Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target
Identifieur interne : 000123 ( Istex/Corpus ); précédent : 000122; suivant : 000124Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target
Auteurs : N. Agafonova ; A. Aleksandrov ; O. Altinok ; A. Anokhina ; S. Aoki ; A. Ariga ; T. Ariga ; D. Autiero ; A. Badertscher ; A. Bagulya ; A. Ben Dhahbi ; A. Bertolin ; M. Besnier ; C. Bozza ; T. Brugire ; R. Brugnera ; F. Brunet ; G. Brunetti ; S. Buontempo ; A. Cazes ; L. Chaussard ; M. Chernyavskiy ; V. Chiarella ; A. Chukanov ; N. D'Ambrosio ; F. Dal Corso ; G. De Lellis ; P. Del Amo Sanchez ; Y. Dclais ; M. De Serio ; F. Di Capua ; A. Di Crescenzo ; D. Di Ferdinando ; N. Di Marco ; S. Dmitrievski ; M. Dracos ; D. Duchesneau ; S. Dusini ; T. Dzhatdoev ; J. Ebert ; O. Egorov ; R. Enikeev ; A. Ereditato ; L. S Esposito ; J. Favier ; T. Ferber ; R. A Fini ; D. Frekers ; T. Fukuda ; A. Garfagnini ; G. Giacomelli ; M. Giorgini ; C. Gllnitz ; J. Goldberg ; D. Golubkov ; L. Goncharova ; Y. Gornushkin ; G. Grella ; F. Grianti ; A. M Guler ; C. Gustavino ; C. Hagner ; K. Hamada ; T. Hara ; M. Hierholzer ; A. Hollnagel ; K. Hoshino ; M. Ieva ; H. Ishida ; K. Jakovcic ; C. Jollet ; F. Juget ; M. Kamiscioglu ; K. Kazuyama ; S. H Kim ; M. Kimura ; N. Kitagawa ; B. Klicek ; J. Knuesel ; K. Kodama ; M. Komatsu ; U. Kose ; I. Kreslo ; H. Kubota ; C. Lazzaro ; J. Lenkeit ; I. Lippi ; A. Ljubicic ; A. Longhin ; P. Loverre ; G. Lutter ; A. Malgin ; G. Mandrioli ; K. Manai ; J. Marteau ; T. Matsuo ; V. Matveev ; N. Mauri ; E. Medinaceli ; F. Meisel ; A. Meregaglia ; P. Migliozzi ; S. Mikado ; S. Miyamoto ; P. Monacelli ; K. Morishima ; U. Moser ; M. T Muciaccia ; N. Naganawa ; T. Naka ; M. Nakamura ; T. Nakano ; D. Naumov ; V. Nikitina ; K. Niwa ; Y. Nonoyama ; S. Ogawa ; N. Okateva ; A. Olshevskiy ; M. Paniccia ; A. Paoloni ; B. D Park ; I. G Park ; A. Pastore ; L. Patrizii ; E. Pennacchio ; H. Pessard ; K. Pretzl ; V. Pilipenko ; C. Pistillo ; N. Polukhina ; M. Pozzato ; F. Pupilli ; R. Rescigno ; T. Roganova ; H. Rokujo ; G. Romano ; G. Rosa ; I. Rostovtseva ; A. Rubbia ; A. Russo ; V. Ryasny ; O. Ryazhskaya ; O. Sato ; Y. Sato ; A. Schembri ; W. Schmidt-Parzefall ; H. Schroeder ; L. Scotto Lavina ; A. Sheshukov ; H. Shibuya ; G. Shoziyoev ; S. Simone ; M. Sioli ; C. Sirignano ; G. Sirri ; J. S Song ; M. Spinetti ; L. Stanco ; N. Starkov ; M. Stipcevic ; T. Strauss ; P. Strolin ; S. Takahashi ; M. Tenti ; F. Terranova ; I. Tezuka ; V. Tioukov ; P. Tolun ; A. Trabelsi ; T. Tran ; S. Tufanli ; P. Vilain ; M. Vladimirov ; L. Votano ; J. L Vuilleumier ; G. Wilquet ; B. Wonsak ; V. Yakushev ; C. S Yoon ; T. Yoshioka ; J. Yoshida ; Y. Zaitsev ; S. Zemskova ; A. Zghiche ; R. ZimmermannSource :
- New Journal of Physics [ 1367-2630 ] ; 2012-01.
Abstract
A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.
Url:
DOI: 10.1088/1367-2630/14/1/013026
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Anokhina</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Aoki, S" sort="Aoki, S" uniqKey="Aoki S" first="S" last="Aoki">S. Aoki</name><affiliation><mods:affiliation>57-8501 Kobe, Japan</mods:affiliation></affiliation></author><author><name sortKey="Ariga, A" sort="Ariga, A" uniqKey="Ariga A" first="A" last="Ariga">A. Ariga</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Ariga, T" sort="Ariga, T" uniqKey="Ariga T" first="T" last="Ariga">T. Ariga</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Autiero, D" sort="Autiero, D" uniqKey="Autiero D" first="D" last="Autiero">D. Autiero</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Badertscher, A" sort="Badertscher, A" uniqKey="Badertscher A" first="A" last="Badertscher">A. 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Zemskova</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Zghiche, A" sort="Zghiche, A" uniqKey="Zghiche A" first="A" last="Zghiche">A. Zghiche</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author><author><name sortKey="Zimmermann, R" sort="Zimmermann, R" uniqKey="Zimmermann R" first="R" last="Zimmermann">R. Zimmermann</name><affiliation><mods:affiliation></mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">New Journal of Physics</title><idno type="eISSN">1367-2630</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2012-01">2012-01</date><biblScope unit="volume">14</biblScope><biblScope unit="issue">1</biblScope></imprint></series><idno type="istex">7705F1E1B67BCD89127D1990F9986F8DD9B44DFA</idno><idno type="DOI">10.1088/1367-2630/14/1/013026</idno><idno type="href">http://stacks.iop.org/NJP/14/013026</idno><idno type="ArticleID">nj398914</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>N Agafonova</name><affiliations><json:string>INRInstitute for Nuclear Research of the Russian Academy of Sciences, RUS-117312 Moscow, Russia</json:string></affiliations></json:item><json:item><name>A Aleksandrov</name><affiliations><json:string>INFN Sezione di Napoli, I-80125 Napoli, Italy</json:string><json:string>LPILebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russia</json:string></affiliations></json:item><json:item><name>O Altinok</name><affiliations><json:string>METUMiddle East Technical University, TR-06531 Ankara, Turkey</json:string></affiliations></json:item><json:item><name>A Anokhina</name><affiliations><json:string>SINP MSUSkobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, RUS-119992 Moscow, Russia</json:string></affiliations></json:item><json:item><name>S Aoki</name><affiliations><json:string>Kobe University, J-657-8501 Kobe, Japan</json:string></affiliations></json:item><json:item><name>A Ariga</name><affiliations><json:string>Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, CH-3012 Bern, Switzerland</json:string></affiliations></json:item><json:item><name>T Ariga</name><affiliations><json:string>Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, CH-3012 Bern, Switzerland</json:string></affiliations></json:item><json:item><name>D Autiero</name><affiliations><json:string>IPNL, Universit Claude Bernard Lyon 1, CNRSIN2P3, F-69622 Villeurbanne, France</json:string></affiliations></json:item><json:item><name>A Badertscher</name><affiliations><json:string>ETH Zurich, Institute for Particle Physics, CH-8093 Zurich, Switzerland</json:string></affiliations></json:item><json:item><name>A Bagulya</name><affiliations><json:string>LPILebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russia</json:string></affiliations></json:item><json:item><name>A Ben Dhahbi</name><affiliations><json:string>Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, CH-3012 Bern, Switzerland</json:string><json:string>Unit de Physique Nuclaire et des Hautes Energies (UPNHE), Tunis, Tunisia</json:string></affiliations></json:item><json:item><name>A Bertolin</name><affiliations><json:string>INFN Sezione di Padova, I-35131 Padova, Italy</json:string></affiliations></json:item><json:item><name>M Besnier</name><affiliations><json:string>LAPP, Universit de Savoie, CNRSIN2P3, F-74941 Annecy-le-Vieux, France</json:string></affiliations></json:item><json:item><name>C Bozza</name><affiliations><json:string>Dipartimento di Fisica dell'Universit di Salerno and INFN, I-84084 Fisciano, Salerno, Italy</json:string></affiliations></json:item><json:item><name>T Brugire</name><affiliations><json:string>IPNL, Universit Claude Bernard Lyon 1, CNRSIN2P3, F-69622 Villeurbanne, France</json:string></affiliations></json:item><json:item><name>R Brugnera</name><affiliations><json:string>INFN Sezione di Padova, I-35131 Padova, Italy</json:string><json:string>Dipartimento di Fisica dell'Universit di Padova, I-35131 Padova, Italy</json:string></affiliations></json:item><json:item><name>F Brunet</name><affiliations><json:string>LAPP, Universit de Savoie, CNRSIN2P3, F-74941 Annecy-le-Vieux, France</json:string></affiliations></json:item><json:item><name>G Brunetti</name><affiliations><json:string>IPNL, Universit Claude Bernard Lyon 1, CNRSIN2P3, F-69622 Villeurbanne, France</json:string><json:string>Dipartimento di Fisica dell'Universit di Bologna, I-40127 Bologna, Italy</json:string><json:string>INFN Sezione di Bologna, I-40127 Bologna, 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Tezuka</name><affiliations><json:string>Utsunomiya University, J-321-8505 Tochigi-Ken, Utsunomiya, Japan</json:string></affiliations></json:item><json:item><name>V Tioukov</name><affiliations><json:string>INFN Sezione di Napoli, I-80125 Napoli, Italy</json:string></affiliations></json:item><json:item><name>P Tolun</name><affiliations><json:string>METUMiddle East Technical University, TR-06531 Ankara, Turkey</json:string></affiliations></json:item><json:item><name>A Trabelsi</name><affiliations><json:string>Unit de Physique Nuclaire et des Hautes Energies (UPNHE), Tunis, Tunisia</json:string></affiliations></json:item><json:item><name>T Tran</name><affiliations><json:string>IPNL, Universit Claude Bernard Lyon 1, CNRSIN2P3, F-69622 Villeurbanne, France</json:string></affiliations></json:item><json:item><name>S Tufanli</name><affiliations><json:string>METUMiddle East Technical University, TR-06531 Ankara, Turkey</json:string></affiliations></json:item><json:item><name>P Vilain</name><affiliations><json:string>IIHE, Universit Libre de Bruxelles, B-1050 Brussels, Belgium</json:string></affiliations></json:item><json:item><name>M Vladimirov</name><affiliations><json:string>LPILebedev Physical Institute of the Russian Academy of Sciences, 119991 Moscow, Russia</json:string></affiliations></json:item><json:item><name>L Votano</name><affiliations><json:string>INFNLaboratori Nazionali di Frascati dell'INFN, I-00044 Frascati (Roma), Italy</json:string></affiliations></json:item><json:item><name>J L Vuilleumier</name><affiliations><json:string>Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, CH-3012 Bern, Switzerland</json:string></affiliations></json:item><json:item><name>G Wilquet</name><affiliations><json:string>IIHE, Universit Libre de Bruxelles, B-1050 Brussels, Belgium</json:string></affiliations></json:item><json:item><name>B Wonsak</name><affiliations><json:string>Hamburg University, D-22761 Hamburg, Germany</json:string></affiliations></json:item><json:item><name>V Yakushev</name><affiliations><json:string>INRInstitute for Nuclear Research of the Russian Academy of Sciences, RUS-117312 Moscow, Russia</json:string></affiliations></json:item><json:item><name>C S Yoon</name><affiliations><json:string>Gyeongsang National University, ROK-900 Gazwa-dong, Jinju 660-701, Korea</json:string></affiliations></json:item><json:item><name>T Yoshioka</name><affiliations><json:string>Nagoya University, J-464-8602 Nagoya, Japan</json:string></affiliations></json:item><json:item><name>J Yoshida</name><affiliations><json:string>Nagoya University, J-464-8602 Nagoya, Japan</json:string></affiliations></json:item><json:item><name>Y Zaitsev</name><affiliations><json:string>ITEP-Institute for Theoretical and Experimental Physics, RUS-117259 Moscow, Russia</json:string></affiliations></json:item><json:item><name>S Zemskova</name><affiliations><json:string>JINR-Joint Institute for Nuclear Research, RUS-141980 Dubna, Russia</json:string></affiliations></json:item><json:item><name>A Zghiche</name><affiliations><json:string>LAPP, Universit de Savoie, CNRSIN2P3, F-74941 Annecy-le-Vieux, France</json:string></affiliations></json:item><json:item><name>R Zimmermann</name><affiliations><json:string>Hamburg University, D-22761 Hamburg, Germany</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.</abstract><qualityIndicators><score>6.904</score><pdfVersion>1.4</pdfVersion><pdfPageSize>595.276 x 841.89 pts (A4)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>800</abstractCharCount><pdfWordCount>6757</pdfWordCount><pdfCharCount>36787</pdfCharCount><pdfPageCount>19</pdfPageCount><abstractWordCount>117</abstractWordCount></qualityIndicators><title>Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target</title><genre><json:string>research-article</json:string></genre><host><volume>14</volume><issue>1</issue><genre></genre><language><json:string>unknown</json:string></language><eissn><json:string>1367-2630</json:string></eissn><title>New Journal of Physics</title></host><publicationDate>2012</publicationDate><copyrightDate>2012</copyrightDate><doi><json:string>10.1088/1367-2630/14/1/013026</json:string></doi><id>7705F1E1B67BCD89127D1990F9986F8DD9B44DFA</id><fulltext><json:item><original>true</original><mimetype>application/pdf</mimetype><extension>pdf</extension><uri>https://api.istex.fr/document/7705F1E1B67BCD89127D1990F9986F8DD9B44DFA/fulltext/pdf</uri></json:item><json:item><original>false</original><mimetype>application/zip</mimetype><extension>zip</extension><uri>https://api.istex.fr/document/7705F1E1B67BCD89127D1990F9986F8DD9B44DFA/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/7705F1E1B67BCD89127D1990F9986F8DD9B44DFA/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>IOP Publishing</publisher><availability><p>IOP</p></availability><date>2012-01-16</date></publicationStmt><notesStmt><note>Author to whom any correspondence should be addressed.</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target</title><author><persName><forename type="first">N</forename><surname>Agafonova</surname></persName><affiliation>17312 Moscow, Russia</affiliation></author><author><persName><forename type="first">A</forename><surname>Aleksandrov</surname></persName><affiliation>5 Napoli, Italy</affiliation><affiliation></affiliation></author><author><persName><forename type="first">O</forename><surname>Altinok</surname></persName><affiliation></affiliation></author><author><persName><forename type="first">A</forename><surname>Anokhina</surname></persName><affiliation></affiliation></author><author><persName><forename 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type="first">T</forename><surname>Yoshioka</surname></persName><affiliation></affiliation></author><author><persName><forename type="first">J</forename><surname>Yoshida</surname></persName><affiliation></affiliation></author><author><persName><forename type="first">Y</forename><surname>Zaitsev</surname></persName><affiliation>9 Moscow, Russia</affiliation></author><author><persName><forename type="first">S</forename><surname>Zemskova</surname></persName><affiliation></affiliation></author><author><persName><forename type="first">A</forename><surname>Zghiche</surname></persName><affiliation></affiliation></author><author><persName><forename type="first">R</forename><surname>Zimmermann</surname></persName><affiliation></affiliation></author></analytic><monogr><title level="j">New Journal of Physics</title><idno type="eISSN">1367-2630</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2012-01"></date><biblScope unit="volume">14</biblScope><biblScope unit="issue">1</biblScope></imprint></monogr><idno type="istex">7705F1E1B67BCD89127D1990F9986F8DD9B44DFA</idno><idno type="DOI">10.1088/1367-2630/14/1/013026</idno><idno type="href">http://stacks.iop.org/NJP/14/013026</idno><idno type="ArticleID">nj398914</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2012-01-16</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.</p></abstract><textClass><keywords scheme="keyword"><list><head>article-type</head><item><term>Paper</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2012-01-16">Created</change><change when="2012-01">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/7705F1E1B67BCD89127D1990F9986F8DD9B44DFA/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1" </istex:xmlDeclaration><istex:docType PUBLIC="-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" URI="http://ej.iop.org/dtd/nlm-3.0/journalpublishing3.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article"><front><journal-meta><journal-id journal-id-type="publisher-id">nj</journal-id><journal-id journal-id-type="coden">NJOPFM</journal-id><journal-title-group><journal-title>New Journal of Physics</journal-title><abbrev-journal-title abbrev-type="IOP">NJP</abbrev-journal-title><abbrev-journal-title abbrev-type="publisher">New J. Phys.</abbrev-journal-title></journal-title-group><issn pub-type="epub">1367-2630</issn><publisher><publisher-name>IOP Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">nj398914</article-id><article-id pub-id-type="doi">10.1088/1367-2630/14/1/013026</article-id><article-id pub-id-type="manuscript">398914</article-id><article-categories><subj-group subj-group-type="article-type"><subject>Paper</subject></subj-group></article-categories><title-group><article-title>Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target</article-title><alt-title alt-title-type="ascii">Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target</alt-title><alt-title alt-title-type="short">Momentum measurement by the multiple Coulomb scattering method</alt-title><alt-title alt-title-type="short-ascii">Momentum measurement by the multiple Coulomb scattering method in the 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rid="nj398914af17">17</xref></contrib><contrib contrib-type="author"><name><surname>L Vuilleumier</surname><given-names>J</given-names></name><xref ref-type="aff" rid="nj398914af7">7</xref></contrib><contrib contrib-type="author"><name><surname>Wilquet</surname><given-names>G</given-names></name><xref ref-type="aff" rid="nj398914af38">38</xref></contrib><contrib contrib-type="author"><name><surname>Wonsak</surname><given-names>B</given-names></name><xref ref-type="aff" rid="nj398914af24">24</xref></contrib><contrib contrib-type="author"><name><surname>Yakushev</surname><given-names>V</given-names></name><xref ref-type="aff" rid="nj398914af1">1</xref></contrib><contrib contrib-type="author"><name><surname>S Yoon</surname><given-names>C</given-names></name><xref ref-type="aff" rid="nj398914af32">32</xref></contrib><contrib contrib-type="author"><name><surname>Yoshioka</surname><given-names>T</given-names></name><xref ref-type="aff" rid="nj398914af30">30</xref></contrib><contrib contrib-type="author"><name><surname>Yoshida</surname><given-names>J</given-names></name><xref ref-type="aff" rid="nj398914af30">30</xref></contrib><contrib contrib-type="author"><name><surname>Zaitsev</surname><given-names>Y</given-names></name><xref ref-type="aff" rid="nj398914af25">25</xref></contrib><contrib contrib-type="author"><name><surname>Zemskova</surname><given-names>S</given-names></name><xref ref-type="aff" rid="nj398914af18">18</xref></contrib><contrib contrib-type="author"><name><surname>Zghiche</surname><given-names>A</given-names></name><xref ref-type="aff" rid="nj398914af12">12</xref></contrib><contrib contrib-type="author"><name><surname>Zimmermann</surname><given-names>R</given-names></name><xref ref-type="aff" rid="nj398914af24">24</xref></contrib><aff id="nj398914af1"><label>1</label><institution>INR—Institute for Nuclear Research of the Russian Academy of Sciences</institution>, RUS-117312 Moscow, <country>Russia</country></aff><aff id="nj398914af2"><label>2</label>INFN Sezione di Napoli, I-80125 Napoli, <country>Italy</country></aff><aff id="nj398914af3"><label>3</label><institution>LPI—Lebedev Physical Institute of the Russian Academy of Sciences</institution>, 119991 Moscow, <country>Russia</country></aff><aff id="nj398914af4"><label>4</label><institution>METU—Middle East Technical University</institution>, TR-06531 Ankara, <country>Turkey</country></aff><aff id="nj398914af5"><label>5</label><institution>SINP MSU—Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University</institution>, RUS-119992 Moscow, <country>Russia</country></aff><aff id="nj398914af6"><label>6</label><institution>Kobe University</institution>, J-657-8501 Kobe, <country>Japan</country></aff><aff id="nj398914af7"><label>7</label>Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), <institution>University of Bern</institution>, CH-3012 Bern, <country>Switzerland</country></aff><aff id="nj398914af8"><label>8</label>IPNL, <institution>Université Claude Bernard Lyon 1</institution>, CNRS/IN2P3, F-69622 Villeurbanne, <country>France</country></aff><aff id="nj398914af9"><label>9</label>ETH Zurich, <institution>Institute for Particle Physics</institution>, CH-8093 Zurich, <country>Switzerland</country></aff><aff id="nj398914af10"><label>10</label><institution>Unité de Physique Nucléaire et des Hautes Energies (UPNHE)</institution>, Tunis, <country>Tunisia</country></aff><aff id="nj398914af11"><label>11</label>INFN Sezione di Padova, I-35131 Padova, <country>Italy</country></aff><aff id="nj398914af12"><label>12</label>LAPP, <institution>Université de Savoie</institution>, CNRS/IN2P3, F-74941 Annecy-le-Vieux, <country>France</country></aff><aff id="nj398914af13"><label>13</label><institution>Dipartimento di Fisica dell'Università di Salerno and INFN</institution>, I-84084 Fisciano, Salerno, <country>Italy</country></aff><aff id="nj398914af14"><label>14</label><institution>Dipartimento di Fisica dell'Università di Padova</institution>, I-35131 Padova, <country>Italy</country></aff><aff id="nj398914af15"><label>15</label><institution>Dipartimento di Fisica dell'Università di Bologna</institution>, I-40127 Bologna, <country>Italy</country></aff><aff id="nj398914af16"><label>16</label>INFN Sezione di Bologna, I-40127 Bologna, <country>Italy</country></aff><aff id="nj398914af17"><label>17</label>INFN—Laboratori Nazionali di Frascati dell'INFN, I-00044 Frascati (Roma), <country>Italy</country></aff><aff id="nj398914af18"><label>18</label><institution>JINR-Joint Institute for Nuclear Research</institution>, RUS-141980 Dubna, <country>Russia</country></aff><aff id="nj398914af19"><label>19</label>INFN—Laboratori Nazionali del Gran Sasso, I-67010 Assergi (L'Aquila), <country>Italy</country></aff><aff id="nj398914af20"><label>20</label><institution>Dipartimento di Scienze Fisiche dell'Università Federico II di Napoli</institution>, I-80125 Napoli, <country>Italy</country></aff><aff id="nj398914af21"><label>21</label>INFN Sezione di Bari, I-70126 Bari, <country>Italy</country></aff><aff id="nj398914af22"><label>22</label><institution>Dipartimento di Fisica dell'Università dell'Aquila and INFN</institution>, I-67100 L'Aquila, <country>Italy</country></aff><aff id="nj398914af23"><label>23</label>IPHC, <institution>Université de Strasbourg</institution>, CNRS/IN2P3, F-67037 Strasbourg, <country>France</country></aff><aff id="nj398914af24"><label>24</label><institution>Hamburg University</institution>, D-22761 Hamburg, <country>Germany</country></aff><aff id="nj398914af25"><label>25</label><institution>ITEP-Institute for Theoretical and Experimental Physics</institution>, RUS-117259 Moscow, <country>Russia</country></aff><aff id="nj398914af26"><label>26</label><institution>University of Münster</institution>, D-48149 Münster, <country>Germany</country></aff><aff id="nj398914af27"><label>27</label><institution>Toho University</institution>, J-274-8510 Funabashi, <country>Japan</country></aff><aff id="nj398914af28"><label>28</label>Department of Physics, Technion, IL-32000 Haifa, <country>Israel</country></aff><aff id="nj398914af29"><label>29</label><institution>Università degli Studi di Urbino ‘Carlo Bo’</institution>, I-61029 Urbino, <country>Italy</country></aff><aff id="nj398914af30"><label>30</label><institution>Nagoya University</institution>, J-464-8602 Nagoya, <country>Japan</country></aff><aff id="nj398914af31"><label>31</label><institution>IRB-Rudjer Boskovic Institute</institution>, HR-10002 Zagreb, <country>Croatia</country></aff><aff id="nj398914af32"><label>32</label><institution>Gyeongsang National University</institution>, ROK-900 Gazwa-dong, Jinju 660-701, <country>Korea</country></aff><aff id="nj398914af33"><label>33</label><institution>Aichi University of Education</institution>, J-448-8542 Kariya (Aichi-Ken), <country>Japan</country></aff><aff id="nj398914af34"><label>34</label><institution>Dipartimento di Fisica dell'Università di Roma ‘La Sapienza’ and INFN</institution>, I-00185 Roma, <country>Italy</country></aff><aff id="nj398914af35"><label>35</label><institution>Dipartimento di Fisica dell'Università di Bari</institution>, I-70126 Bari, <country>Italy</country></aff><aff id="nj398914af36"><label>36</label><institution>Utsunomiya University</institution>, J-321-8505 Tochigi-Ken, Utsunomiya, <country>Japan</country></aff><aff id="nj398914af37"><label>37</label><institution>Fachbereich Physik der Universität Rostock</institution>, D-18051 Rostock, <country>Germany</country></aff><aff id="nj398914af38"><label>38</label>IIHE, <institution>Université Libre de Bruxelles</institution>, B-1050 Brussels, <country>Belgium</country></aff><ext-link ext-link-type="email" id="nj398914em1">duchesneau@lapp.in2p3.fr</ext-link><author-comment content-type="short-author-list"><p>N Agafonova <italic>et al</italic></p></author-comment></contrib-group><author-notes><fn id="nj398914afn1"><label>39</label><p>Author to whom any correspondence should be addressed.</p></fn><fn id="nj398914afn2"><label>40</label><p>Present address: Laboratoire Leprince-Ringuet, CNRS/IN2P3 Ecole polytechnique, F-91128 Palaiseau, France.</p></fn><fn id="nj398914afn3"><label>41</label><p>Present address: INFN—Laboratori Nazionali del Gran Sasso, I-67010 Assergi (L'Aquila), Italy.</p></fn><fn id="nj398914afn4"><label>42</label><p>Present address: INAF/IASF, Sezione di Milano, I-20133 Milano, Italy.</p></fn><fn id="nj398914afn5"><label>43</label><p>Present address: Dipartimento di Fisica dell'Università di Roma ‘La Sapienza’ and INFN, I-00185 Roma, Italy.</p></fn><fn id="nj398914afn6"><label>44</label><p>Present address: Pusan National University, Geumjeong-Gu Busan 609-735, Korea.</p></fn><fn id="nj398914afn7"><label>45</label><p>Present address: INFN—Laboratori Nazionali di Frascati dell'INFN, I-00044 Frascati (Roma), Italy.</p></fn><fn id="nj398914afn8"><label>46</label><p>Present address: Asan Medical Center, 388-1 Pungnap-2 Dong, Songpa-Gu, Seoul 138-736, Korea.</p></fn><fn id="nj398914afn9"><label>47</label><p>Present address: SUBATECH, CNRS/IN2P3, F-44307 Nantes, France.</p></fn><fn id="nj398914afn10"><label>48</label><p>Present address: Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics (LHEP), University of Bern, CH-3012 Bern, Switzerland.</p></fn></author-notes><pub-date pub-type="ppub"><month>1</month><year>2012</year></pub-date><pub-date pub-type="epub"><day>16</day><month>1</month><year>2012</year></pub-date><volume>14</volume><issue>1</issue><elocation-id content-type="artnum">013026</elocation-id><history><date date-type="received"><day>1</day><month>7</month><year>2011</year></date></history><permissions><copyright-statement>© IOP Publishing and Deutsche Physikalische Gesellschaft</copyright-statement><copyright-year>2012</copyright-year></permissions><self-uri xlink:href="http://stacks.iop.org/NJP/14/013026"></self-uri><abstract><title>Abstract</title><p>A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.</p></abstract><counts><page-count count="19"></page-count></counts><custom-meta-group><custom-meta><meta-name>ccc</meta-name><meta-value>1367-2630/12/013026+19$33.00</meta-value></custom-meta><custom-meta><meta-name>table-of-contents</meta-name><meta-value>yes</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="nj398914s1"><label>1.</label><title>Introduction</title><p>The multiple Coulomb scattering (MCS) process offers a means of estimating the momentum of charged particles in any detectors able to measure precisely particle trajectories even in the absence of a magnetic field. This technique has been used in the past in a large variety of tracking technologies. Early applications of the multiple scattering theory to measure momentum have been developed for cloud chambers [<xref ref-type="bibr" rid="nj398914bib01">1</xref>], emulsion detectors [<xref ref-type="bibr" rid="nj398914bib02">2</xref>] and spark chambers [<xref ref-type="bibr" rid="nj398914bib03">3</xref>], the latter being essentially for balloon-borne cosmic ray experiments. This technique is still widely used and is continuously adapted for new detector technologies and concepts, such as for the recent measurements of the momenta of through-going atmospheric muons from MCS carried out by the MACRO collaboration [<xref ref-type="bibr" rid="nj398914bib04">4</xref>] that used streamer tubes, and by the ICARUS collaboration with the T600 liquid argon TPC [<xref ref-type="bibr" rid="nj398914bib05">5</xref>]. Alternatively, the MCS of cosmic ray muons passing through dense material is used to develop novel methods for muon tomography as described in [<xref ref-type="bibr" rid="nj398914bib06">6</xref>].</p><p>The study described in this paper is an application of the MCS process to momentum measurement in a new generation emulsion experiment. The momentum of charged particles can be measured in emulsion cloud chambers (ECC) [<xref ref-type="bibr" rid="nj398914bib07">7</xref>] made of massive material plates, used as the target, interleaved with nuclear emulsion films acting as high-resolution tracking devices. This technique was exploited by the DONUT experiment [<xref ref-type="bibr" rid="nj398914bib08">8</xref>, <xref ref-type="bibr" rid="nj398914bib09">9</xref>] and is currently used in the OPERA experiment searching for <italic>ν</italic><sub><italic>μ</italic></sub> → <italic>ν</italic><sub><italic>τ</italic></sub> oscillations in the CNGS neutrino beam [<xref ref-type="bibr" rid="nj398914bib10">10</xref>]. The study uses the geometry and the characteristics of the OPERA neutrino target ECC elements called ‘bricks’. They have dimensions of 12.7 × 10.2 × 7.5 cm<sup>3</sup> and are composed of a sequence of 56 lead plates (1 mm thick) and 57 emulsion films (44 <italic>μ</italic>m thick emulsion layers on each side of a 205 <italic>μ</italic>m thick plastic base). The total length of a brick corresponds to about 10<italic>X</italic><sub>0</sub>.</p><p>Charged particles crossing the emulsions ionize silver bromide crystals, and clusters of silver grains, appearing as black dots, are formed along their paths after film processing. Automatic microscopes [<xref ref-type="bibr" rid="nj398914bib11">11</xref>] are used to reconstruct three-dimensional (3D) particle track segments. Micro-track segments are reconstructed in single-emulsion layers as sequences of aligned grains. Two matching micro-tracks in a film define a base-track, obtained as the straight line connecting the grains closest to the plastic base in the two emulsion layers.</p><p>A track reconstructed through connecting segments in two or more films is called a volume-track.</p><p>The momentum measurement by MCS can be carried out by either the track position (coordinate method) [<xref ref-type="bibr" rid="nj398914bib12">12</xref>] or the track angle (angular method) [<xref ref-type="bibr" rid="nj398914bib13">13</xref>] measured in each emulsion film. The two methods determine the deviations of the trajectory from a straight line on the basis of position or angle measurements, respectively. The use of one method rather than the other depends on the required accuracy, and on the achievable spatial and angular resolutions. In OPERA ECC bricks, base-track directions are measured with a precision of a few mrad. Moreover, the angular method does not depend on a precise knowledge of the relative alignment of the different emulsion films. The evolution of slopes of consecutive base-tracks forming a volume-track can thus be used to compute the mean Coulomb scattering angle in a given lead thickness, which is directly related to the particle momentum. The angular resolution of the emulsions allows the determination of charged particle momentum from several hundreds of MeV c<sup>−1</sup> to a few GeV c<sup>−1</sup>, which corresponds to the momentum range of secondary hadrons produced in neutrino interactions in the OPERA experiment. Several approaches to making angular deviation measurements in lead have been tested and compared in previous studies. The method presented in this paper is based on the work detailed in [<xref ref-type="bibr" rid="nj398914bib14">14</xref>], and is used for the analysis of the neutrino events observed in OPERA [<xref ref-type="bibr" rid="nj398914bib15">15</xref>].</p><p>The first part describes the method and the special treatment used for the large angle tracks. Results from Monte Carlo (MC) and from data analysis with pions from 1 to 8 GeV c<sup>−1</sup> momentum for various track lengths are summarized in sections <xref ref-type="sec" rid="nj398914s3">3</xref> and <xref ref-type="sec" rid="nj398914s4">4</xref>. In the last section, the results of the application of the algorithm to muon tracks reconstructed independently in the OPERA electronic detectors with momenta below 6 GeV c<sup>−1</sup> are presented.</p></sec><sec id="nj398914s2"><label>2.</label><title>Measurement method</title><sec id="nj398914s2-1"><label>2.1.</label><title>The scattering angle dependence on lead thickness</title><p>The main ingredient of the angular method measurement is the availability of several angular measurements along a volume-track. The present approach uses the angle differences measured in pairs of emulsion films separated by lead. In the following, one cell corresponds to one lead plate and one film. Figure <xref ref-type="fig" rid="nj398914fig1">1</xref> provides a schematic view of a volume-track and its associated base-tracks in the <italic>XZ</italic> projection plane. Let <italic>θ</italic><sub><italic>i</italic></sub> be the angle of a given base-track in the <italic>i</italic>th emulsion film, <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn1.gif"></inline-graphic></inline-formula> in the <italic>XZ</italic> or <italic>Y</italic><italic>Z</italic> projection plane. Defining <italic>θ</italic><sub><italic>ik</italic></sub> = <italic>θ</italic><sub><italic>i</italic>+<italic>k</italic></sub> − <italic>θ</italic><sub><italic>i</italic></sub> as the scattering angle after crossing a number <italic>k</italic> of cells, its distribution is peaked at zero and has a shape that can be approximated by a Gaussian with a standard deviation given by [<xref ref-type="bibr" rid="nj398914bib16">16</xref>] <disp-formula id="nj398914eqn1"><label>1</label><tex-math></tex-math><graphic xlink:href="nj398914eqn1.gif"></graphic></disp-formula> where <italic>p</italic> is the particle momentum in MeV c<sup>−1</sup>, <italic>β</italic><italic>c</italic> is its velocity, <italic>x</italic> is the distance traversed and <italic>X</italic><sub>0</sub> is the radiation length in the material. The accuracy of this approximation of Moliere's theory of scattering is better than 11% in any material, with 0.001 < <italic>x</italic>/<italic>X</italic><sub>0</sub> < 100 [<xref ref-type="bibr" rid="nj398914bib17">17</xref>] for single charged particles with <italic>β</italic> ≈ 1.</p><fig id="nj398914fig1" position="float"><label>Figure 1.</label><caption id="nj398914fc1"><p>Sketch of five lead cells in a target brick, where a volume-track and its base tracks are represented in the <italic>XZ</italic> projection.</p></caption><graphic id="nj398914f1_eps" content-type="print" xlink:href="nj398914f1_pr.eps"></graphic><graphic id="nj398914f1_online" content-type="online" xlink:href="nj398914f1_online.jpg"></graphic></fig><p>The scattering is dominated by the lead since the radiation length in the emulsion layers and the plastic base is larger by more than one order of magnitude. For this reason, the value <italic>X</italic><sub>0</sub> = 5.6 mm will be assumed in the analysis and a thickness of 1 mm will be used for each cell, neglecting the emulsion films. By denoting the number of cells crossed by a particle track by <italic>N</italic><sub>cell</sub>, the above-mentioned expression becomes <disp-formula id="nj398914eqn2"><label>2</label><tex-math></tex-math><graphic xlink:href="nj398914eqn2.gif"></graphic></disp-formula> The variance of the scattering angle distribution for a given cell depth <italic>N</italic><sub>cell</sub> = <italic>k</italic> is given by <disp-formula id="nj398914eqn3"><label>3</label><tex-math></tex-math><graphic xlink:href="nj398914eqn3.gif"></graphic></disp-formula> where <italic>N</italic><sub>meas</sub> is the number of scattering angle measurements and <italic>δ</italic><italic>θ</italic> is an additional term corresponding to the base-track angular resolution<xref ref-type="fn" rid="nj398914fn49"><sup>49</sup></xref><fn id="nj398914fn49"><label>49</label><p><italic>δ</italic><italic>θ</italic> is the angular resolution between two base-tracks. The single base-track angular resolution is <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn2.gif"></inline-graphic></inline-formula>.</p></fn>.</p><p>The current experimental value of <italic>δ</italic><italic>θ</italic> is about 2.1 mrad. In order to determine <italic>p</italic> up to a few GeV c<sup>−1</sup> through the scattering angle, a fit of the dependence of <italic>θ</italic><sub>meas</sub> on the number of crossed cells is performed, treating <italic>p</italic> as a free parameter and fixing the angular resolution. With increasing <italic>p</italic>, the MCS starts dominating over <italic>δ</italic><italic>θ</italic> at larger values of <italic>N</italic><sub>cell</sub>, where the number of available measurements decreases, thus increasing the statistical error. In order to improve the sensitivity to high-momentum tracks, it is important to reduce the statistical uncertainty at large crossed thicknesses.</p><p>The method is illustrated in figure <xref ref-type="fig" rid="nj398914fig2">2</xref>. It consists of using the differences between all combinations of pairs of angles separated by <italic>N</italic><sub>cell</sub> cells. For a given cell depth <italic>N</italic><sub>cell</sub> and a total track span <italic>N</italic><sub>pl</sub> measured as the number of lead plates traversed by the particle, the number of available measurements <italic>N</italic><sub>meas</sub> is given by <disp-formula id="nj398914eqn4"><label>4</label><tex-math></tex-math><graphic xlink:href="nj398914eqn4.gif"></graphic></disp-formula></p><fig id="nj398914fig2" position="float"><label>Figure 2.</label><caption id="nj398914fc2"><p>Representation of the number of possible measurements available when applying the MCS method up to <italic>N</italic><sub>cell</sub> = 3.</p></caption><graphic id="nj398914f2_eps" content-type="print" xlink:href="nj398914f2_pr.eps"></graphic><graphic id="nj398914f2_online" content-type="online" xlink:href="nj398914f2_online.jpg"></graphic></fig></sec><sec id="nj398914s2-2"><label>2.2.</label><title>Track angle dependence</title><p>For large-angle tracks the following effects have to be taken into account. Firstly, the crossed lead thickness varies as 1/cos <italic>θ</italic>, with <italic>θ</italic> being the track angle measured with respect to the normal to the emulsion plane (the <italic>Z</italic> coordinate). Secondly, also the angular resolution <italic>δ</italic><italic>θ</italic> depends on <italic>θ</italic>, as the longitudinal uncertainty affects the measured grain positions along the optical <italic>Z</italic>-axis. This effect is dominated by the vertical resolution of the scanning system and is about 2.5 <italic>μ</italic>m [<xref ref-type="bibr" rid="nj398914bib11">11</xref>]. For angles above 200 mrad, this uncertainty is one order of magnitude larger than that in the transverse <italic>X</italic> and <italic>Y</italic> coordinates.</p><p>In order to decouple the intrinsic angular resolution from the slope-dependent contribution, the algorithm is constructed in a new reference coordinate system. It uses transverse and longitudinal coordinates (denoted, respectively, by <italic>T</italic> and <italic>L</italic>) as defined in [<xref ref-type="bibr" rid="nj398914bib11">11</xref>], projected on the <italic>θ</italic><sub><italic>T</italic></sub> and <italic>θ</italic><sub><italic>L</italic></sub> axes of the reference frame schematically shown in figure <xref ref-type="fig" rid="nj398914fig3">3</xref>. The <italic>T</italic> and <italic>L</italic> coordinates are obtained from <italic>X</italic> and <italic>Y</italic> by applying a rotation: <disp-formula id="nj398914eqn5"><label>5</label><tex-math></tex-math><graphic xlink:href="nj398914eqn5.gif"></graphic></disp-formula><disp-formula id="nj398914eqn6"><label>6</label><tex-math></tex-math><graphic xlink:href="nj398914eqn6.gif"></graphic></disp-formula> where <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn3.gif"></inline-graphic></inline-formula>). The 3D space angle can be written as
<disp-formula id="nj398914eqn7"><label>7</label><tex-math></tex-math><graphic xlink:href="nj398914eqn7.gif"></graphic></disp-formula></p><fig id="nj398914fig3" position="float"><label>Figure 3.</label><caption id="nj398914fc3"><p>Schematic view of <italic>T–L</italic> coordinate reference frame, superimposed on the <italic>θ</italic><sub><italic>y</italic></sub> versus <italic>θ</italic><sub><italic>x</italic></sub> plot for the base tracks of 10 GeV c<sup>−1</sup> MC muons at large angle (<italic>θ</italic><sub><italic>X</italic></sub> = <italic>θ</italic><sub><italic>Y</italic></sub> = 500 mrad).</p></caption><graphic id="nj398914f3_eps" content-type="print" xlink:href="nj398914f3_pr.eps"></graphic><graphic id="nj398914f3_online" content-type="online" xlink:href="nj398914f3_online.jpg"></graphic></fig><p>As can be seen in figure <xref ref-type="fig" rid="nj398914fig3">3</xref>, the <italic>T</italic> coordinate gives an angular spread which remains the same for any track angle. The angular dependence of the resolution can be parameterized as [<xref ref-type="bibr" rid="nj398914bib18">18</xref>] <disp-formula id="nj398914eqn8"><label>8</label><tex-math></tex-math><graphic xlink:href="nj398914eqn8.gif"></graphic></disp-formula> and <disp-formula id="nj398914eqn9"><label>9</label><tex-math></tex-math><graphic xlink:href="nj398914eqn9.gif"></graphic></disp-formula> where <italic>ε</italic><sub><italic>z</italic></sub> is a parameter that linearly depends on the longitudinal uncertainty.</p><p>This transformation allows keeping <italic>θ</italic><sub><italic>T</italic></sub> centred around 0 mrad as shown in figure <xref ref-type="fig" rid="nj398914fig4">4</xref>. As discussed in section <xref ref-type="sec" rid="nj398914s3-2">3.2</xref>, an unbiased algorithm would use the 3D coordinate (both <italic>T</italic> and <italic>L</italic> or <italic>X</italic> and <italic>Y</italic> measurements) for small angles, and only the <italic>T</italic> coordinate at large angles. However, the latter choice results in only half the statistics, even though it is angle independent and free of bias. In the following, all the results are obtained using the <italic>T–L</italic> coordinate system.</p><fig id="nj398914fig4" position="float"><label>Figure 4.</label><caption id="nj398914fc4"><p>Angular distributions of base tracks from 4 GeV c<sup>−1</sup> MC pions simulated with <italic>θ</italic><sub><italic>X</italic></sub> = 400 mrad and <italic>θ</italic><sub><italic>Y</italic></sub> = 200 mrad in the <italic>XY</italic> (left) and <italic>TL</italic> projection planes (right).</p></caption><graphic id="nj398914f4_eps" content-type="print" xlink:href="nj398914f4_pr.eps"></graphic><graphic id="nj398914f4_online" content-type="online" xlink:href="nj398914f4_online.jpg"></graphic></fig></sec><sec id="nj398914s2-3"><label>2.3.</label><title>Momentum and resolution estimate</title><p>In order to estimate the momentum resolution, samples of the same-momentum tracks can be analysed. Assuming a Gaussian distribution for <italic>θ</italic><sub>0</sub>, the shape of the momentum distribution can be approximated by the function <disp-formula id="nj398914eqn10"><label>10</label><tex-math></tex-math><graphic xlink:href="nj398914eqn10.gif"></graphic></disp-formula> where <italic>p</italic><sub>0</sub>, <italic>p</italic><sub>1</sub> and <italic>p</italic><sub>2</sub> are free parameters. The parameter <italic>p</italic><sub>1</sub> corresponds to the average of the reconstructed momenta <italic>p</italic><sub>mean</sub>. Figure <xref ref-type="fig" rid="nj398914fig5">5</xref> (left) shows an example of this fitted distribution for tracks of 4 GeV c<sup>−1</sup> MC pions passing through 56 cells. In order to take into account possible uncertainties coming from the Gaussian analytic approximation of 1/<italic>p</italic>, the mean reconstructed momentum is obtained from the average fits of the distributions of both momentum and inverted momentum (figure <xref ref-type="fig" rid="nj398914fig5">5</xref> (right)). The first one has sensitivity to the high reconstructed momentum tail while the second is more sensitive to the lower reconstructed momentum values. The difference of the two results is the systematic uncertainty of the average fitted momentum determination. In the previous example, the results give ⟨<italic>p</italic>⟩ = 3.97 ± 0.01(stat) ± 0.08(syst) GeV c<sup>−1</sup>.</p><fig id="nj398914fig5" position="float"><label>Figure 5.</label><caption id="nj398914fc5"><p>Momentum distribution (left) and inverted momentum distribution (right) for about 4000 tracks of 4 GeV c<sup>−1</sup> MC pions reconstructed in an ECC brick.</p></caption><graphic id="nj398914f5_eps" content-type="print" xlink:href="nj398914f5_pr.eps"></graphic><graphic id="nj398914f5_online" content-type="online" xlink:href="nj398914f5_online.jpg"></graphic></fig><p>Since the inverted momentum distribution 1/<italic>p</italic> has a Gaussian shape, the width of the Gaussian divided by 1/<italic>p</italic><sub>mean</sub> directly gives the momentum resolution estimate <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn4.gif"></inline-graphic></inline-formula>. Its uncertainty can be obtained by propagating the errors on the two components, which are the width of the distribution and the reconstructed momentum. Therefore, the momentum resolution of the 4 GeV c<sup>−1</sup> MC sample of pions passing through an entire OPERA target brick is 20.1 ± 0.6%.</p></sec></sec><sec id="nj398914s3"><label>3.</label><title>Monte Carlo results</title><p>In this section, the results obtained from MC simulations are reported. The MC data correspond to 2, 4, 6 and 8 GeV c<sup>−1</sup> pion samples of 1000 events each that have been generated with the simulation tool ORFEO, based on GEANT and developed in the OPERA framework [<xref ref-type="bibr" rid="nj398914bib18">18</xref>]. It simulates particle interactions inside a brick and includes the main experimental effects such as the track efficiency and spatial resolution.</p><p>This section is divided into two parts: the first gives the results for small incident angles (<italic>θ</italic> < 200 mrad) and the second for large incident angles (<italic>θ</italic> > 200 mrad).</p><sec id="nj398914s3-1"><label>3.1.</label><title>Tracks at small incident angles</title><p>Figure <xref ref-type="fig" rid="nj398914fig6">6</xref> shows the dependence of the scattering angle on <italic>N</italic><sub>cell</sub> for different momenta from 1 to 8 GeV c<sup>−1</sup> <xref ref-type="fn" rid="nj398914fn50"><sup>50</sup></xref><fn id="nj398914fn50"><label>50</label><p>The MC samples have been tuned in order to reproduce the measured <italic>δ</italic><italic>θ</italic><sub>s</sub>, obtained in the scanning of the test beam data samples with the same momenta.</p></fn>. Since the MC samples contain a large number of tracks with the same momentum, the single base-track angular resolution <italic>δ</italic><italic>θ</italic><sub>s</sub> can be directly determined together with the particle momentum from the fits of figure <xref ref-type="fig" rid="nj398914fig6">6</xref>. The results are summarized in table <xref ref-type="table" rid="nj398914t1">1</xref>.</p><fig id="nj398914fig6" position="float"><label>Figure 6.</label><caption id="nj398914fc6"><p>The <italic>θ</italic><sub>meas</sub> dependence on <italic>N</italic><sub>cell</sub> for MC pions of different energies, where <italic>δ</italic><italic>θ</italic><sub>s</sub> has been simulated at a value of <italic>δ</italic><italic>θ</italic><sup>MC</sup><sub>s</sub> = 1.67 mrad. The solid curves correspond to the fitted expectations.</p></caption><graphic id="nj398914f6_eps" content-type="print" xlink:href="nj398914f6_pr.eps"></graphic><graphic id="nj398914f6_online" content-type="online" xlink:href="nj398914f6_online.jpg"></graphic></fig><table-wrap id="nj398914t1" position="float"><label>Table 1.</label><caption id="nj398914tc1"><p>Reconstructed values of the single base-track resolution <italic>δ</italic><italic>θ</italic><sub>s</sub>, the average momentum ⟨<italic>p</italic>⟩ and the momentum resolution <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn5.gif"></inline-graphic></inline-formula> for MC samples of tracks crossing an entire brick and for different energies simulated with <italic>δ</italic><italic>θ</italic><sup>MC</sup><sub>s</sub> = 1.67 mrad.</p></caption><table frame="hsides"><colgroup><col align="left"></col><col align="left"></col><col align="left"></col><col align="left"></col></colgroup><thead><tr><th><italic>p</italic><sub>MC</sub> (GeV c<sup>−1</sup>)</th><th><italic>δ</italic><italic>θ</italic><sub>s</sub> (mrad)</th><th>⟨<italic>p</italic>⟩ (GeV c<sup>−1</sup>)</th><th><inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn6.gif"></inline-graphic></inline-formula>)</th></tr></thead><tbody><tr><td>1</td><td>1.80±0.20</td><td>1.03±0.01</td><td>14.2±0.3</td></tr><tr><td>2</td><td>1.76±0.05</td><td>2.04±0.03</td><td>15.4±0.3</td></tr><tr><td>3</td><td>1.67±0.02</td><td>3.01±0.05</td><td>17.6±0.5</td></tr><tr><td>4</td><td>1.68±0.01</td><td>3.97±0.09</td><td>20.1±0.6</td></tr><tr><td>6</td><td>1.66±0.01</td><td>5.99±0.17</td><td>22.0±0.7</td></tr><tr><td>8</td><td>1.66±0.01</td><td>8.13±0.30</td><td>26.0±1.0</td></tr></tbody></table></table-wrap><p>The values of ⟨<italic>p</italic>⟩ and <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn7.gif"></inline-graphic></inline-formula> have been obtained with the method described in section <xref ref-type="sec" rid="nj398914s2">2</xref>. It appears that the linearity between reconstructed and MC momenta is kept over the whole range and that the momentum resolution worsens with the momentum, as expected. The linearity of the MC reconstructed momentum and the evolution of the momentum resolution show the consistency of the method. They also demonstrate that the approximation of lead as the main scattering element is well suited for the OPERA ECC configuration.</p><p>These results were obtained for tracks passing through 56 cells of an ECC brick. Figure <xref ref-type="fig" rid="nj398914fig7">7</xref> shows how the resolution worsens with increasing momentum and with decreasing track span.</p><fig id="nj398914fig7" position="float"><label>Figure 7.</label><caption id="nj398914fc7"><p>Momentum resolution dependence on track span <italic>N</italic><sub>pl</sub> for MC pions with <italic>δ</italic><italic>θ</italic><sup>MC</sup><sub>s</sub> = 1.67 mrad. The solid lines correspond to the fitted parameterized resolution function of equation (<xref ref-type="disp-formula" rid="nj398914eqn11">11</xref>).</p></caption><graphic id="nj398914f7_eps" content-type="print" xlink:href="nj398914f7_pr.eps"></graphic><graphic id="nj398914f7_online" content-type="online" xlink:href="nj398914f7_online.jpg"></graphic></fig><p>Using all the MC results for different track spans and momenta values, the momentum resolution <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn8.gif"></inline-graphic></inline-formula> has been parameterized in terms of the momentum <italic>p</italic> and track span <italic>N</italic><sub>pl</sub> as <disp-formula id="nj398914eqn11"><label>11</label><tex-math></tex-math><graphic xlink:href="nj398914eqn11.gif"></graphic></disp-formula> The fitted function describes well all momentum measurements from 1 to 8 GeV c<sup>−1</sup> for various track lengths.</p></sec><sec id="nj398914s3-2"><label>3.2.</label><title>Tracks at large incident angles</title><p>A first sample of 2, 4 and 6 GeV c<sup>−1</sup> MC pions has been generated at angles of <italic>θ</italic><sub><italic>X</italic></sub> = 200 and 400 mrad and <italic>θ</italic><sub><italic>Y</italic></sub> = 0 mrad. The <italic>δ</italic><italic>θ</italic><sub><italic>T</italic></sub> and <italic>δ</italic><italic>θ</italic><sub><italic>L</italic></sub> angular dependences have been parameterized according to equations (<xref ref-type="disp-formula" rid="nj398914eqn8">8</xref>) and (<xref ref-type="disp-formula" rid="nj398914eqn9">9</xref>) using the resolution parameters measured with a special brick consisting of a sequence of emulsion films, without lead exposed to 7 GeV c<sup>−1</sup> pions at several incident angles. The track resolution parameters are measured to be <italic>δ</italic><italic>θ</italic><sub><italic>L</italic></sub>(0) = <italic>δ</italic><italic>θ</italic><sub><italic>T</italic></sub>(0) = 2.1 mrad and <italic>ε</italic><sub><italic>z</italic></sub> = 9.3.</p><p>Different MC samples have been simulated using this parameterization of the angular resolution. For the MC event samples at <italic>θ</italic><sub><italic>X</italic></sub> = 200 mrad, the measured values of ⟨<italic>p</italic>⟩ in 3D and 2D projections <italic>T</italic>,<italic>L</italic> are consistent with the expected values. The values of ⟨<italic>p</italic>⟩ in the 3D and <italic>L</italic> projections for 4 and 6 GeV c<sup>−1</sup> pions at <italic>θ</italic><sub><italic>X</italic></sub> = 400 mrad are 10 and 20%, respectively, lower than the true momentum, while there is agreement in the <italic>T</italic> projection. This is explained by the angular dependence of longitudinal resolution, which increases linearly with the angle reaching already a factor of two for track angles of 200 mrad. Note that the <italic>T</italic> projection is not affected since it is angle independent.</p><p>For the same reason, the momentum resolution is stable, as can be observed in figure <xref ref-type="fig" rid="nj398914fig8">8</xref> depicting the dependence of <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn9.gif"></inline-graphic></inline-formula> on angle in the <italic>T</italic> projection. This plot also shows that the momentum resolution in the <italic>T</italic> projection is worse than in the 3D case for tracks at 0 mrad, due to the 50% reduced statistics when using only one projection.</p><fig id="nj398914fig8" position="float"><label>Figure 8.</label><caption id="nj398914fc8"><p>Momentum resolution with respect to the 3D angle <italic>θ</italic> for different MC pion momenta, obtained using only the <italic>T</italic> projection. As a reference, the values obtained at 0 mrad in 3D are indicated by the open symbols.</p></caption><graphic id="nj398914f8_eps" content-type="print" xlink:href="nj398914f8_pr.eps"></graphic><graphic id="nj398914f8_online" content-type="online" xlink:href="nj398914f8_online.jpg"></graphic></fig><p>All the previous considerations lead to the conclusion that, at large angles, the optimal method for estimating the momentum is to use the <italic>T</italic> projection, which is not biased and not angle dependent. However, at small angles, the 3D calculation remains statistically more accurate, resulting in improved momentum resolution. In the algorithm, the threshold for large angles is set to 200 mrad, such that the angular resolution <italic>δ</italic><italic>θ</italic> is kept independent and always equal to the value for <italic>θ</italic> = 0.</p><p>A second sample of 2 and 4 GeV c<sup>−1</sup> MC pions has been generated with <italic>θ</italic><sub><italic>X</italic></sub> = 400 mrad and <italic>θ</italic><sub><italic>Y</italic></sub> = 200 mrad. Since the 3D angle is above 200 mrad, we report only the results obtained with the <italic>T</italic> projection. The value of <italic>δ</italic><italic>θ</italic><sub><italic>T</italic></sub> is fixed at 2.1 mrad. The measured values of ⟨<italic>p</italic>⟩ and <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn10.gif"></inline-graphic></inline-formula> are given in table <xref ref-type="table" rid="nj398914t2">2</xref>. The momentum measurements are consistent with the input values, and the momentum resolutions agree with previous estimates.</p><table-wrap id="nj398914t2" position="float"><label>Table 2.</label><caption id="nj398914tc2"><p>The results on ⟨<italic>p</italic>⟩ and <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn11.gif"></inline-graphic></inline-formula> with the <italic>T</italic> projection for 2 and 4 GeV c<sup>−1</sup> pions, with <italic>θ</italic><sub><italic>X</italic></sub> = 400 mrad and <italic>θ</italic><sub><italic>Y</italic></sub> = 200 mrad.</p></caption><table frame="hsides"><colgroup><col align="left"></col><col align="left"></col><col align="left"></col></colgroup><thead><tr><th><italic>p</italic><sub>MC</sub> (GeV c<sup>−1</sup>)</th><th>⟨<italic>p</italic>⟩ (GeV c<sup>−1</sup>)</th><th><inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn12.gif"></inline-graphic></inline-formula></th></tr></thead><tbody><tr><td>2</td><td>1.9±0.1</td><td>22±1</td></tr><tr><td>4</td><td>3.9±0.2</td><td>26±1</td></tr></tbody></table></table-wrap><p>The method of using the <italic>T</italic> projection for angles larger than 200 mrad is thus validated. Similarly to equation (<xref ref-type="disp-formula" rid="nj398914eqn11">11</xref>) for small angles, it is now possible to parameterize this dependence at large angles as well, using the <italic>T</italic> projection and a similar analytic formula. It gives <disp-formula id="nj398914eqn12"><label>12</label><tex-math></tex-math><graphic xlink:href="nj398914eqn12.gif"></graphic></disp-formula></p><p>This single function, shown in figure <xref ref-type="fig" rid="nj398914fig9">9</xref>, describes all the MC results from 1 to 8 GeV c<sup>−1</sup> for various <italic>p</italic> and <italic>N</italic><sub>pl</sub> values. As in equation (<xref ref-type="disp-formula" rid="nj398914eqn11">11</xref>), it is used to assign the confidence level ranges of single-track momentum measurement.</p><fig id="nj398914fig9" position="float"><label>Figure 9.</label><caption id="nj398914fc9"><p>The momentum resolution dependence on track span <italic>N</italic><sub>pl</sub> for MC pions using the <italic>T</italic> projection with <italic>δ</italic><italic>θ</italic><sup>MC</sup><sub>s</sub> = 1.67 mrad. The solid lines correspond to the fitted parameterized resolution function of equation (<xref ref-type="disp-formula" rid="nj398914eqn12">12</xref>).</p></caption><graphic id="nj398914f9_eps" content-type="print" xlink:href="nj398914f9_pr.eps"></graphic><graphic id="nj398914f9_online" content-type="online" xlink:href="nj398914f9_online.jpg"></graphic></fig></sec><sec id="nj398914s3-3"><label>3.3.</label><title>Comments on method comparisons and systematics</title><p>Various MC studies concerning systematic errors and comparisons with other methods have been carried out in [<xref ref-type="bibr" rid="nj398914bib14">14</xref>]: <list id="nj398914l1" list-type="bullet"><list-item id="nj398914l1.1"><label>•</label><p>As explained in section <xref ref-type="sec" rid="nj398914s2">2</xref>, using the differences between all combinations of pairs of angles separated by <italic>N</italic><sub>cell</sub> cells increases the number of measurements. It has been established that when using only the differences between successive pairs of angles, the fit of the momentum distributions diverges above 4 GeV c<sup>−1</sup>. Moreover, the momentum resolutions are 1.5 times worse.</p></list-item><list-item id="nj398914l1.2"><label>•</label><p>A track momentum <italic>p</italic> can be measured with both <italic>δ</italic><italic>θ</italic> (angular base-track resolution) and <italic>p</italic> as free parameters in the fit procedure. However, an error of a few per cent on <italic>δ</italic><italic>θ</italic> can affect the momentum reconstruction by more than 10% for high-energy tracks (above 4 GeV c<sup>−1</sup>). The best results are obtained with the proposed method keeping <italic>δ</italic><italic>θ</italic> constant. The physical value of the base-track angular resolution is usually between 1 and 2 mrad and depends mainly on the experimental conditions. The value of <italic>δ</italic><italic>θ</italic> can be determined or verified with reference measurements of angular deviations in emulsion films, without scattering in heavy materials.</p></list-item><list-item id="nj398914l1.3"><label>•</label><p>Effects from the correlations among the <italic>θ</italic><sub>meas</sub> values measured at different <italic>N</italic><sub>cell</sub> cells have been estimated by building covariance matrices at different energies and track lengths with MC samples. Fits of the track scattering angle dependence on <italic>N</italic><sub>cell</sub> have been repeated by incorporating the covariance matrix in the minimization function used to compute the track momentum. The difference from the uncorrelated fit is found to be less than a few per cent for the absolute momentum value determination for pion momenta ranging from 2 to 8 GeV c<sup>−1</sup> and the resolution stays unchanged.</p></list-item></list></p></sec></sec><sec id="nj398914s4"><label>4.</label><title>Analysis of pion test beam data</title><p>We report here the results obtained with real data collected in a test beam exposure of OPERA bricks to 2, 4, 6 and 8 GeV c<sup>−1</sup> pions produced by the CERN PS accelerator. Figures <xref ref-type="fig" rid="nj398914fig10">10</xref> and <xref ref-type="fig" rid="nj398914fig11">11</xref> compare the momentum distributions of MC (red solid line) to real data (black crosses) for pions crossing the entire brick with momenta of 2 and 6 GeV c<sup>−1</sup>, respectively. Table <xref ref-type="table" rid="nj398914t3">3</xref> summarizes the values of the single base-track resolution <italic>δ</italic><italic>θ</italic><sub>s</sub>, the average momentum ⟨<italic>p</italic>⟩ and the resolution <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn13.gif"></inline-graphic></inline-formula> obtained for each data sample.</p><fig id="nj398914fig10" position="float"><label>Figure 10.</label><caption id="nj398914fc10"><p>Data/MC comparison for 2 GeV c<sup>−1</sup> pions. Left: momentum distribution. Right: inverted momentum distribution (⟨<italic>p</italic>⟩/<italic>p</italic> − 1).</p></caption><graphic id="nj398914f10_eps" content-type="print" xlink:href="nj398914f10_pr.eps"></graphic><graphic id="nj398914f10_online" content-type="online" xlink:href="nj398914f10_online.jpg"></graphic></fig><fig id="nj398914fig11" position="float"><label>Figure 11.</label><caption id="nj398914fc11"><p>Data/MC comparison for 6 GeV c<sup>−1</sup> pions. Left: momentum distribution. Right: inverted momentum distribution (⟨<italic>p</italic>⟩/<italic>p</italic> − 1).</p></caption><graphic id="nj398914f11_eps" content-type="print" xlink:href="nj398914f11_pr.eps"></graphic><graphic id="nj398914f11_online" content-type="online" xlink:href="nj398914f11_online.jpg"></graphic></fig><table-wrap id="nj398914t3" position="float"><label>Table 3.</label><caption id="nj398914tc3"><p>Reconstructed values of <italic>δ</italic><italic>θ</italic><sub>s</sub>, ⟨<italic>p</italic>⟩ and <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn14.gif"></inline-graphic></inline-formula> obtained with pion test beam data.</p></caption><table frame="hsides"><colgroup><col align="left"></col><col align="left"></col><col align="left"></col><col align="left"></col></colgroup><thead><tr><th><italic>p</italic><sub><italic>π</italic></sub> (GeV c<sup>−1</sup>)</th><th><italic>δ</italic><italic>θ</italic><sub>s</sub> (mrad)</th><th>⟨<italic>p</italic>⟩ (GeV c<sup>−1</sup>)</th><th><inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn15.gif"></inline-graphic></inline-formula></th></tr></thead><tbody><tr><td>2</td><td>2.26±0.01</td><td>2.08±0.05</td><td>19.6±0.4</td></tr><tr><td>4</td><td>1.72±0.01</td><td>4.32±0.08</td><td>19.4±0.4</td></tr><tr><td>6</td><td>1.90±0.01</td><td>5.9±0.2</td><td>21.0±3.0</td></tr><tr><td>8</td><td>1.48±0.01</td><td>7.2±0.5</td><td>32.0±2.0</td></tr></tbody></table></table-wrap><p>The results for real and simulated data are consistent within 11%. Concerning additional systematic uncertainties coming from beam composition, it appears that while the 4 and 6 GeV c<sup>−1</sup> data samples have the expected <italic>p</italic> resolution, the momentum resolution for 2 and 8 GeV c<sup>−1</sup> data is measured to be 4 and 10%, respectively, worse than for the MC expectations. The discrepancy at 8 GeV c<sup>−1</sup> has been understood to come from a higher muon contamination produced after the momentum selection collimators in the pion beam, which was not taken into account in the simulation. In the case of the 2 GeV c<sup>−1</sup> sample, the resolution is slightly worse due to scattering on different materials placed along the beam line in front of the bricks.</p><p>Data at large angles from test beam pions of several energies and different incident angles recorded in one OPERA brick have also been analysed. Figure <xref ref-type="fig" rid="nj398914fig12">12</xref> shows the angular distribution in <italic>θ</italic><sub><italic>X</italic></sub> for reconstructed tracks with length (<italic>N</italic><sub>pl</sub>) ranging from 25 to 30 plates. The different peaks correspond to <list id="nj398914l2" list-type="bullet"><list-item id="nj398914l2.1"><label>•</label><p>2 GeV c<sup>−1</sup> pions at 200 and 400 mrad,</p></list-item><list-item id="nj398914l2.2"><label>•</label><p>4 GeV c<sup>−1</sup> pions at −200 and −400 mrad,</p></list-item><list-item id="nj398914l2.3"><label>•</label><p>6 GeV c<sup>−1</sup> pions at 100, 300 and 600 mrad,</p></list-item><list-item id="nj398914l2.4"><label>•</label><p>8 GeV c<sup>−1</sup> pions at 50 mrad, used as reference data at small angles.</p></list-item></list></p><fig id="nj398914fig12" position="float"><label>Figure 12.</label><caption id="nj398914fc12"><p>Angular distribution in <italic>θ</italic><sub><italic>X</italic></sub> for pion tracks reconstructed in the brick with a span between 25 and 30 plates.</p></caption><graphic id="nj398914f12_eps" content-type="print" xlink:href="nj398914f12_pr.eps"></graphic><graphic id="nj398914f12_online" content-type="online" xlink:href="nj398914f12_online.jpg"></graphic></fig><p>The results for large angles are summarized in table <xref ref-type="table" rid="nj398914t4">4</xref>. The values of ⟨<italic>p</italic>⟩ are compatible with the expected pion beam momentum. The reconstructed momentum resolution can be compared with the one parameterized in equation (<xref ref-type="disp-formula" rid="nj398914eqn12">12</xref>), also given in table <xref ref-type="table" rid="nj398914t4">4</xref>. The measured values are compatible with the expectations except for the 2 GeV c<sup>−1</sup> samples, where the measured value of <inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn16.gif"></inline-graphic></inline-formula> is overestimated by 25–40%. This effect is also due to the scattering on different materials, placed along the beam line in front of the brick during the test beam. The 2 GeV c<sup>−1</sup> pions have been particularly affected, as can be seen from the broad peaks in figure <xref ref-type="fig" rid="nj398914fig12">12</xref>: the interactions on materials lead to a dispersion in angle and in energy, which deteriorates the results on momentum resolution at low energies.</p><table-wrap id="nj398914t4" position="float"><label>Table 4.</label><caption id="nj398914tc4"><p>Results of momentum measurements obtained with the pion test beam at different angles and energies. The calculation was performed in the <italic>T</italic> projection, with <italic>δ</italic><italic>θ</italic><sub><italic>T</italic></sub> fixed at 2.1 mrad.</p></caption><table frame="hsides"><colgroup><col align="left"></col><col align="left"></col><col align="left"></col><col align="left"></col><col align="left"></col><col align="left"></col></colgroup><thead><tr><th><italic>p</italic><sub>true</sub> (GeV c<sup>−1</sup>)</th><th><italic>N</italic><sub>pl</sub></th><th><italic>θ</italic><sub>3D</sub> (rad)</th><th>⟨<italic>p</italic>⟩ (GeV c<sup>−1</sup>)</th><th><inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn17.gif"></inline-graphic></inline-formula> (%)</th><th><inline-formula><tex-math></tex-math><inline-graphic xlink:href="nj398914ieqn18.gif"></inline-graphic></inline-formula> (%)</th></tr></thead><tbody><tr><td>2</td><td>36</td><td>0.2</td><td>2.2±0.2</td><td>37±5</td><td>26</td></tr><tr><td>2</td><td>28</td><td>0.4</td><td>2.1±0.1</td><td>38±3</td><td>30</td></tr><tr><td align="left" colspan="6"></td></tr><tr><td>4</td><td>36</td><td>0.2</td><td>4.3±0.3</td><td>32±2</td><td>32</td></tr><tr><td>4</td><td>28</td><td>0.4</td><td>4.0±0.5</td><td>42±6</td><td>37</td></tr><tr><td align="left" colspan="6"></td></tr><tr><td>6</td><td>36</td><td>0.1</td><td>6.3±0.6</td><td>44±5</td><td>38</td></tr><tr><td>6</td><td>36</td><td>0.3</td><td>6.1±0.6</td><td>38±4</td><td>38</td></tr><tr><td>6</td><td>28</td><td>0.5</td><td>5.7±0.5</td><td>45±4</td><td>44</td></tr></tbody></table></table-wrap><p>Taking into account these effects, one can conclude that MC and test beam data are compatible and give consistent results at both small and large angles.</p><p>The results obtained in this study at different track angles are in agreement with the 23% resolution obtained at small angles (<300 mrad) by Kodama <italic>et al</italic> [<xref ref-type="bibr" rid="nj398914bib09">9</xref>] with similar emulsion stacks of 24 plates exposed to pions of 0.8 and 1.5 GeV c<sup>−1</sup>. The present work adds a major contribution to the use of MCS for momentum measurement in ECC by extending the method to track angles larger than 300 mrad keeping the momentum resolution at large angle better than 40% for momentum less than 6 GeV c<sup>−1</sup>.</p></sec><sec id="nj398914s5"><label>5.</label><title>Soft muon momentum measurement in OPERA</title><p>In order to validate the algorithm with charged particles produced in neutrino interactions, a sample of muons recorded in the 2008 run originating from charged current interactions (<italic>ν</italic><sup>CC</sup><sub><italic>μ</italic></sub>) in the OPERA target bricks was selected. Details of the detector characteristics, data acquisition, event reconstruction and analysis procedures can be found in [<xref ref-type="bibr" rid="nj398914bib19">19</xref>]. More details of the performance of the OPERA electronic detectors can be found in [<xref ref-type="bibr" rid="nj398914bib20">20</xref>].</p><p>The muon momentum in the electronic detectors was obtained either from the range of the particle in the OPERA target tracker or in the spectrometer yoke or from the magnetic spectrometer measurement. The corresponding momentum resolution Δ<italic>p</italic>/<italic>p</italic> is estimated at about 10% for the sample analysed. In order to match the momentum range accessible with the MCS algorithm, charged current interactions where a muon was reconstructed in the electronic detectors with a momentum below 6 GeV c<sup>−1</sup> were selected. The corresponding neutrino interaction vertices were located in the emulsion target, and one emulsion track per event was matched to the muon track predicted by the electronic detectors. Additional selection criteria have been applied on track quality and length. The required minimum track span is 10 cells. The final sample corresponds to 43 events. Figure <xref ref-type="fig" rid="nj398914fig13">13</xref> shows the dependence of the angular deviation on the thickness of lead traversed in the 3D (left) and the <italic>T</italic> (right) coordinates for two different muon tracks. The dashed line shows the expected angular dependence obtained with the momentum measured by the electronic detectors, while the solid line is the result of the fit of the momentum by the MCS method described in this paper. The two momentum measurements from MCS and electronic detectors are fully compatible.</p><fig id="nj398914fig13" position="float"><label>Figure 13.</label><caption id="nj398914fc13"><p>The angular deviation dependence on the thickness of lead traversed by a muon track with an incident angle of 98 mrad using the 3D coordinates (left) and for a muon track with an incident angle of 321 mrad using the <italic>T</italic> coordinate (right). The dashed line shows the expected angular dependence obtained with the momentum measured by the electronic detectors, while the solid line corresponds to the momentum measured by the MCS algorithm in emulsion.</p></caption><graphic id="nj398914f13_eps" content-type="print" xlink:href="nj398914f13_pr.eps"></graphic><graphic id="nj398914f13_online" content-type="online" xlink:href="nj398914f13_online.jpg"></graphic></fig><p>The muon momenta in the selected sample range from 2 to 6 GeV c<sup>−1</sup>, as can be seen in the left plot of figure <xref ref-type="fig" rid="nj398914fig14">14</xref>, which shows the correlation between the two measurements: the right plot shows the relative difference with respect to the electronic detector value.</p><fig id="nj398914fig14" position="float"><label>Figure 14.</label><caption id="nj398914fc14"><p>Left: muon momenta measured by MCS (<italic>P</italic><sub>MCS</sub>) as a function of the momenta obtained from the electronic detectors (<italic>P</italic><sub>ED</sub>). The error bars correspond to the 68% confidence level range. Right: the relative difference between the two measurements with respect to the electronic detector measurement.</p></caption><graphic id="nj398914f14_eps" content-type="print" xlink:href="nj398914f14_pr.eps"></graphic><graphic id="nj398914f14_online" content-type="online" xlink:href="nj398914f14_online.jpg"></graphic></fig><p>The distribution is a Gaussian centred at zero. The width gives an average resolution of (22 ± 4)%, compatible with the expectation obtained by folding the track sample characteristics with the parameterized resolution functions. The width includes also a contribution from the electronic detector resolution. In order to cross-check the estimate of the experimental uncertainty, the differences of the measured inverted momenta have been normalized to the uncertainty estimates on 1/<italic>p</italic>, given by equations (<xref ref-type="disp-formula" rid="nj398914eqn11">11</xref>) and (<xref ref-type="disp-formula" rid="nj398914eqn12">12</xref>) for the different track spans and angles. The resulting Gaussian distribution has a standard deviation of 1.10 ± 0.24, compatible with unity. This shows that the uncertainty for each track is properly estimated.</p></sec><sec id="nj398914s6"><label>6.</label><title>Conclusions</title><p>An improved angular method has been developed to exploit MCS for the momentum measurement of charged particles in ECC detectors. The results of MC studies and pion test beam data show that momenta up to 8 GeV c<sup>−1</sup> can be measured with a resolution better than 30%. The approach has been optimized for small incident angles, as well as for large-angle tracks entering the OPERA lead-emulsion target elements, and is well suited for the neutrino interaction analysis. The results obtained with muons measured with the OPERA electronic detectors have confirmed the validity of the approach and assessed the performance of the algorithm.</p></sec></body><back><ack><title>Acknowledgments</title><p>We thank CERN for the successful operation of the CNGS facility and INFN for the continuous support given to the experiment during the construction, installation and commissioning phases through its LNGS laboratory. We acknowledge funding from the following national agencies: Fonds de la Recherche Scientifique—FNRS and Institut Interuniversitaire des Sciences Nucléaires of Belgium; MoSES of Croatia; CNRS and IN2P3 of France; BMBF of Germany; INFN of Italy; JSPS (Japan Society for the Promotion of Science), MEXT (Ministry of Education, Culture, Sports, Science and Technology), QFPU (Global COE programme of Nagoya University ‘Quest for Fundamental Principles in the Universe’ supported by JSPS and MEXT) and the Promotion and Mutual Aid Corporation for Private Schools of Japan; SNF, the Canton of Bern and the ETH Zurich of Switzerland; the Russian Foundation for Basic Research (grant no. 09-02-00300 a), the programmes of the Presidium of the Russian Academy of Sciences ‘Neutrino Physics’ and ‘Experimental and theoretical researches of fundamental interactions connected with work on the accelerator of CERN’, Programs of Support of Leading Schools (grant no. 3517.2010.2) and the Ministry of Education and Science of the Russian Federation; a Korea Research Foundation grant (KRF-2008-313-C00201); and TUBITAK, the Scientific and Technological Research Council of Turkey. We are also indebted to INFN for providing fellowships and grants to non-Italian researchers. We thank the IN2P3 Computing Centre (CC-IN2P3) for providing computing resources for the analysis and hosting of the central database for the OPERA experiment. We are indebted to our technical collaborators for the excellent quality of their work over many years of the design, prototyping and construction of the detector and of its facilities. Finally, we thank our industrial partners.</p></ack><ref-list content-type="numerical"><title>References</title><ref id="nj398914bib01"><label>1</label><element-citation publication-type="journal" id="nj398914bib01a"><person-group person-group-type="author"><name><surname>Olbert</surname><given-names>S</given-names></name></person-group><year>1952</year><source>Phys. 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type="personal"><namePart type="given">V</namePart><namePart type="family">Yakushev</namePart><affiliation>17312 Moscow, Russia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C</namePart><namePart type="family">S Yoon</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">T</namePart><namePart type="family">Yoshioka</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J</namePart><namePart type="family">Yoshida</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Y</namePart><namePart type="family">Zaitsev</namePart><affiliation>9 Moscow, Russia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S</namePart><namePart type="family">Zemskova</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A</namePart><namePart type="family">Zghiche</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">R</namePart><namePart type="family">Zimmermann</namePart><affiliation></affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><subject><genre>article-type</genre><topic>Paper</topic></subject><originInfo><publisher>IOP Publishing</publisher><dateIssued encoding="w3cdtf">2012-01</dateIssued><dateCreated encoding="w3cdtf">2012-01-16</dateCreated><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.</abstract><note type="footnotes">Author to whom any correspondence should be addressed.</note><relatedItem type="host"><titleInfo><title>New Journal of Physics</title></titleInfo><genre type="Journal">journal</genre><identifier type="eISSN">1367-2630</identifier><identifier type="PublisherID">nj</identifier><part><date>2012</date><detail type="volume"><caption>vol.</caption><number>14</number></detail><detail type="issue"><caption>no.</caption><number>1</number></detail><extent unit="pages"><total>19</total></extent></part></relatedItem><identifier type="istex">7705F1E1B67BCD89127D1990F9986F8DD9B44DFA</identifier><identifier type="DOI">10.1088/1367-2630/14/1/013026</identifier><identifier type="href">http://stacks.iop.org/NJP/14/013026</identifier><identifier type="ArticleID">nj398914</identifier><accessCondition type="use and reproduction" contentType="copyright">IOP Publishing and Deutsche Physikalische Gesellschaft</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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|texte= Momentum measurement by the multiple Coulomb scattering method in the OPERA lead-emulsion target
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