Measurement of inclusive jet production and nuclear modifications in pPb collisions at sqrt(s[NN]) = 5.02 TeV
V Khachatryan, R Erbacher, Camilo Andres Carrillo Montoya, Wagner Carvalho, Maciej Gorski,Danek Kotlinski, Pavel Jez, B Ujvari,Samuel Bein, S Ozturk, R Lander, N C Smith,Y Choi, Roumyana Hadjiiska, Rachel Bartek, A Lath,Willard Johns, P Gras,Pierre Van Hove, Alberto Orso Maria Iorio, U Heintz, Alessandro Thea,Andrew Hart,Sinan Sagir,Kunal Kothekar,Jennifer Chu,Olga Driga,Cristian Pena,Jozsef Molnar,Soureek Mitra,Dominik Nowatschin, P Mine,Ece Asilar, M Rodozov, M Tytgat, Dooyeon Gyun, Robert Schofbeck, L Pape, J F Hirschauer,Burak Bilki,Sachiko Toda, F Yumiceva, V Giakoumopoulou,Reza Goldouzian, C Jorda,Ram Krishna Dewanjee, C Rovelli,Eliza Melo Da Costa,Daniele Fasanella, R Hirosky, J C Sanabria, H Reithler, L M Pant, Danila Tlisov, Austin Baty, Tomas Linden,Zachary Lesko,G G Hanson,G Selvaggi,Fabio Colombo, J Lim, Bhawandeep Bhawandeep,Alexandra Junkes,Yue Shi Lai, W Zeuner, T Camporesi, Raphael Granier De Cassagnac, G Daskalakis,Kin Ho Lo, E Migliore, Ilknur Hos,Giacomo Ortona,Maria Chamizo Llatas, Marcos Correa Martins Junior, Andras Hazi, N Cavallo, Annemarie Magnan, Christopher Mcginn, A Adair,Andre Holzner, Tayung Ling, M Nguyen, D P Stickland, G Apollinari,Ashish Kumar, M Felcini, D Lelas, Selcuk Bilmis,Michal Olszewski, J L Rodriguez,P Lujan, A M Sirunyan, M Mulders, F Palla,Satoshi Hasegawa,Lorenzo Uplegger,David Curry,Sunil Bansal,Roberval Walsh, Victor Krychkine,Christopher Palmer, Kristan Allan Hahn,Tao Huang, P Traczyk,Niklas Pietsch,Willi Bertl, Jesse Heilman,G S F Stephans,Olena Karacheban, Alicia Calderon, T Peiffer,Thomas Kress,Georgia Karapostoli, Niladribihari Sahoo, Fotios Ptochos, N Beni, A Zanetti, M M Baarmand,Valerio Calvelli, Achille Petrilli, Andreas Kornmayer, Clint Richardson, G Anagnostou,Maria Cepeda,Gregory Habib Hammad, Cecile Caillol, Wee Don Teo, J P Chou,Peicho Petkov, N Demaria, D Piccolo,Lukas Vanelderen, Pawel De Barbaro, N Akchurin,P Verdier, R R Betts, V Innocente,Attila Racz, P Baillon, Viktor Savrin,Jyothsna Rani Komaragiri,Matteo Marone, Mario Masciovecchio, Adam Dishaw, Rylan Conway, Michael Northup,Kaya Tatar, Alexx Perloff, Dustin Anderson, A Safonov, Bibhuprasad Mahakud,Viktor Khristenko, S Tkaczyk,Alan Campbell,Arabella Martelli,Arno Heister,Devdatta Majumder, Isidro Gonzalez Caballero, Kelly Beernaert,Sudeshna Banerjee, S Buontempo,Silvia Taroni, C Dragoiu,Evangelos Paradas, Andrea Massironi,Tobias Lapsien,David Lange,Roberto Guida,Ryan Mueller, Gigi Cappello, C Kleinwort, Robert Fischer, Kuntal Mondal, Benjamin Michlin, Maximilian Heindl, P Wittich, G Abbiendi, M Paulini, Diego Matos Figueiredo, Altan Cakir, P Lariccia,Stefan Piperov, J M Hernandez, Lauri Wendland, Yusuf Erdogan,Huaqiao Zhang, Yutaro Iiyama,Vladimir Petrov,Emine Gurpinar,Mario Galanti, Alberto Sanchez Hernandez, Roko Plestina, G A Alves,Iurii Antropov,Mark Turner, Alexander Nikitenko, K Burkett,Seth Cooper, R Demina,Wuming Luo, Federico Nguyen,J R Dittmann,Chunjie Wang,Elvire Bouvier, D Krofcheck,Claudia Pistone,Z A Ibrahim, Timo Peltola, Raymond Patrick Kenny,Helen F Heath,S Ahuja, Annik Olbrechts,Matthias Hamer, Pedro Silva,Christopher West, S Wasserbaech,Alexey Svyatkovskiy, J Malcles, E Butz,P Kyberd,Boris Mangano, Richard Loveless, Alexander Dermenev,Dezso Horvath,Andrea Delgado, Andres Tiko, T J Orimoto, David Romero Abad, Alex Garabedian, A V Gritsan, Rachel Yohay, W Lohmann, Riccardo Andrea Manzoni,Francesco Fiori,Gaia Maria Berruti, Benjamin Charles Radburnsmith,Yi Chen, Apostolos Panagiotou, L J Gutay,Igor Smirnov, Frank Jm Geurts,Carlos Florez, Lucija Sudic, Martin Lipinski, Charles Harrington, Claudio Caputo,Filip Thyssen,Muhammad Waqas, Evan Wolfe,Bibhuti Parida, Giancarlo Mantovani, Philip Symonds, Evrim Ersin Kangal, Maryam Zeinali, Antonio Maria Perezcalero Yzquierdo, K Kaadze,Renato Campanini,Alexander Schmidt,F L Navarria, Matthias Schroder,Federica Primavera,Ashim Roy, Klaas Padeken, C Civinini,Alexey Kamenev,Konstantin Kanishchev, Matthieu Marionneau, Ivo Nicolas Naranjo, Malte Hoffmann,Rizki Syarif,Manoj Sharan, I Papadopoulos, M Schmitt, Patricia Rebello Teles,P Paolucci, Deniz Sunar Cerci, Ayman Mahrous,Javier Duarte, L Moroni, E Auffray, K Nawrocki, J Conway, I Fisk, P Garciaabia, Pablo Martinez Ruiz Del Arbol, Mukund Varma,Hasan Ogul, O Gutsche, Alexis Fagot,Burin Asavapibhop,I Vardanyan, Andreas Guth, Q Ingram,Thomas Eichhorn,Stanislav Lisniak, Lana Beck,Gianluca Cerminara, S Lacaprara,Matteo Sani,A Zghiche,D Abbaneo, P Sphicas, Willis Lin, Nairit Sur, S Maselli,Begona De La Cruz,Joaquin Emilo Siado,Maria Florencia Canelli,C Hensel,S Z Shalhout, Martin Kirakosyan,Esa Tuovinen, C Tully, A Santocchia, John Bradmillerfeld,Yanchu Wang,G Masetti, D Son,Tristan Du Pree,Rishi Patel, N Neumeister,Hamit Mermerkaya, Colin Bernet, C H Shepherdthemistocleous, S My, E Torassa, E O Olaiya, Ilaria Vai, Douglas Rank, Y Sirois,Qiao Xu, Viktor Matveev, W Erdmann, V Ciulli,Daniele Del Re, F Cavallari,Giuseppe Codispoti, Lina Milena Huertas Guativa,Erhan Gulmez,Min Sang Ryu, J Schieck,Sue Ann Koay,Jacopo Bernardini, Kittikul Kovitanggoon, J Ellison, L Benussi, K Mazumdar, Christina Snyder,Enrique Calvo, C P Jessop,Anthony Moeller, Annika Vanhoefer,Stefan Gundacker,Matthew Snowball, Vladimir Mossolov, P Ronchese, Jonatan Piedra Gomez, K Krajczar,Wei Xie,Sara Fiorendi,Eike Schlieckau,Michael Wang, I Golutvin, N Zaganidis, Chamath Kottachchi Kankanamge Don,Anna Teresa Meneguzzo, Pooja Saxena, Emrah Tiras, Carley De Oliveira Martins, T Rodrigo,Johannes Brandstetter, U Joshi, T Aziz, F Meijers, Milos Dordevic,Gennady Mesyats, M Diemoz,B Choudhary, V Bhatnagar,A Ahmad, G Benelli, Joao Rodrigues Antunes,N Terentyev, T Bergauer, Sergei Bitioukov, J Wagnerkuhr,Markus Klute, A Belyaev, Andrea Carlo Marini,Robert Bainbridge, G B Mohanty, W Adam, T Sarangi, Paul David Luckey, J Flix,Soren Erdweg,Mohsen Naseri,Sergey Troshin,G Sguazzoni,Matthias Komm, M Margoni,Michele De Gruttola, Norbert Tambe,Thi Hien Doan, Werner Sun, H Jung, Dan Knowlton, Oleksii Toldaiev,Wajid Ali Khan, D Bloch, T Rohe,Ran Bi,Alain Herve, D Kovalskyi, Kuanhsin Chen, C Charlot, Darren Puigh, Gyorgy Bencze, Louis Antonelli, H B Newman, Alexander Ershov,Christian Barth, Apichart Hortiangtham, Anterpreet Kaur, Deniz Poyraz, Michael Wayne Arenton, Juan Ramon Castineiras De Saa,Michael Krohn, L Teodorescu,Giacomo Fedi,Maurizio Lo Vetere, Seth Conrad Zenz,Vincenzo Daponte,Keith Rose, Guillelmo Gomez Ceballos, R Eusebi,Christopher Brew, A Soha,Tyler Ruggles, A Kharchilava, G Zumerle, Florian Scheuch,Marius Preuten,Weifeng Ji, D Ryckbosch, A Askew, Vassili Kachanov, I P J Shipsey, C Campagnari,Alexander Savin,Clemens Lange, Adish Vartak, D Gele, L Uvarov,Rebeca Gonzalez Suarez,B Betchart,Egidio Longo,Luca Cadamuro, Laurent Thomas,Tobias Pook, F Simonetto,M Chadeeva, I M Nugent, Ferdos Rezaei Hosseinabadi, G Eckerlin,Isabel Ojalvo,Y D Oh,Can You,German Martinez, S Tosi, M Kasemann, Dinyar Rabady,Jia Fu Low, Pramod Lamichhane, Pedro Guilherme Ferreira Parracho, M Maggi, Rocio Vilar Cortabitarte, Yee Hsiung, Felix Frensch, Claudia Seitz,Thomas Esch, K A Ulmer,Christian Sander,Peter Thomassen, Qamar Hassan, P Bloch,Philip Harris, F Chlebana, Nathaniel Pastika, M Besancon, Jonathan Hollar, S J Wimpenny,Jennifer Poehlsen, Christian Contrerascampana,Bhawna Gomber, K F Johnson, Gian Luca Pinna Angioni,Dan Klein,L Spiegel, Francesco Pandolfi, G R Snow,Christof Roland, S Jindariani,David Sheffield,A C Bundock, M Finger,Georg Auzinger, Terence Libeiro, P Schleper,Xinmei Niu, P K Mal,Shivali Malhotra, S Malik, Christopher Anelli,Vitaly Smirnov, Petr Levchenko, Mikhail Gavrilenko, S Ganjour, F Fabozzi, Giuseppe Benedetto Cerati,Monoranjan Guchait,Ben Bylsma, S Czellar, Daniele Marconi,Thomas Reis,Damir Devetak, Mikhail Makouski, Roman Ryutin, Thomas Lenzi,Sadia Khalil,Nayana Majumdar, Luca Pernie, D Cutts,Hannes Sakulin, D Saltzberg, Paolo Gunnellini,Martti Raidal, Taimoor Khurshid,B L Winer, Phillip Russell Dudero,Yuri Musienko, Javier Andres Brochero Cifuentes, A Gribushin, G Rakness, B Kilminster, P Merkel,Simon Spannagel, M Chiorboli, Darin Baumgartel, Nikolai Skatchkov, E Vlasov,Sven Dildick,Marc Osherson, Shawn Williamson, Adrian Quintario Olmeda, Carsten Heidemann, Ievgen Korol, Valentin Sulimov,Jeffrey Richman, G Bagliesi,Norraphat Srimanobhas,Aniello Spiezia,Yongsun Kim,Kenneth Long, Marion Murumaa, S Gninenko, Xavier Coubez, Tomasz Frueboes, J Letts, U Goerlach, L Barone, D Carlsmith,Leonardo Di Matteo,Marton Bartok, Shihchuan Kao,Deepak Kumar Sahoo,Alexandre Leonard, A Givernaud, Chuanzhe Lin, Amithabh Shrinivas, Giuseppe Fasanella, P Vitulo, Alice Cocoros,Jose Monroy,R M Harris,Junquan Tao, Pablo De Castro Manzano,E Chapon, Alajos Makovec, M Spiropulu, R Sacchi,Dominique Gigi,Giacomo Bruno,Zuhal Seyma Demiroglu,Rebecca Lane, H Bialkowska, Fionn Ball,Niki Saoulidou, P A Piroue, A Geiser,Martin Gorner, P Jarry,J Vaitkus,P Cirkovic,David Barney,Robert Stringer,Steve Schnetzer,Tejinder Virdee,Vallary Bhopatkar, Emmanuel Contrerascampana, C Amsler, Manuel Olmedo Negrete, Shilpi Jain,A Santoro, Catherine Vander Velde,Kevin Stenson,Batool Safarzadeh, C Hill, K Maeshima, A Randleconde,Benjamin Carlson,Christian Hartl,Yao Weng, C Schwick, E Halkiadakis,S Dey,B Calpas, R Stone, G Bolla,Silvio Donato,Marek Walczak,E B Hughes, O Pooth, Andrey Marinov,Taylan Yetkin, Kamuran Dilsiz,Fabrizio Fabbri, Rebekka Sophie Hoing, Michael Brodski, E Conte,P Mcbride, Aaron Levine, R G Kellogg,Matti J Kortelainen,A Triossi, G Mitselmakher, Deborah Duchardt, F Hartmann, Fuat Ilkehan Vardarli, V E Barnes, U Behrens, Boris Grynyov, Owen Baron,Ajeeta Khatiwada, Leonid Tourtchanovitch, Sunil Dogra,Daniel Arcaro,Yetkin Yilmaz, A Colaleo,Victoria Zhukova, E Gottschalk, Laurent Forthomme,Johannes Hauk, Mariarosaria Dalfonso, M U Mozer, Nil Valls, Wenxing Fang, J Rander,Joosep Pata, Joshua Bendavid,Marc Dobson,Barbara Clerbaux, Valerio Re,Claudiaelisabeth Wulz, Jordan Damgov, S Dasu, Shimaa Abu Zeid, Pieter Everaerts,Thomas Williams,Morris Swartz, Otto Hindrichs,Sebastian Naumannemme, Cesar Augusto Bernardes,Siddharth Narayanan, James Zabel, Suvankar Roy Chowdhury, Analu Custodio, R Wallny, Joram Berger, S Obraztsov,Ridhi Chawla, Andreas Kunsken, P R Hobson, S Jabeen, F Beaudette,Abdulla Abdulsalam, Edouard Boos,Rosamaria Venditti, Miguel Vidal Marono,Zhenyu Chen,Luigi Fiore, Junghwan Goh, P Iaydjiev,Sergey Vavilov, Nadir Daci,Ryo Yonamine,Stefano Mersi, Ivan Marchesini,Ferhat Ozok,Yuta Takahashi,Robin Aggleton, Sho Maruyama, A Venturi, P G Mercadante,Sebastien Brochet,Anita Topkar, S Somalwar, D Liko, F Couderc, Andrea Gozzelino, Joanne Cole, Arnerasmus Draeger, S Sarkar, Niels Dupont,S Grunendahl, A Mohapatra, James John Brooke,Juan Alcaraz Maestre, L Brigliadori, Dominic Smith, Anshul Kapoor,Andrea Benaglia, Angelo De Souza Santos,Wit Busza,Yeonju Go,Jianguo Bian,Heiko Geenen,Denis Favart,Cristina Fernandez Bedoya,Thomas Muller, Jose Chinellato, D Menasce,Quan Wang, V Sordini, I Vorobiev, P Maksimovic, M W Grunewald,Frank Golf, V J Smith,J Keaveney,Alfredo Gurrola, Ludivine Ceard, Conor Henderson,Silvia Goy Lopez, K Sumorok, D Denegri,Suchandra Dutta, Hafeez R Hoorani,Victor Murzin, Nazar Bartosik, Richard Vidal, E Focardi,Alessio Ghezzi,N Krasnikov, Kirika Uchida, Juska Pekkanen, Sanmay Ganguly, M Gallinaro, L Mundim,I Macneill, Artur Lobanov, Jason Gran, Dmitri Konstantinov,Paul Papacz, N Chanon,Paolo Montagna, D H Miller, B Dahmes, Christine Obrien, Gregor Mittag, Alberto Escalante Del Valle, E Meschi,Luca Brianza,Nabarun Dev,Jay Roberts,N Stefaniuk,Stefaan Tavernier, L Scodellaro, H Stadie,Susan Dittmer, Nicolo Tosi,Pelin Kurt, A Ledovskoy,Mohd Adli Bin Md Ali,Thea Klaeboe Aarrestad,Bastian Kargoll, D Bonacorsi, J A Coughlan,Marcin Konecki, A C Mignerey, Benedikt Maier,Lingshan Xu, C Grandi, Nikita Beliy,Andrew Levin,Young Ho Shin,M Girone, A Messineo, Axel Konig, Bajrang Sutar, M Paganoni,Narumon Suwonjandee,Igor Miagkov,Kyong Sei Lee,Anatoli Zarubin, T Lomtadze,Sergey 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Kumar,Daniel Meister,Mauro Verzetti, B Ille, V Blobel, Alex Van Spilbeeck,Simon Regnard,Avishek Chatterjee, David Petyt,F Fanzago, M Arneodo,Hannsjoerg Artur Weber, Emanuele Usai,Amandeep Kaur Kalsi,V Perelygin,Andrea Giammanco, Jorgen Dhondt, Anthony Poll,Manoj Jha, R Covarelli, C Newmanholmes,Sandeep Bhowmik, Vivian Odell,S Wilbur, Bugra Bilin,Kamal Lamichhane, D J Kong,Clemencia Mora Herrera, P Adzic,Benoit Roland, Raghav Kunnawalkam Elayavalli, J Bunn,Seema Sharma,Stefano Ragazzi, A Dierlamm, Wan Ahmad Tajuddin Wan Abdullah, C Biino, M Zeyrek, A Belloni,Kurt Jung,Luciano Orsini, Jesus Manuel Vizan Garcia, G Majumder, Carmen Diez Pardos, P Zotto, T Dorland,Joseph Mccartin, Martin Delcourt, Bilal Kiani,Andres G Delannoy, Seyed Mohsen Etesami,Michel Della Negra, Aytul Adiguzel, Rudolf Fruehwirth, J Linacre, S Gascon, Ryan Kelley,Ali Celik, T Sakuma,Paoti Chang, Metin Yalvac, Hannes Mildner, Marcello Mannelli, Gerrit Patrick Van Onsem,Vishwajeet Jha, Christine Mclean, Matthew Jones,Thomas J Weiler, Z Zolkapli, Celso Martinez Rivero, Dave M Newbold, P Markowitz, Bernardo Gomez Moreno, Patrick Dunne,Karol Bunkowski, Ali Fahim,Harry Cheung, H Topakli, R Dalessandro, M Flechl,Mojtaba Mohammadi Najafabadi,J D Lewis,Matthias Wolf,V Rusinov, Joshua Kunkle, P Lecoq, Felix Bachmair,Annecatherine Le Bihan, E Barberis, A Mott, Nikitas Loukas, T Lampen, Erik Dietzlaursonn, Nikoloz Skhirtladze, Candan Dozen, A Kyriakis, Ted Kolberg, Y Gershtein, S Petrushanko, Adel Awad, M Abbrescia,Elizabeth Sextonkennedy, Anatoli Pashenkov, Federico De Guio, A H Ball,Konstantinos Theofilatos,Paolo Meridiani, B Casal, Charles Mueller, Rocky Bala Garg, Annelaure Pequegnot,Maxim Konyushikhin,Andrea Rizzi, Semiray Girgis, Jamal Rorie, Francesca Riccitam, C Mariotti, Hyunsoo Kim, D Bisello, Oleg Prokofyev, Tomislav Seva, Yenjie Lee, Nathaniel Woods,Ashutosh Bhardwaj, A Gaz, P Salvini, D Acosta, A Pfeiffer, S Hewamanage, M Erdmann, L Mirabito, Pohsun Chen, Martin Bodlak, Raffaella Radogna,Robert J Cousins, Giulia Dimperio,Renyuan Zhu, Jorge F De Troconiz, Alexey Volkov, Jaehyeok Yoo, Jeanlouis Faure, Geonmo Ryu,Andreas Hinzmann, Fredmarkus Helmut Stober, Sergey Shmatov, Jennifer Ngadiuba,Ijaz Ahmed, Krishna Thapa, Edmilson Jose Tonelli Manganote, A Montanari, S Hagopian, Marco Esposito, James Dolen, Georg Steinbruck, William Mcbrayer,Wolfgang Waltenberger, Bayram Tali,Piet Verwilligen, Alessio Boletti, J Thom, Walter Luiz Alda Junior, Ankita Mehta, A Toropin, T Dorigo, Michael Mooney, F Nessitedaldi, D R Wood, Jessica Leonard, A Korytov, Tengizi Toriashvili, D Cussans, Valentina Gori, Patricia Lobelle Pardo, Sinem Salva Diblen,Jacopo Pazzini, I Dumanoglu, Shuai Liu, Matthew Chasco,Jim Freeman, Ewerton Belchior Batista Das Chagas,R Rossin, Muhammad Shoaib, Ekaterina Avdeeva, J Nash, S Salur, Hua Wei,M Danilov, Pawandeep Jandir,Jessica Brinson,Mario Kadastik, Joern Schwandt, Pierluigi Bortignon, Vyacheslav Valuev,G Pugliese, G B Smith,Abideh Jafari, Victor Golovtsov, Robyn Lucas, Emyr Clement, Valentin Knunz,Ganna Dolinska, Andrey Pozdnyakov, Ekaterina Kuznetsova,Joao Varela, M G Albrow,Rino Castaldi, Sean Flowers, Zaixing Mao,Christophe Delaere,Paula Eerola,P Barria, F R Cavallo, Pavel Sorokin, Jose Cupertino Ruiz Vargas,Alice Florent, Vincenzo Monaco, Oscar Gonzalez Lopez, M A Ciocci, Hengne Li, Tobias Verlage,Livia Soffi, M Bluj, Roger Wolf, Brian Calvert,Hesheng Chen, T Hebbeker, Charles Maguire, Nikolay Tyurin, P Hidas, Daniele Vadruccio,Orduna Jesus,Giovanni Petrucciani, Bora Akgun, Myriam Schonenberger, Matthew Walker,Ping Tan, Hannes Neugebauer, S W Lee,Andrew D Johnson, T Tuuva,Hamed Bakhshiansohi, Karim Damun Trippkewitz, Himali Kalakhety,Piergiulio Lenzi, Deborah Pinna,F Wurthwein, Sam Daniel Mullin, M Chertok,Olga Evdokimov, Thomas Schoernersadenius, Xin Sun, Marco Rossini, J Mousa, G Vesztergombi, M Guilbaud, Christopher Cowden, F Sikler, Maximilian Knut Kiesel, Salvatore Costa, Vladimir Andreev, Halil Saka, C Seez,Jasbir 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Margherita Obertino, P Kokkas, Stefano Casasso, Igor Azhgirey, Jochen Ott, K Borras, D Treille, Allison Reinsvold, S Malvezzi, F Pauss,S R Dugad, Maiko Takahashi,Babak Rahbaran, M Kaur, M Grothe, G Flucke, Benoit Courbon, Kevin Sung
mag（2016）
引用 82|浏览291
摘要
Inclusive jet production in pPb collisions at a nucleon-nucleon (NN) center-of-mass energy of sqrt(s[NN])=5.02 TeV is studied with the CMS detector at the LHC. A data sample corresponding to an integrated luminosity of 35 inverse nanobarns is analyzed.The jet transverse momentum spectra are studied in seven pseudorapidity intervals covering the range -2.0 u003ceta[CM]u003c 1.5 in the NN center-of-mass frame. The jet production yields at forward and backward pseudorapidity are compared and no significant asymmetry about eta[CM] = 0 is observed in the measured kinematic range. The measurements in the pPb system are compared to reference jet spectra obtained by extrapolation from previous measurements in pp collisions at sqrt(s)=7 TeV. In all pseudorapidity ranges, nuclear modifications in inclusive jet production are found to be small, similar to the predictions from next-to-leading order perturbative QCD calculations that incorporate nuclear effects in the parton distribution functions.
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