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Charge correlations using the balance function in

Pb–Pb collisions at√sNN = 2.76 TeV

Betty Abelevbs, Jaroslav Adamak, Dagmar Adamovabz, Andrew MarshallAdaredw, Madan Aggarwalcd, Gianluca Aglieri Rinellaag, Michelangelo

Agnellocx,cj, Andras Gabor Agocsdv, Andrea Agostinelliaa, ZubayerAhammeddr, Nazeer Ahmadq, Arshad Ahmadq, Sang Un Ahnan,bl, Sul-AhAhnbl, Muhammad Ajazo, Alexander Akindinovax, Dmitry Aleksandrovcp,

Bruno Alessandrocx, Andrea Alicict,l, Anton Alkinc, Erick JonathanAlmaraz Avinabh, Johan Almeai, Torsten Altam, Valerio Altiniae, SedatAltinpinarr, Igor Altsybeevds, Cristian Andreibv, Anton Androniccm,

Venelin Anguelovci, Jonas Anielskibf, Christopher Daniel Ansons, TomeAnticiccn, Federico Antinoricu, Pietro Antoniolict, Laurent Bernard

Aphecetchedc, Harald Appelshauserbd, Nicolas Arborbo, Silvia Arcelliaa,Andreas Arendbd, Nestor Armestop, Roberta Arnaldicx, Tomas Robert

Aronssondw, Ionut Cristian Arsenecm, Mesut Arslandokbd, AndzheyAsryands, Andre Augustinusag, Ralf Peter Averbeckcm, Terry Awesca, JuhaHeikki Aystoap, Mohd Danish Azmiq,cf, Matthias Jakob Bacham, Angela

Badalada, Yong Wook Baekbn,an, Raphaelle Marie Bailhachebd, RenuBalacg,cx, Rinaldo Baldini Ferrolil, Alberto Baldisserin, Fernando BaltasarDos Santos Pedrosaag, Jaroslav Banay, Rama Chandra Baralaz, RobertoBarberaz, Francesco Barileae, Gergely Gabor Barnafoldidv, Lee StuartBarnbycr, Valerie Barretbn, Jerzy Gustaw Bartkedf, Maurizio Basileaa,

Nicole Bastidbn, Sumit Basudr, Bastian Bathenbf, Guillaume Batignedc,Boris Batyunyabj, Christoph Heinrich Baumannbd, Ian Gardner Beardenbx,Hans Beckbd, Nirbhay Kumar Beheraar, Iouri Belikovbi, Francesca Belliniaa,

Rene Bellwieddl, Ernesto Belmont-Morenobh, Gyula Bencedidv, StefaniaBeolev, Ionela Berceanubv, Alexandru Bercucibv, Yaroslav Berdnikovcb,Daniel Berenyidv, Anais Annick Erica Bergognondc, Dario Berzanov,cx,

Latchezar Betevag, Anju Bhasincg, Ashok Kumar Bhaticd, Jihyun Bhomdp,Nicola Bianchibp, Livio Bianchiv, Jaroslav Bielcikak, Jana Bielcikovabz, Ante

Bilandzicbx, Sandro Bjelogrlicaw, Francesco Blancodl, F. Blancoj, Dmitry

1M.V.Lomonosov Moscow State University, D.V.Skobeltsyn Institute of NuclearPhysics, Moscow, Russia

2University of Belgrade, Faculty of Physics and "Vinča" Institute of Nuclear Sciences,Belgrade, Serbia

Preprint submitted to Physics Letters B October 17, 2018

Blaucp, Christoph Blumebd, Marco Boccioliag, Stefan Boettgerbc, AlexeyBogdanovbt, Hans Boggildbx, Mikhail Bogolyubskyau, Laszlo Boldizsardv,Marek Bombaraal, Julian Bookbd, Herve Boreln, Alexander Borissovdu,

Francesco Bossucf, Michiel Botjeby, Elena Bottav, Ermes Braidotbr, PeterBraun-Munzingercm, Marco Bregantdc, Timo Gunther Breitnerbc, Theo

Alexander Brokerbd, Tyler Allen Browningck, Michal Brozaj, Rene Brunag,Elena Brunav,cx, Giuseppe Eugenio Brunoae, Dmitry Budnikovco, Henner

Bueschingbd, Stefania Bufalinov,cx, Predrag Buncicag, Oliver Buschci, EdithZinhle Buthelezicf, Diego Caballero Ordunadw, Davide Caffarriab,cu, XuCaig, Helen Louise Cainesdw, Ernesto Calvo Villarcs, Paolo Camerinix,Veronica Canoa Romank, Giovanni Cara Romeoct, Francesco Carenaag,

Wisla Carenaag, Nelson Carlin Filhodi, Federico Carminatiag, Amaya OfeliaCasanova Diazbp, Javier Ernesto Castillo Castellanosn, Juan FranciscoCastillo Hernandezcm, Ester Anna Rita Casulaw, Vasile Catanescubv,

Costanza Cavicchioliag, Cesar Ceballos Sanchezi, Jan Cepilaak, PiergiorgioCerellocx, Beomsu Changap,dy, Sylvain Chapelandag, Jean-Luc FernandCharvetn, Subhasis Chattopadhyaydr, Sukalyan Chattopadhyaycq, IshaChawlacd, Michael Gerard Cherneycc, Cvetan Cheshkovag,dk, Brigitte

Cheynisdk, Vasco Miguel Chibante Barrosoag, David Chinellatodl, PeterChochulaag, Marek Chojnackibx, Subikash Choudhurydr, Panagiotis

Christakoglouby, Christian Holm Christensenbx, Peter Christiansenaf,Tatsuya Chujodp, Suh-Urk Chungcl, Corrado Cicalocw, Luisa Cifarelliaa,ag,l,Federico Cindoloct, Jean Willy Andre Cleymanscf, Fabrizio Coccettil, Fabio

Colamariaae, Domenico Colellaae, Alberto Colluw, Gustavo ConesaBalbastrebo, Zaida Conesa del Valleag, Megan Elizabeth Connorsdw,

Giacomo Continx, Jesus Guillermo Contrerask, Thomas Michael Cormierdu,Yasser Corrales Moralesv, Pietro Cortesead, Ismael Cortes Maldonadob,Mauro Rogerio Cosentinobr, Filippo Costaag, Manuel Enrique Cotalloj,

Elisabetta Cresciok, Philippe Crochetbn, Emilia Cruz Alanizbh, RigobertoCruz Albinok, Eleazar Cuautlebg, Leticia Cunqueirobp, Andrea Daineseab,cu,Hans Hjersing Dalsgaardbx, Andrea Danubb, Supriya Dasd, Debasish Dascq,

Kushal Dascq, Indranil Dasat, Sadhana Dashar, Ajay Kumar Dashdj,Sudipan Dedr, Gabriel de Barrosdi, Annalisa De Caroac,l, Giacinto de

Cataldocz, Jan de Cuvelandam, Alessandro De Falcow, Daniele DeGruttolaac,l, Hugues Delagrangedc, Andrzej Deloffbu, Nora De Marcocx,Ervin Denesdv, Salvatore De Pasqualeac, Airton Deppmandi, GinevraD’Erasmoae, Raoul Stefan de Rooijaw, Miguel Angel Diaz Corcheroj,Domenico Di Bariae, Thomas Dietelbf, Carmelo Di Giglioae, Sergio Di

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Libertocv, Antonio Di Mauroag, Pasquale Di Nezzabp, Roberto Diviaag,Oeystein Djuvslandr, Alexandru Florin Dobrindu,af, Tadeusz Antoni

Dobrowolskibu, Benjamin Doniguscm, Olja Dordicu, Olga Drigadc, AnandKumar Dubeydr, Andrea Dublaaw, Laurent Ducrouxdk, Pascal Dupieuxbn,A.K. Dutta Majumdarcq, Domenico Eliacz, David Philip Emschermannbf,

Heiko Engelbc, Barbara Erazmusag,dc, Hege Austrheim Erdalai, BrunoEspagnonat, Magali Danielle Estiennedc, Shinichi Esumidp, David Evanscr,

Gyulnara Eyyubovau, Daniela Fabrisab,cu, Julien Faivrebo, DavideFalchieriaa, Alessandra Fantonibp, Markus Faselcm,ci, Roger Worsley

Fearickcf, Dominik Fehlkerr, Linus Feldkampbf, Daniel Feleabb, AlessandroFeliciellocx, Bo Fenton-Olsenbr, Grigory Feofilovds, Arturo FernandezTellezb, Alessandro Ferrettiv, Andrea Festantiab, Jan Figieldf, MarcelFigueredodi, Sergey Filchaginco, Dmitry Finogeevav, Fiorella Fiondaae,

Enrichetta Maria Fioreae, Emmanuel Floratosce, Michele Florisag, SiegfriedValentin Foertschcf, Panagiota Fokacm, Sergey Fokincp, Enrico

Fragiacomocy, Andrea Francesconag,ab, Ulrich Michael Frankenfeldcm, UlrichFuchsag, Christophe Furgetbo, Mario Fusco Girardac, Jens Joergen

Gaardhojebx, Martino Gagliardiv, Alberto Gagocs, Mauro Galliov, DhevanRaja Gangadharans, Paraskevi Ganotica, Jose Garabatoscm, Edmundo

Garcia-Solism, Corrado Gargiuloag, Irakli Garishvilibs, Jochen Gerhardam,Marie Germaindc, Claudio Geunan, Andrei George Gheataag, Mihaela

Gheatabb,ag, Bruno Ghidiniae, Premomoy Ghoshdr, Paola Gianottibp, MartinRobert Girarddt, Paolo Giubellinoag, Ewa Gladysz-Dziadusdf, Peter

Glasselci, Ramon Gomezdh,k, Elena Gonzalez Ferreirop, Laura HelenaGonzalez-Truebabh, Pedro Gonzalez-Zamoraj, Sergey Gorbunovam, Ankita

Goswamich, Sven Gotovacde, Lukasz Kamil Graczykowskidt, RobertGrajcarekci, Alessandro Grelliaw, Costin Grigorasag, Alina Gabriela

Grigorasag, Vladislav Grigorievbt, Ara Grigoryana, Smbat Grigoryanbj,Boris Grinyovc, Nevio Grioncy, Philippe Grosaf, Jan Fiete

Grosse-Oetringhausag, Jean-Yves Grossiorddk, Raffaele Grossoag, FedorGuberav, Rachid Guernanebo, Barbara Guerzoniaa, Maxime Rene JosephGuilbauddk, Kristjan Herlache Gulbrandsenbx, Hrant Gulkanyana, Taku

Gunjido, Anik Guptacg, Ramni Guptacg, Rudiger Haakebf, Oystein SennesetHaalandr, Cynthia Marie Hadjidakisat, Maria Haiducbb, Hideki Hamagakido,

Gergoe Hamardv, Byounghee Hant, Luke David Hanrattycr, AlexanderHansenbx, Zuzana Harmanovaal, John William Harrisdw, Matthias Hartigbd,

Austin Hartonm, Despoina Hatzifotiadouct, Shinichi Hayashido, ArsenHayrapetyanag,a, Stefan Thomas Heckelbd, Markus Ansgar Heidebf, Haavard

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Helstrupai, Andrei Ionut Herghelegiubv, Gerardo Antonio Herrera Corralk,Norbert Herrmannci, Benjamin Andreas Hessdq, Kristin Fanebust Hetlandai,

Bernard Hicksdw, Boris Hippolytebi, Yasuto Horido, Peter ZaharievHristovag, Ivana Hrivnacovaat, Meidana Huangr, Thomas Humanics, Dae

Sung Hwangt, Raphaelle Ichoubn, Radiy Ilkaevco, Iryna Ilkivbu, MotoiInabadp, Elisa Incaniw, Pier Giorgio Innocentiag, Gian Michele Innocentiv,Mikhail Ippolitovcp, Muhammad Irfanq, Cristian George Ivancm, VladimirIvanovcb, Andrey Ivanovds, Marian Ivanovcm, Oleksii Ivanytskyic, Adam

Wlodzimierz Jacholkowskiz, Peter Jacobsbr, Haeng Jin Jangbl, MalgorzataAnna Janikdt, Rudolf Janikaj, Sandun Jayarathnadl, Satyajit Jenaar,

Deeptanshu Manu Jhadu, Raul Tonatiuh Jimenez Bustamantebg, PeterGraham Jonescr, Hyung Taik Jungan, Anton Juskocr, Alexei Kaidalovax,Sebastian Kalcheram, Peter Kalinakay, Tuomo Esa Aukusti Kalliokoskiap,

Alexander Philipp Kalweitbe,ag, Ju Hwan Kangdy, Vladimir Kaplinbt, AybenKarasu Uysalag,dx,bm, Oleg Karavichevav, Tatiana Karavichevaav, Evgeny

Karpechevav, Andrey Kazantsevcp, Udo Wolfgang Kebschullbc, RalfKeideldz, Palash Khancq, Shuaib Ahmad Khandr, Mohisin MohammedKhanq, Kamal Hussain Khano, Alexei Khanzadeevcb, Yury Kharlovau,

Bjarte Kilengai, Taesoo Kimdy, Se Yong Kimt, Minwoo Kimdy, BeomkyuKimdy, Mimae Kiman, Jin Sook Kiman, Jonghyun Kimt, Dong Jo Kimap, Do

Won Kiman,bl, Stefan Kirscham, Ivan Kiselam, Sergey Kiselevax, AdamRyszard Kisieldt, Jennifer Lynn Klayf, Jochen Kleinci, Christian

Klein-Bosingbf, Michael Kliemantbd, Alexander Klugeag, Michael LinusKnichelcm, Anders Garritt Knospedg, Markus Kohlercm, ThorstenKolleggeram, Anatoly Kolojvarids, Mikhail Kompanietsds, Valery

Kondratievds, Natalia Kondratyevabt, Artem Konevskihav, VladimirKovalenkods, Marek Kowalskidf, Serge Koxbo, Greeshma Koyithatta

Meethaleveeduar, Jiri Kralap, Ivan Kralikay, Frederick Kramerbd, AdelaKravcakovaal, Tobias Krawutschkeci,ah, Michal Krelinaak, Matthias Kretzam,

Marian Krivdacr,ay, Filip Krizekap, Miroslav Krusak, Evgeny Kryshencb,Mikolaj Krzewickicm, Yury Kucheriaevcp, Thanushan Kugathasanag,

Christian Claude Kuhnbi, Paul Kuijerby, Igor Kulakovbd, Jitendra Kumarar,Podist Kurashvilibu, A.B. Kurepinav, A. Kurepinav, Alexey Kuryakinco,

Vasily Kushpilbz, Svetlana Kushpilbz, Henning Kvaernou, Min JungKweonci, Youngil Kwondy, Pedro Ladron de Guevarabg, Igor Lakomovat,

Rune Langoyr, Sarah Louise La Pointeaw, Camilo Ernesto Larabc, AntoineXavier Lardeuxdc, Paola La Roccaz, Ramona Leax, Mateusz Lechmanag, KiSang Leean, Sung Chul Leean, Graham Richard Leecr, Iosif Legrandag, Joerg

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Walter Lehnertbd, Matthieu Laurent Lenhardtcm, Vito Lenticz, HermesLeonbh, Ildefonso Leon Monzondh, Hermes Leon Vargasbd, Peter Levaidv,

Shuang Lig, Jorgen Lienr, Roman Lietavacr, Svein Lindalu, VolkerLindenstrutham, Christian Lippmanncm,ag, Michael Annan Lisas, Hans

Martin Ljunggrenaf, Davide Francesco Lodatoaw, Per-Ivar Loenner, VeraLogginsdu, Vitaly Loginovbt, Daniel Lohnerci, Constantinos Loizidesbr, Kai

Krister Looap, Xavier Bernard Lopezbn, Ernesto Lopez Torresi, GunnarLovhoidenu, Xianguo Luci, Philipp Luettigbd, Marcello Lunardonab, JiebinLuog, Grazia Luparelloaw, Cinzia Luzziag, Rongrong Madw, Ke Mag, DilanMinthaka Madagodahettige-Dondl, Alla Maevskayaav, Magnus Magerbe,ag,Durga Prasad Mahapatraaz, Antonin Maireci, Mikhail Malaevcb, Ivonne

Alicia Maldonado Cervantesbg, Ludmila Malininabj,1, Dmitry Mal’Kevichax,Peter Malzachercm, Alexander Mamonovco, Loic Henri Antoine Manceaucx,

Lalit Kumar Mangotracg, Vladislav Mankocp, Franck Mansobn, VitoManzaricz, Yaxian Maog, Massimiliano Marchisonebn,v, Jiri Maresba,

Giacomo Vito Margagliottix,cy, Anselmo Margottict, Ana Maria Marincm,Christina Markertdg, Marco Marquardbd, Irakli Martashvilidn, Nicole AliceMartincm, Paolo Martinengoag, Mario Ivan Martinezb, Arnulfo Martinez

Davalosbh, Gines Martinez Garciadc, Yevgen Martynovc, Alexis Jean-MichelMasdc, Silvia Masciocchicm, Massimo Maserav, Alberto Masonicw, Laure

Marie Massacrierdc, Annalisa Mastroserioae, Adam Tomasz Matyjadf,Christoph Mayerdf, Joel Mazerdn, Alessandra Maria Mazzonicv, FrancoMeddiy, Arturo Alejandro Menchaca-Rochabh, Jorge Mercado Perezci,Michal Meresaj, Yasuo Miakedp, Leonardo Milanov, Jovan Milosevicu,2,

Andre Mischkeaw, Aditya Nath Mishrach,as, Dariusz Miskowieccm, CiprianMihai Mitubb, Sanshiro Mizunodp, Jocelyn Mlynarzdu, Bedangadas

Mohantydr,bw, Levente Molnardv,ag,bi, Luis Manuel Montano Zetinak, MarcoMontenocx, Esther Montesj, Taebong Moondy, Maurizio Morandoab, Denise

Aparecida Moreira De Godoydi, Sandra Morettoab, Astrid Morrealeap,Andreas Morschag, Valeria Mucciforabp, Eugen Mudnicde, Sanjib Muhuridr,Maitreyee Mukherjeedr, Hans Mullerag, Marcelo Munhozdi, Sean Murraycf,

Luciano Musaag, Jan Musinskyay, Alfredo Mussocx, Basanta KumarNandiar, Rosario Naniact, Eugenio Nappicz, Christine Nattrassdn, Tapan

Kumar Nayakdr, Sergey Nazarenkoco, Alexander Nedosekinax, MariaNicassioae,cm, Mihai Niculescubb,ag, Borge Svane Nielsenbx, Takafumi

Niidadp, Sergey Nikolaevcp, Vedran Nikoliccn, Sergey Nikulincp, VladimirNikulincb, Bjorn Steven Nilsencc, Mads Stormo Nilssonu, Francesco

Noferinict,l, Petr Nomokonovbj, Gerardus Noorenaw, Norbert Novitzkyap,

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Alexandre Nyanincp, Anitha Nyathaar, Casper Nygaardbx, Joakim IngemarNystrandr, Alexander Ochirovds, Helmut Oskar Oeschlerbe,ag, Saehanseul

Ohdw, Sun Kun Ohan, Janusz Oleniaczdt, Antonio Carlos Oliveira DaSilvadi, Chiara Oppedisanocx, Antonio Ortiz Velasquezaf,bg, Anders Nils

Erik Oskarssonaf, Piotr Krystian Ostrowskidt, Jacek Tomasz Otwinowskicm,Ken Oyamaci, Kyoichiro Ozawado, Yvonne Chiara Pachmayerci, Milos

Pachrak, Fatima Padillav, Paola Paganoac, Guy Paicbg, Florian Painkeam,Carlos Pajaresp, Susanta Kumar Paldr, Arvinder Singh Palahacr, ArmandoPalmerida, Vardanush Papikyana, Giuseppe Pappalardoda, Woo Jin Parkcm,

Annika Passfeldbf, Blahoslav Pastircakay, Dmitri Ivanovich Patalakhaau,Vincenzo Paticchiocz, Biswarup Paulcq, Alexei Pavlinovdu, Tomasz Jan

Pawlakdt, Thomas Peitzmannaw, Hugo Denis Antonio Pereira Da Costan,Elienos Pereira De Oliveira Filhodi, Dmitri Peresunkocp, Carlos Eugenio

Perez Laraby, Diego Periniag, Davide Perrinoae, Wiktor Stanislaw Perytdt,Alessandro Pescict, Vladimir Peskovag,bg, Yury Pestove, Vojtech Petracekak,

Michal Petranak, Mariana Petrisbv, Plamen Rumenov Petrovcr, MihaiPetrovicibv, Catia Pettaz, Stefano Pianocy, Miroslav Piknaaj, Philippe

Pillotdc, Ombretta Pinazzaag, Lawrence Pinskydl, Nora Pitzbd,Danthasinghe Piyarathnadl, Mirko Planiniccn, Mateusz Andrzej Ploskonbr,Jan Marian Plutadt, Timur Pocheptsovbj, Sona Pochybovadv, Pedro Luis

Manuel Podesta Lermadh, Martin Poghosyanag, Karel Polakba, BorisPolichtchoukau, Amalia Popbv, Sarah Porteboeuf-Houssaisbn, Vladimir

Pospisilak, Baba Potukuchicg, Sidharth Kumar Prasaddu, RobertoPreghenellact,l, Francesco Prinocx, Claude Andre Pruneaudu, Igor

Pshenichnovav, Giovanna Pudduw, Valery Puninco, Marian Putisal, JornHenning Putschkedu, Emanuele Quercighag, Henrik Qvigstadu, AlexandreRachevskicy, Alphonse Rademakersag, Tomi Samuli Raihaap, Jan Rakap,Andry Malala Rakotozafindraben, Luciano Ramelload, Abdiel Ramirez

Reyesk, Rashmi Raniwalach, Sudhir Raniwalach, Sami Sakari Rasanenap,Bogdan Theodor Rascanubd, Deepika Ratheecd, Kenneth Francis Readdn,Jean-Sebastien Realbo, Krzysztof Redlichbu,1,1,1,1, Rosi Jan Reeddw, AttiqUr Rehmanr, Patrick Reicheltbd, Martijn Reicheraw, Rainer Arno Ernst

Renfordtbd, Anna Rita Reolonbp, Andrey Reshetinav, Felix VincenzRettigam, Jean-Pierre Revolag, Klaus Johannes Reygersci, LodovicoRiccaticx, Renato Angelo Riccibq, Tuva Richertaf, Matthias Rudolph

Richteru, Petra Riedlerag, Werner Rieglerag, Francesco Riggiz,da, MarioRodriguez Cahuantzib, Alis Rodriguez Mansoby, Ketil Roedr,u, David

Rohram, Dieter Rohrichr, Rosa Romitacm,db, Federico Ronchettibp, Philippe

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Rosnetbn, Stefan Rosseggerag, Andrea Rossiag,ab, Pradip Kumar Roycq,Christelle Sophie Roybi, Antonio Juan Rubio Monteroj, Rinaldo Ruix,

Riccardo Russov, Evgeny Ryabinkincp, Andrzej Rybickidf, SergeySadovskyau, Karel Safarikag, Raghunath Sahooas, Pradip Kumar Sahuaz,Jogender Sainidr, Hiroaki Sakaguchiaq, Shingo Sakaibr, Dosatsu Sakatadp,

Carlos Albert Salgadop, Jai Salzwedels, Sanjeev Singh Sambyalcg, VladimirSamsonovcb, Xitzel Sanchez Castrobi, Ladislav Sandoray, Andres

Sandovalbh, Masato Sanodp, Gianluca Santagatiz, Romualdo Santoroag,l,Juho Jaako Sarkamoap, Eugenio Scapparonect, Fernando Scarlassaraab, RolfPaul Scharenbergck, Claudiu Cornel Schiauabv, Rainer Martin Schickerci,

Hans Rudolf Schmidtdq, Christian Joachim Schmidtcm, SimoneSchuchmannbd, Jurgen Schukraftag, Tim Schusterdw, Yves Roland

Schutzag,dc, Kilian Eberhard Schwarzcm, Kai Oliver Schwedacm, GildaScioliaa, Enrico Scomparincx, Rebecca Scottdn, Patrick Aaron Scottcr,

Gianfranco Segatoab, Ilya Selyuzhenkovcm , Serhiy Senyukovbi, Jeewon Seocl,Sergio Serciw, Eulogio Serradillaj,bh, Adrian Sevcencobb, Alexandre

Shabetaidc, Galina Shabratovabj, Ruben Shahoyanag, Natasha Sharmacd,dn,Satish Sharmacg, Rohini Sharmacg, Kenta Shigakiaq, Katherin Shtejeri,

Yury Sibiriakcp, Eva Sickingbf, Sabyasachi Siddhantacw, TeodorSiemiarczukbu, David Olle Rickard Silvermyrca, Catherine Silvestrebo,

Goran Simatovicbg,cn, Giuseppe Simonettiag, Rama Narayana Singarajudr,Ranbir Singhcg, Subhash Singhadr,bw, Vikas Singhaldr, Tinku Sinhacq,

Bikash Sinhadr, Branislav Sitaraj, Mario Sittaad, Bernhard Skaaliu, KyrreSkjerdalr, Radek Smakalak, Nikolai Smirnovdw, Raimond Snellingsaw,Carsten Sogaardbx,af, Ron Ariel Soltzbs, Hyungsuk Sont, Jihye Songcl,

Myunggeun Songdy, Csaba Soosag, Francesca Soramelab, IwonaSputowskadf, Martha Spyropoulou-Stassinakice, Brijesh Kumar Srivastavack,Johanna Stachelci, Ionel Stanbb, Grzegorz Stefanekbu, Matthew Steinpreiss,

Evert Anders Stenlundaf, Gideon Francois Steyncf, Johannes HendrikStillerci, Diego Stoccodc, Mikhail Stolpovskiyau, Peter Strmenaj, Alexandre

Alarcon do Passo Suaidedi, Martin Alfonso Subieta Vasquezv, ToruSugitateaq, Christophe Pierre Suireat, Rishat Sultanovax, Michal Sumberabz,Tatjana Susacn, Timothy Symonsbr, Alejandro Szanto de Toledodi, Imrich

Szarkaaj, Adam Szczepankiewiczdf,ag, Maciej Szymanskidt, Jun Takahashidj,Marco-Antonio Tangaroae, Daniel Jesus Tapia Takakiat, Attilio TarantolaPelonibd, Alfonso Tarazona Martinezag, Arturo Tauroag, Guillermo Tejeda

Munozb, Adriana Telescaag, Astkhik Ter-Minasyanbt,cp, Cristina Terrevoliae,Jochen Mathias Thadercm, Deepa Thomasaw, Raphael Noel Tieulentdk,

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Anthony Timminsdl, David Tlustyak, Alberica Toiaam,ab,cu, Hisayuki Toriido,Luca Toscanocx, Victor Trubnikovc, David Christopher Truesdales,

Wladyslaw Henryk Trzaskaap, Tomoya Tsujido, Alexandr Tumkinco, RosarioTurrisicu, Trine Spedstad Tveteru, Jason Glyndwr Ulerybd, Kjetil Ullalandr,Jochen Ulrichbk,bc, Antonio Urasdk, Jozef Urbanal, Guido Marie Urciuolicv,

Gianluca Usaiw, Michal Vajzerak,bz, Martin Valabj,ay, Lizardo ValenciaPalomoat, Sara Valleroci, Pierre Vande Vyvreag, Marco van Leeuwenaw,Luigi Vannuccibq, Aurora Diozcora Vargasb, Raghava Varmaar, Maria

Vasileiouce, Andrey Vasilievcp, Vladimir Vecherninds, Misha Veldhoenaw,Massimo Venaruzzox, Ermanno Vercellinv, Sergio Vergarab, RenaudVerneth, Marta Verweijaw, Linda Vickovicde, Giuseppe Viestiab, JussiViinikainenap, Zabulon Vilakazicf, Orlando Villalobos Bailliecr, Yury

Vinogradovco, Alexander Vinogradovcp, Leonid Vinogradovds, TizianoVirgiliac, Yogendra Viyogidr, Alexander Vodopianovbj, Kirill Voloshinax,

Sergey Voloshindu, Giacomo Volpeag, Barthelemy von Hallerag, IvanVorobyevds, Danilo Vraniccm, Janka Vrlakovaal, Bogdan Vulpescubn, Alexey

Vyushinco, Vladimir Wagnerak, Boris Wagnerr, Renzhuo Wang, DongWangg, Yifei Wangci, Mengliang Wangg, Yaping Wangg, Kengo

Watanabedp, Michael Weberdl, Johannes Wesselsag,bf, Uwe Westerhoffbf,Jens Wiechuladq, Jon Wikneu, Martin Rudolf Wildebf, Grzegorz Andrzej

Wilkbu, Alexander Wilkbf, Crispin Williamsct, Bernd Stefan Windelbandci,Leonidas Xaplanteris Karampatsosdg, Chris G Yaldodu, Yorito

Yamaguchido, Shiming Yangr, Hongyan Yangn,aw, Stanislav Yasnopolskycp,JunGyu Yicl, Zhongbao Ying, In-Kwon Yoocl, Jongik Yoondy, Weilin Yubd,

Xianbao Yuang, Igor Yushmanovcp, Valentina Zaccolobx, Cenek Zachak,Chiara Zampollict, Sergey Zaporozhetsbj, Andrey Zarochentsevds, Petr

Zavadaba, Nikolai Zaviyalovco, Hanna Paulina Zbroszczykdt, PierreZelnicekbc, Sorin Ion Zgurabb, Mikhail Zhalovcb, Xiaoming Zhangbr,bn,g,

Haitao Zhangg, Fengchu Zhoug, You Zhouaw, Daicui Zhoug, Jianlin Zhug,Jianhui Zhug, Xiangrong Zhug, Hongsheng Zhug, Antonino Zichichiaa,l,Alice Zimmermannci, Gennady Zinovjevc, Yannick Denis Zoccaratodk,

Mykhaylo Zynovyevc, Maksym Zyzakbd

aA. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation,Yerevan, Armenia

bBenemérita Universidad Autónoma de Puebla, Puebla, MexicocBogolyubov Institute for Theoretical Physics, Kiev, Ukraine

dBose Institute, Department of Physics and Centre for Astroparticle Physics and SpaceScience (CAPSS), Kolkata, India

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eBudker Institute for Nuclear Physics, Novosibirsk, RussiafCalifornia Polytechnic State University, San Luis Obispo, California, United States

gCentral China Normal University, Wuhan, ChinahCentre de Calcul de l’IN2P3, Villeurbanne, France

iCentro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, CubajCentro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT),

Madrid, SpainkCentro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and

Mérida, MexicolCentro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”,

Rome, ItalymChicago State University, Chicago, United States

nCommissariat à l’Energie Atomique, IRFU, Saclay, FranceoCOMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

pDepartamento de Física de Partículas and IGFAE, Universidad de Santiago deCompostela, Santiago de Compostela, Spain

qDepartment of Physics Aligarh Muslim University, Aligarh, IndiarDepartment of Physics and Technology, University of Bergen, Bergen, NorwaysDepartment of Physics, Ohio State University, Columbus, Ohio, United States

tDepartment of Physics, Sejong University, Seoul, South KoreauDepartment of Physics, University of Oslo, Oslo, Norway

vDipartimento di Fisica dell’Università and Sezione INFN, Turin, ItalywDipartimento di Fisica dell’Università and Sezione INFN, Cagliari, ItalyxDipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

yDipartimento di Fisica dell’Università ‘La Sapienza’ and Sezione INFN, Rome, ItalyzDipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, ItalyaaDipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, ItalyabDipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, ItalyacDipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN,

Salerno, ItalyadDipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte

Orientale and Gruppo Collegato INFN, Alessandria, ItalyaeDipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy

afDivision of Experimental High Energy Physics, University of Lund, Lund, SwedenagEuropean Organization for Nuclear Research (CERN), Geneva, Switzerland

ahFachhochschule Köln, Köln, GermanyaiFaculty of Engineering, Bergen University College, Bergen, Norway

ajFaculty of Mathematics, Physics and Informatics, Comenius University, Bratislava,Slovakia

akFaculty of Nuclear Sciences and Physical Engineering, Czech Technical University inPrague, Prague, Czech Republic

alFaculty of Science, P.J. Šafárik University, Košice, SlovakiaamFrankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität

Frankfurt, Frankfurt, GermanyanGangneung-Wonju National University, Gangneung, South Korea

9

aoGauhati University, Department of Physics, Guwahati, IndiaapHelsinki Institute of Physics (HIP) and University of Jyväskylä, Jyväskylä, Finland

aqHiroshima University, Hiroshima, JapanarIndian Institute of Technology Bombay (IIT), Mumbai, IndiaasIndian Institute of Technology Indore, Indore, India (IITI)

atInstitut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-IN2P3,Orsay, France

auInstitute for High Energy Physics, Protvino, RussiaavInstitute for Nuclear Research, Academy of Sciences, Moscow, Russia

awNikhef, National Institute for Subatomic Physics and Institute for Subatomic Physicsof Utrecht University, Utrecht, Netherlands

axInstitute for Theoretical and Experimental Physics, Moscow, RussiaayInstitute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia

azInstitute of Physics, Bhubaneswar, IndiabaInstitute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech

RepublicbbInstitute of Space Sciences (ISS), Bucharest, Romania

bcInstitut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt,Germany

bdInstitut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt,Germany

beInstitut für Kernphysik, Technische Universität Darmstadt, Darmstadt, GermanybfInstitut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster,

GermanybgInstituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico

City, MexicobhInstituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

biInstitut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg,CNRS-IN2P3, Strasbourg, France

bjJoint Institute for Nuclear Research (JINR), Dubna, RussiabkKirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg,

GermanyblKorea Institute of Science and Technology Information, Daejeon, South Korea

bmKTO Karatay University, Konya, TurkeybnLaboratoire de Physique Corpusculaire (LPC), Clermont Université, Université Blaise

Pascal, CNRS–IN2P3, Clermont-Ferrand, FranceboLaboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Joseph

Fourier, CNRS-IN2P3, Institut Polytechnique de Grenoble, Grenoble, FrancebpLaboratori Nazionali di Frascati, INFN, Frascati, ItalybqLaboratori Nazionali di Legnaro, INFN, Legnaro, Italy

brLawrence Berkeley National Laboratory, Berkeley, California, United StatesbsLawrence Livermore National Laboratory, Livermore, California, United States

btMoscow Engineering Physics Institute, Moscow, RussiabuNational Centre for Nuclear Studies, Warsaw, Poland

bvNational Institute for Physics and Nuclear Engineering, Bucharest, Romania

10

bwNational Institute of Science Education and Research, Bhubaneswar, IndiabxNiels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

byNikhef, National Institute for Subatomic Physics, Amsterdam, NetherlandsbzNuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u Prahy,

Czech RepubliccaOak Ridge National Laboratory, Oak Ridge, Tennessee, United States

cbPetersburg Nuclear Physics Institute, Gatchina, RussiaccPhysics Department, Creighton University, Omaha, Nebraska, United States

cdPhysics Department, Panjab University, Chandigarh, IndiacePhysics Department, University of Athens, Athens, Greece

cfPhysics Department, University of Cape Town and iThemba LABS, National ResearchFoundation, Somerset West, South Africa

cgPhysics Department, University of Jammu, Jammu, IndiachPhysics Department, University of Rajasthan, Jaipur, India

ciPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, GermanycjPolitecnico di Torino, Turin, Italy

ckPurdue University, West Lafayette, Indiana, United StatesclPusan National University, Pusan, South Korea

cmResearch Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fürSchwerionenforschung, Darmstadt, GermanycnRudjer Bošković Institute, Zagreb, Croatia

coRussian Federal Nuclear Center (VNIIEF), Sarov, RussiacpRussian Research Centre Kurchatov Institute, Moscow, Russia

cqSaha Institute of Nuclear Physics, Kolkata, IndiacrSchool of Physics and Astronomy, University of Birmingham, Birmingham, United

KingdomcsSección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú,

Lima, PeructSezione INFN, Bologna, ItalycuSezione INFN, Padova, ItalycvSezione INFN, Rome, Italy

cwSezione INFN, Cagliari, ItalycxSezione INFN, Turin, ItalycySezione INFN, Trieste, ItalyczSezione INFN, Bari, Italy

daSezione INFN, Catania, ItalydbNuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

dcSUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,Nantes, France

ddSuranaree University of Technology, Nakhon Ratchasima, ThailanddeTechnical University of Split FESB, Split, Croatia

dfThe Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences,Cracow, Poland

dgThe University of Texas at Austin, Physics Department, Austin, TX, United StatesdhUniversidad Autónoma de Sinaloa, Culiacán, Mexico

11

diUniversidade de São Paulo (USP), São Paulo, BrazildjUniversidade Estadual de Campinas (UNICAMP), Campinas, Brazil

dkUniversité de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, FrancedlUniversity of Houston, Houston, Texas, United States

dmUniversity of Technology and Austrian Academy of Sciences, Vienna, AustriadnUniversity of Tennessee, Knoxville, Tennessee, United States

doUniversity of Tokyo, Tokyo, JapandpUniversity of Tsukuba, Tsukuba, Japan

dqEberhard Karls Universität Tübingen, Tübingen, GermanydrVariable Energy Cyclotron Centre, Kolkata, India

dsV. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, RussiadtWarsaw University of Technology, Warsaw, Poland

duWayne State University, Detroit, Michigan, United StatesdvWigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest,

HungarydwYale University, New Haven, Connecticut, United States

dxYildiz Technical University, Istanbul, TurkeydyYonsei University, Seoul, South Korea

dzZentrum für Technologietransfer und Telekommunikation (ZTT), FachhochschuleWorms, Worms, Germany

Abstract

In high–energy heavy–ion collisions, the correlations between the emittedparticles can be used as a probe to gain insight into the charge creationmechanisms. In this article, we report the first results of such studies usingthe electric charge balance function in the relative pseudorapidity (∆η) andazimuthal angle (∆ϕ) in Pb–Pb collisions at

√sNN = 2.76 TeV with the

ALICE detector at the Large Hadron Collider. The width of the balancefunction decreases with growing centrality (i.e. for more central collisions) inboth projections. This centrality dependence is not reproduced by HIJING,while AMPT, a model which incorporates strings and parton rescattering,exhibits qualitative agreement with the measured correlations in ∆ϕ but failsto describe the correlations in ∆η. A thermal blast wave model incorporat-ing local charge conservation and tuned to describe the pT spectra and v2

measurements reported by ALICE, is used to fit the centrality dependenceof the width of the balance function and to extract the average separationof balancing charges at freeze–out. The comparison of our results with mea-surements at lower energies reveals an ordering with

√sNN : the balance

12

functions become narrower with increasing energy for all centralities. Thisis consistent with the effect of larger radial flow at the LHC energies butalso with the late stage creation scenario of balancing charges. However, therelative decrease of the balance function widths in ∆η and ∆ϕ with central-ity from the highest SPS to the LHC energy exhibits only small differences.This observation cannot be interpreted solely within the framework wherethe majority of the charge is produced at a later stage in the evolution of theheavy–ion collision.

Keywords: Balance function, charge correlations, ALICE LHC

1. Introduction

According to Quantum ChromoDynamics (QCD), the theory that de-scribes the strong interaction, at sufficiently high energy densities and tem-peratures, a new phase of matter exists in which the constituents, the quarksand the gluons, are deconfined [1]. This new state of matter is called theQuark Gluon Plasma (QGP). Its creation in the laboratory, the correspond-ing verification of its existence and the subsequent study of its properties arethe main goals of the ultrarelativistic heavy–ion collision programs. Con-vincing experimental evidences for the existence of a deconfined phase havebeen published already at RHIC energies [2]. Recently, the first experimentalresults from the heavy–ion program of the LHC experiments provided addi-tional indication [3, 4] for the existence of this state of matter at this newenergy regime.

Among the different observables, such as the anisotropic flow [3] or theenergy loss of high transverse momentum particles [4], the charge balancefunctions are suggested to be sensitive probes of the properties of the system,providing valuable insight into the charge creation mechanism and can beused to address fundamental questions concerning hadronization in heavy–ion collisions [5].

The system that is produced in a heavy–ion collision undergoes an ex-pansion, during which it exhibits collective behavior and can be describedin terms of hydrodynamics [6]. A pair of particles of opposite charge that iscreated during this stage is subject to the collective motion of the system,which transforms the correlations in coordinate space into correlations in mo-mentum space. The subsequent rescattering phase after the hadronizationwill also affect the final measured degree of correlation. The balance function

13

being a sensitive probe of the balancing charge distribution in momentumspace, quantifies these effects. The final degree of correlation is reflected inthe balance function distribution and consequently in its width. It was sug-gested in [5] that narrow distributions correspond to a system that consistsof particles that are created close to the end of the evolution. It was alsosuggested that a larger width may signal the creation of balancing chargesat the first stages of the system’s evolution [5].

The balance function describes the conditional probability that a particlein a bin P1 in momentum space will be accompanied (balanced) by a particleof opposite charge with momentum P2. The general definition is given inEq. 1:

Bab(P2|P1) =1

2

(

Cab(P2|P1) + Cba(P2|P1)

− Cbb(P2|P1)− Caa(P2|P1))

, (1)

where Cab(P2|P1) = Nab(P2|P1)/Nb(P1) is the distribution of pairs of parti-cles, of type a and b, with momenta P2 and P1, respectively, normalized tothe number of particles b. Particles a and b could come from different particlespecies (e.g. π+–π−, K+–K−, p–p). In this article, a refers to all positive andb to all negative particles. This analysis is performed for both particles inthe pseudorapiity intervals |η| < 0.8. We assume that the balance function isinvariant over pseudorapidity in this region, and report the results in termsof the relative pseudorapidity ∆η = ηb − ηa and the relative azimuthal angle∆ϕ = ϕb − ϕa, by averaging the balance function over the position of one ofthe particles (similar equation is used for B(∆ϕ)):

B+−(∆η) =1

2

(

C+−(∆η) + C−+(∆η)− C−−(∆η)− C++(∆η))

. (2)

Each term of Eq. 2, is corrected for detector and tracking inefficiencies aswell as for acceptance effects, similar to what is proposed in [7], and can bewritten as Cab = (Nab/Nb)/fab. The factors fab (where in the case of chargedparticles, a and b correspond to the charge i.e. f+−, f−+, f++ and f−−)represent the probability that given a particle a is reconstructed, a second

14

particle emitted at a relative pseudorapidity or azimuthal angle (∆η or ∆ϕ,respectively), would also be detected. These terms are defined as the productof the single particle tracking efficiency ε(η, ϕ, pT) and the acceptance termα(∆η,∆ϕ). The way they are extracted in this analysis is described in oneof the following sections.

For a neutral system, every charge has an opposite balancing partner andthe balance function would integrate to unity. However, this normalizationdoes not hold if not all charged particles are included in the calculation dueto specific momentum range or particle type selection.

The width of the balance function distribution can be used to quantifyhow tightly the balancing charges are correlated. It can be characterizedby the average 〈∆η〉 or 〈∆ϕ〉 in case of studies in pseudorapidity or theazimuthal angle, respectively. The mathematical expression for the case ofcorrelations in pseudorapidity is given in Eq. 3 (similar for 〈∆ϕ〉).

〈∆η〉 =k

∑

i=1

[B+−(∆ηi) ·∆ηi]/

k∑

i=1

B+−(∆ηi), (3)

where B+−(∆ηi) is the balance function value for each bin ∆ηi, with the sumrunning over all bins k.

Experimentally, the balance function for non–identified particles was stud-ied by the STAR collaboration in Au–Au collisions at

√sNN = 130 GeV [8],

followed by the NA49 experiment in Pb–Pb collisions at the highest SPSenergy [9]. Both experiments reported the narrowing of the balance func-tion in ∆η in more central compared to peripheral collisions. The resultswere qualitatively in agreement with theoretical expectations for a systemwith a long-lived QGP phase and exhibiting delayed hadronization. Theseresults triggered an intense theoretical investigation of their interpretation[10, 11, 12, 13, 14, 15, 16]. In [10], it was suggested that the balance func-tion could be distorted by the excess of positive charges due to the protonsof the incoming beams (unbalanced charges). This effect is expected to bereduced at higher collision energy, leaving a system at mid–rapidity that isnet–baryon free. Also in [10], it was proposed to perform balance functionstudies in terms of the relative invariant momentum of the particle pair, toeliminate the sensitivity to collective flow. In [11], it was shown that purelyhadronic models predict a modest broadening of the balance function for

15

central heavy–ion collisions, contrary to the experimentally measured nar-rowing. It was also shown that thermal models were in agreement with the(at that time) published data, concluding that charge conservation is local atfreeze–out, consistent with the delayed charged-creation scenario [11]. Sim-ilar agreement with the STAR data was reported in [12], where a thermalmodel that included resonances was used. In [13], the author showed thatthe balance function, when measured in terms of the relative azimuthal an-gle of the pair, is a sensitive probe of the system’s collective motion andin particular of its radial flow. In [14], it was suggested that radial flow isalso the driving force of the narrowing of the balance function in pseudo-rapidity, with its width being inversely proportional to the transverse mass,mT =

√

m2 + p2T. In parallel in [15, 16], the authors attributed the narrowingof the balance function for more central collisions to short range correlationsin the QGP at freeze–out.

Recently, the STAR collaboration extended their balance function studiesin Au–Au collisions at

√sNN = 200 GeV [17], confirming the strong centrality

dependence of the width in ∆η but also revealing a similar dependence in ∆ϕ,the latter being mainly attributed to radial flow. Finally, in [18] the authorsfitted the experimentally measured balance function at the top RHIC energieswith a blast–wave parameterization and argued that in ∆ϕ the results couldbe explained by larger radial flow in more central collisions. However theresults in ∆η could only be reproduced when considering the separation ofcharges at freeze–out implemented in the model. They also stressed theimportance of performing a multi–dimensional analysis. In particular, theypresented how the balance function measured with respect to the orientationof the reaction plane (i.e. the plane of symmetry of a collision defined by theimpact parameter vector and the beam direction) could probe potentiallyone of the largest sources of background in studies related to parity violatingeffects in heavy–ion collisions [19].

In this article we report the first results of the balance function measure-ments in Pb–Pb collisions at

√sNN = 2.76 TeV with the ALICE detector

[20, 21]. The article is organized as follows: Section 2 briefly describes theexperimental setup, while details about the data analysis are presented inSection 3. In Section 4 we discuss the main results followed by a detailedcomparison with different models in Section 5. In the same section we presentthe energy dependence of the balance function. We conclude with the sum-mary and a short outlook.

16

2. Experimental setup

ALICE [21] is the dedicated heavy–ion detector at the LHC, designedto cope with the high charged–particle densities measured in central Pb–Pb collisions [22]. The experiment consists of a large number of detectorsubsystems inside a solenoidal magnet (0.5 T). The central tracking systemsof ALICE provide full azimuthal coverage within a pseudorapidity window|η| < 0.9. They are also optimized to provide good momentum resolution(≈ 1% at pT < 1 GeV/c) and particle identification (PID) over a broadmomentum range, the latter being important for the future, particle typedependent balance function studies.

For this analysis, the charged particles were reconstructed using the Time

Projection Chamber (TPC) [23], which is the main tracking detector of thecentral barrel. In addition, a complementary analysis relying on the combinedtracking of the TPC and the Inner Tracking System (ITS) was performed.The ITS consists of six layers of silicon detectors employing three differenttechnologies. The two innermost layers are Silicon Pixel Detectors (SPD),followed by two layers of Silicon Drift Detectors (SDD). Finally the twooutermost layers are double–sided Silicon Strip Detectors (SSD).

The position of the primary interaction was determined by the TPC andby the SPD, depending on the tracking mode used. A set of forward detec-tors, namely the VZERO scintillator arrays, were used in the trigger logicand also for the centrality determination [22]. The VZERO detector consistsof two arrays of scintillator counters, the VZERO–A and the VZERO–C, po-sitioned on each side of the interaction point. They cover the pseudorapidityranges of 2.8 < η < 5.1 and −3.7 < η < −1.7 for VZERO–A and VZERO–C,respectively.

For more details on the ALICE experimental setup, see [21].

3. Data analysis

Approximately 15 × 106 Pb–Pb events, recorded during the first LHCheavy–ion run in 2010 at

√sNN = 2.76 TeV, were analyzed. A minimum bias

trigger was used, requiring two pixel chips hit in the SPD in coincidence witha signal in the VZERO–A and VZERO–C detectors. Measurements were alsomade with the requirement changed to a coincidence between signals fromthe two sides of the VZERO detectors. An offline event selection was alsoapplied in order to reduce the contamination from background events, such as

17

electromagnetic and beam–gas interactions. All events were required to havea reconstructed vertex position along the beam axis (Vz) with |Vz| < 10 cmfrom the nominal interaction point.

η∆-1.5-1-0.5

00.51

1.5

(deg.)ϕ∆

-150-100-50050100150

)ϕ∆,η∆(+

-f

0

0.2

0.4

0.6

0.8

= 2.76 TeVNNsPb-Pb

Centrality 0-5%

Figure 1: (color online). The correction factor f+−(∆η,∆ϕ) for the 5% most central Pb–

Pb collisions, extracted from the single particle tracking efficiencies ε(η, ϕ, pT) and theacceptance terms α(∆η,∆ϕ) (see text for details).

The data were sorted according to centrality classes, reflecting the ge-ometry of the collision (i.e. impact parameter), which span 0 − 80% of theinelastic cross section. The 0 − 5% bin corresponds to the most central(i.e. small impact parameter) and the 70 − 80% class to the most periph-eral (i.e. large impact parameter) collisions. The centrality of the collisionwas estimated using the charged particle multiplicity distribution and thedistribution of signals from the VZERO scintillator detectors. Fitting thesedistributions with a Glauber model [24], the centrality classes are mapped to

18

0 0.5 1 1.5

)η ∆(+

-B

0

0.5

1

1.5Centrality 0-5%(a)

0 0.5 1 1.5

0

0.5

1

1.5Centrality 30-40%(b)

η ∆0 0.5 1 1.5

0

0.5

1

1.5

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

Centrality 70-80%(c)

Figure 2: (color online). Balance function as a function of ∆η for different centralityclasses: 0–5% (a), 30–40% (b) and 70–80%. Mixed events results, not corrected for thedetector effects, are shown by open squares. See text for details.

the corresponding mean number of participating nucleons 〈Npart〉 [25]. Dif-ferent centrality estimators (i.e. TPC tracks, SPD clusters) were used toinvestigate the systematic uncertainties.

To select charged particles with high efficiency and to minimize the con-tribution from background tracks (i.e. secondary particles originating eitherfrom weak decays or from the interaction of particles with the material), allselected tracks were required to have at least 70 reconstructed space pointsout of the maximum of 159 possible in the TPC. The 〈χ2〉 per degree offreedom the momentum fit was required to be below 2. To further reducethe contamination from background tracks, a cut on the distance of clos-est approach between the tracks and the primary vertex (dca) was applied(dcaxy/dxy)

2 + (dcaz/dz)2 < 1 with dxy = 2.4 cm and dz = 3.2 cm. In the

parallel analysis, with the combined tracking of the TPC and the ITS, thevalues of dxy = 0.3 cm and dz = 0.3 cm were used, profiting from the betterdca resolution that the ITS provides. Finally, we report the results for theregion of |η| < 0.8 and 0.3 < pT < 1.5 GeV/c. The pT range is chosen toensure a high tracking efficiency (lower cut) and a minimum contributionfrom (mini–)jet correlations (upper cut).

19

0 50 100 150

)

-1

) (d

egϕ ∆(

+-

B

0

0.005

0.01

0.015Centrality 0-5%(a)

0 50 100 150

0

0.005

0.01

0.015

Centrality 30-40%(b)

(deg.)ϕ ∆

0 50 100 150

0

0.005

0.01

0.015

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

= 2.76 TeVNNsPb-Pb @

ALICE data

ALICE event mixing data

Centrality 70-80%(c)

Figure 3: (color online). Balance function as a function of ∆ϕ for different centralityclasses: 0–5% (a), 30–40% (b) and 70–80%. Mixed events results, not corrected for thedetector effects, are shown by open squares. See text for details.

4. Results

As discussed in the introduction, the correction factors f+−, f−+, f++,and f−− are needed to eliminate the dependence of the balance function onthe detector acceptance and tracking inefficiencies. The tracking inefficienciesare extracted from a detailed Monte Carlo simulation of the ALICE detec-tor based on GEANT3 [26]. The acceptance part of the correction factors,α(∆η,∆ϕ), is extracted from mixed events. The mixed events are generatedby taking all two–particle non–same–event combinations for a collection ofa few (≈ 5) events with similar values of the z position of the reconstructedvertex (|∆Vz| < 5 cm). In addition, the events used for the event mixing be-longed to the same centrality class and had multiplicities that did not differby more than 1–2%, depending on the centrality. Figure 1 presents the cor-rection factor for the distribution of pairs of particles with opposite charge asa function of the relative pseudorapidity and azimuthal angle differences forthe 5% most central Pb–Pb collisions. The maximum value is observed for∆η = 0 and is equal to the pT–integrated single particle efficiency. The distri-bution decreases to ≈ 0 near the edge of the acceptance i.e. |∆η| ≈ 1.6. This

20

reduction reflects the decrease of the probability of detecting both balancingcharges as the relative pseudorapidity difference increases. The correctionfactor is constant as a function of ∆ϕ.

The measured balance function is averaged over positive and negativevalues of ∆η (∆ϕ) and reported only for positive values. The integrals of thebalance function over the reported region are close to 0.5, reflecting the factthat most of the balancing charges are distributed in the measured region.

Figure 2 presents the balance functions as a function of the relative pseu-dorapidity ∆η for three different centrality classes: the 0–5% (most central),the 30–40% (mid–central) and the 70–80% (most peripheral) centrality bins.It is seen that the balance function, in full circles, gets narrower for more cen-tral collisions. Figure 2 presents also the balance functions for mixed events,not corrected for detector effects, represented by the open squares. These bal-ance functions, fluctuate around zero as expected for a totally uncorrelatedsample where the charge is not conserved.

Figure 3 presents the balance functions as a function of the relative az-imuthal angle for the same centrality classes as in Fig. 2. The balance func-tions calculated using mixed events and not corrected for the tracking effi-ciency exhibit a distinct modulation originating from the 18 sectors of theTPC. This modulation is more pronounced for more central collisions, sincethe charge dependent acceptance differences scale with multiplicity. Theefficiency-corrected balance functions, represented by the full markers, indi-cate that these detector effects are successfully removed. Narrowing of thebalance function in more central events has been also observed in this repre-sentation. A decrease of the balance function at small ∆ϕ (i.e. for ∆ϕ ≤ 10◦)can be observed for the mid–central and peripheral collisions. This can beattributed to short–range correlations between pairs of same and oppositecharge, such as HBT and Coulomb effects [18].

In both Fig. 2 and Fig. 3 as well as in the next figures, the error barof each point corresponds to the statistical uncertainty (typically the size ofthe marker). The systematic uncertainty is represented by the shaded bandaround each point. The origin and the value of the assigned systematic un-certainty on the width of the balance function, calculated for each centralityand for both ∆η and ∆ϕ, will be discussed in the next paragraph.

The data sample was analyzed separately for two magnetic field config-urations. The two data samples had comparable statistics. The maximumvalue of the systematic uncertainty, defined as half of the difference betweenthe balance functions in these two cases, is found to be less than 1.3% over

21

all centralities. In addition, we estimated the contribution to the system-atic uncertainty originating from the centrality selection, by determiningthe centrality not only with the VZERO detector but alternatively usingthe multiplicity of the TPC tracks or the number of clusters of the secondSPD layer. This resulted in an additional maximum contribution to the esti-mated systematic uncertainty of 0.8% over all centralities. Furthermore, weinvestigated the influence of the ranges of the cuts in parameters such as theposition of the primary vertex in the z coordinate, the dca, and the numberof required TPC clusters. This was done by varying the relevant ranges,one at a time, and again assigning half of the difference between the lowerand higher value of the width to the systematic uncertainty. The maximumcontribution from these sources was estimated to be 1.3%, 1.1% and 1.3%for the three parameters, respectively. We also studied the influence of thedifferent tracking modes used by repeating the analysis using tracks recon-structed by the combination of the TPC and the ITS (global tracking). Theresulting maximum contribution to the systematic uncertainty of the widthfrom this source is 1.1%, again over all centralities. Finally, the appliedacceptance corrections result in large fluctuations of the balance functionpoints for some centralities towards the edge of the acceptance (i.e. largevalues of ∆η), which originates from the division of two small numbers. Toaccount for this, we average over several bins at these high values of ∆η toextract the weighted average. This procedure results in an uncertainty thathas a maximum value of 5% over all centralities. All these contributions aresummarized in Table 1. The final systematic uncertainty for each centralitybin was calculated by adding all the different sources in quadrature. Theresulting values for the 0–5%, 30–40% and 70–80% centrality bins were es-timated to be 2.5%, 3.0% and 3.6%, respectively, in 〈∆η〉 (1.9%, 1.2% and2.4%, respectively, in 〈∆ϕ〉).

5. Discussion

5.1. Centrality dependence

The width of the balance function (Eq. 3) as a function of the centralitypercentile is presented in Fig. 4. Central (peripheral) collisions correspondto small (large) centrality percentile. The width is calculated in the entireinterval where the balance function was measured (i.e. 0.0 < ∆η < 1.6and 0o < ∆ϕ < 180o). Both results in terms of correlations in the relativepseudorapidity (〈∆η〉–upper panel, Fig. 4–a) and the relative azimuthal angle

22

Table 1: The maximum value of the systematic uncertainties on the width of the balancefunction over all centralities for each of the sources studied.

Systematic Uncertainty

Category Source Value (max)Magnetic field (++)/(- -) 1.3%

Centrality estimator VZERO, TPC, SPD 0.8%dca 1.3%

Cut variation Nclusters(TPC) 1.1%∆Vz 1.3%

Tracking TPC, Global 1.1%Binning Extrapolation to large ∆η 5.0%

(〈∆ϕ〉–lower panel, Fig. 4–b) are shown. The experimental data points,represented by the full red circles, exhibit a strong centrality dependence:more central collisions correspond to narrower distributions (i.e. movingfrom right to left along the x–axis) for both ∆η and ∆ϕ. Our results arecompared to different model predictions, such as HIJING [27] and differentversions of a multi–phase transport model (AMPT) [28]. The error bars inthe results from these models represent the statistical uncertainties.

The points from the analysis of HIJING Pb–Pb events at√sNN = 2.76 TeV,

represented by the blue triangles, show little centrality dependence in bothprojections. The slightly narrower balance functions for central collisionsmight be related to the fact that HIJING is not just a simple superpositionof single pp collisions; jet–like effects as well as increased resonance yields incentral collisions could be reflected as additional correlations. The balancefunction widths generated by HIJING are much larger than those measuredin the data, consistent with the fact that the model lacks collective flow.

In addition, we compare our data points to the results from the analysisof events from three different versions of AMPT in Fig. 4. The AMPT modelconsists of two different configurations: the default and the string melting.Both are based on HIJING to describe the initial conditions. The partonicevolution is described by the Zhang’s parton cascade (ZPC) [29]. In the de-

fault AMPT model, partons are recombined with their parent strings whenthey stop interacting, and the resulting strings are converted to hadrons us-ing the Lund string fragmentation model. In the string melting configurationa quark coalescence model is used instead to combine partons into hadrons.The final part of the whole process, common between the two configura-

23

⟩ η ∆ ⟨

0.4

0.6

0.8

ALICE HIJING AMPT (String melting) AMPT (String melting w/o rescattering) AMPT (Default)

ALICE HIJING AMPT (String melting) AMPT (String melting w/o rescattering) AMPT (Default)

ALICE HIJING AMPT (String melting) AMPT (String melting w/o rescattering) AMPT (Default)

= 2.76 TeVNNsPb-Pb @

(a)

Centrality percentile0 20 40 60 80

(de

g.)

⟩ ϕ ∆ ⟨

40

60

80

(b)

Figure 4: (color online). The centrality dependence of the width of the balance function〈∆η〉 and 〈∆ϕ〉, for the correlations studied in terms of the relative pseudorapidity andthe relative azimuthal angle, respectively. The data points are compared to the predictionsfrom HIJING [27], and AMPT [28].

24

η ∆0 0.5 1 1.5

)η ∆(+

-B

0

0.5

1

1.5 = 2.76 TeVNNsPb-Pb @

Centrality 0-5%

(deg.)ϕ ∆0 50 100 150

)-1

) (d

egϕ ∆(

+-

B

0

0.005

0.01

0.015 ALICE data

Blast Wave

HIJING

AMPT (string melting)

ALICE data

Blast Wave

HIJING

AMPT (string melting)

ALICE data

Blast Wave

HIJING

AMPT (string melting)

Figure 5: (color online). The balance functions for the 5% most central Pb–Pb collisionsmeasured by ALICE as a function of the relative pseudorapidity (a) and the relativeazimuthal angle (b). The experimental points are compared to predictions from HIJING[27], AMPT [28] and from a thermal blast wave [31, 32].

25

tions, consists of the hadronic rescattering which also includes the decay ofresonances.

The filled green squares represent the results of the analysis of the string

melting AMPT events with parameters tuned [30] to reproduce the measuredelliptic flow (v2) values of non–identified particles at the LHC [3]. The widthof the balance functions when studied in terms of the relative pseudorapidityexhibit little centrality dependence despite the fact that the produced systemexhibits significant collective behavior [30]. However, the width of the balancefunction in ∆ϕ is in qualitative agreement with the centrality dependence ofthe experimental points. This is consistent with the expectation that thebalance function when studied as a function of ∆ϕ can be used as a measureof radial flow of the system, as suggested in [13, 18]. We also studied thesame AMPT configuration, i.e. the string melting, this time switching offthe last part where the hadronic rescattering takes place, without alteringthe decay of resonances. The resulting points, indicated with the orangefilled stars in Fig. 4, demonstrate a similar qualitative behavior as in theprevious case: no centrality dependence of 〈∆η〉 and a significant decreaseof 〈∆ϕ〉 for central collisions. On a quantitative level though, the widths inboth projections are larger than the ones obtained in the case where hadronicrescattering is included. This can be explained by the fact that within thismodel, a significant part of radial flow of the system is built during this verylast stage of the system’s evolution. Therefore, the results are consistentwith the picture of having the balancing charges more focused under theinfluence of this collective motion, which is reflected in a narrower balancefunction distribution. In addition, we analyzed AMPT events produced usingthe default configuration, which results in smaller vn flow coefficients butharder spectra than the string melting. The extracted widths of the balancefunctions are represented by the open brown squares and exhibit similarbehavior as the results from the string melting configuration. In particular,the width in ∆η shows little centrality dependence while the values are inagreement with the ones calculated from the string melting. The width in∆ϕ shows similar (within the statistical uncertainties) quantitative centralitydependence as the experimental data points. However, these latter resultsexhibit a systematically lower value of the width for this version of AMPTcompared to the string melting configuration. This latter effect is consistentwith the observation of having a system exhibiting larger radial flow with

26

the default version.3

Finally, we fit the experimentally measured values with a thermal blast–wave model [31, 32]. This model, assumes that the radial expansion velocityis proportional to the distance from the center of the system and takes intoaccount the resonance production and decay. It also incorporates the lo-cal charge conservation, by generating ensembles of particles with zero totalcharge. Each particle of an ensemble is emitted by a fluid element with acommon collective velocity following the single–particle blast–wave parame-terization with the additional constraint of being emitted with a separationat kinetic freeze–out from the neighboring particle sampled from a Gaussianwith a width denoted as ση and σϕ in the pseudorapidity space and the az-imuthal angle, respectively. The procedure that we followed started fromtuning the input parameters of the model to match the average pT valuesextracted from the analysis of identified particle spectra [34] as well as thev2 values for non–identified particles reported by ALICE [3]. We then adjustthe widths of the parameters ση and σϕ to match the experimentally mea-sured widths of the balance function, 〈∆η〉 and 〈∆ϕ〉. The resulting valuesof ση and σϕ are listed in Table 2. We find that ση starts from 0.28±0.05 forthe most central Pb–Pb collisions reaching 0.52 ± 0.07 for the most periph-eral, while σϕ starts from 0.30± 0.10 evolving to 0.76± 0.01 for the 60–70%centrality bin.

Figure 5 presents the detailed comparison of the model results with themeasured balance functions as a function of ∆η (a) and ∆ϕ (b) for the5% most central Pb–Pb collisions. The data points are represented by thefull markers and are compared with HIJING (dotted blue line), AMPT string

melting (dashed green line) and the thermal blast–wave (full black line). Thedistributions for HIJING and AMPT are normalized to the same integral tofacilitate the direct comparison of the shapes and the widths. It is seenthat for correlations in the relative pseudorapidity, both HIJING and AMPTresult in similarly wider distributions. As mentioned before, the blast–wavemodel is tuned to reproduce the experimental points, so it is not surprisingthat the relevant curve not only reproduces the same narrow distribution butdescribes fairly well also its shape. For the correlations in ∆ϕ the HIJING

3We recently confirmed that AMPT does not conserve the charge. The influence ofthis effect to our measurement can not be easily quantified. However we still considerinteresting and worthwhile to point out that this model describes in a qualitative (and tosome extent quantitative) way the centrality dependence of 〈∆ϕ〉.

27

Table 2: The values of ση and σϕ extracted by fitting the centrality dependence of both〈∆η〉 and 〈∆ϕ〉 with the blast–wave parameterization of [31, 32].

Results from the fit with the blast–wave model

Centrality ση σϕ

0–5% 0.28± 0.05 0.30± 0.105–10% 0.32± 0.05 0.35± 0.0710–20% 0.31± 0.05 0.36± 0.0820–30% 0.36± 0.03 0.43± 0.0530–40% 0.43± 0.04 0.52± 0.0540–50% 0.42± 0.04 0.54± 0.0650–60% 0.44± 0.07 0.64± 0.0660–70% 0.52± 0.07 0.76± 0.01

curve clearly results in a wider balance function distribution. On the otherhand, there is a very good agreement between the AMPT curve and themeasured points, with the exception of the first bins (i.e. small relativeazimuthal angles) where the magnitude of B+−(∆ϕ) is significantly largerin real data. This suggests that there are additional correlations present inthese small ranges of ∆ϕ in data than what the model predicts.

5.2. Energy dependence

Figure 6 presents the comparison of our results for the centrality depen-dence (i.e. as a function of the centrality percentile) of the width of the bal-ance function, 〈∆η〉 (Fig. 6–a) and 〈∆ϕ〉 (Fig. 6–b), with results from STAR[17] in Au–Au collisions at

√sNN = 200 GeV (stars). The ALICE points

have been corrected for acceptance and detector effects, using the correctionfactors fab, discussed in the introduction. To make a proper comparison withthe STAR measurement, where such a correction was not applied, we employthe procedure suggested in [7] to the RHIC points. Based on the assumptionof a boost–invariant system the balance function studied in a given pseudo-rapidity window B+−(∆η|ηmax) can be related to the balance function for aninfinite interval according to the formula of Eq. 4

B+−(∆η|ηmax) = B+−(∆η|∞) ·(

1− ∆η

ηmax

)

. (4)

28

This procedure results in similar corrections as to the case where the fab areused, if the acceptance is flat in η (which is a reasonable assumption for theacceptance of STAR).4

While the centrality dependence is similar for both measurements, thewidths are seen to be significantly narrower at the LHC energies. This isconsistent with the idea of having a system exhibiting larger radial flow atthe LHC with respect to RHIC [3] while having a longer–lived QGP phase[33] with the consequence of a smaller separation between charge pairs whencreated at hadronization. However, it is seen that the relative decrease of thewidth between central and peripheral collisions seems to be similar betweenthe two energies. This observation could challenge the interpretation of thenarrowing of the width in ∆η as primarily due to the late stage creation ofbalancing charges.

To further quantify the previous observation, Fig. 7 presents the relativedecrease of 〈∆η〉 (a) and 〈∆ϕ〉 (b) from peripheral to central collisions as afunction of the mean number of participating nucleons, 〈Npart〉, for the high-est SPS5 [9] and RHIC [17] energies, compared to the values reported in thisarticle. In this figure, central (peripheral) collisions correspond to high (low)number of 〈Npart〉. The choice of the representation as a function of 〈Npart〉 ismainly driven by the apparent better scaling compared to the centrality per-centile. It is seen that in terms of correlations in relative pseudorapidity thedata points at the different energies are in fairly good agreement within theuncertainties, resulting though into an additional, marginal decrease for the0–5% most central collisions of ≈ (9.5 ± 2.0 (stat) ± 2.5 (syst))% comparedto the RHIC point. On the other hand, 〈∆ϕ〉/〈∆ϕ〉peripheral exhibits a de-crease of ≈ (14.0±1.3 (stat)±1.9 (syst))% between the most central Au–Aucollisions at

√sNN = 200 GeV and the results reported in this article. This

could be attributed to the additional increase in radial flow between centraland peripheral collisions at the LHC compared to RHIC energies. Anothercontribution might come from the bigger influence from jet–like structures atthe LHC with respect to RHIC that results in particles being emitted prefer-

4We do not compare our results to the data from the NA49 experiment at SPS inthis figure, for two reasons. Firstly, the balance function in that experiment was notmeasured at mid-rapidity. Secondly, the non-uniform acceptance in pseudorapidity makesthe simplified correction of Eq. 4 invalid.

5We include the NA49 points in this representation since the ratio to the peripheralresults should cancel out the acceptance effects to first order.

29

⟩ η ∆ ⟨

0.5

0.6

0.7

(a)

Centrality percentile0 20 40 60 80

(de

g.)

⟩ ϕ ∆ ⟨

40

60

80

(b)

= 2.76 TeVNN

sALICE: Pb-Pb

= 200 GeVNN

sSTAR: Au-Au

= 2.76 TeVNN

sALICE: Pb-Pb

= 200 GeVNN

sSTAR: Au-Au

= 2.76 TeVNN

sALICE: Pb-Pb

= 200 GeVNN

sSTAR: Au-Au

Figure 6: (color online). The centrality dependence of the balance function width 〈∆η〉(a) and 〈∆ϕ〉 (b). The ALICE points are compared to results from STAR [17]. The STARresults have been corrected for the finite acceptance as suggested in [7].

30

perip

hera

l⟩ η ∆ ⟨/⟩ η ∆ ⟨

0.7

0.8

0.9

1

1.1 = 2.76 TeVNNsPb-Pb @

= 200 GeVNNsAu-Au @

= 17.2 GeVNNsPb-Pb @

= 2.76 TeVNNsPb-Pb @

= 200 GeVNNsAu-Au @

= 17.2 GeVNNsPb-Pb @

= 2.76 TeVNNsPb-Pb @

= 200 GeVNNsAu-Au @

= 17.2 GeVNNsPb-Pb @

(a)

⟩ part.

N⟨0 100 200 300 400

perip

hera

l⟩ ϕ ∆ ⟨/⟩ ϕ ∆ ⟨

0.6

0.8

1(b)

Figure 7: (color online). The centrality dependence of the relative decrease of the widthof the balance function in the relative pseudorapidity (a) and relative azimuthal angle (b).The ALICE points are compared to results for the highest SPS [9] and RHIC [17] energies.

31

entially in cones with small opening angles. Contrary to 〈∆ϕ〉/〈∆ϕ〉peripheral,this strikingly marginal decrease of 〈∆η〉/〈∆η〉peripheral between the three col-liding energy regimes that differ more than an order of magnitude, can notbe easily understood solely within the framework of the late stage creationof charges.

6. Summary

This article reported the first measurements of the balance function forcharged particles in Pb–Pb collisions at the LHC using the ALICE detector.The balance function was studied both, in relative pseudorapidity (∆η) andazimuthal angle (∆ϕ). The widths of the balance functions, 〈∆η〉 and 〈∆ϕ〉,are found to decrease when moving from peripheral to central collisions. Theresults are consistent with the picture of a system exhibiting larger radialflow in central collisions but also whose charges are created at a later stageof the collision. While HIJING is not able to reproduce the observed central-ity dependence of the width in either projection, AMPT tuned to describethe v2 values reported by ALICE seems to agree qualitatively with the cen-trality dependence of 〈∆ϕ〉 but fails to reproduce the dependence of 〈∆η〉.A thermal blast–wave model incorporating the principle of local charge con-servation was fitted to the centrality dependence of 〈∆η〉 and 〈∆ϕ〉. Theresulting values of the charge separation at freeze–out can be used to con-strain models describing the hadronization processes. The comparison of theresults with those from lower energies showed that the centrality dependenceof the width, in both the relative pseudorapidity and azimuthal angle, whenscaled by the most peripheral widths, exhibits minor differences betweenRHIC and LHC.

These studies will soon be complemented by and extended to the correla-tions of identified particles in an attempt to probe the chemical evolution ofthe produced system, to quantify the influence of radial flow to the narrow-ing of the balance function width in more central collisions and to furtherconstrain the parameters of the models used to describe heavy–ion collisions.

We would like to thank Scott Pratt for providing us with the blast wavemodel calculations and fruitful discussions. The ALICE collaboration wouldlike to thank all its engineers and technicians for their invaluable contribu-tions to the construction of the experiment and the CERN accelerator teamsfor the outstanding performance of the LHC complex.The ALICE collaboration acknowledges the following funding agencies for

32

their support in building and running the ALICE detector:State Committee of Science, Calouste Gulbenkian Foundation from Lisbonand Swiss Fonds Kidagan, Armenia;Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Fi-nanciadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisado Estado de São Paulo (FAPESP);National Natural Science Foundation of China (NSFC), the Chinese Ministryof Education (CMOE) and the Ministry of Science and Technology of China(MSTC);Ministry of Education and Youth of the Czech Republic;Danish Natural Science Research Council, the Carlsberg Foundation and theDanish National Research Foundation;The European Research Council under the European Community’s SeventhFramework Programme;Helsinki Institute of Physics and the Academy of Finland;French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘RegionAuvergne’ and CEA, France;German BMBF and the Helmholtz Association;General Secretariat for Research and Technology, Ministry of Development,Greece;Hungarian OTKA and National Office for Research and Technology (NKTH);Department of Atomic Energy and Department of Science and Technologyof the Government of India;Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi - MuseoStorico della Fisica e Centro Studi e Ricerche "Enrico Fermi", Italy;MEXT Grant-in-Aid for Specially Promoted Research, Japan;Joint Institute for Nuclear Research, Dubna;National Research Foundation of Korea (NRF);CONACYT, DGAPA, México, ALFA-EC and the HELEN Program (High-Energy physics Latin-American–European Network);Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Neder-landse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands;Research Council of Norway (NFR);Polish Ministry of Science and Higher Education;National Authority for Scientific Research - NASR (Autoritatea Naţionalăpentru Cercetare Ştiinţifică - ANCS);Ministry of Education and Science of Russian Federation, International Sci-ence and Technology Center, Russian Academy of Sciences, Russian Federal

33

Agency of Atomic Energy, Russian Federal Agency for Science and Innova-tions and CERN-INTAS;Ministry of Education of Slovakia;Department of Science and Technology, South Africa;CIEMAT, EELA, Ministerio de Educación y Ciencia of Spain, Xunta de Gali-cia (Consellería de Educación), CEADEN, Cubaenergía, Cuba, and IAEA(International Atomic Energy Agency);Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation(KAW);Ukraine Ministry of Education and Science;United Kingdom Science and Technology Facilities Council (STFC);The United States Department of Energy, the United States National ScienceFoundation, the State of Texas, and the State of Ohio.

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