Two-pion Bose-Einstein correlations in pp collisions at sqrt(s)=900 GeV

arXiv:1007.0516v2 [hep-ex] 28 Sep 2017

Submitted to: PRD

Two-pion Bose-Einstein correlations in

pp

collisions at

√

s

= 900

GeV

ALICE Collaboration

Abstract

We report on the measurement of two-pion correlation functions from

pp

collisions at

√

s

= 900

GeV per-formed by the ALICE experiment at the Large Hadron Collider. Our analysis shows an increase of the HBT radius with increasing event multiplicity, in line with other measurements done in particle- and nuclear collisions. Conversely, the strong decrease of the radius with increasing transverse momentum, as observed at RHIC and at Tevatron, is not manifest in our data.

Two-pion Bose-Einstein correlations in pp collisions at

s

= 900 GeV

(ALICE Collaboration)

K. Aamodt,1N. Abel,2U. Abeysekara,3A. Abrahantes Quintana,4A. Abramyan,5D. Adamov´a,6M.M. Aggarwal,7 G. Aglieri Rinella,8_{A.G. Agocs,}9_{S. Aguilar Salazar,}10_{Z. Ahammed,}11_{A. Ahmad,}12_{N. Ahmad,}12_{S.U. Ahn,}13, a_{R. Akimoto,}14

A. Akindinov,15D. Aleksandrov,16B. Alessandro,17R. Alfaro Molina,10A. Alici,18E. Almar´az Avi˜na,10J. Alme,19T. Alt,2, b V. Altini,20S. Altinpinar,21C. Andrei,22A. Andronic,21G. Anelli,8V. Angelov,2, bC. Anson,23T. Antiˇci´c,24F. Antinori,8, c

S. Antinori,18_{K. Antipin,}25_{D. Anto´nczyk,}25_{P. Antonioli,}26_{A. Anzo,}10_{L. Aphecetche,}27_{H. Appelsh¨auser,}25_{S. Arcelli,}18 R. Arceo,10_{A. Arend,}25_{N. Armesto,}28_{R. Arnaldi,}17_{T. Aronsson,}29_{I.C. Arsene,}1, d_{A. Asryan,}30_{A. Augustinus,}8 R. Averbeck,21T.C. Awes,31J. ¨Ayst¨o,32M.D. Azmi,12S. Bablok,19M. Bach,33A. Badal`a,34Y.W. Baek,13, aS. Bagnasco,17 R. Bailhache,21, e_{R. Bala,}35_{A. Baldisseri,}36_{A. Baldit,}37_{J. B´an,}38_{R. Barbera,}39_{G.G. Barnaf¨oldi,}9_{L.S. Barnby,}40_{V. Barret,}37

J. Bartke,41_{F. Barile,}20_{M. Basile,}18_{V. Basmanov,}42_{N. Bastid,}37_{B. Bathen,}43_{G. Batigne,}27_{B. Batyunya,}44_{C. Baumann,}43, e I.G. Bearden,45B. Becker,46, fI. Belikov,47R. Bellwied,48E. Belmont-Moreno,10A. Belogianni,49L. Benhabib,27

S. Beole,35I. Berceanu,22A. Bercuci,21, gE. Berdermann,21Y. Berdnikov,50L. Betev,8A. Bhasin,51A.K. Bhati,7 L. Bianchi,35_{N. Bianchi,}52_{C. Bianchin,}53_{J. Bielˇc´ık,}54_{J. Bielˇc´ıkov´a,}6_{A. Bilandzic,}55_{L. Bimbot,}56_{E. Biolcati,}35 A. Blanc,37F. Blanco,39, hF. Blanco,57D. Blau,16C. Blume,25M. Boccioli,8N. Bock,23A. Bogdanov,58H. Bøggild,45 M. Bogolyubsky,59J. Bohm,60L. Boldizs´ar,9M. Bombara,61C. Bombonati,53, iM. Bondila,32H. Borel,36A. Borisov,62

C. Bortolin,53, j_{S. Bose,}63_{L. Bosisio,}64_{F. Boss´u,}35_{M. Botje,}55_{S. B¨ottger,}2_{G. Bourdaud,}27_{B. Boyer,}56_{M. Braun,}30 P. Braun-Munzinger,21, 65, bL. Bravina,1M. Bregant,64, kT. Breitner,2G. Bruckner,8R. Brun,8E. Bruna,29G.E. Bruno,20

D. Budnikov,42_{H. Buesching,}25_{P. Buncic,}8_{O. Busch,}66_{Z. Buthelezi,}67_{D. Caffarri,}53_{X. Cai,}68_{H. Caines,}29_{E. Calvo,}69 E. Camacho,70_{P. Camerini,}64_{M. Campbell,}8_{V. Canoa Roman,}8_{G.P. Capitani,}52_{G. Cara Romeo,}26_{F. Carena,}8_{W. Carena,}8

F. Carminati,8A. Casanova D´ıaz,52M. Caselle,8J. Castillo Castellanos,36J.F. Castillo Hernandez,21V. Catanescu,22 E. Cattaruzza,64C. Cavicchioli,8P. Cerello,17V. Chambert,56B. Chang,60S. Chapeland,8A. Charpy,56J.L. Charvet,36 S. Chattopadhyay,63_{S. Chattopadhyay,}11_{M. Cherney,}3_{C. Cheshkov,}8_{B. Cheynis,}71_{E. Chiavassa,}35_{V. Chibante Barroso,}8

D.D. Chinellato,72P. Chochula,8K. Choi,73M. Chojnacki,74P. Christakoglou,74C.H. Christensen,45P. Christiansen,75 T. Chujo,76F. Chuman,77C. Cicalo,46L. Cifarelli,18F. Cindolo,26J. Cleymans,67O. Cobanoglu,35J.-P. Coffin,47S. Coli,17

A. Colla,8_{G. Conesa Balbastre,}52_{Z. Conesa del Valle,}27, l_{E.S. Conner,}78_{P. Constantin,}66_{G. Contin,}64, i_{J.G. Contreras,}70 Y. Corrales Morales,35T.M. Cormier,48P. Cortese,79I. Cort´es Maldonado,80M.R. Cosentino,72F. Costa,8M.E. Cotallo,57 E. Crescio,70P. Crochet,37E. Cuautle,81L. Cunqueiro,52J. Cussonneau,27A. Dainese,82H.H. Dalsgaard,45A. Danu,83

I. Das,63_{A. Dash,}84_{S. Dash,}84_{G.O.V. de Barros,}85_{A. De Caro,}86_{G. de Cataldo,}87_{J. de Cuveland,}2, b_{A. De Falco,}88 M. De Gaspari,66_{J. de Groot,}8_{D. De Gruttola,}86_{N. De Marco,}17_{S. De Pasquale,}86_{R. De Remigis,}17_{R. de Rooij,}74 G. de Vaux,67H. Delagrange,27Y. Delgado,69G. Dellacasa,79A. Deloff,89V. Demanov,42E. D´enes,9A. Deppman,85 G. D’Erasmo,20_{D. Derkach,}30_{A. Devaux,}37_{D. Di Bari,}20_{C. Di Giglio,}20, i_{S. Di Liberto,}90_{A. Di Mauro,}8_{P. Di Nezza,}52 M. Dialinas,27L. D´ıaz,81R. D´ıaz,32T. Dietel,43R. Divi`a,8Ø. Djuvsland,19V. Dobretsov,16A. Dobrin,75T. Dobrowolski,89

B. D¨onigus,21I. Dom´ınguez,81D.M.M. Don,91O. Dordic,1A.K. Dubey,11J. Dubuisson,8L. Ducroux,71P. Dupieux,37 A.K. Dutta Majumdar,63_{M.R. Dutta Majumdar,}11_{D. Elia,}87_{D. Emschermann,}66, m_{A. Enokizono,}31_{B. Espagnon,}56 M. Estienne,27S. Esumi,76D. Evans,40S. Evrard,8G. Eyyubova,1C.W. Fabjan,8, nD. Fabris,82J. Faivre,92D. Falchieri,18 A. Fantoni,52M. Fasel,21O. Fateev,44R. Fearick,67A. Fedunov,44D. Fehlker,19V. Fekete,93D. Felea,83B. Fenton-Olsen,45, o

G. Feofilov,30_{A. Fern´andez T´ellez,}80_{E.G. Ferreiro,}28_{A. Ferretti,}35_{R. Ferretti,}79, p_{M.A.S. Figueredo,}85_{S. Filchagin,}42 R. Fini,87_{F.M. Fionda,}20_{E.M. Fiore,}20_{M. Floris,}88, i_{Z. Fodor,}9_{S. Foertsch,}67_{P. Foka,}21_{S. Fokin,}16_{F. Formenti,}8 E. Fragiacomo,94M. Fragkiadakis,49U. Frankenfeld,21A. Frolov,95U. Fuchs,8F. Furano,8C. Furget,92M. Fusco Girard,86

J.J. Gaardhøje,45_{S. Gadrat,}92_{M. Gagliardi,}35_{A. Gago,}69_{M. Gallio,}35_{P. Ganoti,}49_{M.S. Ganti,}11_{C. Garabatos,}21 C. Garc´ıa Trapaga,35_{J. Gebelein,}2_{R. Gemme,}79_{M. Germain,}27_{A. Gheata,}8_{M. Gheata,}8_{B. Ghidini,}20_{P. Ghosh,}11 G. Giraudo,17P. Giubellino,17E. Gladysz-Dziadus,41R. Glasow,43, qP. Gl¨assel,66A. Glenn,96R. G´omez Jim´enez,97 H. Gonz´alez Santos,80L.H. Gonz´alez-Trueba,10P. Gonz´alez-Zamora,57S. Gorbunov,2, bY. Gorbunov,3S. Gotovac,98 H. Gottschlag,43_{V. Grabski,}10_{R. Grajcarek,}66_{A. Grelli,}74_{A. Grigoras,}8_{C. Grigoras,}8_{V. Grigoriev,}58_{A. Grigoryan,}5 S. Grigoryan,44B. Grinyov,62N. Grion,94P. Gros,75J.F. Grosse-Oetringhaus,8J.-Y. Grossiord,71R. Grosso,82F. Guber,99

R. Guernane,92C. Guerra,69B. Guerzoni,18K. Gulbrandsen,45H. Gulkanyan,5T. Gunji,14A. Gupta,51R. Gupta,51 H.-A. Gustafsson,75, q_{H. Gutbrod,}21_{Ø. Haaland,}19_{C. Hadjidakis,}56_{M. Haiduc,}83_{H. Hamagaki,}14_{G. Hamar,}9 J. Hamblen,100B.H. Han,101J.W. Harris,29M. Hartig,25A. Harutyunyan,5D. Hasch,52D. Hasegan,83D. Hatzifotiadou,26

A. Hayrapetyan,5M. Heide,43M. Heinz,29H. Helstrup,102A. Herghelegiu,22C. Hern´andez,21G. Herrera Corral,70 N. Herrmann,66_{K.F. Hetland,}102_{B. Hicks,}29_{A. Hiei,}77_{P.T. Hille,}1, r_{B. Hippolyte,}47_{T. Horaguchi,}77, s_{Y. Hori,}14_{P. Hristov,}8

I. Ilkiv,89M. Inaba,76P.G. Innocenti,8M. Ippolitov,16M. Irfan,12C. Ivan,74A. Ivanov,30M. Ivanov,21V. Ivanov,50 T. Iwasaki,77A. Jachołkowski,8P. Jacobs,104L. Janˇcurov´a,44S. Jangal,47R. Janik,93C. Jena,84S. Jena,105L. Jirden,8 G.T. Jones,40_{P.G. Jones,}40_{P. Jovanovi´c,}40_{H. Jung,}13_{W. Jung,}13_{A. Jusko,}40_{A.B. Kaidalov,}15_{S. Kalcher,}2, b_{P. Kaliˇn´ak,}38 M. Kalisky,43T. Kalliokoski,32A. Kalweit,65A. Kamal,12R. Kamermans,74K. Kanaki,19E. Kang,13J.H. Kang,60J. Kapitan,6

V. Kaplin,58S. Kapusta,8O. Karavichev,99T. Karavicheva,99E. Karpechev,99A. Kazantsev,16U. Kebschull,2R. Keidel,78 M.M. Khan,12_{S.A. Khan,}11_{A. Khanzadeev,}50_{Y. Kharlov,}59_{D. Kikola,}106_{B. Kileng,}102_{D.J Kim,}32_{D.S. Kim,}13_{D.W. Kim,}13

H.N. Kim,13J. Kim,59J.H. Kim,101J.S. Kim,13M. Kim,13M. Kim,60S.H. Kim,13S. Kim,101Y. Kim,60S. Kirsch,8 I. Kisel,2, dS. Kiselev,15A. Kisiel,23, iJ.L. Klay,107J. Klein,66C. Klein-B¨osing,8, mM. Kliemant,25A. Klovning,19 A. Kluge,8_{M.L. Knichel,}21_{S. Kniege,}25_{K. Koch,}66_{R. Kolevatov,}1_{A. Kolojvari,}30_{V. Kondratiev,}30_{N. Kondratyeva,}58

A. Konevskih,99E. Korna´s,41R. Kour,40M. Kowalski,41S. Kox,92K. Kozlov,16J. Kral,54, kI. Kr´alik,38F. Kramer,25 I. Kraus,65, dA. Kravˇc´akov´a,61T. Krawutschke,108M. Krivda,40D. Krumbhorn,66M. Krus,54E. Kryshen,50M. Krzewicki,55

Y. Kucheriaev,16_{C. Kuhn,}47_{P.G. Kuijer,}55_{L. Kumar,}7_{N. Kumar,}7_{R. Kupczak,}106_{P. Kurashvili,}89_{A. Kurepin,}99 A.N. Kurepin,99_{A. Kuryakin,}42_{S. Kushpil,}6_{V. Kushpil,}6_{M. Kutouski,}44_{H. Kvaerno,}1_{M.J. Kweon,}66_{Y. Kwon,}60 P. La Rocca,39, tF. Lackner,8P. Ladr´on de Guevara,57V. Lafage,56C. Lal,51C. Lara,2D.T. Larsen,19G. Laurenti,26 C. Lazzeroni,40_{Y. Le Bornec,}56_{N. Le Bris,}27_{H. Lee,}73_{K.S. Lee,}13_{S.C. Lee,}13_{F. Lef`evre,}27_{M. Lenhardt,}27_{L. Leistam,}8 J. Lehnert,25_{V. Lenti,}87_{H. Le´on,}10_{I. Le´on Monz´on,}97_{H. Le´on Vargas,}25_{P. L´evai,}9_{X. Li,}103_{Y. Li,}103_{R. Lietava,}40_{S. Lindal,}1

V. Lindenstruth,2, bC. Lippmann,8M.A. Lisa,23L. Liu,19V. Loginov,58S. Lohn,8X. Lopez,37M. L´opez Noriega,56 R. L´opez-Ram´ırez,80E. L´opez Torres,4G. Løvhøiden,1A. Lozea Feijo Soares,85S. Lu,103M. Lunardon,53G. Luparello,35 L. Luquin,27_{J.-R. Lutz,}47_{K. Ma,}68_{R. Ma,}29_{D.M. Madagodahettige-Don,}91_{A. Maevskaya,}99_{M. Mager,}65, i_{D.P. Mahapatra,}84

A. Maire,47I. Makhlyueva,8D. Mal’Kevich,15M. Malaev,50K.J. Malagalage,3I. Maldonado Cervantes,81M. Malek,56 L. Malinina,44, u_{T. Malkiewicz,}32_{P. Malzacher,}21_{A. Mamonov,}42_{L. Manceau,}37_{L. Mangotra,}51_{V. Manko,}16_{F. Manso,}37

V. Manzari,87_{Y. Mao,}68, v_{J. Mareˇs,}109_{G.V. Margagliotti,}64_{A. Margotti,}26_{A. Mar´ın,}21_{I. Martashvili,}100_{P. Martinengo,}8 M.I. Mart´ınez Hern´andez,80A. Mart´ınez Davalos,10G. Mart´ınez Garc´ıa,27Y. Maruyama,77A. Marzari Chiesa,35 S. Masciocchi,21_{M. Masera,}35_{M. Masetti,}18_{A. Masoni,}46_{L. Massacrier,}71_{M. Mastromarco,}87_{A. Mastroserio,}20, i

Z.L. Matthews,40_{A. Matyja,}41, w_{D. Mayani,}81_{G. Mazza,}17_{M.A. Mazzoni,}90_{F. Meddi,}110_{A. Menchaca-Rocha,}10 P. Mendez Lorenzo,8M. Meoni,8J. Mercado P´erez,66P. Mereu,17Y. Miake,76A. Michalon,47N. Miftakhov,50L. Milano,35

J. Milosevic,1F. Minafra,20A. Mischke,74D. Mi´skowiec,21C. Mitu,83K. Mizoguchi,77J. Mlynarz,48B. Mohanty,11 L. Molnar,9, i_{M.M. Mondal,}11_{L. Monta˜no Zetina,}70, x_{M. Monteno,}17_{E. Montes,}57_{M. Morando,}53_{S. Moretto,}53_{A. Morsch,}8

T. Moukhanova,16V. Muccifora,52E. Mudnic,98S. Muhuri,11H. M¨uller,8M.G. Munhoz,85J. Munoz,80L. Musa,8 A. Musso,17B.K. Nandi,105R. Nania,26E. Nappi,87F. Navach,20S. Navin,40T.K. Nayak,11S. Nazarenko,42G. Nazarov,42

A. Nedosekin,15_{F. Nendaz,}71_{J. Newby,}96_{A. Nianine,}16_{M. Nicassio,}87, i_{B.S. Nielsen,}45_{S. Nikolaev,}16_{V. Nikolic,}24 S. Nikulin,16V. Nikulin,50B.S. Nilsen,3M.S. Nilsson,1F. Noferini,26P. Nomokonov,44G. Nooren,74N. Novitzky,32 A. Nyatha,105C. Nygaard,45A. Nyiri,1J. Nystrand,19A. Ochirov,30G. Odyniec,104H. Oeschler,65M. Oinonen,32 K. Okada,14_{Y. Okada,}77_{M. Oldenburg,}8_{J. Oleniacz,}106_{C. Oppedisano,}17_{F. Orsini,}36_{A. Ortiz Velasquez,}81_{G. Ortona,}35 A. Oskarsson,75F. Osmic,8L. ¨Osterman,75P. Ostrowski,106I. Otterlund,75J. Otwinowski,21G. Øvrebekk,19K. Oyama,66

K. Ozawa,14Y. Pachmayer,66M. Pachr,54F. Padilla,35P. Pagano,86G. Pai´c,81F. Painke,2C. Pajares,28S. Pal,63, y S.K. Pal,11_{A. Palaha,}40_{A. Palmeri,}34_{R. Panse,}2_{V. Papikyan,}5_{G.S. Pappalardo,}34_{W.J. Park,}21_{B. Pastirˇc´ak,}38_{C. Pastore,}87

V. Paticchio,87A. Pavlinov,48T. Pawlak,106T. Peitzmann,74A. Pepato,82H. Pereira,36D. Peressounko,16C. P´erez,69 D. Perini,8D. Perrino,20, iW. Peryt,106J. Peschek,2, bA. Pesci,26V. Peskov,81, iY. Pestov,95A.J. Peters,8V. Petr´aˇcek,54 A. Petridis,49, q_{M. Petris,}22_{P. Petrov,}40_{M. Petrovici,}22_{C. Petta,}39_{J. Peyr´e,}56_{S. Piano,}94_{A. Piccotti,}17_{M. Pikna,}93_{P. Pillot,}27

O. Pinazza,26, iL. Pinsky,91N. Pitz,25F. Piuz,8R. Platt,40M. Płosko´n,104J. Pluta,106T. Pocheptsov,44, zS. Pochybova,9 P.L.M. Podesta Lerma,97F. Poggio,35M.G. Poghosyan,35K. Pol´ak,109B. Polichtchouk,59P. Polozov,15V. Polyakov,50

B. Pommeresch,19_{A. Pop,}22_{F. Posa,}20_{V. Posp´ıˇsil,}54_{B. Potukuchi,}51_{J. Pouthas,}56_{S.K. Prasad,}11_{R. Preghenella,}18, t F. Prino,17_{C.A. Pruneau,}48_{I. Pshenichnov,}99_{G. Puddu,}88_{P. Pujahari,}105_{A. Pulvirenti,}39_{A. Punin,}42_{V. Punin,}42_{M. Putiˇs,}61 J. Putschke,29E. Quercigh,8A. Rachevski,94A. Rademakers,8S. Radomski,66T.S. R¨aih¨a,32J. Rak,32A. Rakotozafindrabe,36

L. Ramello,79_{A. Ram´ırez Reyes,}70_{M. Rammler,}43_{R. Raniwala,}111_{S. Raniwala,}111_{S.S. R¨as¨anen,}32_{I. Rashevskaya,}94 S. Rath,84_{K.F. Read,}100_{J.S. Real,}92_{K. Redlich,}89, aa_{R. Renfordt,}25_{A.R. Reolon,}52_{A. Reshetin,}99_{F. Rettig,}2, b_{J.-P. Revol,}8

K. Reygers,43, bbH. Ricaud,65L. Riccati,17R.A. Ricci,112M. Richter,19P. Riedler,8W. Riegler,8F. Riggi,39A. Rivetti,17 M. Rodriguez Cahuantzi,80K. Røed,102D. R¨ohrich,8, ccS. Rom´an L´opez,80R. Romita,20, dF. Ronchetti,52P. Rosinsk´y,8 P. Rosnet,37_{S. Rossegger,}8_{A. Rossi,}64, dd_{F. Roukoutakis,}8, ee_{S. Rousseau,}56_{C. Roy,}27, l_{P. Roy,}63_{A.J. Rubio-Montero,}57

R. Rui,64I. Rusanov,66G. Russo,86E. Ryabinkin,16A. Rybicki,41S. Sadovsky,59K. ˇSafaˇr´ık,8R. Sahoo,53J. Saini,11 P. Saiz,8D. Sakata,76C.A. Salgado,28R. Salgueiro Domingues da Silva,8S. Salur,104T. Samanta,11S. Sambyal,51 V. Samsonov,50_{L. ˇS´andor,}38_{A. Sandoval,}10_{M. Sano,}76_{S. Sano,}14_{R. Santo,}43_{R. Santoro,}20_{J. Sarkamo,}32_{P. Saturnini,}37

E. Scapparone,26F. Scarlassara,53R.P. Scharenberg,113C. Schiaua,22R. Schicker,66H. Schindler,8C. Schmidt,21 H.R. Schmidt,21K. Schossmaier,8S. Schreiner,8S. Schuchmann,25J. Schukraft,8Y. Schutz,27K. Schwarz,21K. Schweda,66

G. Scioli,18_{E. Scomparin,}17_{P.A. Scott,}40_{G. Segato,}53_{D. Semenov,}30_{S. Senyukov,}79_{J. Seo,}13_{S. Serci,}88_{L. Serkin,}81 E. Serradilla,57A. Sevcenco,83I. Sgura,20G. Shabratova,44R. Shahoyan,8G. Sharkov,15N. Sharma,7S. Sharma,51 K. Shigaki,77M. Shimomura,76K. Shtejer,4Y. Sibiriak,16M. Siciliano,35E. Sicking,8, ffE. Siddi,46T. Siemiarczuk,89

A. Silenzi,18_{D. Silvermyr,}31_{E. Simili,}74_{G. Simonetti,}20, i_{R. Singaraju,}11_{R. Singh,}51_{V. Singhal,}11_{B.C. Sinha,}11 T. Sinha,63B. Sitar,93M. Sitta,79T.B. Skaali,1K. Skjerdal,19R. Smakal,54N. Smirnov,29R. Snellings,55H. Snow,40 C. Søgaard,45A. Soloviev,59H.K. Soltveit,66R. Soltz,96W. Sommer,25C.W. Son,73H. Son,101M. Song,60C. Soos,8 F. Soramel,53_{D. Soyk,}21_{M. Spyropoulou-Stassinaki,}49_{B.K. Srivastava,}113_{J. Stachel,}66_{F. Staley,}36_{E. Stan,}83_{G. Stefanek,}89

G. Stefanini,8T. Steinbeck,2, bE. Stenlund,75G. Steyn,67D. Stocco,35, wR. Stock,25P. Stolpovsky,59P. Strmen,93 A.A.P. Suaide,85M.A. Subieta V´asquez,35T. Sugitate,77C. Suire,56M. ˇSumbera,6T. Susa,24D. Swoboda,8J. Symons,104

A. Szanto de Toledo,85_{I. Szarka,}93_{A. Szostak,}46_{M. Szuba,}106_{M. Tadel,}8_{C. Tagridis,}49_{A. Takahara,}14_{J. Takahashi,}72 R. Tanabe,76_{J.D. Tapia Takaki,}56_{H. Taureg,}8_{A. Tauro,}8_{M. Tavlet,}8_{G. Tejeda Mu˜noz,}80_{A. Telesca,}8_{C. Terrevoli,}20 J. Th¨ader,2, bR. Tieulent,71D. Tlusty,54A. Toia,8T. Tolyhy,9C. Torcato de Matos,8H. Torii,77G. Torralba,2L. Toscano,17

F. Tosello,17_{A. Tournaire,}27, gg_{T. Traczyk,}106_{P. Tribedy,}11_{G. Tr¨oger,}2_{D. Truesdale,}23_{W.H. Trzaska,}32_{G. Tsiledakis,}66 E. Tsilis,49_{T. Tsuji,}14_{A. Tumkin,}42_{R. Turrisi,}82_{A. Turvey,}3_{T.S. Tveter,}1_{H. Tydesj¨o,}8_{K. Tywoniuk,}1_{J. Ulery,}25 K. Ullaland,19A. Uras,88J. Urb´an,61G.M. Urciuoli,90G.L. Usai,88A. Vacchi,94M. Vala,44, hhL. Valencia Palomo,10 S. Vallero,66N. van der Kolk,55P. Vande Vyvre,8M. van Leeuwen,74L. Vannucci,112A. Vargas,80R. Varma,105A. Vasiliev,16

I. Vassiliev,2, ee_{M. Vasileiou,}49_{V. Vechernin,}30_{M. Venaruzzo,}64_{E. Vercellin,}35_{S. Vergara,}80_{R. Vernet,}39, ii_{M. Verweij,}74 I. Vetlitskiy,15L. Vickovic,98G. Viesti,53O. Vikhlyantsev,42Z. Vilakazi,67O. Villalobos Baillie,40A. Vinogradov,16 L. Vinogradov,30_{Y. Vinogradov,}42_{T. Virgili,}86_{Y.P. Viyogi,}11_{A. Vodopianov,}44_{K. Voloshin,}15_{S. Voloshin,}48_{G. Volpe,}20 B. von Haller,8_{D. Vranic,}21_{J. Vrl´akov´a,}61_{B. Vulpescu,}37_{B. Wagner,}19_{V. Wagner,}54_{L. Wallet,}8_{R. Wan,}68, l_{D. Wang,}68 Y. Wang,66Y. Wang,68K. Watanabe,76Q. Wen,103J. Wessels,43U. Westerhoff,43J. Wiechula,66J. Wikne,1A. Wilk,43

G. Wilk,89_{M.C.S. Williams,}26_{N. Willis,}56_{B. Windelband,}66_{C. Xu,}68_{C. Yang,}68_{H. Yang,}66_{S. Yasnopolskiy,}16 F. Yermia,27_{J. Yi,}73_{Z. Yin,}68_{H. Yokoyama,}76_{I-K. Yoo,}73_{X. Yuan,}68, jj_{V. Yurevich,}44_{I. Yushmanov,}16_{E. Zabrodin,}1

B. Zagreev,15A. Zalite,50C. Zampolli,8, kkYu. Zanevsky,44S. Zaporozhets,44A. Zarochentsev,30P. Z´avada,109 H. Zbroszczyk,106P. Zelnicek,2A. Zenin,59A. Zepeda,70I. Zgura,83M. Zhalov,50X. Zhang,68, aD. Zhou,68S. Zhou,103

J. Zhu,68_{A. Zichichi,}18, t_{A. Zinchenko,}44_{G. Zinovjev,}62_{Y. Zoccarato,}71_{V. Zych´aˇcek,}54_{and M. Zynovyev}62

1_{Department of Physics, University of Oslo, Oslo, Norway}

2_{Kirchhoff-Institut f¨ur Physik, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany} 3_{Physics Department, Creighton University, Omaha, NE, United States}

4_{Centro de Aplicaciones Tecnol´ogicas y Desarrollo Nuclear (CEADEN), Havana, Cuba} 5_{Yerevan Physics Institute, Yerevan, Armenia}

6_{Nuclear Physics Institute, Academy of Sciences of the Czech Republic, ˇReˇz u Prahy, Czech Republic} 7_{Physics Department, Panjab University, Chandigarh, India}

8_{European Organization for Nuclear Research (CERN), Geneva, Switzerland}

9_{KFKI Research Institute for Particle and Nuclear Physics, Hungarian Academy of Sciences, Budapest, Hungary} 10_{Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico}

11_{Variable Energy Cyclotron Centre, Kolkata, India} 12_{Department of Physics Aligarh Muslim University, Aligarh, India} 13_{Gangneung-Wonju National University, Gangneung, South Korea}

14_{University of Tokyo, Tokyo, Japan}

15_{Institute for Theoretical and Experimental Physics, Moscow, Russia} 16_{Russian Research Centre Kurchatov Institute, Moscow, Russia}

17_{Sezione INFN, Turin, Italy}

18_{Dipartimento di Fisica dell’Universit`a and Sezione INFN, Bologna, Italy} 19_{Department of Physics and Technology, University of Bergen, Bergen, Norway} 20_{Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy}

21_{Research Division and ExtreMe Matter Institute EMMI,}

GSI Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, Germany

22_{National Institute for Physics and Nuclear Engineering, Bucharest, Romania} 23_{Department of Physics, Ohio State University, Columbus, OH, United States}

24_{Rudjer Boˇskovi´c Institute, Zagreb, Croatia}

25_{Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany} 26_{Sezione INFN, Bologna, Italy}

27_{SUBATECH, Ecole des Mines de Nantes, Universit´e de Nantes, CNRS-IN2P3, Nantes, France}

28_{Departamento de F´ısica de Part´ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain} 29_{Yale University, New Haven, CT, United States}

30_{V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia} 31_{Oak Ridge National Laboratory, Oak Ridge, TN, United States}

32_{Helsinki Institute of Physics (HIP) and University of Jyv¨askyl¨a, Jyv¨askyl¨a, Finland}

33_{Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany} 34_{Sezione INFN, Catania, Italy}

35_{Dipartimento di Fisica Sperimentale dell’Universit`a and Sezione INFN, Turin, Italy</sub> 36<sub>Commissariat `a l’Energie Atomique, IRFU, Saclay, France}

37_{Laboratoire de Physique Corpusculaire (LPC), Clermont Universit´e,}

Universit´e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

38_{Institute of Experimental Physics, Slovak Academy of Sciences, Koˇsice, Slovakia} 39_{Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy} 40_{School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom} 41_{The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland}

42_{Russian Federal Nuclear Center (VNIIEF), Sarov, Russia}

43_{Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at M¨unster, M¨unster, Germany} 44_{Joint Institute for Nuclear Research (JINR), Dubna, Russia}

45_{Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark} 46_{Sezione INFN, Cagliari, Italy}

47_{Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´e de Strasbourg, CNRS-IN2P3, Strasbourg, France} 48_{Wayne State University, Detroit, MI, United States}

49_{Physics Department, University of Athens, Athens, Greece} 50_{Petersburg Nuclear Physics Institute, Gatchina, Russia} 51_{Physics Department, University of Jammu, Jammu, India}

52_{Laboratori Nazionali di Frascati, INFN, Frascati, Italy} 53_{Dipartimento di Fisica dell’Universit`a and Sezione INFN, Padova, Italy}

54_{Faculty of Nuclear Sciences and Physical Engineering,}

Czech Technical University in Prague, Prague, Czech Republic

55_{Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands}

56_{Institut de Physique Nucl´eaire d’Orsay (IPNO), Universit´e Paris-Sud, CNRS-IN2P3, Orsay, France} 57_{Centro de Investigaciones Energ´eticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain}

58_{Moscow Engineering Physics Institute, Moscow, Russia} 59_{Institute for High Energy Physics, Protvino, Russia}

60_{Yonsei University, Seoul, South Korea}

61_{Faculty of Science, P.J. ˇSaf´arik University, Koˇsice, Slovakia} 62_{Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine}

63_{Saha Institute of Nuclear Physics, Kolkata, India}

64_{Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy} 65_{Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, Darmstadt, Germany} 66_{Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany} 67_{Physics Department, University of Cape Town, iThemba Laboratories, Cape Town, South Africa}

68_{Hua-Zhong Normal University, Wuhan, China}

69_{Secci´on F´ısica, Departamento de Ciencias, Pontificia Universidad Cat´olica del Per´u, Lima, Peru} 70_{Centro de Investigaci´on y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico}

71_{Universit´e de Lyon, Universit´e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France} 72_{Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil}

73_{Pusan National University, Pusan, South Korea}

74_{Nikhef and Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands} 75_{Division of Experimental High Energy Physics, University of Lund, Lund, Sweden}

76_{University of Tsukuba, Tsukuba, Japan} 77_{Hiroshima University, Hiroshima, Japan}

78_{Zentrum f¨ur Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany}

79_{Dipartimento di Scienze e Tecnologie Avanzate dell’Universit`a del Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy} 80_{Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico}

81_{Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico} 82_{Sezione INFN, Padova, Italy}

83_{Institute of Space Sciences (ISS), Bucharest, Romania} 84_{Institute of Physics, Bhubaneswar, India} 85_{Universidade de S˜ao Paulo (USP), S˜ao Paulo, Brazil}

86_{Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit`a and Sezione INFN, Salerno, Italy} 87_{Sezione INFN, Bari, Italy}

88_{Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy} 89_{Soltan Institute for Nuclear Studies, Warsaw, Poland}

90_{Sezione INFN, Rome, Italy}

92_{Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit´e Joseph Fourier,}

CNRS-IN2P3, Institut Polytechnique de Grenoble, Grenoble, France

93_{Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia} 94_{Sezione INFN, Trieste, Italy}

95_{Budker Institute for Nuclear Physics, Novosibirsk, Russia} 96_{Lawrence Livermore National Laboratory, Livermore, CA, United States}

97_{Universidad Aut´onoma de Sinaloa, Culiac´an, Mexico} 98_{Technical University of Split FESB, Split, Croatia}

99_{Institute for Nuclear Research, Academy of Sciences, Moscow, Russia} 100_{University of Tennessee, Knoxville, TN, United States} 101_{Department of Physics, Sejong University, Seoul, South Korea} 102_{Faculty of Engineering, Bergen University College, Bergen, Norway}

103_{China Institute of Atomic Energy, Beijing, China}

104_{Lawrence Berkeley National Laboratory, Berkeley, CA, United States} 105_{Indian Institute of Technology, Mumbai, India}

106_{Warsaw University of Technology, Warsaw, Poland}

107_{California Polytechnic State University, San Luis Obispo, CA, United States} 108_{Fachhochschule K¨oln, K¨oln, Germany}

109_{Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic} 110_{Dipartimento di Fisica dell’Universit`a ‘La Sapienza’ and Sezione INFN, Rome, Italy}

111_{Physics Department, University of Rajasthan, Jaipur, India} 112_{Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy}

113_{Purdue University, West Lafayette, IN, United States}

(Dated: August 12, 2018)

We report on the measurement of two-pion correlation functions from pp collisions at√s= 900 GeV per-formed by the ALICE experiment at the Large Hadron Collider. Our analysis shows an increase of the HBT radius with increasing event multiplicity, in line with other measurements done in particle- and nuclear colli-sions. Conversely, the strong decrease of the radius with increasing transverse momentum, as observed at RHIC and at Tevatron, is not manifest in our data.

PACS numbers: 25.75.-q, 25.75.Gz, 25.70.Pq

a_{Also at Laboratoire de Physique Corpusculaire (LPC), Clermont}

Univer-sit´e, Universit´e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

b_{Also at Frankfurt Institute for Advanced Studies, Johann Wolfgang}

Goethe-Universit¨at Frankfurt, Frankfurt, Germany

c_{Now at Sezione INFN, Padova, Italy}

d_{Now at Research Division and ExtreMe Matter Institute EMMI, GSI}

Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, Germany

e_{Now at Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at}

Frankfurt, Frankfurt, Germany

f_{Now at Physics Department, University of Cape Town, iThemba}

Labora-tories, Cape Town, South Africa

g_{Now at National Institute for Physics and Nuclear Engineering, Bucharest,}

Romania

h_{Also at University of Houston, Houston, TX, United States}

i_{Now at European Organization for Nuclear Research (CERN), Geneva,}

Switzerland

j_{Also at Dipartimento di Fisica dell´Universit`a, Udine, Italy}

k_{Now at Helsinki Institute of Physics (HIP) and University of Jyv¨askyl¨a,}

Jyv¨askyl¨a, Finland

l_{Now at Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´e de}

Strasbourg, CNRS-IN2P3, Strasbourg, France

m_{Now at Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at}

M¨unster, M¨unster, Germany

n_{Now at : University of Technology and Austrian Academy of Sciences,}

Vienna, Austria

o_{Also at Lawrence Livermore National Laboratory, Livermore, CA, United}

States

p_{Also at European Organization for Nuclear Research (CERN), Geneva,}

Switzerland

q_Deceased

r_{Now at Yale University, New Haven, CT, United States}

s_{Now at University of Tsukuba, Tsukuba, Japan}

t_{Also at Centro Fermi – Centro Studi e Ricerche e Museo Storico della}

Fisica “Enrico Fermi”, Rome, Italy

u_{Also at Moscow State University, Moscow, Russia}

v_{Also at Laboratoire de Physique Subatomique et de Cosmologie (LPSC),}

Universit´e Joseph Fourier, CNRS-IN2P3, Institut Polytechnique de Greno-ble, GrenoGreno-ble, France

w_{Now at SUBATECH, Ecole des Mines de Nantes, Universit´e de Nantes,}

CNRS-IN2P3, Nantes, France

x_{Now at Dipartimento di Fisica Sperimentale dell’Universit`a and Sezione}

INFN, Turin, Italy

y_{Now at Commissariat `a l’Energie Atomique, IRFU, Saclay, France}

z_{Also at Department of Physics, University of Oslo, Oslo, Norway}

aa_{Also at Wrocław University, Wrocław, Poland}

bb_{Now at Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg,}

Heidelberg, Germany

cc_{Now at Department of Physics and Technology, University of Bergen,}

Bergen, Norway

dd_{Now at Dipartimento di Fisica dell’Universit`a and Sezione INFN, Padova,}

Italy

ee_{Now at Physics Department, University of Athens, Athens, Greece}

ff_{Also at Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at}

M¨unster, M¨unster, Germany

gg_{Now at Universit´e de Lyon, Universit´e Lyon 1, CNRS/IN2P3, IPN-Lyon,}

Villeurbanne, France

hh_{Now at Faculty of Science, P.J. ˇSaf´arik University, Koˇsice, Slovakia}

ii_{Now at : Centre de Calcul IN2P3, Lyon, France}

jj_{Also at Dipartimento di Fisica dell’Universit`a and Sezione INFN, Padova,}

Italy

I. INTRODUCTION

Proton-proton collisions at √s = 900 GeV have been recorded by ALICE (A Large Ion Collider Experiment) at the Large Hadron Collider (LHC) at CERN [1]. Hadron colli-sions at these energies provide an opportunity to probe Quan-tum Chromodynamics (QCD) under extreme conditions. The distinguishing feature of QCD is the mechanism of color con-finement, the physics of which is not fully understood, due in part to its theoretical intractability [2]. The confinement mechanism has a physical scale on the order of the proton ra-dius and is especially important at low momentum.

Bose-Einstein enhancement of identical-pion pairs at low relative momentum was first observed in p ¯p collisions by Goldhaber, Goldhaber, Lee and Pais 50 years ago [3]. Since then, two-pion correlations have been successfully applied to assess the spatial scale of the emitting source in e+e− [4], hadron-hadron and lepton-hadron [5], and heavy ion [6] col-lisions. Especially in the latter case, this technique, known as Hanbury Brown - Twiss (HBT) interferometry [7, 8] and being a special case of femtoscopy [9, 10], has been developed into a precision tool to probe the dynamically-generated geometry of the emitting system. In particular, a first order phase tran-sition between the color-deconfined and -confined states was precluded by the observation of short timescales [6]. At the same time, femtoscopic measurement of bulk collective flow, manifesting itself via dynamical dependences of femtoscopic scales (“homogeneity lengths” [11, 12]), provided hints that a strongly self-interacting system was created in the collision. This was further corroborated by the positive correlation be-tween the HBT radius and the multiplicity of the event [6].

In particle physics, overviews of femtoscopic measure-ments in hadron- and lepton-induced collisions [4, 5, 13] reveal systematics surprisingly similar to those mentioned above for heavy-ion collisions. Moreover, in the first direct comparison of femtoscopy in heavy-ion collisions at RHIC, and proton collisions in the same apparatus, a virtually identi-cal multiplicity- and momentum-dependence was reported in the two systems [14].

A systematic program of femtoscopic measurements in pp and heavy-ion collisions at the LHC will shed consider-able light on the nature, the similarities, and the differences of their dynamics. With the present work, we begin this program.

II. EXPERIMENT AND DATA ANALYSIS

The data discussed in this article were collected in Decem-ber 2009, during the first stable-beam period of the LHC com-missioning. The two beams were at the LHC injection energy of 450 GeV and each had 2-4 bunches, one of them collid-ing at the ALICE intersection point. The bunch intensity was typically 5_{× 10}9protons, giving a luminosity of the order of 1026_cm−2_s−1_{and a rate for inelastic proton-proton collisions} of a few Hz.

Approximately 3_{× 10}5minimum bias pp collision events were identified by signals measured in the forward

scintilla-tors (VZERO) and the two layers of the Silicon Pixel Detec-tor (SPD) [15]. The VZERO counters are placed on either side of the interaction region at z = 3.3 m and z = -0.9 m. They cover the region 2_{.8 < η < 5.1 and −3.7 < η < −1.7} and record both amplitude and time of signals produced by charged particles. The minimum-bias trigger required a hit in one of the VZERO counters or in one of the two SPD layers which cover the central pseudorapidity regions_{|η| < 2 (inner)} and_{|η| < 1.4 (outer). The events were collected in} coinci-dence with the signals from two beam pick-up counters, one on each side of the interaction region, indicating the presence of passing bunches. The trigger selection efficiency for inelas-tic collisions was estimated to be 95-97% [16].

The VZERO counters were used also to discriminate against beam-gas and beam-halo events by requiring a strict matching between their timing signals (see Ref. [1] for de-tails). This background was also rejected by exploiting the correlation between the number of clusters of pixels and the number of tracklets pointing to a reconstructed vertex. After these selections the fraction of background events remaining in the sample of events with at least one charged particle track was estimated to be below 0.1%. The trigger and run condi-tions are discussed in detail in Ref. [16].

The 250 k events used in the analysis were required to have a primary vertex (collision position) within 10 cm of the cen-ter of the 5 m long Time Projection Chamber (TPC) [17]. This provides almost uniform acceptance for particles within the pseudorapidity range_{|η| < 0.8 for all events in the} sam-ple. Within this sample, we have selected events based on the measured charged-particle multiplicity M. The three multi-plicity classes were M_{≤ 6, 7 ≤ M ≤ 11, and M ≥ 12; about} 70% of all events were falling into the first multiplicity class. The tracks used in determining the multiplicity were the same as those used for correlation analysis (see below) except that particle identification cuts were not applied. The measured multiplicity was converted to the charged-particle pseudora-pidity density dNch/dη by normalizing it to the pseudorapid-ity acceptance and by correcting it for the reconstruction ef-ficiency and contamination. The correction factor was deter-mined from a Monte Carlo simulation with thePHOJETevent generator [18, 19] and with the full description of the AL-ICE apparatus and is 0.71, 0.78, and 0.81, respectively, for the three multiplicity bins. The estimated systematic error is be-low 4%. The average charged-particle pseudorapidity density of the analyzed event sample is_hdNch/dη_{i=3.6. An alternative} method based on SPD tracklets [16] gave the same result.

The ALICE Time Projection Chamber (TPC) [17] was used to record charged particle tracks as they leave ionization trails in the Ne-CO2-N2gas. The ionization electrons drift up to 2.5 m to be measured on 159 pad rows; the position resolu-tion is better than 2 mm. Combined with a solenoidal mag-netic field of B=0.5 T this leads to a momentum resolution ∼ 1% for pions with pT< 1 GeV/c. The ALICE Inner Track-ing System (ITS) has also been used for trackTrack-ing. It consists of six silicon layers, two innermost pixel detectors, two lay-ers of drift detectors, and two outer laylay-ers of strip detectors, which provide up to six space points for each track. The tracks used in this analysis were reconstructed using the information

from both the TPC (signals from at least 90 pad rows required) and the ITS. Separate studies have been done with TPC-only and ITS-only tracks, and were found to give results consistent with the combined ITS+TPC analysis. The tracks were re-quired to project back to the primary interaction vertex within 0.2 cm (2.4 cm) in the transverse plane and 0.25 cm (3.2 cm) in longitudinal direction, if ITS+TPC (TPC only) information is used, thereby rejecting most secondary pions from weak decays. The pion tracks used in the correlation analysis had transverse momenta between 0.15 GeV/c and 1.0 GeV/c.

ALICE provides excellent particle identification capability. In this analysis the particle identification was achieved by cor-relating the magnetic rigidity of a track with its specific ion-ization (dE/dx) in the TPC gas. The dE/dx of the TPC was calibrated using cosmic rays and its resolution was shown to be better than 5.5%, the design value. The contamination of the pion sample is negligible within the momentum range of 0.25 GeV/c< p < 0.65 GeV/c. Below and above this range it is on the order of 5% and is caused by electrons and kaons, respectively.

III. TWO-PION CORRELATION FUNCTIONS

The two-particle correlation function is defined as the ratio C(q) = A (q) /B (q), where A (q) is the measured distribution of pair momentum difference q= p2− p1, and B(q) is a simi-lar distribution formed by using pairs of particles from differ-ent evdiffer-ents (evdiffer-ent mixing) [20]. The limited statistics available (520 k identical-pion pairs with qinv< 0.5 GeV/c) allowed us to perform a detailed analysis only for the one-dimensional two-pion correlation function C(qinv). The qinv is, for iden-tical mass particles, equal to the modulus of the momentum difference|q| in the pair rest frame.

The correlation functions were studied in bins of event multiplicity and of transverse momentum, defined as half of the vector sum of the two transverse momenta, kT=|pT,1+pT,2|/2. During event mixing, all pion tracks from one event were paired with all pion tracks from another event. Every event was mixed with five other events with similar multiplicities; ten multiplicity bins were introduced for this purpose. The multiplicity binning improved the flatness of the correlation function at qinv> 1.5 GeV/c. Binning events according to their vertex position, on the other hand, had no effect on the correlation function and therefore was not used. Alternatively to event mixing, the denominator can be ob-tained by rotating one of the two tracks by 180oin azimuth. The correlation functions obtained using this technique are generally flatter at high qinv than those from event mixing. The difference between the results obtained utilizing the two techniques was used in estimating the systematic errors.

For the correlation structures measured here, with charac-teristic widths∼ 0.2 GeV/c, track splitting and track merging in the event reconstruction are small effects overall. Their im-pact on the results was carefully studied with the Monte Carlo simulation and turned out to be negligible.

Another apparatus effect considered is the momentum res-olution. Momentum smearing for single particles has similar

effect on the correlation structures in two-particle correlations i.e. it smears the correlation peak, making it appear lower and wider. We have studied this effect with the Monte-Carlo simu-lation of the ALICE detector and have found that for the width of the correlation peak expected here the effect is on the order of 1%.

Fig. 1 presents two-pion correlation functions measured by ALICE in pp collisions at√s= 900 GeV, as a function of event multiplicity and transverse momentum kT. The denom-inator of the correlation function was obtained via event mix-ing and normalized such that the numbers of true and mixed pairs with 0.4 GeV/c< qinv< 0.6 GeV/c were equal. The q_invrange used for normalization was chosen to be outside of the Bose-Einstein peak but as close as possible to it. The nor-malized distributions of positive and negative pion pairs were added together before building the ratio of true and mixed pairs. The Bose-Einstein enhancement is manifest at low q_inv. A slight decrease of the correlation peak width is seen as mul-tiplicity grows. The kT dependence is less obvious because

0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 experiment simulation <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 _<dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 <dN <k λ R 0 0.20.40.60.8 0 0.20.40.60.8 0 0.20.40.60.8 1 0.8 0.8 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 1.4 1.6 1.6 1.6 1.6 1.6 1.8 (GeV/c) inv q (GeV/c) inv q (GeV/c) inv q ) inv C(q ) inv C(q ) inv C(q ) inv C(q ) inv C(q 6 ≤ M 7 ≤ M ≤ 11 M ≥ 12 <0.25 T 0.10<k <0.40 T 0.25<k <0.55 T 0.40<k <0.7 T 0.55<k <1.0 T 0.70<k

FIG. 1. Correlation functions for identical pions from pp colli-sions at√s= 900 GeV (full dots) and those obtained from a simu-lation usingPHOJET(open circles). Positive and negative pion pairs were combined. The three columns represent collisions with differ-ent charged-particle multiplicities M; the transverse momdiffer-entum of pion pairs kT(GeV/c) increases from top to bottom. The lines going

the correlation baseline – the underlying two particle correla-tion without any Bose-Einstein enhancement – is systemati-cally changing its shape between the low and high transverse momenta.

The correlation functions were fitted by a function account-ing for the Bose-Einstein enhancement and for the mutual Coulomb interaction between the two particles:

C(qinv) = (1 − λ) + λK(qinv)1 + exp(−R2invq2inv)
D(qinv), (1) withλ describing the correlation strength and Rinvbeing the Gaussian HBT radius [21]. The factor K is the Coulomb func-tion integrated over a spherical source of the size 1 fm. It is at-tenuated by the same factorλ as the Bose-Einstein peak. The factor D(qinv) accounts for long-range correlations, like those arising from jets and/or from energy and momentum conser-vation, and plays an important role in the analysis as will be discussed later.

Neglecting the Coulomb interaction K(qinv) ≡ 1 the fit function reduces to

C(qinv) =1 + λ exp(−R2invq2inv) D(qinv) . (2) The difference between the R_inv values obtained with and without the Coulomb correction is less than 0.05 fm.

While the Gaussian fit captures the bulk scales of the cor-relation, at low qinvthe data points lie above the fit line. This feature was observed previously in pion correlations from par-ticle collisions. An exponential fit

C(qinv) = [1 + λ exp(−Rinvqinv)] D(qinv) (3) matches the data better. However, contrary to the Gaussian Rinv, the Rinvparameter from Eq. (3) does not have a straight-forward interpretation as the “radius of the source”. We have used both functional forms and leave a detailed investigation of the correlation peak shape to future studies. In order to make the connection to established systematics at lower en-ergy particle and heavy-ion collisions, a careful treatment of the long-range correlations, visible as a slope in the baseline of the correlation developing with increasing transverse mo-mentum and represented by the factor D(qinv) in Eqs. (1-3), is crucial.

In order to better understand the shape of the correlation baseline we have calculated correlation functions for pp col-lisions events generated by the modelPHOJETand propagated through the ALICE detectors, performing an identical analy-sis for the simulated events as for the measured ones. The re-sults are shown as open circles in Fig. 1. The model does not contain the Bose-Einstein effect, hence the lack of the peak at low q_invis expected. At low kTand low multiplicity, the model predicts a flat correlation function. However, as kTincreases, long-range correlations start becoming visible as a distortion of the correlation function baseline similar to that seen in the experimental data.

The accuracy of our simulation in describing the correlation baseline was verified with unlike-sign pion pairs. The multi-plicity and kTdependence of theπ+π−functions is shown in Fig. 2. Correlation structures for non-identical pions include a

0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 experiment simulation 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.2 0.4 0.6 0.8 1 0.8 1 1.2 1.4 1.6 1.8 0 0.20.40.60.8 0 0.20.40.60.8 0 0.20.40.60.8 1 0.8 0.8 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 1.4 1.6 1.6 1.6 1.6 1.6 1.8 (GeV/c) inv q (GeV/c) inv q (GeV/c) inv q ) inv C(q ) inv C(q ) inv C(q ) inv C(q ) inv C(q 6 ≤ M 7 ≤ M ≤ 11 M ≥ 12 <0.25 T 0.10<k <0.40 T 0.25<k <0.55 T 0.40<k <0.7 T 0.55<k <1.0 T 0.70<k

FIG. 2. One-dimensional correlation functions forπ+π−pairs from ppcollisions at√s= 900 GeV. The columns and rows are defined as in Fig. 1.

mutual Coulomb interaction peak, here limited to the first bin at lowest qinv, and peaks coming from meson decays which should be correctly modeled in the event generator. Therefore, one can directly compare simulations with data. In Fig. 2, the simulated correlation functions agree reasonably well with the experimental data. This suggests that the same model (PHO -JET) can be used as a reasonable estimate also for identical particles to describe the correlation baseline under the Bose-Einstein peak. The presence of resonance peaks (like the K0 S one at qinv= 412 MeV/c) and the fact that the simulated corre-lations for identical and non-identical pion pairs have different slopes, on the other hand, indicate that unlike-sign pion pairs cannot be directly used for the denominator of the identical pion correlations.

The procedure employed to extract the HBT radii with Eq. (1) using thePHOJET baseline is as follows. First, the simulation points shown in Fig. 1 are fitted with the 2nd-order polynomial

D(qinv) = a + bqinv+ cq2inv. (4) Subsequently, the experimental correlation function is fitted by Eq. (1), taking the D(qinv) from thePHOJETfit and adjust-ingλ and Rinv. The two fits are represented in Fig. 1 by the

lines going through the simulation and experiment data points, respectively.

In order to estimate the systematic error from the baseline determination we repeated the fitting procedure using a sim-ulation performed with the PYTHIA [22] generator (version 6.4.21, Perugia-0 (320) tune [23]) instead of PHOJET. The HBT radii obtained in the two ways differ by up to 10%. In the following we use the average between them and we estimate the systematic error related to the baseline shape assumption to be half of the difference.

It is interesting to see what happens with the radii if the slope of the baseline is neglected. Assuming a flat baseline D(qinv) ≡ a and treating a as the third fit parameter in Eq. (1) leads to Rinvvalues that are similar to those obtained with the

PHOJETorPYTHIAbaseline at low kTvalues but smaller by

up to 30% at high transverse momenta. This is because the broad enhancement caused by long-range correlations will be attributed to Bose-Einstein correlations, giving rise to smaller radii (wider correlation function). The resulting apparent kT dependence will be discussed in Section V.

The Rinvobtained from the fit (the two highest multiplic-ity bins combined) is shown in Fig. 3. In order to reduce the statistical errors and to compare to other experiments, in the following sections of this article we analyze separately the multiplicity and the transverse momentum dependences.

> (GeV/c) T <k 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (fm) inv R 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 6 ≤ multiplicity M 7 ≥ multiplicity M

FIG. 3. Extracted HBT radius as a function of kTfor low (black

cir-cles) and high (red squares) multiplicity events. The error bars are statistical. The shaded bands represent the systematic errors related to the baseline shape assumption and to the fit range, added quadrat-ically.

IV. MULTIPLICITY DEPENDENCE OF THE HBT RADIUS

The multiplicity dependence of the obtained HBT radius is shown in Fig. 4 and Table I. The analysis here was

re-> η /d ch <dN 0 5 10 15 20 (fm) inv R 0 0.5 1 1.5 2 2.5 3 =900 GeV s ALICE pp at =44 GeV s ABCDHW pp at =62 GeV s ABCDHW pp at =1.8 TeV s at p E735 p =200 GeV s STAR pp at

FIG. 4. One-dimensional Gaussian HBT radius in pp collisions at √s= 900 GeV determined using pion pairs with kT =

0.1-0.55 GeV/c, hkTi= 0.32 GeV/c, and shown as a function of the

charged-particle multiplicity at midrapidity (full dots). The shaded band represents the systematic errors (see text). For comparison, open symbols, red stars, and green filled boxes represent the data taken at the ISR [24], RHIC [14], and Tevatron [25], respectively.

TABLE I. One-dimensional HBT radius in pp collisions at√s= 900 GeV determined using pion pairs with kT = 0.1-0.55 GeV/c,

hkTi= 0.32 GeV/c, as a function of the charged-particle

pseudorapid-ity denspseudorapid-ity at midrapidpseudorapid-ity. The radii were obtained using the Gaus-sian fit function defined by Eq. (1).

hdNch/dηi λ Rinv(fm)

3.2 0.386± 0.022 0.874± 0.047 (stat.)+0.047_−0.181(syst.) 7.7 0.331± 0.023 1.082± 0.068 (stat.)+0.069_−0.206(syst.) 11.2 0.310± 0.026 1.184± 0.092 (stat.)+0.067_−0.168(syst.)

stricted to the first three transverse momentum bins kT= 0.1-0.55 GeV/c. The mean transverse momentum for pairs with q_{inv< 0.2 GeV/c is hk}Ti= 0.32 GeV/c. The HBT radii were obtained by usingPHOJETandPYTHIAto estimate the shape of the baseline, as explained in the previous section. The sys-tematic errors related to the baseline assumption reflect the difference between the two. The systematic error related to the

choice of the normalization and/or fit range was estimated to be 5%. An additional downward systematic error of 13-20% accounts for the difference between the event mixing and the rotation denominator techniques. The shaded area represents the three systematic errors added in quadrature.

The charged-particle pseudorapidity density_hdNch/dηi of the lowest multiplicity bin was calculated excluding events with multiplicities M< 2 because these events do not con-tribute to the numerator of the correlation function. Including all events and including only events with at least one like-sign pair would shift the point by 0.8 to the left and to the right, respectively.

An increase of the HBT radius with multiplicity is ob-served, consistent with the hadron-hadron collision system-atics above√s_{∼ 50 GeV [13]. While the average transverse} momentum is similar in all four data sets, other aspects of the analysis, e.g. the average orientation of the momentum differ-ence vector, can differ so the trends, not the absolute values, should be compared. In heavy-ion collisions, this multiplicity dependence has been associated with the particle composition and overall volume of the final state system [6, 26, 27] or with final-state hadronic rescattering [28]. The relation observed in heavy-ion collision data [6], R_{∼ a + b(dN}ch/dη)1/3, where aand b are constants, appears to be consistent with our data within our systematic errors. For high energy pp collisions, it has been suggested that a similar behavior could originate from final-state hadronic rescattering for short hadronization times [29]. In an alternative scenario, the increase of the HBT radius with multiplicity results from the fact that the high mul-tiplicity pp events mostly come from hard parton scattering, and the hadronization length, i.e. the distance travelled by a parton before hadronization, is roughly proportional to the parton energy [30].

The fitted correlation strength λ is lower than unity, the value expected for the ideal Bose-Einstein case. One rea-son for this is the non-Gaussian shape of the peak, caused at least partially by pions from decays of short- (∆, ρ) and long-lived resonances (ω, η, η′). On the detector side, λ can be reduced by the particle misidentification; this effect is how-ever small in our data sample. In ALICE,λ decreases from 0.37±0.03 to 0.32±0.03 between the lowest and the highest multiplicity, in close agreement with the E735 measurements at Tevatron [25]. A similar trend was observed by UA1 in pp¯ collisions at √s= 630 GeV/c [31]; the fact that their λ values were lower may have to do with the lack of the par-ticle identification and the resulting dilution of the correla-tion peak. In a final-state hadronic rescattering model [29], a correlation strength dropping with multiplicity in high-energy ppcollisions was attributed to the increased contribution from long-lived resonances in higher multiplicity events.

An increase of the HBT radius with increasing particle multiplicity was recently reported by the CMS Collabora-tion for the same collision system and energy [32]. The authors fit the correlation peak by an exponential (Eq. (3)). An analogous approach in our case (Table II) yields radii that are rather similar to the Gaussian ones (Table I) once scaled down by√π [32]. In order to compare between the two experiments we perform a fit to an inclusive

correla-tion (all multiplicities and kT’s). The exponential fit to the correlation functions obtained using event mixing and using rotation yields Rinv=1.61±0.07 (stat.)±0.05 (syst.) fm and R_inv=1.31_{±0.05 (stat.)±0.22 (syst.) fm, respectively. This is} in close agreement with the corresponding values quoted by CMS, 1.72_{±0.06 fm and 1.29±0.04 fm.}

TABLE II. One-dimensional HBT radius in pp collisions at√s= 900 GeV determined using pion pairs with kT = 0.1-0.55 GeV/c,

hkTi= 0.32 GeV/c, as a function of the charged-particle

pseudorapid-ity denspseudorapid-ity at midrapidpseudorapid-ity. The radii were obtained using the expo-nential fit function defined by Eq. (3).

hdNch/dηi λ Rinv/√π (fm)

3.2 0.704± 0.048 0.809± 0.061 (stat.)+0.049_−0.208(syst.) 7.7 0.577± 0.054 0.967± 0.095 (stat.)+0.071_−0.206(syst.) 11.2 0.548± 0.051 1.069± 0.104 (stat.)+0.063_−0.203(syst.)

V. TRANSVERSE MOMENTUM DEPENDENCE OF THE HBT RADIUS

One of the key features of the bulk system created in nu-clear collisions is its large collective flow. The fingerprint of this flow is a specific space-momentum correlation signa-ture, revealed in the transverse momentum dependence of the Gaussian HBT radius [6]. While quantitative comparison be-tween particle and heavy ion studies is complicated by exper-iments using different acceptances and techniques, a recent comparison of the HBT radii from pp and Au+Au collisions at RHIC indicates an almost identical pTdependence between these collision systems [14]. Again, this raises the interesting question whether hadron collisions at the highest energies al-ready develop a bulk, collective behavior.

The kTdependence of our measured HBT radius is shown in Fig. 5. The choice of the fitting method, which only weakly affects the multiplicity dependence of the HBT radius dis-cussed in the previous section, is of crucial importance for the transverse momentum dependence. Taking the baseline shape from the Monte Carlo leads to an HBT radius that is nearly independent of kT(filled black circles and red boxes forPHO

-JETandPYTHIA, respectively). Assuming a flat baseline, on

the other hand, results in a radius falling with kT(green stars). As discussed in the previous section, the experimental unlike-sign pion correlation functions are close to the predictions of

PHOJETandPYTHIAand we consider using the average

be-tween the two cases as baseline to be a reliable estimate for the HBT radii.

The radii obtained in this fashion are summarized in Ta-bles III and IV and shown in Fig. 6 where we compare them to RHIC and Tevatron data [13]. Like for the multiplicity dependence, the systematic error band represents a quadratic sum of the error related to the baseline assumption (0-10%), the fit range (10%), and the denominator construction method (mixing/rotating, 7-17%). The lowest-kTpoint is significantly below the RHIC and Tevatron results. It should be noted that

> (GeV/c) T <k 0 0.2 0.4 0.6 0.8 1 (fm) inv R 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 phojet baseline pythia baseline flat baseline

FIG. 5. One-dimensional Gaussian HBT radius in pp collisions at √

s= 900 GeV as a function of transverse momentum kT. Three

fit-ting methods, differing by the choice of the baseline parametrization, are compared.

the ALICE analysis was performed on a minimum bias event sample and the averaged charged-particle pseudorapidity den-sity ishdNch/dηi=3.6 while the Tevatron events are biased to high multiplicity,hdNch/dηi=14.4, similar to our highest mul-tiplicity bin. As visible in Fig. 3, the lowest-kT point at the high multiplicity is at Rinv≈1.2 fm, approaching the Tevatron points. The STAR results, on the other hand, were obtained from events with_hdNch/dη_{i= 4.3 i.e. similar to the ALICE} case and thus a similar reasoning cannot explain the differ-ence.

Two tests were performed to make sure that the low HBT radius value at low transverse momenta is not caused by ap-paratus effects. First, the analysis was repeated using only the ITS and thus reducing the low-momentum cut-off by about

TABLE III. One-dimensional HBT radius in pp collisions at√s= 900 GeV as a function of the pair kT. The radii were obtained using

the Gaussian fit function defined by Eq. (1).

hkTi (GeV/c) λ Rinv(fm) 0.20 0.35± 0.03 1.00± 0.06 (stat.)+0.10_−0.20(syst.) 0.32 0.33± 0.03 1.06± 0.06 (stat.)+0.11_−0.19(syst.) 0.47 0.30± 0.04 0.99± 0.09 (stat.)+0.10_−0.14(syst.) 0.62 0.35± 0.06 0.99± 0.11 (stat.)+0.10_−0.13(syst.) 0.81 0.31± 0.06 0.91± 0.12 (stat.)+0.10_−0.12(syst.)

TABLE IV. One-dimensional HBT radius in pp collisions at√s= 900 GeV as a function of the pair kT. The radii were obtained using

the exponential fit function defined by Eq. (3).

hkTi(GeV/c) λ Rinv/√π (fm) 0.20 0.63± 0.05 0.94± 0.07 (stat.)+0.09_−0.20(syst.) 0.32 0.58± 0.04 0.93± 0.07 (stat.)+0.09_−0.20(syst.) 0.47 0.55± 0.07 0.92± 0.10 (stat.)+0.09_−0.14(syst.) 0.62 0.70± 0.11 0.98± 0.14 (stat.)+0.10_−0.14(syst.) 0.81 0.60± 0.12 0.90± 0.16 (stat.)+0.12_−0.15(syst.) > (GeV/c) T <k 0 0.2 0.4 0.6 0.8 1 (fm) inv R 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 =900 GeV s ALICE pp at = 200 GeV s STAR pp at = 1.8 TeV s at p E735 p

FIG. 6. One-dimensional Gaussian HBT radius in pp collisions at √

s= 900 GeV as a function of transverse momentum kT(full dots).

The mean charged-particle multiplicity density washdNch/dηi=3.6. PHOJETsimulation was used to determine the baseline of the cor-relations. UsingPYTHIAand a flat baseline leads to systematic de-viations up and down, respectively; the related systematic errors as indicated by the shaded area. Stars and filled boxes represent the radii measured at RHIC [14] and Tevatron [25], respectively.

50 MeV. This analysis yielded the same HBT radius which demonstrates that the energy loss is not an issue. Second, as seen in Fig. 3 the low-kT point is mostly driven down by the contribution of the low multiplicity events. Since the ver-tex resolution in these events is worse this might in principle deteriorate the momentum resolution and smear out the cor-relation function peak. In order to test this the analysis was performed without using the event vertex constraint for mo-mentum determination. The results, again, were unchanged. This, and the distinct K0

corre-lation functions in the low-multiplicity low-kT bin of Fig. 2, indicate that the momentum resolution is not spoiled in low multiplicity events.

Even more important than the position of the first point, albeit related to it, is the question of the slope of the points in Fig. 6. Our measured HBT radius is practically indepen-dent of kT within the studied transverse momentum range. The slope crucially depends on the baseline shape assump-tion, as was shown in Fig. 5. The results from the experiments to which we are comparing in Fig. 6 were extracted using a flat background (although the STAR experiment also studied the effects of using other types of backgrounds for their data to account for the non-femtoscopic effects [14]). Assuming

thatPHOJET andPYTHIAare correct such a procedure may

lead to a misinterpretation of the low-q enhancement of the correlation function, that is coming from long-range corre-lations (most probably mini-jet like), as a Bose-Einstein en-hancement. As the impact of this may depend on the details of each experiment (certainly on the collision energy) we do not attempt to resolve this question quantitatively. However, we stress again the usefulness of non-identical pion correla-tion in constraining the correlacorrela-tion baseline.

VI. SUMMARY

In summary, ALICE has measured two-pion correlation functions in pp collisions at√s= 900 GeV at the LHC. Con-sistent with previous measurements of high-energy hadron-hadron and nuclear collisions, the extracted HBT radius Rinv increases with event multiplicity. Less consistent is the rela-tion between Rinvand the pion transverse momentum where the ALICE measured HBT radius in minimum bias events is practically constant within our errors and within the transverse momentum range studied.

ACKNOWLEDGMENTS

The ALICE collaboration would like to thank all its en-gineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.

The ALICE collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector:

• Calouste Gulbenkian Foundation from Lisbon and Swiss Fonds Kidagan, Armenia;

• Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq), Financiadora de Estudos e Pro-jetos (FINEP), Fundac¸˜ao de Amparo `a Pesquisa do Es-tado de S˜ao Paulo (FAPESP);

• National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC);

• Ministry of Education and Youth of the Czech Repub-lic;

• Danish Natural Science Research Council, the Carls-berg Foundation and the Danish National Research Foundation;

• The European Research Council under the European Community’s Seventh Framework Programme; • Helsinki Institute of Physics and the Academy of

Fin-land;

• French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re-gion Alsace’, ‘Re‘Re-gion Auvergne’ and CEA, France; • German BMBF and the Helmholtz Association; • Hungarian OTKA and National Office for Research and

Technology (NKTH);

• Department of Atomic Energy and Department of Sci-ence and Technology of the Government of India; • Istituto Nazionale di Fisica Nucleare (INFN) of Italy; • MEXT Grant-in-Aid for Specially Promoted Research,

Japan;

• Joint Institute for Nuclear Research, Dubna;

• Korea Foundation for International Cooperation of Sci-ence and Technology (KICOS);

• CONACYT, DGAPA, M´exico, ALFA-EC and the HE-LEN Program (High-Energy physics Latin-American– European Network);

• Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Weten-schappelijk Onderzoek (NWO), Netherlands;

• Research Council of Norway (NFR);

• Polish Ministry of Science and Higher Education; • National Authority for Scientific Research - NASR

(Autoritatea Nat¸ional˘a pentru Cercetare S¸tiint¸ific˘a -ANCS);

• Federal Agency of Science of the Ministry of Educa-tion and Science of Russian FederaEduca-tion, InternaEduca-tional Science and Technology Center, Russian Acedemy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and CERN-INTAS;

• Ministry of Education of Slovakia;

• CIEMAT, EELA, Ministerio de Educaci´on y Ciencia of Spain, Xunta de Galicia (Conseller´ıa de Educaci´on), CEADEN, Cubaenerg´ıa, Cuba, and IAEA (Interna-tional Atomic Energy Agency);

• Swedish Reseach Council (VR) and Knut & Alice Wal-lenberg 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 Science Foundation, the State of Texas, and the State of Ohio.

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