System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes in Cu+Cu and Au+Au Collisions at $\sqrt{s_{NN}}$ = 200 and 62.4 GeV

Abstract

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from dijets in Cu+Cu and Au+Au collisions at square root sNN=62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from Delta phi=pi in central and semicentral collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.

Full text

arXiv:nucl-ex/0611019v1 12 Nov 2006
System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes
in Cu+Cu and Au+Au Collisions at √sNN = 200 and 62.4 GeV.
A. Adare,10 S.S. Adler,5S. Afanasiev,24 C. Aidala,11 N.N. Ajitanand,51 Y. Akiba,26, 45, 46 H. Al-Bataineh,40
J. Alexander,51 A. Al-Jamel,40 K. Aoki,30, 45 L. Aphecetche,53 R. Armendariz,40 S.H. Aronson,5J. Asai,46
E.T. Atomssa,31 R. Averbeck,52 T.C. Awes,41 B. Azmoun,5V. Babintsev,20 G. Baksay,16 L. Baksay,16
A. Baldisseri,13 K.N. Barish,6P.D. Barnes,33 B. Bassalleck,39 S. Bathe,6, 36 S. Batsouli,11, 41 V. Baublis,44
F. Bauer,6A. Bazilevsky,5, 46 S. Belikov,5, 20, 23 R. Bennett,52 Y. Berdnikov,48 A.A. Bickley,10 M.T. Bjorndal,11
J.G. Boissevain,33 H. Borel,13 K. Boyle,52 M.L. Brooks,33 D.S. Brown,40 N. Bruner,39 D. Bucher,36 H. Buesching,5,36
V. Bumazhnov,20 G. Bunce,5, 46 J.M. Burward-Hoy,32,33 S. Butsyk,33, 52 X. Camard,53 S. Campbell,52 J.-S. Chai,25
P. Chand,4B.S. Chang,60 W.C. Chang,2J.-L. Charvet,13 S. Chernichenko,20 J. Chiba,26 C.Y. Chi,11 M. Chiu,11, 21
I.J. Choi,60 R.K. Choudhury,4T. Chujo,5, 57 P. Chung,51 A. Churyn,20 V. Cianciolo,41 C.R. Cleven,18 Y. Cobigo,13
B.A. Cole,11 M.P. Comets,42 P. Constantin,23, 33 M. Csan´ad,15 T. Cs¨org˝o,27 J.P. Cussonneau,53 T. Dahms,52
K. Das,17 G. David,5F. De´ak,15 M.B. Deaton,1K. Dehmelt,16 H. Delagrange,53 A. Denisov,20 D. d’Enterria,11
A. Deshpande,46, 52 E.J. Desmond,5A. Devismes,52 O. Dietzsch,49 A. Dion,52 M. Donadelli,49 J.L. Drachenberg,1
O. Drapier,31 A. Drees,52 A.K. Dubey,59 A. Durum,20 D. Dutta,4V. Dzhordzhadze,6, 54 Y.V. Efremenko,41
J. Egdemir,52 F. Ellinghaus,10 W.S. Emam,6A. Enokizono,19, 32 H. En’yo,45, 46 B. Espagnon,42 S. Esumi,56
K.O. Eyser,6D.E. Fields,39, 46 C. Finck,53 M. Finger, Jr.,7, 24 M. Finger,7, 24 F. Fleuret,31 S.L. Fokin,29 B. Forestier,34
B.D. Fox,46 Z. Fraenkel,59 J.E. Frantz,11, 52 A. Franz,5A.D. Frawley,17 K. Fujiwara,45 Y. Fukao,30, 45, 46 S.-Y. Fung,6
T. Fusayasu,38 S. Gadrat,34 I. Garishvili,54 F. Gastineau,53 M. Germain,53 A. Glenn,10,54 H. Gong,52 M. Gonin,31
J. Gosset,13 Y. Goto,45, 46 R. Granier de Cassagnac,31 N. Grau,23 S.V. Greene,57 M. Grosse Perdekamp,21, 46
T. Gunji,9H.-˚
A. Gustafsson,35 T. Hachiya,19, 45 A. Hadj Henni,53 C. Haegemann,39 J.S. Haggerty,5M.N. Hagiwara,1
H. Hamagaki,9R. Han,43 A.G. Hansen,33 H. Harada,19 E.P. Hartouni,32 K. Haruna,19 M. Harvey,5E. Haslum,35
K. Hasuko,45 R. Hayano,9M. Heffner,32 T.K. Hemmick,52 T. Hester,6J.M. Heuser,45 X. He,18 P. Hidas,27
H. Hiejima,21 J.C. Hill,23 R. Hobbs,39 M. Hohlmann,16 M. Holmes,57 W. Holzmann,51 K. Homma,19 B. Hong,28
A. Hoover,40 T. Horaguchi,45, 46, 55 D. Hornback,54 M.G. Hur,25 T. Ichihara,45,46 V.V. Ikonnikov,29 K. Imai,30, 45
M. Inaba,56 Y. Inoue,47, 45 M. Inuzuka,9D. Isenhower,1L. Isenhower,1M. Ishihara,45 T. Isobe,9M. Issah,51
A. Isupov,24 B.V. Jacak,52 J. Jia,11, 52 J. Jin,11 O. Jinnouchi,45, 46 B.M. Johnson,5S.C. Johnson,32 K.S. Joo,37
D. Jouan,42 F. Kajihara,9, 45 S. Kametani,9, 58 N. Kamihara,45, 55 J. Kamin,52 M. Kaneta,46 J.H. Kang,60
H. Kanou,45, 55 K. Katou,58 T. Kawabata,9T. Kawagishi,56 D. Kawall,46 A.V. Kazantsev,29 S. Kelly,10,11
B. Khachaturov,59 A. Khanzadeev,44 J. Kikuchi,58 D.H. Kim,37 D.J. Kim,60 E. Kim,50 G.-B. Kim,31 H.J. Kim,60
Y.-S. Kim,25 E. Kinney,10 A. Kiss,15 E. Kistenev,5A. Kiyomichi,45 J. Klay,32 C. Klein-Boesing,36 H. Kobayashi,46
L. Kochenda,44 V. Kochetkov,20 R. Kohara,19 B. Komkov,44 M. Konno,56 D. Kotchetkov,6A. Kozlov,59 A. Kr´al,12
A. Kravitz,11 P.J. Kroon,5J. Kubart,7, 22 C.H. Kuberg,1, ∗G.J. Kunde,33 N. Kurihara,9K. Kurita,45, 47
M.J. Kweon,28 Y. Kwon,54, 60 G.S. Kyle,40 R. Lacey,51 Y.-S. Lai,11 J.G. Lajoie,23 A. Lebedev,23, 29 Y. Le Bornec,42
S. Leckey,52 D.M. Lee,33 M.K. Lee,60 T. Lee,50 M.J. Leitch,33 M.A.L. Leite,49 B. Lenzi,49 H. Lim,50 T. Liˇska,12
A. Litvinenko,24 M.X. Liu,33 X. Li,8X.H. Li,6B. Love,57 D. Lynch,5C.F. Maguire,57 Y.I. Makdisi,5A. Malakhov,24
M.D. Malik,39 V.I. Manko,29 Y. Mao,43, 45 G. Martinez,53 L. Maˇsek,7, 22 H. Masui,56 F. Matathias,11, 52
T. Matsumoto,9, 58 M.C. McCain,1, 21 M. McCumber,52 P.L. McGaughey,33 Y. Miake,56 P. Mikeˇs,7, 22 K. Miki,56
T.E. Miller,57 A. Milov,52 S. Mioduszewski,5G.C. Mishra,18 M. Mishra,3J.T. Mitchell,5M. Mitrovski,51
A.K. Mohanty,4A. Morreale,6D.P. Morrison,5J.M. Moss,33 T.V. Moukhanova,29 D. Mukhopadhyay,57,59
M. Muniruzzaman,6J. Murata,47, 45 S. Nagamiya,26 Y. Nagata,56 J.L. Nagle,10, 11 M. Naglis,59 I. Nakagawa,45,46
Y. Nakamiya,19 T. Nakamura,19 K. Nakano,45, 55 J. Newby,32, 54 M. Nguyen,52 B.E. Norman,33 A.S. Nyanin,29
J. Nystrand,35 E. O’Brien,5S.X. Oda,9C.A. Ogilvie,23 H. Ohnishi,45 I.D. Ojha,3, 57 H. Okada,30, 45 K. Okada,45, 46
M. Oka,56 O.O. Omiwade,1A. Oskarsson,35 I. Otterlund,35 M. Ouchida,19 K. Oyama,9K. Ozawa,9R. Pak,5
D. Pal,57, 59 A.P.T. Palounek,33 V. Pantuev,52 V. Papavassiliou,40 J. Park,50 W.J. Park,28 S.F. Pate,40 H. Pei,23
V. Penev,24 J.-C. Peng,21 H. Pereira,13 V. Peresedov,24 D.Yu. Peressounko,29 A. Pierson,39 C. Pinkenburg,5
R.P. Pisani,5M.L. Purschke,5A.K. Purwar,33, 52 J.M. Qualls,1H. Qu,18 J. Rak,23, 39 A. Rakotozafindrabe,31
I. Ravinovich,59 K.F. Read,41,54 S. Rembeczki,16 M. Reuter,52 K. Reygers,36 V. Riabov,44 Y. Riabov,44 G. Roche,34
A. Romana,31, ∗M. Rosati,23 S.S.E. Rosendahl,35 P. Rosnet,34 P. Rukoyatkin,24 V.L. Rykov,45 S.S. Ryu,60
B. Sahlmueller,36 N. Saito,30, 45, 46 T. Sakaguchi,5, 9, 58 S. Sakai,56 H. Sakata,19 V. Samsonov,44 L. Sanfratello,39

2
R. Santo,36 H.D. Sato,30, 45 S. Sato,5, 26, 56 S. Sawada,26 Y. Schutz,53 J. Seele,10 R. Seidl,21 V. Semenov,20 R. Seto,6
D. Sharma,59 T.K. Shea,5I. Shein,20 A. Shevel,44, 51 T.-A. Shibata,45, 55 K. Shigaki,19 M. Shimomura,56
T. Shohjoh,56 K. Shoji,30, 45 A. Sickles,52 C.L. Silva,49 D. Silvermyr,33,41 C. Silvestre,13 K.S. Sim,28 C.P. Singh,3
V. Singh,3S. Skutnik,23 M. Sluneˇcka,7,24 W.C. Smith,1A. Soldatov,20 R.A. Soltz,32 W.E. Sondheim,33
S.P. Sorensen,54 I.V. Sourikova,5F. Staley,13 P.W. Stankus,41 E. Stenlund,35 M. Stepanov,40 A. Ster,27
S.P. Stoll,5T. Sugitate,19 C. Suire,42 J.P. Sullivan,33 J. Sziklai,27 T. Tabaru,46 S. Takagi,56 E.M. Takagui,49
A. Taketani,45, 46 K.H. Tanaka,26 Y. Tanaka,38 K. Tanida,45, 46 M.J. Tannenbaum,5A. Taranenko,51 P. Tarj´an,14
T.L. Thomas,39 M. Togawa,30, 45 A. Toia,52 J. Tojo,45 L. Tom´aˇsek,22 H. Torii,30, 45, 46 R.S. Towell,1V-N. Tram,31
I. Tserruya,59 Y. Tsuchimoto,19, 45 S.K. Tuli,3H. Tydesj¨o,35 N. Tyurin,20 T.J. Uam,37 C. Vale,23 H. Valle,57
H.W. vanHecke,33 J. Velkovska,5,57 M. Velkovsky,52 R. Vertesi,14 V. Veszpr´emi,14 A.A. Vinogradov,29 M. Virius,12
M.A. Volkov,29 V. Vrba,22 E. Vznuzdaev,44 M. Wagner,30, 45 D. Walker,52 X.R. Wang,18, 40 Y. Watanabe,45, 46
J. Wessels,36 S.N. White,5N. Willis,42 D. Winter,11 F.K. Wohn,23 C.L. Woody,5M. Wysocki,10 W. Xie,6, 46
Y. Yamaguchi,58 A. Yanovich,20 Z. Yasin,6J. Ying,18 S. Yokkaichi,45, 46 G.R. Young,41 I. Younus,39
I.E. Yushmanov,29 W.A. Zajc,11, †O. Zaudtke,36 C. Zhang,11, 41 S. Zhou,8J. Zim´anyi,27, ∗L. Zolin,24 and X. Zong23
(PHENIX Collaboration)
1Abilene Christian University, Abilene, TX 79699, U.S.
2Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
3Department of Physics, Banaras Hindu University, Varanasi 221005, India
4Bhabha Atomic Research Centre, Bombay 400 085, India
5Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
6University of California - Riverside, Riverside, CA 92521, U.S.
7Charles University, Ovocn´y trh 5, Praha 1, 116 36, Prague, Czech Republic
8China Institute of Atomic Energy (CIAE), Beijing, People’s Republic of China
9Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
10University of Colorado, Boulder, CO 80309, U.S.
11Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, U.S.
12Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic
13Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France
14Debrecen University, H-4010 Debrecen, Egyetem t´er 1, Hungary
15ELTE, E¨otv¨os Lor´and University, H - 1117 Budapest, P´azm´any P. s. 1/A, Hungary
16Florida Institute of Technology, Melbourne, FL 32901, U.S.
17Florida State University, Tallahassee, FL 32306, U.S.
18Georgia State University, Atlanta, GA 30303, U.S.
19Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
20IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia
21University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.
22Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
23Iowa State University, Ames, IA 50011, U.S.
24Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
25KAERI, Cyclotron Application Laboratory, Seoul, South Korea
26KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
27KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy
of Sciences (MTA KFKI RMKI), H-1525 Budapest 114, POBox 49, Budapest, Hungary
28Korea University, Seoul, 136-701, Korea
29Russian Research Center “Kurchatov Institute”, Moscow, Russia
30Kyoto University, Kyoto 606-8502, Japan
31Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France
32Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.
33Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.
34LPC, Universit´e Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France
35Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
36Institut f¨ur Kernphysik, University of Muenster, D-48149 Muenster, Germany
37Myongji University, Yongin, Kyonggido 449-728, Korea
38Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan
39University of New Mexico, Albuquerque, NM 87131, U.S.
40New Mexico State University, Las Cruces, NM 88003, U.S.
41Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.
42IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France
43Peking University, Beijing, People’s Republic of China
44PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia

3
45RIKEN, The Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan
46RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
47Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
48Saint Petersburg State Polytechnic University, St. Petersburg, Russia
49Universidade de S˜ao Paulo, Instituto de F´ısica, Caixa Postal 66318, S˜ao Paulo CEP05315-970, Brazil
50System Electronics Laboratory, Seoul National University, Seoul, South Korea
51Chemistry Department, Stony Brook University, Stony Brook, SUNY, NY 11794-3400, U.S.
52Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, U.S.
53SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes) BP 20722 - 44307, Nantes, France
54University of Tennessee, Knoxville, TN 37996, U.S.
55Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
56Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
57Vanderbilt University, Nashville, TN 37235, U.S.
58Waseda University, Advanced Research Institute for Science and
Engineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan
59Weizmann Institute, Rehovot 76100, Israel
60Yonsei University, IPAP, Seoul 120-749, Korea
(Dated: February 6, 2008)
We present azimuthal angle correlations of intermediate transverse momentum (1 −4 GeV/c)
hadrons from dijets in Cu+Cu and Au+Au collisions at √sNN = 62.4 and 200 GeV. The away-side
dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from ∆φ=π
in central and semi-central collisions in all the systems. The broadening and peak location are
found to depend upon the number of participants in the collision, but not on the collision energy or
beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to
Cherenkov gluon radiation models.
PACS numbers: 25.75.Dw
Heavy ion collisions at the Relativistic Heavy Ion Col-
lider (RHIC) produce QCD matter at enormous energy
density [1], exceeding that required for a phase transition
to partonic, rather than hadronic, matter. The produced
matter exhibits collective motion [2] and is opaque to
scattered quarks and gluons. The opacity is observed via
suppression of high momentum hadrons and intermedi-
ate energy dijets [3], and provides clear evidence of large
energy loss by partons (quarks or gluons) traversing the
medium. A key question is how the hot, dense medium
transports the deposited energy.
As partons fragment into back-to-back jets of hadrons,
angular correlations of the hadrons are used to study
medium effects upon hard scattered parton pairs.
Hadron pairs from the same parton appear at ∆φ∼0
(the near-side), while those with one hadron from each
parton in the hard scattered pair appear at ∆φ∼π(the
away-side). For brevity, we will refer to these dijet in-
duced dihadron azimuthal correlations with the abbrevi-
ation ”dijet correlations”.
Of great interest are intermediate transverse momen-
tum (pT) hadrons, as they can arise from intermediate
energy jets or involve partons from the medium [4, 5].
Their correlations can provide information about energy
loss mechanisms, dissipation of the radiated energy in the
medium, and collective modes induced by the deposited
energy. Theoretical ideas include: Mach cones from den-
sity waves induced by supersonic partons [4], co-moving
radiated gluons producing ”wakes” in the medium [5],
ultrarelativistic partons creating Cherenkov gluon radi-
ation [6], and medium-induced gluon radiation at large
emission angles [7, 8]. They all imply significant modi-
fications of dijet correlations in the away-side, when the
parton path through the medium is long. In particular,
some of these theoretical models [4, 6, 7] imply a transi-
tion from the peaked distribution at ∆φ∼πcharacter-
istic of p+p and p+A collisions to a distribution with a
peak away from ∆φ∼πin head-on Au+Au collisions.
Low pT(≥0.15 GeV/c) hadrons associated with high
pThadrons (≥4 GeV/c) have modified away-side di-
jet correlations and softened pTdistributions relative to
those in p+p collisions, suggesting that at least some of
the lost energy is thermalized in the medium [9]. At in-
termediate pT, a strong non-Gaussian shape modification
of the dijet away-side correlation [10] indicates the possi-
ble existence of a local minimum at ∆φ=π. This Letter
introduces new parameters to quantify this shape modi-
fication and reports their dependence on collision energy,
system size, transverse momentum and centrality mea-
sured by the PHENIX experiment at RHIC.
The minimum bias data were collected in the years
2005 (Cu+Cu at √sN N = 200 and 62.4 GeV), 2004
(Au+Au at √sN N = 200 and 62.4 GeV), and 2003
(d+Au at √sN N = 200 GeV). Charged hadrons are
tracked using the Drift Chambers and Pad Chambers
of the PHENIX central arm spectrometers at midrapid-
ity (|η|<0.35) in the same way as described in [10].
The number of events in the Au+Au data at √sNN =
200 GeV used here is about 30 times higher than that in
[10]. Collision centrality and the number of participant

4
nucleons (Npart) are determined using the Beam-Beam
Counters (BBCs) and Zero Degree Calorimeters [11].
Relative azimuthal distributions Ysame(∆φ) between
”trigger” hadrons with 2.5< pT<4 GeV/c and ”associ-
ated” hadrons with 1 < pT<2.5 GeV/c are formed. We
correct their shape for the non-uniform azimuthal accep-
tance of the PHENIX central arms by using the mixed
event pairs Ymixed(∆φ) [10] from the same data sample:
C(∆φ)≡Ysame(∆φ)
Ymixed(∆φ)×RYmixed (∆φ)d∆φ
RYsame(∆φ)d∆φ(1)
Extensive Monte-Carlo simulations were performed to
ensure that the true pair distribution shape is recovered
through this procedure.
In Au+Au and Cu+Cu collisions, hadrons have an az-
imuthal correlation with the reaction plane orientation
ΦRP which is proportional to 1 + 2v2cos(2(φ−ΦRP )).
This generates a significant correlated background to our
dijet source J(∆φ) of azimuthal correlations:
C(∆φ) = b0(1+ 2hvassoc
2ihvtrigg
2icos(2∆φ))+ J(∆φ) (2)
The charged hadron hv2i, where ”hi” signifies an event
average, was measured through a reaction plane analysis
using the BBCs (3 <|η|<4) as in [10, 12].
Hadrons have also a much smaller fourth order az-
imuthal correlation with the reaction plane orientation.
Its effect was studied with the Au+Au data at 200 GeV
by including the corresponding 2hvassoc
4ihvtrigg
4icos(4∆φ)
component in the background term of Eq. 2, where the
hv4ivalues have also been measured through the reaction-
plane analysis [12]. No significant v4systematic effects
on the shape of the dijet correlations were found.
The background subtraction generates point-by-point
(∆φdependent) systematic errors from hvassoc
2ihvtrigg
2i
uncertainty and an overall (∆φindependent) systematic
error from b0uncertainty. The sources of hvassoc
2ihvtrigg
2i
uncertainty are the hv2isystematic error [10], domi-
nated by the reaction plane resolution uncertainty, the
hv2istatistical error, and the systematic error from the
hvassoc
2·vtrigg
2i ≈ hvassoc
2i · hvtrigg
2ifactorization approxi-
mation made in Eq. 2. The latter is estimated to be at
most 5% of the hv2iproduct for the most central events.
The b0uncertainty is estimated by using three inde-
pendent methods to calculate b0. The first, called Zero
Yield At Minimum (ZYAM), assumes that there is a re-
gion in ∆φwhere the dijet source of particle pairs is neg-
ligible. b0is varied until the background component in
Eq. 2 matches the measured correlation C(∆φ) at some
value of ∆φ. In the second method a functional form for
J(∆φ) is added to the background, and the sum fitted
to the measured correlation with b0as a free parameter.
Motivated by the theoretical ideas discussed in the in-
troduction, we use a function that contains a near-side
Gaussian, and two symmetric away-side Gaussians:
J(∆φ) = G(∆φ) + G(∆φ−π−D) + G(∆φ−π+D) (3)
While the choice of this functional form is not unique,
it does provide a reasonable fit to the measured correla-
tions, as shown by the dotted line in Fig. 1. The pa-
rameter D, or peak angle, is motivated by an attempt
to describe the away-side dijet correlation in terms of its
symmetry around ∆φ∼π. We note that it also tends to
absorb any non-Gaussian character of the dijet correla-
tion. The third method is independent of the measured
C(∆φ). We calculate b0=ξκhntrigg ihnassoc i/hnsamei
with hadron production rates measured from all events
within each centrality class and scale by the same-event
pair rate. κis a correction for pair-cut bias and ξis a
correction for residual correlations due to averaging pro-
duction rates from events of different multiplicity within
the same centrality class [13].
As shown in Table I for the Au+Au data at 200 GeV,
there are slight b0variations depending on which method
is used to extract its value. However, the resulting shape
of the dijet correlations is essentially independent of these
variations.
TABLE I: b0values in Au+Au data at √sN N = 200 GeV:
ZYAM values (first row); variation of fit values from the
ZYAM values (second row); variation of combinatorial val-
ues from the ZYAM values (third row).
Centrality 60-90% 40-60% 20-40% 10-20% 5-10% 0-5%
ZYAM b00.861 0.942 0.960 0.971 0.982 0.988
fit δb0-0.003 -0.003 -0.006 -0.028 -0.035 -0.022
comb. δb0-0.086 -0.013 -0.004 +0.002 +0.001 +0.001
Figure 1 summarizes the extraction with the ZYAM
method of the dijet correlations using the central (0-5%)
Au+Au data at √sN N = 200 GeV: the measured corre-
lation is shown with squares, the background term with
a full line, and the background subtracted dijet correla-
tion with circles for values and boxes for the point-by-
point systematic errors. The systematic errors are cor-
related since they depend on the same parameter - the
hvassoc
2ihvtrigg
2iuncertainty. For clarity, J(∆φ) is shifted
up by b0, shown with dashed line, hence its amplitude
should be read from the right axis. We note that, in this
case, the measured correlation is flat near ∆φ∼π, even
before any background subtraction. Due to the cosine
modulation of the background, a local minimum should
develop at ∆φ∼πin the dijet away-side correlation.
Figure 2 shows a central and a peripheral dijet correla-
tion for each colliding system and energy. A remarkable
away-side feature in central and semi-central collisions
(<40%) is the peak location away from ∆φ=π, and
the appearance of a local minimum at ∆φ=π. To quan-
tify the significance of this minimum in the Au+Au data
at 200 GeV, we have studied how much hvassoc
2ihvtrig
2i
would need to change for the away-side to be flat. For
the four most central bins (0-5%, 5-10%, 10-20%, and 20-

5
(rad)φ∆
0 0.5 1 1.5 2 2.5 3
)φ
∆C(
0.99
1
1.01
1.02
)φ
∆J(
0
0.01
0.02
0.03
<4GeV/c
trigg
T
<2.5<p
assoc
T
1<p
Au+Au 200 GeV 0-5%
FIG. 1: (Color online) The measured correlation C(∆φ)
(squares) and the dijet correlation J(∆φ) (circles with boxes
for point-to-point systematic errors) in central Au+Au colli-
sions at √sNN = 200 GeV. The full line shows the background
term and the dotted line shows a C(∆φ) fit with Eqs. (2)+(3).
The left axis shows the measured correlation amplitude and
the right axis shows the dijet correlation amplitude.
40%) it would have to decrease by 85%(5.1σ), 41%(4.2σ),
20%(2.3σ), and 23%(2.7σ), respectively, where σis the
total hvassoc
2ihvtrig
2iuncertainty.
)φ
∆J(
0
0.01
0.02
0.03
0.04
Au+Au 200 GeV 5-10%
<4GeV/c
trigg
T
<2.5<p
assoc
T
1<p
0
0.1
0.2
0.3 Au+Au 200 GeV 60-90%
<4GeV/c
trigg
T
<2.5<p
assoc
T
1<p
)φ
∆J(
0
0.01
0.02
0.03 Au+Au 62.4 GeV 0-10%
0
0.05
0.1 Au+Au 62.4 GeV 40-80%
)φ
∆J(
0
0.02
0.04
0.06 Cu+Cu 200 GeV 0-10%
0
0.1
0.2
0.3 Cu+Cu 200 GeV 40-80%
(rad)φ∆
0 0.5 1 1.5 2 2.5 3
)φ
∆J(
0
0.02
0.04
0.06 Cu+Cu 62.4 GeV 0-10%
(rad)φ∆
0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3 Cu+Cu 62.4 GeV 40-80%
FIG. 2: (Color online) (Di)jet correlations (circles with boxes
for point-to-point systematic errors) in Au+Au and Cu+Cu
collisions at √sNN = 62.4 and 200 GeV. Left panels show
central collisions, while right panels show peripheral collisions.
We parameterize the away-side shape change and de-
viation from a Gaussian distribution by extracting the
second and fourth central moments around ∆φ∼π
(µn≡ h(∆φ−π)ni, n = 2,4), in the standard form of
the following statistical quantities: the root mean square
rms ≡√µ2and the kurtosis ≡µ4/µ2
2. The away-side
is defined here as all ∆φvalues above the dijet function
J(∆φ) minimum, typically one rad. We extract these
statistics on only the away-side jet peaks in J(∆φ); possi-
ble jet-associated flat underlying distributions, which are
highly sensitive to the uncertainty in b0and precluded
by the ZYAM assumption, are not included.
The rms and kurtosis centrality dependence is shown
in Fig. 3(a). The rms increases with centrality, indicat-
ing broadening of the away-side dijet correlation, while
the kurtosis decreases from the value characteristic of
a Gaussian shape (three), suggesting a flattening of its
shape beyond an increase in the Gaussian width.
rms (rad) or kurtosis
1
2
3
<4GeV/c
trigg
T
<2.5<p
assoc
T
1<p
filled symbols - kurtosis
open symbols - rms
(a)
part
N
0 100 200 300 400
D (rad)
0
0.5
1
d+Au 200 GeV
Au+Au 200 GeV
Cu+Cu 200 GeV
Au+Au 62.4 GeV
Cu+Cu 62.4 GeV
(b)
FIG. 3: (Color online) Collision centrality, energy, and sys-
tem size dependence of shape parameters: (a) kurtosis (filled
symbols) and rms (open symbols); (b) peak angle D. Bars
show statistical errors, shaded bands systematic errors.
TABLE II: Dependence of away-side shape parameters on as-
sociated hadron pTin central (0-20%) Au+Au collisions at
√sNN = 200 GeV for 3 < ptrigg
T<5 GeV/c. First error is
statistical and second error is systematic.
passoc
TD [rad] rms [rad] kurtosis
1-1.5 1.04±0.03±0.03 1.02±0.02±0.05 1.68±0.04±0.10
1.5-2 1.07±0.04±0.04 1.06±0.02±0.05 1.58±0.05±0.10
2-2.5 1.05±0.03±0.06 1.08±0.04±0.08 1.38±0.11±0.12
2.5-3 1.07±0.06±0.06 1.09±0.07±0.07 1.35±0.17±0.12
3-5 0.88±0.13±0.16 1.01±0.11±0.14 1.31±0.23±0.25
The peak angle D centrality dependence, extracted by
fitting dijet correlations with Eq. 3, is shown in Fig.
3(b). It is consistent with zero radians in d+Au and pe-
ripheral nuclear collisions, but rapidly grows to a value
around one radian in central nuclear collisions. Some
deviation from zero radians of the peak angle may be

6
related to slight non-Gaussian shapes of the dijet corre-
lations even without medium modification. This can be
seen in the kurtosis values for d+Au and peripheral nu-
clear collisions, which have values somewhat lower than
three. For details on dijet correlations in d+Au see [14].
The systematic errors in Fig. 3 come exclusively from v2
uncertainty. No apparent dependence of rms, kurtosis, or
peak angle D on collision energy or species is observed.
Table II shows the dependence of the away-side shape
parameters on the associated hadron pTin the Au+Au
data at 200 GeV for a 0-20% centrality bin, 3 < ptrigg
T<5
GeV/c, and the following passoc
Tbins: 1 −1.5, 1.5−2,
2−2.5, 2.5−3, and 3 −5 GeV/c. The peak angle D
and the rms have no pTdependence, while the kurtosis
is consistent with a slow decrease with pT.
Several phenomenological models for modification of
the away-side jet have been proposed; all involve a strong
response of the medium to the traversing jet. Bow shocks
propagating as sound, or density, waves in the medium
produce a peak located away from ∆φ=πat approx-
imately the same angle as seen in the data [4, 15]. If
the peak indeed arises from a sound wave, its location at
one radian away from the nominal jet direction implies
a speed of sound intermediate between that expected in
a hadron gas and quark-gluon plasma [4]. A first or-
der phase transition would cause a region with speed of
sound identically zero. This region was postulated [4] to
reflect sound waves and cause a second away-side peak
located at about 1.4 radians away from ∆φ=π. No clear
evidence for a distinct peak is seen in our data.
If the coupling among partons in the medium is strong,
then the high momentum parton may induce non-sound
wave collective plasma excitations [5]. In the strong cou-
pling limit the AdS/CFT correspondence was applied to
calculate the wake of directional emission from a heavy
quark traversing the medium, where a peak angle is found
at values slightly larger than in these data [16].
The peak may also arise from Cherenkov gluon radi-
ation [6]. Such a mechanism should disappear for high
energy gluons, implying that the peak angle D should
gradually approach zero with increasing momentum of
associated hadrons. Table II shows that this is not sup-
ported by the data. The medium may induce gluon radia-
tion at large angles by mechanisms other than Cherenkov
radiation [7, 8]. Such models can reproduce the observed
peak if the density of scattering centers is large and the
gluon splitting sufficiently asymmetric [7]. However, the
predicted radiation is very sensitive to the treatment of
geometry, expansion and radiative energy loss framework
used. Our detailed measurements constrain the options.
An important issue is whether the density wave cor-
relations can survive the underlying medium expansion.
It was shown that the interplay of the longitudinal ex-
pansion and limited experimental ηacceptance preserves,
and even amplifies, the signal of directed collective exci-
tations [15]. However, the creation of a shock wave con-
sistent with our data requires that 75-90% of the jet’s lost
energy be transferred to the collective mode [4, 15, 17].
We have presented azimuthal angle correlations of in-
termediate transverse momentum hadrons from dijets in
Cu+Cu and Au+Au collisions at √sN N = 62.4 and 200
GeV. The away-side dijet correlation is seen to be broad-
ened, non-Gaussian and peaked away from ∆φ=πin
central and semi-central collisions. The away-side shape
depends on the number of participants in the collision,
and not on the beam nuclei or energy. The general
features of the observed shape can be qualitatively ac-
counted for by a number of phenomenological models,
all having in common a strong medium response to the
energy deposited by the traversing parton. The system-
atic data presented here provide quantitative tests that
could discriminate between these models.
We thank the staff of the Collider-Accelerator and
Physics Departments at BNL for their vital contribu-
tions. We acknowledge support from the Department of
Energy and NSF (U.S.A.), MEXT and JSPS (Japan),
CNPq and FAPESP (Brazil), NSFC (China), MSMT
(Czech Republic), IN2P3/CNRS and CEA (France),
BMBF, DAAD, and AvH (Germany), OTKA (Hungary),
DAE (India), ISF (Israel), KRF and KOSEF (Korea),
MES, RAS, and FAAE (Russia), VR and KAW (Swe-
den), U.S. CRDF for the FSU, US-Hungarian NSF-
OTKA-MTA, and US-Israel BSF.
∗Deceased
†PHENIX Spokesperson: zajc@nevis.columbia.edu
[1] K. Adcox et al., Nucl. Phys. A 757, 184 (2005).
[2] S. S. Adler et al., Phys. Rev. Lett. 91, 182301 (2003).
[3] S. S. Adler et al., Phys. Rev. Lett. 91, 072301 (2003);
S. S. Adler et al., Phys. Rev. C 69, 034910 (2004).
[4] J. Casalderrey-Solana, E. V. Shuryak and D. Teaney,
Nucl. Phys. A 774, 577 (2006) and hep-ph/0511263.
[5] J. Ruppert, B. Mueller, Phys. Lett. B 618, 123 (2005).
[6] V. Koch, A. Majumder, and X.-N. Wang, Phys. Rev.
Lett. 96, 172302 (2006).
[7] A. D. Polosa and C. A. Salgado, hep-ph/0607295.
[8] I. Vitev, Phys. Lett. B 630, 78 (2005).
[9] J. Adams et al., Phys. Rev. Lett. 95, 152301 (2005).
[10] S. S. Adler et al., Phys. Rev. Lett. 97, 052301 (2006).
[11] K. Adcox et al., Phys. Rev. C 69, 024904 (2004).
[12] H. Masui, nucl-ex/0510018; M. D. Oldenburg, J. Phys.
G31, S437 (2005) and nucl-ex/0412001.
[13] S. S. Adler et al., Phys. Rev. C 71, 051902 (2005).
[14] S. S. Adler et al., Phys. Rev. C 73, 054903 (2006).
[15] T. Renk and J. Ruppert, hep-ph/0605330.
[16] J. J. Friess, S. S. Gubser, G. Michalogiorgakis and
S. S. Pufu, hep-th/0607022.
[17] A. K. Chaudhuri and U. W. Heinz, Phys. Rev. Lett. 97,
062301 (2006).