Incident energy dependence of p(t) correlations at relativistic energies

Abstract

We present results for two-particle transverse momentum correlations, <Delta p(t,i)Delta p(t,j)>, as a function of event centrality for Au+Au collisions at root SNN = 20, 62, 130, and 200 GeV at the BNL Relativistic Heavy Ion Collider. We observe correlations decreasing with centrality that are similar at all four incident energies. The correlations multiplied by the multiplicity density increase with incident energy, and the centrality dependence may show evidence of processes such as thermalization, jet production, or the saturation of transverse flow. The square root of the correlations divided by the event-wise average transverse momentum per event shows little or no beam energy dependence and generally agrees with previous measurements made at the CERN Super Proton Synchrotron.

Full text

Physics
Physics Research Publications
Purdue University Year 
Incident energy dependence of p(t)
correlations at relativistic energies
J. Adams, M. M. Aggarwal, Z. Ahammed, J. Amonett, B. D. Anderson, D.
Arkhipkin, G. S. Averichev, S. K. Badyal, Y. Bai, J. Balewski, O. Barannikova,
L. S. Barnby, J. Baudot, S. Bekele, V. V. Belaga, A. Bellingeri-Laurikainen, R.
Bellwied, J. Berger, B. I. Bezverkhny, S. Bharadwaj, A. Bhasin, A. K. Bhati,
V. S. Bhatia, H. Bichsel, J. Bielcik, J. Bielcikova, A. Billmeier, L. C. Bland, C.
O. Blyth, B. E. Bonner, M. Botje, A. Boucham, J. Bouchet, A. V. Brandin, A.
Bravar, M. Bystersky, R. V. Cadman, X. Z. Cai, H. Caines, M. C. D. B. Sanchez,
J. Castillo, O. Catu, D. Cebra, Z. Chajecki, P. Chaloupka, S. Chattopadhyay,
H. F. Chen, Y. Chen, J. Cheng, M. Cherney, A. Chikanian, W. Christie, J.
P. Coffin, T. M. Cormier, J. G. Cramer, H. J. Crawford, D. Das, S. Das, M.
Daugherity, M. M. de Moura, T. G. Dedovich, A. A. Derevschikov, L. Didenko,
T. Dietel, S. M. Dogra, W. J. Dong, X. Dong, J. E. Draper, F. Du, A. K. Dubey,
V. B. Dunin, J. C. Dunlop, M. R. D. Mazumdar, V. Eckardt, W. R. Edwards,
L. G. Efimov, V. Emelianov, J. Engelage, G. Eppley, B. Erazmus, M. Estienne,
P. Fachini, J. Faivre, R. Fatemi, J. Fedorisin, K. Filimonov, P. Filip, E. Finch,
V. Fine, Y. Fisyak, J. Fu, C. A. Gagliardi, L. Gaillard, J. Gans, M. S. Ganti,
F. Geurts, V. Ghazikhanian, P. Ghosh, J. E. Gonzalez, H. Gos, O. Grachov, O.
Grebenyuk, D. Grosnick, S. M. Guertin, Y. Guo, A. Gupta, T. D. Gutierrez, T.
J. Hallman, A. Hamed, D. Hardtke, J. W. Harris, M. Heinz, T. W. Henry, S.
Hepplemann, B. Hippolyte, A. Hirsch, E. Hjort, G. W. Hoffmann, H. Z. Huang,
S. L. Huang, E. W. Hughes, T. J. Humanic, G. Igo, A. Ishihara, P. Jacobs, W.
W. Jacobs, M. Jedynak, H. Jiang, P. G. Jones, E. G. Judd, S. Kabana, K. Kang,
M. Kaplan, D. Keane, A. Kechechyan, V. Y. Khodyrev, J. Kiryluk, A. Kisiel,
E. M. Kislov, J. Klay, S. R. Klein, D. D. Koetke, T. Kollegger, M. Kopytine, L.
Kotchenda, K. L. Kowalik, M. Kramer, P. Kravtsov, V. I. Kravtsov, K. Krueger,
C. Kuhn, A. I. Kulikov, A. Kumar, R. K. Kutuev, A. A. Kuznetsov, M. A. C.
Lamont, J. M. Landgraf, S. Lange, F. Laue, J. Lauret, A. Lebedev, R. Lednicky,
S. Lehocka, M. J. LeVine, C. Li, Q. Li, Y. Li, G. Lin, S. J. Lindenbaum, M. A.
Lisa, F. Liu, H. Liu, L. Liu, Q. J. Liu, Z. Liu, T. Ljubicic, W. J. Llope, H. Long,
R. S. Longacre, M. Lopez-Noriega, W. A. Love, Y. Lu, T. Ludlam, D. Lynn,
G. L. Ma, J. G. Ma, Y. G. Ma, D. Magestro, S. Maha jan, D. P. Mahapatra,
R. Majka, L. K. Mangotra, R. Manweiler, S. Margetis, C. Markert, L. Martin,

J. N. Marx, H. S. Matis, Y. A. Matulenko, C. J. McClain, T. S. McShane, F.
Meissner, Y. Melnick, A. Meschanin, M. L. Miller, N. G. Minaev, C. Mironov, A.
Mischke, D. K. Mishra, J. Mitchell, B. Mohanty, L. Molnar, C. F. Moore, D. A.
Morozov, M. G. Munhoz, B. K. Nandi, S. K. Nayak, T. K. Nayak, J. M. Nelson,
P. K. Netrakanti, V. A. Nikitin, L. V. Nogach, S. B. Nurushev, G. Odyniec,
A. Ogawa, V. Okorokov, M. Oldenburg, D. Olson, S. K. Pal, Y. Panebratsev,
S. Y. Panitkin, A. I. Pavlinov, T. Pawlak, T. Peitzmann, V. Perevoztchikov,
C. Perkins, W. Peryt, V. A. Petrov, S. C. Phatak, R. Picha, M. Planinic, J.
Pluta, N. Porile, J. Porter, A. M. Poskanzer, M. Potekhin, E. Potrebenikova,
B. V. K. S. Potukuchi, D. Prindle, C. Pruneau, J. Putschke, G. Rakness, R.
Raniwala, S. Raniwala, O. Ravel, R. L. Ray, S. V. Razin, D. Reichhold, J.
G. Reid, J. Reinnarth, G. Renault, F. Retiere, A. Ridiger, H. G. Ritter, J. B.
Roberts, O. V. Rogachevskiy, J. L. Romero, A. Rose, C. Roy, L. Ruan, M.
Russcher, R. Sahoo, I. Sakrejda, S. Salur, J. Sandweiss, M. Sarsour, I. Savin, P.
S. Sazhin, J. Schambach, R. P. Scharenberg, N. Schmitz, K. Schweda, J. Seger,
P. Seyboth, E. Shahaliev, M. Shao, W. Shao, M. Sharma, W. Q. Shen, K. E.
Shestermanov, S. S. Shimanskiy, E. Sichtermann, F. Simon, R. N. Singaraju,
N. Smirnov, R. Snellings, G. Sood, P. Sorensen, J. Sowinski, J. Speltz, H. M.
Spinka, B. Srivastava, A. Stadnik, T. D. S. Stanislaus, R. Stock, A. Stolpovsky,
M. Strikhanov, B. Stringfellow, A. A. P. Suaide, E. Sugarbaker, C. Suire, M.
Sumbera, B. Surrow, M. Swanger, T. J. M. Symons, A. S. de Toledo, A. Tai, J.
Takahashi, A. H. Tang, T. Tarnowsky, D. Thein, J. H. Thomas, S. Timoshenko,
M. Tokarev, S. Trentalange, R. E. Tribble, O. D. Tsai, J. Ulery, T. Ullrich, D.
G. Underwood, G. V. Buren, G. Van Buren, A. M. Vander Molen, R. Varma, I.
M. Vasilevski, A. N. Vasiliev, R. Vernet, S. E. Vigdor, Y. P. Viyogi, S. Vokal,
S. A. Voloshin, W. T. Waggoner, F. Wang, G. Wang, X. L. Wang, Y. Wang, Z.
M. Wang, H. Ward, J. W. Watson, J. C. Webb, G. D. Westfall, A. Wetzler, C.
Whitten, H. Wieman, S. W. Wissink, R. Witt, J. Wood, J. Wu, N. Xu, Z. Xu,
Z. Z. Xu, E. Yamamoto, P. Yepes, V. I. Yurevich, I. Zborovsky, H. Zhang, W.
M. Zhang, Y. Zhang, Z. P. Zhang, R. Zoulkarneev, Y. Zoulkarneeva, and A. N.
Zubarev
This paper is posted at Purdue e-Pubs.
http://docs.lib.purdue.edu/physics articles/89

PHYSICAL REVIEW C 72, 044902 (2005)
Incident energy dependence of ptcorrelations at relativistic energies
J. Adams,3M. M. Aggarwal,29 Z. Ahammed,43 J. Amonett,20 B. D. Anderson,20 D. Arkhipkin,13 G. S. Averichev,12
S. K. Badyal,19 Y. B a i , 27 J. Balewski,17 O. Barannikova,32 L. S. Barnby,3J. Baudot,18 S. Bekele,28 V. V. B e l a g a , 12
A. Bellingeri-Laurikainen,38 R. Bellwied,46 J. Berger,14 B. I. Bezverkhny,48 S. Bharadwaj,33 A. Bhasin,19 A. K. Bhati,29
V. S. Bhatia,29 H. Bichsel,45 J. Bielcik,48 J. Bielcikova,48 A. Billmeier,46 L. C. Bland,4C. O. Blyth,3B. E. Bonner,34 M. Botje,27
A. Boucham,38 J. Bouchet,38 A. V. Brandin,25 A. Bravar,4M. Bystersky,11 R. V. Cadman,1X. Z. Cai,37 H. Caines,48
M. Calder´
on de la Barca S´
anchez,17 J. Castillo,21 O. Catu,48 D. Cebra,7Z. Chajecki,28 P. Chaloupka,11 S. Chattopadhyay,43
H. F. Chen,36 Y. Chen,8J. Cheng,41 M. Cherney,10 A. Chikanian,48 W. Christie,4J. P. Coffin,18 T. M. Cormier,46 J. G. Cramer,45
H. J. Crawford,6D. Das,43 S. Das,43 M. Daugherity,40 M. M. de Moura,35 T. G. Dedovich,12 A. A. Derevschikov,31
L. Didenko,4T. Dietel,14 S. M. Dogra,19 W. J. Dong,8X. Dong,36 J. E. Draper,7F. Du,48 A. K. Dubey,15 V. B. Dunin,12
J. C. Dunlop,4M. R. Dutta Mazumdar,43 V. Eckardt,23 W. R. Edwards,21 L. G. Efimov,12 V. Emelianov,25 J. Engelage,6
G. Eppley,34 B. Erazmus,38 M. Estienne,38 P. Fachini,4J. Faivre,18 R. Fatemi,17 J. Fedorisin,12 K. Filimonov,21 P. Filip,11
E. Finch,48 V. Fine,4Y. Fisyak,4J. Fu,41 C. A. Gagliardi,39 L. Gaillard,3J. Gans,48 M. S. Ganti,43 F. Geurts,34 V. Ghazikhanian,8
P. Ghosh,43 J. E. Gonzalez,8H. Gos,44 O. Grachov,46 O. Grebenyuk,27 D. Grosnick,42 S. M. Guertin,8Y. Guo,46 A. Gupta,19
T. D. Gutierrez,7T. J. Hallman,4A. Hamed,46 D. Hardtke,21 J. W. Harris,48 M. Heinz,2T. W. Henry,39 S. Hepplemann,30
B. Hippolyte,18 A. Hirsch,32 E. Hjort,21 G. W. Hoffmann,40 H. Z. Huang,8S. L. Huang,36 E. W. Hughes,5T. J. Humanic,28
G. Igo,8A. Ishihara,40 P. Jacobs,21 W. W. Jacobs,17 M. Jedynak,44 H. Jiang,8P. G. Jones,3E. G. Judd,6S. Kabana,2K. Kang,41
M. Kaplan,9D. Keane,20 A. Kechechyan,12 V. Yu. Khodyrev,31 J. Kiryluk,22 A. Kisiel,44 E. M. Kislov,12 J. Klay,21
S. R. Klein,21 D. D. Koetke,42 T. Kollegger,14 M. Kopytine,20 L. Kotchenda,25 K. L. Kowalik,21 M. Kramer,26
P. Kr a v ts o v ,25 V. I . K r a v t s o v , 31 K. Krueger,1C. Kuhn,18 A. I. Kulikov,12 A. Kumar,29 R. Kh. Kutuev,13 A. A. Kuznetsov,12
M. A. C. Lamont,48 J. M. Landgraf,4S. Lange,14 F. Laue,4J. Lauret,4A. Lebedev,4R. Lednicky,12 S. Lehocka,12
M. J. LeVine,4C. Li,36 Q. Li,46 Y. Li , 41 G. Lin,48 S. J. Lindenbaum,26 M. A. Lisa,28 F. L i u , 47 H. Liu,36 L. Liu,47 Q. J. Liu,45
Z. Liu,47 T. Ljubicic,4W. J. Llope,34 H. Long,8R. S. Longacre,4M. Lopez-Noriega,28 W. A. Love,4Y. L u , 47 T. Ludlam,4
D. Lynn,4G. L. Ma,37 J. G. Ma,8Y. G. M a , 37 D. Magestro,28 S. Mahajan,19 D. P. Mahapatra,15 R. Majka,48 L. K. Mangotra,19
R. Manweiler,42 S. Margetis,20 C. Markert,20 L. Martin,38 J. N. Marx,21 H. S. Matis,21 Yu. A. Matulenko,31 C. J. McClain,1
T. S. McShane,10 F. Meissner,21 Yu. Melnick,31 A. Meschanin,31 M. L. Miller,22 N. G. Minaev,31 C. Mironov,20 A. Mischke,27
D. K. Mishra,15 J. Mitchell,34 B. Mohanty,43 L. Molnar,32 C. F. Moore,40 D. A. Morozov,31 M. G. Munhoz,35 B. K. Nandi,43
S. K. Nayak,19 T. K. Nayak,43 J. M. Nelson,3P. K. Netrakanti,43 V. A. Nikitin,13 L. V. Nogach,31 S. B. Nurushev,31
G. Odyniec,21 A. Ogawa,4V. Okorokov,25 M. Oldenburg,21 D. Olson,21 S. K. Pal,43 Y. Panebratsev,12 S. Y. Panitkin,4
A. I. Pavlinov,46 T. Pawlak,44 T. Peitzmann,27 V. Perevoztchikov,4C. Perkins,6W. Peryt,44 V. A. Petrov,46 S. C. Phatak,15
R. Picha,7M. Planinic,49 J. Pluta,44 N. Porile,32 J. Porter,45 A. M. Poskanzer,21 M. Potekhin,4E. Potrebenikova,12
B. V. K. S. Potukuchi,19 D. Prindle,45 C. Pruneau,46 J. Putschke,21 G. Rakness,30 R. Raniwala,33 S. Raniwala,33 O. Ravel,38
R. L. Ray,40 S. V. Razin,12 D. Reichhold,32 J. G. Reid,45 J. Reinnarth,38 G. Renault,38 F. Retiere,21 A. Ridiger,25 H. G. Ritter,21
J. B. Roberts,34 O. V. Rogachevskiy,12 J. L. Romero,7A. Rose,21 C. Roy,38 L. Ruan,36 M. Russcher,27 R. Sahoo,15 I. Sakrejda,21
S. Salur,48 J. Sandweiss,48 M. Sarsour,17 I. Savin,13 P. S. Sazhin,12 J. Schambach,40 R. P. Scharenberg,32 N. Schmitz,23
K. Schweda,21 J. Seger,10 P. Seyboth,23 E. Shahaliev,12 M. Shao,36 W. Shao,5M. Sharma,29 W. Q. Shen,37 K. E. Shestermanov,31
S. S. Shimanskiy,12 E. Sichtermann,21 F. Simon,23 R. N. Singaraju,43 N. Smirnov,48 R. Snellings,27 G. Sood,42 P. Sorensen,21
J. Sowinski,17 J. Speltz,18 H. M. Spinka,1B. Srivastava,32 A. Stadnik,12 T. D. S. Stanislaus,42 R. Stock,14 A. Stolpovsky,46
M. Strikhanov,25 B. Stringfellow,32 A. A. P. Suaide,35 E. Sugarbaker,28 C. Suire,4M. Sumbera,11 B. Surrow,22 M. Swanger,10
T. J. M. Symons,21 A. Szanto de Toledo,35 A. Tai,8J. Takahashi,35 A. H. Tang,27 T. Tarnow s ky,32 D. Thein,8J. H. Thomas,21
S. Timoshenko,25 M. Tokarev,12 S. Trentalange,8R. E. Tribble,39 O. D. Tsai,8J. Ulery,32 T. Ullrich,4D. G. Underwood,1
G. Van Buren,4M. van Leeuwen,21 A. M. Vander Molen,24 R. Varma,16 I. M. Vasilevski,13 A. N. Vasiliev,31 R. Vernet,18
S. E. Vigdor,17 Y. P. Viyogi,43 S. Vokal,12 S. A. Voloshin,46 W. T. Waggoner,10 F. Wang,32 G. Wang,20 G. Wang,5X. L. Wang,36
Y. Wang,40 Y. Wang,41 Z. M. Wang,36 H. Ward,40 J. W. Watson,20 J. C. Webb,17 G. D. Westfall,24 A. Wetzler,21 C. Whitten Jr.,8
H. Wieman,21 S. W. Wissink,17 R. Witt,2J. Wood,8J. Wu,36 N. Xu,21 Z. Xu,4Z. Z. Xu,36 E. Yamamoto,21 P. Yepes,34
V. I. Yurevich,12 I. Zborovsky,11 H. Zhang,4W. M. Zhang,20 Y. Zhang,36 Z. P. Zhang,36 R. Zoulkarneev,13 Y. Zoulkarneeva,13
and A. N. Zubarev12
(STAR Collaboration)
1Argonne National Laboratory, Argonne, Illinois 60439, USA
2University of Bern, CH-3012 Bern, Switzerland
3University of Birmingham, Birmingham, United Kingdom
4Brookhaven National Laboratory, Upton, New York 11973, USA
5California Institute of Technology, Pasadena, California 91125, USA
6University of California, Berkeley, California 94720, USA
7University of California, Davis, California 95616, USA
8University of California, Los Angeles, California 90095, USA
9Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
0556-2813/2005/72(4)/044902(6)/$23.00 044902-1 ©2005 The American Physical Society

J. ADAMS et al. PHYSICAL REVIEW C 72, 044902 (2005)
10Creighton University, Omaha, Nebraska 68178, USA
11Nuclear Physics Institute AS CR, 250 68 ˇ
Reˇ
z/Prague, Czech Republic
12Laboratory for High Energy, Dubna, Russia
13Particle Physics Laboratory, Dubna, Russia
14University of Frankfurt, Frankfurt, Germany
15Institute of Physics, Bhubaneswar 751005, India
16Indian Institute of Technology, Mumbai, India
17Indiana University, Bloomington, Indiana 47408, USA
18Institut de Recherches Subatomiques, Strasbourg, France
19University of Jammu, Jammu 180001, India
20Kent State University, Kent, Ohio 44242, USA
21Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
22Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
23Max-Planck-Institut f ¨
ur Physik, Munich, Germany
24Michigan State University, East Lansing, Michigan 48824, USA
25Moscow Engineering Physics Institute, Moscow, Russia
26City College of New York, New York City, New York 10031, USA
27NIKHEF and Utrecht University, Amsterdam, The Netherlands
28Ohio State University, Columbus, Ohio 43210, USA
29Panjab University, Chandigarh 160014, India
30Pennsylvania State University, University Park, Pennsylvania 16802, USA
31Institute of High Energy Physics, Protvino, Russia
32Purdue University, West Lafayette, Indiana 47907, USA
33University of Rajasthan, Jaipur 302004, India
34Rice University, Houston, Texas 77251, USA
35Universidade de S ˜
ao Paulo, S˜
ao Paulo, Brazil
36University of Science & Technology of China, Anhui 230027, China
37Shanghai Institute of Applied Physics, Shanghai 201800, China
38SUBATECH, Nantes, France
39Texas A&M University, College Station, Texas 77843, USA
40University of Texas, Austin, Texas 78712, USA
41Tsinghua University, Beijing 100084, China
42Valparaiso University, Valparaiso, Indiana 46383, USA
43Variable Energy Cyclotron Centre, Kolkata 700064, India
44Warsaw University of Technology, Warsaw, Poland
45University of Washington, Seattle, Washington 98195, USA
46Wayne State University, Detroit, Michigan 48201, USA
47Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China
48Yale University, New Haven, Connecticut 06520, USA
49University of Zagreb, Zagreb, HR-10002, Croatia
(Received 25 April 2005; published 19 October 2005)
We present results for two-particle transverse momentum correlations, p t,ip t,j, as a function of event
centrality for Au+Au collisions at √sNN =20, 62, 130, and 200 GeV at the BNL Relativistic Heavy Ion Collider.
We observe correlations decreasing with centrality that are similar at all four incident energies. The correlations
multiplied by the multiplicity density increase with incident energy, and the centrality dependence may show
evidence of processes such as thermalization, jet production, or the saturation of transverse flow. The square
root of the correlations divided by the event-wise average transverse momentum per event shows little or no
beam energy dependence and generally agrees with previous measurements made at the CERN Super Proton
Synchrotron.
DOI: 10.1103/PhysRevC.72.044902 PACS number(s): 25.75.Gz
The study of event-by-event fluctuations in global quan-
tities, which are intimately related to correlations in particle
production, may provide evidence for the production of quark-
gluon plasma (QGP) in relativistic heavy-ion collisions [1–15].
Various theoretical works predict that the production of a
QGP phase in relativistic heavy-ion collisions could produce
significant dynamic event-by-event fluctuations in apparent
temperature, mean transverse momentum, multiplicity, and
conserved quantities such as net charge. Several recent exper-
imental studies at the CERN Super Proton Synchrotron (SPS)
044902-2

INCIDENT ENERGY DEPENDENCE OF pt. . . PHYSICAL REVIEW C 72, 044902 (2005)
[16–18] and at the BNL Relativistic Heavy Ion Collider
(RHIC) [19–24] have focused on the study of fluctuations and
correlations in relativistic heavy-ion collisions. One possible
signal of the QGP would be a nonmonotonic change in pt
correlations as a function of centrality and/or as the incident
energy is raised [8].
Here we report an experimental study of the incident energy
dependence of ptcorrelations we obtained by using Au+Au
collisions ranging in center-of-mass energy from the highest
SPS energy to the highest RHIC energy, which we measured
by using the solenoidal tracker at RHIC (STAR) detector.
Fluctuations involve a purely statistical component arising
from the stochastic nature of particle production and detection
processes, as well as a dynamic component determined by
correlations arising in various particle production processes.
In this paper we first unambiguously demonstrate the exis-
tence of a finite dynamical component at all four incident
energies by comparing the distribution of measured event-wise
average transverse momentum per event, pt, with the same
quantity from mixed events. We then analyze these dynamical
fluctuations by using the two-particle transverse momentum
correlations defined as covariance,
pt,ipt,j= 1
Nevent
Nevent

k=1
Ck
Nk(Nk−1) ,(1)
where
Ck=
Nk

i=1
Nk

j=1,i=j
(pt,i −pt)(pt,j −pt),(2)
Nevent is the number of events, pt,i is the transverse momentum
of the ith track in each event, and Nkis the number of tracks in
the kth event. The overall event average transverse momentum
pt is given by
pt =Nevent

k=1ptkNevent,(3)
where ptkis the average transverse momentum per event
given by
ptk=Nk

i=1
pt,iNk.(4)
pt,ipt,jis independent, to first order, of detection effi-
ciencies because both the numerator Ckand the denominator
Nk(Nk−1) are proportional to the square of the particle
detection efficiency. Therefore the efficiency cancels. By
construction, pt,ipt,jis zero within statistics for properly
mixed events because all correlations are removed. Note that
we use mixed events only in Fig. 1.
We measured the data used in this analysis by using the
solenoidal tracker at RHIC (STAR) detector to study Au+Au
collisions at √sNN =20, 62, 130, and 200 GeV [25]. The main
detector was the time-projection chamber (TPC) located in a
solenoidal magnetic field. The magnetic field was 0.25 T for the
20- and 130-GeV data and 0.5 T for the 62- and 200-GeV data.
Tracks from the TPC with 0.15 GeV/cpt2.0GeV/cwith
|η|<1.0 were used in the analysis. All tracks were required
Data
Mixed
20 GeV
62 GeV
130 GeV
200 GeV
|η| < 1
0.15 < pt < 2.0 GeV/c
0.48 0.52 0.56 0.60 0.64
<pt> (GeV/c)
Counts
1
10
102
103
1
10
102
103
104
1
10
102
1
10
102
Γ for Mixed
Γ for Data
FIG. 1. (Color online) Histograms of the average transverse
momentum per event for Au+Au at √sNN =20, 62, 130, and
200 GeV for the 5% most central collisions at each energy. Both
data and mixed events are shown for each incident energy. The lines
represent gamma distributions.
to have originated within 1 cm of the measured event vertex.
Events were selected according to their distance of the event
vertex from the center of STAR. Events were accepted within
1 cm of the center of STAR in the plane perpendicular to the
beam direction. For the 20- and 130-GeV data sets, events were
accepted with vertices within 75 cm of the center of STAR in
the beam direction, whereas for the 62- and 200-GeV data sets,
events were accepted within 25 cm of the center.
Data shown for 62, 130 and 200 GeV are from minimum
bias triggers. Minimum bias triggers were defined by the
coincidence of two zero-degree calorimeters (ZDCs) [26]
located ±18 m from the center of the interaction region.
For 20 GeV, a combination of minimum bias and central
triggers was used. Centrality bins were determined by use
of the multiplicity of all charged particles measured in the
TPC with |η|<0.5. The centrality bins were calculated as
fractions of this multiplicity distribution starting with the
044902-3

J. ADAMS et al. PHYSICAL REVIEW C 72, 044902 (2005)
highest multiplicities. The ranges used were 0%–5% (most
central), 5%–10%, 10%–20%, 20%–30%, 30%–40%, 40%–
50%, 50%–60%, 60%–70%, and 70%–80% (most peripheral).
Each centrality was associated with a number of partici-
pating nucleons, Npart, by use of a Glauber Monte Carlo
calculation [27].
We treated the variation of pt within a given centrality
bin by using the following procedure. We calculated pt as
afunctionofNch, the multiplicity used to define the centrality
bin. We fitted this dependence and used the fit in Eqs. (1)–(4)
on an event-by-event basis as a function of Nch. This method
removes the dependence of the experimental results on the
size of the centrality bin and slightly reduces pt,ipt,j
by removing correlations induced by the changing of pt
within the experimental centrality bins. The results pre-
sented in this paper were obtained by use of this fitting
procedure.
Figure 1 shows histograms of ptfor the 5% most central
Au+Au collisions at 20, 62, 130, and 200 GeV. Histograms for
ptare also shown for mixed events. The histograms for the
data are wider than the histograms for mixed events, indicating
that we observe nonstatistical fluctuations at all four incident
energies. Similar results are obtained for all centralities. The
overall normalization reflects the number events taken at each
energy. The values of ptincluded in these histograms are not
corrected for experimental momentum resolution, acceptance,
or efficiency.
We created the mixed events at each energy by randomly
selecting one track from an event chosen from measured events
in the same centrality and event vertex bin. Ten centrality bins
and either 5 or 10 bins (depending on the available number
of events at each energy) in the event vertex position in the
beam direction were used to create mixed events with the same
multiplicity distribution as that of the real events. Note that we
do not use mixed events for the quantitative analysis based on
pt,ipt,j.
The lines in Fig. 1 represent gamma distributions for both
the data and mixed events. The parameters for the gamma
distributions are shown in Table I. According to Ref. [28],
without ptcuts, the parameter αdivided by the average
multiplicity in the centrality bin, N, should be approximately
two and the parameter βmultiplied by Nshould reflect the
temperature parameter of the ptdistributions. We find that
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
10
2
10
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
10
2
10
20 GeV Au+Au
62 GeV Au+Au
130 GeV Au+Au
200 GeV Au+Au
20 GeV HIJING
62 GeV HIJING
130 GeV HIJING
200 GeV HIJING
<∆pt,i∆pt,j> [(MeV/c)2]
FIG. 2. (Color online) pt,ip t,j as a function of centrality and
incident energy for Au+Au collisions compared with HIJING results.
α/Nvaries from 2.27 to 1.93 and βNvaries from 0.230
to 0.299 GeV/cas the energy goes from 20 to 200 GeV.
To characterize the transverse momentum correlations, we
use the quantity pt,ipt,j, defined in Eq. (1). Figure 2
shows pt,ip t,jfor Au+Au collisions at √sNN =20, 62,
130, and 200 GeV as functions of centrality. One observes that
pt,ipt,jdecreases with centrality at all four energies as
expected because of a progressive dilution of the correlations
resulting from the increased number of participants if the
correlations are dominated by pairs of particles that originate
from the same nucleon-nucleon collision. The correlations
measured at 62, 130, and 200 GeV are similar, whereas the
correlations for 20 GeV are smaller than those observed at the
higher energies.
To explore the issue of the relative importance of short-
range correlations such as Coulomb interactions and Hanbury
Brown-Twiss (HBT) effects, we extracted the correlations,
excluding pairs with invariant relative momentum qinv,less
than 0.1 GeV/c, assuming that all particles were pions. We
observed that 10% of the measured correlations at 62, 130, and
TABLE I. Parameters for the gamma distributions shown in Fig. 1. The gamma distribution is
given by the form f(x)={xα−1e−x/β/(α)βα}where α=(µ2/σ 2)andβ=(σ2/µ) in GeV/c;
µis the mean in GeV/c;andσis the standard deviation in GeV/c.
Case αβ µσ
20 GeV, real 1096 4.772 ×10−40.5228 0.01579
20 GeV, mixed 1199 4.360 ×10−40.5227 0.01510
62 GeV, real 1445 3.786 ×10−40.5471 0.01439
62 GeV, mixed 1743 3.139 ×10−40.5470 0.01310
130 GeV, real 1556 3.608 ×10−40.5614 0.01423
130 GeV, mixed 1917 2.927 ×10−40.5612 0.01282
200 GeV, real 1853 3.129 ×10−40.5799 0.01347
200 GeV, mixed 2373 2.443 ×10−40.5799 0.01190
044902-4

INCIDENT ENERGY DEPENDENCE OF pt. . . PHYSICAL REVIEW C 72, 044902 (2005)
200 GeV and 20% of measured correlations at 20 GeV could
be attributed to these short-range correlations. These estimates
agree with those extracted for 17-GeV Pb+Pb [16] by use of a
somewhat different method. We also estimated the contribution
of resonances and other charge-ordering effects by studying
the reduction in the correlations for same charge (negative)
particles compared with correlations for all charged particles.
This study indicated that the reduction in pt,ipt,j is 40%
at 20 GeV, 20% at 62 and 130 GeV, and 15% at 200GeV.
We do not correct pt,ipt,jfor short-range correlations or
resonance contributions.
The errors shown in all figures are statistical unless
otherwise noted. We estimate the systematic relative errors for
pt,ipt,jby using studies of the effects of pt-dependent
efficiencies (1.2%) and sensitivity to track merging and
splitting (1.4%). These values give an overall systematic
relative error of 2%. The measured correlations were lowered
approximately 3% when the fitting method rather than the
binning method was used. The reported values are sensitive to
the ptcuts for kinematic and physics reasons. Using HIJING
[29], we observe a 6% increase in correlations when the lower
ptcut is removed. Raising the upper ptcut increases the
correlations. We used 0.15 GeV/cpt2.0GeV/cfor all the
results reported in this paper. The upper ptcut was chosen to
be consistent with previous work [19,24].
Also shown in Fig. 2 are HIJING calculations for Au+Au
collisions at √sNN =20, 62, 130, and 200 GeV [29]. We
used HIJING version 1.36 with the default options, which
include jet quenching. The HIJING results were obtained by
the selection of particles with 0.15 GeV/cpt2.0GeV/c
with |η|<1.0 without further efficiency corrections. HIJING
reproduces correlations in p+pand α+αcollisions at Inter-
secting Storage Rings (ISR) energies [30], p+pcollisions
at RHIC energies, and p+¯
pcollisions at CERN p+¯
p Collider
(SppS) energies [31]. We use HIJING to provide a reference that
incorporates a superposition of nucleon-nucleon interactions.
Any differences between HIJING and the experimental results
might signal phenomena unique to nucleus-nucleus collisions.
The HIJING calculations exhibit little incident energy depen-
dence and decrease with increasing centrality. The values for
pt,ipt,jpredicted by HIJING are always smaller than the
data.
To address the observed dilution of the correlations with
centrality and to check the hypothesis that the correlations
scale as inverse multiplicity, we multiplyp t,ip t,jby the
charged-particle pseudorapidity density at a given centrality,
dN/dη. We use fully corrected values for dN/dη from
published work [32–34]. The quantity (dN/dη)p t,ipt,j 
then is insensitive to efficiency and is similar to the (efficiency-
corrected) quantity σpt [19] that STAR reported previously.
In Fig. 3 we show the quantity (dN/dη)p t,ip t,jfor
Au+Au collisions at 20, 62, 130, and 200 GeV as functions
of centrality. In this figure the errors include the quoted errors
in dN/dη. This quantity increases with incident energy at all
centralities. At each energy this measure of the correlations
increases quickly as the collisions become more central and
then saturates in central collisions. The behavior of this
quantity is similar to that of the quantity σpt previously
studied by STAR [19]. This saturation might indicate effects
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
0
5000
10000
15000
20000
25000
30000
35000
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
0
5000
10000
15000
20000
25000
30000
35000 20 GeV Au+Au
62 GeV Au+Au
130 GeV Au+Au
200 GeV Au+Au
20 GeV HIJING
62 GeV HIJING
130 GeV HIJING
200 GeV HIJING
(dN/dη)<∆pt,i∆pt,j> [(MeV/c)2]
FIG. 3. (Color online) (dN/dη)p t,ip t,jas a function of
centrality and incident energy for Au+Au collisions compared with
HIJING results.
such as the onset of thermalization [15], the onset of jet
quenching [14], the saturation of transverse flow [35] in central
collisions, or other processes.
In Fig. 3 the results of HIJING calculations for
(dN/dη)pt,ipt,j are also shown. In contrast to the
experimental results, the HIJING results show little dependence
on centrality.
To account for possible changes of pt,ipt,jthat are
due to possible changes in pt with incident energy and/or
centrality of the collision, we also study the square root of the
measured correlations scaled by pt. The resulting quantity
pt,ipt,j/ptis shown in Fig. 4 for Au+Au collisions
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
>>
t
/<<p>
t,j
p∆
t,i
p∆<
1
part
N
0 50 100 150 200 250 300 350
part
N
0 50 100 150 200 250 300 350
>> (%)
t
/<<p>
t,j
p∆
t,i
p∆<
1
20 GeV Au+Au
62 GeV Au+Au
130 GeV Au+Au
200 GeV Au+Au
CERES 17 GeV Pb+Pb
20 GeV HIJING
62 GeV HIJING
130 GeV HIJING
200 GeV HIJING
(GeV)
NN
s
10 2
10
>> (%)
t
/<<p>
t,j
p∆
t,i
p∆<
0
0.4
0.8
1.2
1.6
Au+Au
CERES Pb+Pb
0 - 5% Most Central
FIG. 4. (Color online) pt,ip t,j/pt as a function of
centrality and incident energy for Au+Au collisions compared
with HIJING results for corresponding systems. The inset shows the
excitation function for the most central bin.
044902-5

J. ADAMS et al. PHYSICAL REVIEW C 72, 044902 (2005)
at 20, 62, 130, and 200 GeV. Similar results from Pb+Pb
collisions at 17 GeV [16] are also shown in Fig. 4. These
values are consistent with our measured results for Au+Au at
20 GeV. We observe little or no dependence on the incident
energy for this quantity. The inset in Fig. 4 demonstrates the
incident energy dependence of pt,ipt,j /pt for the
0%–5% most central bin, in which the Pb+Pb results are from
Ref. [16].
In contrast to the measured correlations, HIJING predictions
for pt,ipt,j/pt vary with incident energy. HIJING
predicts a different centrality dependence as well as a notice-
able dependence on the incident energy.
In conclusion we observe clear nonzero ptcorrelations,
pt,ipt,jin Au+Au collisions from √sNN =20 to
200 GeV. The quantity (dN/dη)pt,ipt,jincreases
with beam energy. The centrality dependence of
(dN/dη)pt,ipt,j may show signs of effects such
as thermalization [15], the onset of jet suppression [14,24],
the saturation of transverse expansion in central collisions [35],
or other processes. The quantity pt,ipt,j/pt shows
little or no change with beam energy. HIJING model calculations
underpredict the measured correlations and do not predict the
observed centrality dependence.
ACKNOWLEDGMENTS
We thank the RHIC Operations Group and RCF at BNL
and the NERSC Center at Lawrence Berkeley National
Laboratory for their support. This work was supported in
part by the HENP Divisions of the Office of Science of
the U.S. Department of Energy; the U.S. National Science
Foundation; the Bundesministerium f¨
ur Bildung, Forschung
und Technologie; of Germany; IN2P3, RA, RPL, and EMN of
France; Engineering and Physical Sciences Research Council
of the United Kingdom; Fundac˜
ao de Amparo`
a Pesguisa do
Estado de S˜
ao Paulo of Brazil; the Russian Ministry of Science
and Technology; the Ministry of Education and the NNSFC
of China; IRP and GA of the Czech Republic; FOM of the
Netherlands; DAE, DST, and Council of Scientific and Indus-
trial Research of India; the Swiss National Science Foundation;
the Polish State Committee for Scientific Research; and the
STAA of Slovakia.
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