Transverse momentum and centrality dependence of dihadron correlations in Au+Au collisions at = 200 GeV: Jet-quenching and the response of partonic matter
Azimuthal angle () correlations are presented for charged hadrons from dijets for GeV/ in Au+Au collisions at = 200 GeV. With increasing , the away-side distribution evolves from a broad to a concave shape, then to a convex shape. Comparisons to data suggest that the away-side can be divided into a partially suppressed “head” region centered at , and an enhanced “shoulder” region centered at . The spectrum for the “head” region softens toward central collisions, consistent with the onset of jet quenching. The spectral slope for the “shoulder” region is independent of centrality and trigger , which offers constraints on energy transport mechanisms and suggests that the “shoulder” region contains the medium response to energetic jets.
High transverse momentum () partons are valuable probes of the high energy density matter created at the Relativistic Heavy-Ion Collider (RHIC). These partons lose a large fraction of their energy in the matter prior to forming hadrons, a phenomenon known as jet-quenching. Such energy loss is predicted to lead to strong suppression of both single- and correlated away-side dihadron yields at high Gyulassy:2003mc , consistent with experimental findings Adler:2003au ; Adler:2002tq . The exact mechanism for energy loss is not yet understood. Recent results of dihadron azimuthal angle () correlations have indicated strong modification of the away-side jet Adams:2005ph ; Adler:2005ee ; Adler:2002tq ; Adare:2006nr . For high hadron pairs, such modification is manifested by a partially suppressed away-side peak at Adler:2002tq . This has been interpreted as evidence for the fragmentation of jets that survive their passage through the medium.
For intermediate charged hadron pairs, the away-side jet was observed to peak at Adler:2005ee ; Adare:2006nr , suggesting that the energy lost by high partons is transported to lower hadrons at angles away from . The proposed mechanisms for such energy transport include medium deflection of hard Chiu:2006pu or shower partons Armesto:2004pt ,large-angle gluon radiation Vitev:2005yg ; Polosa:2006hb , Cherenkov gluon radiation Koch:2005sx , and “Mach Shock” medium excitations Casalderrey-Solana:2004qm .
In this letter we present a detailed “mapping” of the and centrality dependence of away-side jet shapes and yields. These measurements (1) allow a detailed investigation of the jet distributions centered around and , (2) provide new insight on the interplay between jet quenching and the response of the medium to the lost energy, and (3) provide new constraints for distinguishing the competing mechanisms for energy transport.
The results presented here are based on minimum-bias (MB) Au+Au and p+p datasets as well as a “photon” level-1 triggered (PT) p+p dataset Adare:2006hc collected with the PHENIX detector Adcox:2003zm at =200 GeV, during the 2004-2005 RHIC running periods. The collision vertex was required to be within 30cm of the nominal crossing point. The event centrality was determined via the method in Ref. Adcox:2003zm . A total of 840 million Au+Au events were analyzed. Charged particles were reconstructed in the two central arms of PHENIX, each covering -0.35 to 0.35 in pseudo-rapidity and in azimuth. The tracking system consists of the drift chambers and two layers of multi-wire proportional chambers with pad readout (PC1 and PC3), achieving a momentum resolution of (GeV/) Adler:2003au .
Dihadron azimuthal angle correlations are obtained by correlating “trigger” (type ) hadrons with “partner” (type ) hadrons. The MB and PT p+p datasets are used for trigger GeV/ and GeV/, respectively. To reduce background from decays and conversions, tracks are required to have a matching hit within a window in PC3. For GeV/, additional matching hit at the electromagnetic calorimeter (EMC) was required to suppress background tracks that randomly associate with the PC3 Adler:2003au . For triggers with GeV/, a dependent energy cut in the EMC and a tight matching cut at the PC3 were applied to reduce the background to % Adler:2005ad . This energy cut greatly reduces PT trigger bias effects. The PT p+p results are consistent with the MB p+p data for trigger GeV/.
where is the number of triggers, is the single particle efficiency for partners in the full azimuth and ; and are pair distributions from the same- and mixed-events, respectively. Mixed-event pairs are obtained by selecting partners from different events with similar centrality and vertex. The values include detector acceptance and reconstruction efficiency, with an uncertainty of % Adler:2005in ; Adler:2003au . The harmonic term, , reflects the elliptic flow modulation of the combinatoric pairs in Au+Au collisions Adler:2005ee . Values for and for each centrality class are measured via the reaction plane (RP) method Adler:2003kt using the Beam-Beam Counters at . The systematic errors on are dominated by the RP resolution, and are estimated to be % for central and mid-central collisions, and % for the peripheral collisions Adler:2005ee .
To fix the value of , we followed the subtraction procedure of Refs. Adler:2005ee ; Ajitanand:2005jj and assumed that has zero yield at its minimum (ZYAM). To estimate the possible over-subtraction at , we calculate values independently by fitting to a function consisting of one near-side and two symmetric away-side Gaussians. The fitting procedure is similar to that used in Adare:2006nr , except that a region around () is excluded to avoid “punch-through” jets around (see Fig.1). This fit accounts for the overlap of the near- and away-side Gaussians at , and thus gives systematically lower values than that for ZYAM. We assign the differences as one-sided systematic errors on . This over-subtraction error is only significant in central collisions and at GeV/.
The per-trigger yield distributions for and 0-20% central Au+Au collisions are compared in Fig. 1 for various combinations of trigger and partner ranges () as indicated. The data show essentially Gaussian away-side peaks centered at for all and . In contrast, the Au+Au data show substantial shape modifications dependent on and . For a fixed value of , Figs. 1(a)-(d) reveal a striking evolution from a broad, roughly flat peak to a local minimum at with side-peaks at . Interestingly, the location of the side-peaks in is roughly constant with increasing (see also Adare:2006nr ). Such independence is compatible with the away-side jet modification expected from a medium-induced “Mach Shock” Casalderrey-Solana:2004qm but disfavors models which incorporate large angle gluon radiation Vitev:2005yg ; Polosa:2006hb , Cherenkov gluon radiation Koch:2005sx or deflected jets Armesto:2004pt ; Chiu:2006pu .
For relatively high values of , Figs. 1(e)-(h) show that the away-side jet shape for Au+Au gradually becomes peaked as for , albeit suppressed. This “re-appearance” of the away-side peak seems due to a reduction of the yield centered at relative to that at , rather than a merging of the peaks centered at . This is consistent with the dominance of dijet fragmentation at large , possibly due to jets that “punch-through” the medium Renk:2006pk or those emitted tangentially to the medium’s surface Loizides:2006cs .
The evolution of the away-side jet shape with (cf. Fig. 1) suggests separate contributions from a medium-induced component centered at and a fragmentation component centered at . A model independent study of these contributions can be made by dividing the away-side jet function into equal-sized “head” (, HR) and “shoulder” (, SR) regions, as indicated in Fig. 1(c). We characterize the relative amplitude of these two regions with the ratio, ,
Since in Eq.1 cancels in the ratio, is a pure pair variable and is symmetric and : . For concave and convex shapes, one expects and , respectively.
Figure 2 summarizes the dependence of for both and central Au+Au collisions in four bins. The ratios for are always above one and increase with . This reflects the narrowing of a peaked jet shape with increasing Adler:2005ad . In contrast, the ratios for Au+Au show a non-monotonic dependence on . They evolve from for GeV/ through for GeV/ followed by for GeV/. These trends reflect the competition between medium-induced modification and jet fragmentation, and suggest that the latter dominates at GeV/. The results shown in Fig. 1 indicate that, relative to , the Au+Au yield is suppressed in the HR but is enhanced in the SR. We quantify this suppression/enhancement via , the ratio of jet yield between Au+Au and collisions over a region, W, .
Figure 3 shows as a function of for the HR and the HR+SR, respectively, in four bins. For triggers of GeV/, for HR+SR exceeds one at low , but falls and crosses one at 3.5 GeV/. A similar trend is observed for the higher triggers, but the enhancement (at low ) is smaller and the suppression (at high ) is stronger. The values in HR are lower relative to HR+SR for all . For the low triggers, the suppression sets in around GeV/, followed by a fall-off for GeV/. For higher triggers, a constant level of is observed above GeV/ similar to the suppression level of inclusive hadrons Adler:2003au . These results provide clear evidence for significant yield enhancement in the SR and suppression in the HR. The data suggest that the SR reflects the dissipative processes that redistribute the energy lost in the medium; The suppression for the HR is consistent with jet quenching. However, we note that the values for the HR are upper limit estimates for the jet fragmentation component. This is because the HR yield includes possible contributions from the tails of the SR, as well as from bremsstrahlung gluon radiations Vitev:2005yg .
To further explore the interplay between the HR and the SR, we focus on the intermediate region, GeV/, where the medium-induced component dominates the away-side yield. We characterize the inverse local slope of the partner yield in this range via a truncated mean , - 1 GeV/. is calculated from the jet yields used to make in Fig. 3. Fig. 4 shows the values for the HR, SR and a near-side region (, NR), as a function of the number of participating nucleons, . The values for NR have a weak centrality dependence. Their overall levels for are , and GeV/ for the ranges 2-3, 3-4 and 4-5 GeV/, respectively ridge . This finding is consistent with the dominance of jet fragmentation on the near-side, i.e. a harder spectrum for partner hadrons is expected for higher trigger hadrons.
A very weak centrality dependence is observed for the SR for . In this case, the values for are lower ( GeV/) and do not depend on . They are, however, larger than the values measured for inclusive charged hadrons (0.38 GeV/ shown by solid lines) Adler:2003au . The relatively sharp increase in for may reflect a significant jet fragmentation contribution in peripheral collisions. In contrast, the values for the HR show a gradual decrease with , starting close to that for the near-side jet, and approaches the value for the inclusive spectrum for .
The different patterns observed for the yields in the HR and SR suggest a different origin for these yields. The suppression of the HR yield and the softening of its spectrum are consistent with a depletion of yield due to jet quenching. The observed HR yield could be comprised of contributions from “punch-through” jets, radiated gluons and feed-in from the SR. By contrast, the enhancement of the SR yield for GeV/ suggests a remnant of the lost energy from quenched jets. However, the very weak dependence on and centrality (for ) for its peak location and mean may reflect an intrinsic property of the response of the medium to the energetic jets. These observations are inconsistent with simple deflected jet Armesto:2004pt ; Chiu:2006pu and Cherenkov gluon radiation Koch:2005sx models, since both the deflection/radiation angle and jet spectra slope would depend on the or . However, these results are consistent with expectations for “Mach Shock” in a near-ideal hydrodynamical medium Renk:2005si ; Casalderrey-Solana:2004qm , and thus they can be used to constrain medium transport properties such as speed of sound and viscosity to entropy ratio.
In conclusion, we have observed strong medium modification of away-side shapes and yields for jet-induced pairs in Au+Au collisions at =200 GeV. The detailed dependence of these results on and centrality gives strong evidence for two distinct contributions from the regions of and . The former is consistent with jet quenching. The latter exhibits and centrality independent shape and mean , possibly reflecting an intrinsic property of the medium response to energetic jets. These results provide strong constraints on competing mechanisms for the energy transport.
We thank the staff of the Collider-Accelerator and Physics Departments at BNL for their vital contributions. 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 (Sweden), U.S. CRDF for the FSU, US-Hungarian NSFOTKA- MTA, and US-Israel BSF.
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