Two-Particle Correlations: A Resource for Studying Heavy-Ion Collision Dynamics

1. Two-particle correlations on transverse momentum: an untapped resource for studying relativistic heavy-ion collision dynamics Lanny Ray (U. Texas, Austin) and Alex Jentsch (BNL) ISMD 2019 – Sante Fe, NM, September 9-13, 2019

2. Overview – main points Correlations on 2D transverse momentum have been reported: NA49: J. Reid, Nucl. Phys. A 698, 611 (2002); Nucl. Phys. A 715, 55 (2003); Phys. Rev. C 70, 034902 (2004). CERES: Adamova et al., Nucl. Phys. A 811, 179 (2008) STAR: J. Reid, Ph.D. Thesis (UW), nucl-ex/0302001. Adams et al., J.Phys.G Nucl.Part. 34,799 (2007) Trainor, Prindle, Phys. Rev. D 93, 014031 (2016) E. Oldag, Ph.D. Thesis (UT); J.Phys.Conf.Ser. 446, 012023 (2013) However, the physics impact, so far, has been limited. We show that these correlations: 1) allow access to additional properties of the heavy-ion collisions including the degree of equilibration; fluctuations in soft- and hard QCD processes. 2) enable absolute normalization of the full, two-particle correlation. Details are in: Phys. Rev. C 94, 064902 (2016) Phys. Rev. C 99, 024911 (2019). ISMD 2019 – Ray and Jentsch

3. Introduction: Two-particle correlations Collect all pairs in this event; bin w.r.t., e.g.: pt1,pt2, h1,h2,f1,f2 Dh and/or Df Fill histograms for all same-event pairs using all the events in the centrality bin: Individual heavy-ion collisions within a centrality class Collect all pairs in this event; bin w.r.t., e.g.: pt1,pt2, h1,h2,f1,f2 Dh and/or Df Dominated by the product of single-particle distributions; includes physical correlations plus detector acceptance and tracking inefficiencies etc. ….. ISMD 2019 – Ray and Jentsch

4. Introduction: Two-particle correlations Mixed-event pairs Collect all pairs taking a particle from two events; bin w.r.t., e.g.: pt1,pt2, h1,h2,f1,f2 Dh and/or Df. Repeat for all other pairs of events. Fill histograms for all mixed-event pairs using all the events in the centrality bin, forming an uncorrelated reference: Individual heavy-ion collisions within a centrality class Product of single-particle distribution; includes only detector acceptance and tracking inefficiencies etc. ….. ISMD 2019 – Ray and Jentsch

5. f1-f2 h1-h2 Introduction: Two-particle correlations to approximately cancel acceptance and inefficiencies. Construct ratios when (pt1,pt2) range is fixed: …or when (Dh,Df) range is fixed: Au+Au 200 GeV “easily” interpreted geometrical structures: quantum interferometry (HBT) v2 – quadrupole, elliptic flow, g-interference jets and dijets, modified fragmentation No obvious structures or interpretation Phenomenology required… ISMD 2019 – Ray and Jentsch

6. yt 2 4 3 1 0.17 pt(GeV/c) 0.51 1.4 3.8 Introduction: Two-particle correlations Improve the visual aspects of (pt1,pt2) correlations via two simple changes: Dr/rme is multiplied by an analytic pre-factor function: 1) per-particle measure, and facilitates tests of binary scaling. 2) visual access to structures 3) facilitates scaling tests (e.g. binary scaling) The final quantity used here is: Au+Au 200 GeV (uses single-particle spectra) Phys. Rev. C 99, 024911 (2019). Bias removed and normalization fixed via mean-pt fluctuation measure, see: STAR, Phys. Rev. C 71, 064906 (2005); and Phys. Rev. C 94, 064902 (2016)

7. Theoretical Expectations Datamodeling of STAR preliminary correlations [Oldag (STAR), Hot Quarks, J. Phys. Conf. Ser. 446, 012023 (2013)]. HIJING: (Wang & Gyulassy) LUND color-strings plus PYTHIA; no medium effects EPOS: (K. Werner et al.) e-by-e fluct, hard-scattering, (3+1)D hydro, core+corona, UrQMD. Au+Au 200 GeV “Data” AS-CI 60-80% 40-60% 30-40% 10-20% 0-5% HIJING, 64-100% 46-64% 28-46% 9-28% 0-9% EPOS, 64-100% 46-64% 28-46% 9-28% 0-9%

8. Theoretical Expectations Au+Au 200 GeV, projected onto ytS = yt1+yt2 “Data” AS-CI 60-80% 40-60% 30-40% 10-20% 0-5% HIJING jets on, 64-100% 46-64% 28-46% 9-28% 0-9% HIJING jets off, 64-100% 46-64% 28-46% 9-28% 0-9% EPOS, 64-100% 46-64% 28-46% 9-28% 0-9%

9. Theoretical Expectations - Summary Within the fragmentation approach, jets are essential. In HIJING: peripheral to mid-central are reasonable; NN superposition is OK (?) mid- to more-central are underestimated; medium effects (?) In EPOS: peripheral are poorly described – interactions are too strong (?), more-central collisions are reasonable; strong medium interactions (?) However, it is not obvious what these successes and failures imply for the inner workings of the two approaches. Phenomenology ISMD 2019 – Ray and Jentsch

10. “freeze-out hypersurface” b=1/T ht0 1 Nucleus Nucleus Phenomenological model: Blast-Wave Schnedermann, Sollfrank, Heinz, Phys. Rev. C 48, 2462 (1993) Single-particle: Produces excellent fits to spectra data. ISMD 2019 – Ray and Jentsch

11. Ensemble of globally equilibrated events All pairs sample the same b =1/T Phenomenological model: Blast-Wave Two-particles: Particles 1 and 2 locally sample distributions of temperature and flow rapidity as before, however, these may be correlated. STAR, J. Phys. G: 34, 799 (2007). Example: collisions in Global Equilibrium cold event hot event Example: collisions in Local Equilibrium Ensemble of locally equilibrated events Can data distinguish these? cooler mean warmer mean ISMD 2019 – Ray and Jentsch

12. dsS dsD yt 2 4 3 1 0.17 pt(GeV/c) 0.51 1.4 3.8 Phenomenological model: Blast-Wave Two-particles: Integrate S(x1,p1)S(x2,p2) over (b1,b2) and (ht01,ht02): Au+Au 200 GeV Convolution integral Fit parameters: ISMD 2019 – Ray and Jentsch

13. Phenomenological models: Blast-Wave Smooth, monotonic trend for D(1/q)cov (best determined parameter), consistent disfavored Global thermal equilibration, in the BW, can be falsified for pt = 0.15 to ~6 GeV/c. However, fits with upper pt reduced 1 to 2 GeV/c do not falsify global equil. hypothesis. ISMD 2019 – Ray and Jentsch

14. dsS dsD Phenomenological model: Fragmentation Two component fragmentation (TCF): soft+hard production* Soft production – single particle: Soft production – two particles: J. Phys. G: 34, 799 (2007) Correlations arise when flux-tubes emit multiple particles, or when the flux-tubes in an event tend to be more, or less, energetic than the average. Correl. fit parameters: D(1/qcs)Vol, D(1/qcs)cov *Kharzeev, Nardi, Phys. Lett. B 507, 121 (2001) Color flux-tube (bcs1,bcs2)

15. p p Phenomenological model: Fragmentation Hard production (minijets) – single particle: From: Trainor, Phys. Rev. C 80, 044901 (2009) Fit: shape of rjet, and pQCD low-energy cut-off and slope (nQCD), to spectra data. Hard production (minijets) – two particles: Fit correlations with: shard2 – variance of fluctuating semi-hard multiplicity “Jet correlation” – covarianceof g(Q1,Q2)

16. Phenomenological model: Fragmentation Au+Au 200 GeV Combine “soft” and “hard” contributions and fit “data”: Correl. fit parameters: D(1/qcs)Vol, D(1/qcs)cov shard2 “Jet correlation” BW and TCF models produce similar quality fits. ISMD 2019 – Ray and Jentsch

17. Correlation sources in TCF: color-strings -> saddle-shape shard2 -> saddle-shape Jet correlation -> cov[g(Q1,Q2)] -> peak near (yt1,yt2) = (3,3) Phenomenological model: Fragmentation Jet correlation Saddle shape ISMD 2019 – Ray and Jentsch

18. possibly indicating medium modified fragmentation. Phenomenological model: Fragmentation Fit Fit Fit Jet correlation Poisson Power-law fits to the centrality trends of TCF model parameters ISMD 2019 – Ray and Jentsch

19. Conclusions – Theoretical Predictions The BW and TCF models were also fitted to the EPOS and HIJING predictions, respectively, to get an idea of what these theories might be lacking. BW fits to EPOS EPOS may be too hot in general and too equilibrated in peripheral collisions. TCF fits to HIJING, jets-on Color-string fluctuations are, in general, about ½ of what’s needed; Jet correlations are OK for peripheral, but about ½ too small in more-central. ISMD 2019 – Ray and Jentsch

20. Conclusions – “Data” Correlations on (yt1,yt2) enable access to additional properties of heavy-ion collisions, within a dynamical framework, e.g. equilibration, soft/hard fluctuations. Fluctuating BW and TCF models fit these preliminary correlations fairly well. Global equilibration, in a BW framework, is falsified for pt < 6 GeV/c. These results, plus those from angular correlations [(STAR) Phys. Rev. C 86, 064902 (2012)], imply: more-peripheral collisions ~ S(N+N)collisions (quadrupole?), mid- to most-central collisions require significant medium effects. Watch for 132 new (yt,yt) correlation plots from STAR next year! Thank you! ISMD 2019 – Ray and Jentsch

21. Backup

22. yt 2 4 3 1 0.17 pt(GeV/c) 0.51 1.4 3.8 Introduction: Two-particle correlations Final correlations are displayed with respect to transverse rapidity: to better display the structures at lower and higher momentum; natural coordinate for studying fragmentation. Dr/rme is multiplied by an analytic pre-factor which better displays the correlation structures, gives a per-particle measure, and facilitates tests of binary scaling. The final quantity used here is: Au+Au 200 GeV ISMD 2019 – Ray and Jentsch

23. ? Df Dh Introduction: Two-particle correlations Angular correlations as functions of (pt1,pt2) bins, in principle, fully constrain the two-particle densities. However, the absolute normalization, essentially the constant offset, is undetermined, giving rise to ad hoc normalizations based on, e.g. total number of pairs, per-event averages, ZYAM… Also, it can be shown that (pt1,pt2) correlations as functions of (Dh,Df) are sensitive to different aspects of the heavy-ion collisions, e.g. global vs local-equilibration, fluctuations in hard-scattering vs average hard-scattering yields. Measurement and interpretation of (pt1,pt2) correlations allows absolute normalization of the full, two-particle correlations and opens access to the study of new physical processes in the collision evolution. This new correlation quantity can be derived [Phys. Rev. C 94, 064902 (2016)] from measures of mean-pt fluctuations. In simplest form this is given by

24. f1-f2 h1-h2 Introduction: Two-particle correlations ? However, absolute normalization is unknown, but can be determined via mean-pt fluctuations*. In simplest form, Allows access to new physical properties of the collision system, e.g.: global versus local-equilibration hard-scattering fluctuations versus average yields * STAR, Phys. Rev. C 71, 064906 (2005) ISMD 2019 – Ray and Jentsch

25. yt 2 4 3 1 0.17 pt(GeV/c) 0.51 1.4 3.8 Full BW No flow; include dT No fluctuations; include flow Phenomenological models: Blast-Wave Fits to STAR data in: PRL 91, 172302 (2003). See Phys. Rev. C 99, 024911(2019)

26. yt 2 4 3 1 0.17 pt(GeV/c) 0.51 1.4 3.8 Phenomenological models: TCF Fits to STAR data in: PRL 91, 172302 (2003). fitted nominal rjet~ Trainor, Phys. Rev. C 80, 044901 (2009) See Phys. Rev. C 99, 024911(2019)

27. Phenomenological models: Blast-Wave For two-particles: Convolute the product of BW densities over (b1,b2) and (ht01,ht02): Au+Au 200 GeV

28. Correlation sources in TCF: color-strings -> saddle-shape shard2 -> saddle-shape Jet correlation -> cov[g(Q1,Q2)] -> peak near (yt1,yt2) = (3,3) Phenomenological model: TCF Jet correlation ISMD 2019 – Ray and Jentsch

29. Phenomenological models: EPOS & HIJING The BW and TCF models were also fitted to the EPOS and HIJING predictions, respectively, to get an idea of what these theories might be lacking. BW fits to EPOS: TEPOS ~ 1.3 Tdata; centrality trend is similar sb,EPOS ~ 0.6 to 0.8 sb,data vt are about the same D(1/q)cov,EPOS ~ D(1/q)cov,data TCF fits to HIJING, jets-on: D(1/q)cs,cov,HIJING ~ (1/2)D(1/q)cs,cov,data Jet-related spectra parameters are ~constant with centrality and consistent with data near mid-centrality shard,HIJING2 << shard,data2 The jet-energy-correlation for HIJING and data: are similar for peripheral, ~1/2 that for the data in more-central. ISMD 2019 – Sante Fe, NM, September 9-13, 2019