Future Measurements to Test Recombination Rudolph C. Hwa University of Oregon Workshop on Future Prospects in QCD at High Energy BNL, July 20, 2006

Outline Introduction Recombination model Shower partons 1 xF pT Introduction Recombination model Shower partons Hadron production at low pT Hadron production at large  Hadron production at large pT Summary

I. Introduction What are the properties of recombination that we want to know and test? probability of finding partons at probability for recombination to form a pion at p What partons? Same partons? What is that probability?

Usual strong evidences for recombination number of constituent quarks scaling partons CQ What about gluons? of order 1 or higher impossible by fragmentation Useful to remember in future measurements

Quantitative questions about recombination eventually always become questions about the nature of partons that are to recombine. Two-particle correlation Where are the partons from? Are they independent? Are they from 1 jet, 2 jets, or thermal medium?

Multiparton distributions in terms of the thermal and shower parton distributions

II. Recombination Model Recombination depends on the wave function of the hadron. Constituent quark model describes the bound-state problem of a static hadron. What good is it to help us to know about the distribution of partons in a hadron (proton)? Valons Valons are to the scattering problem what CQs are to the bound-state problem.

Deep inelastic scattering Valon model p U D valons Hwa, PRD 22, 759 (1981) Fq We need a model to relate to the wave function of the proton Fq

Basic assumptions valon distribution is independent of probe parton distribution in a valon is independent of the host hadron U p U D valence quark distr in proton valon distr in proton, independent of Q valance quark distribution in valon, whether in proton or in pion

Hwa & CB Yang, PRC66(2002) using CTEQ4LQ

Recombination function It is the time-reversed process of the valon distributions U U D recombination function U D valon distribution proton pion From  initiated Drell-Yan process valon model

In a pp or AA collision process U + Soft gluon radiation --- color mutation without significant change in momentum D _ Is entropy reduced in recombination? The number of degrees of freedom seems to be reduced. The number of degrees of freedom is not reduced.

How do gluons hadronize? In a proton the parton distributions are x2u(x) x2g(x) Gluons carry ~1/2 momentum of proton but cannot hadronize directly. Gluon conversion to q-qbar x [log] Sea quark dist. Fq ~ c (1-x)7 Saturated sea quark dist. F’q ~ c’ (1-x)7 Recombination of with saturated sea gives pion distribution in agreement with data.

III. Shower Partons from Fragmentation Functions The black box of fragmentation p q A QCD process from quark to pion, not calculable in pQCD z 1 Momentum fraction z < 1

Description of fragmentation by recombination hard parton fragmentation shower partons recombination meson known from data (e+e-, p, … ) can be determined

Meson fragmentation function S(xi) Baryon fragmentation function and can be calculated in the RM

Has never been done before in the 30 years of studying FF. Hwa & CB Yang, PRC 73, 064904 (2006) Has never been done before in the 30 years of studying FF. This is done in the RM with gluon conversion shower partons  valons  hadrons.

IV. Hadron production at low pT First studied in pp collision. Parton distributions at low Q2 p x H(x) Hwa, PRD (1980) .

Hadronic collisions Hwa & CB Yang, PRC 66, 025205 (2002) h + p  h’ +X FNAL PL=100 GeV/c (1982) h h’ p    K+  + K + _ Suggested future measurement Better data at higher energy for p  , K, p, Y

Leading and non-leading D production Leading (same valence quark) non-leading (sea quark) Asymmetry Hwa, PRD 51, 85 (1995) Suggested future measurement:

pA collisions h bears the effect of momentum degradation --- “baryon stopping”. NA49 has good data, but never published. (no target fragmentation, only projectile fragmentation) Hwa & CB Yang, PRC 65, 034905 (2002) Shape depends on degradation. Normalization not adjustable. Suggested future measurement: Measure Need to know well the momentum degradation effect. for all x at higher energy

Transfragmentation Region (TFR) Theoretically, can hadrons be produced at xF > 1? (TFR) It seems to violate momentum conservation, pL > √s/2. In pB collision the partons that recombine must satisfy p B But in AB collision the partons can come from different nucleons B A In the recombination model the produced p and  can have smooth distributions across the xF = 1 boundary.

proton-to-pion ratio is very large. : momentum degradation factor proton pion proton-to-pion ratio is very large. Regeneration of soft parton has not been considered. Particles at xF>1 can be produced only by recombination. Hwa & Yang, PRC 73,044913 (2006) Suggested future measurement Determine the xF distribution in the TFR

BRAHMS data show that in d+Au collisions there is suppression at larger . BRAHMS, PRL 93, 242303 (2004) V. Large  Hwa, Yang, Fries, PRC 71, 024902 (2005). No change in physics from =0 to 3.2 In the RM the soft parton density decreases, as  is increased (faster for more central coll). Suggested future measurement for  and p

AuAu collisions BRAHMS, nucl-ex/0602018

xF = 0.9 xF = 1.0 xF = 0.8 TFR ? TT TS TTT

pT distribution fitted well by recombination of thermal partons Hwa & Yang (2006) pT distribution fitted well by recombination of thermal partons No jet => no associated particles Suggested future measurement Focus on xF>1 region. Determine p/ ratio. Look for associated particles

VI. Hadron production at large pT, small pL A. Cronin Effect Cronin et al, Phys.Rev.D (1975) for h= both  and p This is an exp’tal phenomenon. Not synonymous to initial-state kT broadening. In the RM we have shown that final-state recombination alone (without initial-state broadening) is enough to account for CE. We obtained it for both  and p -- impossible by fragmentation. Hwa & Yang, PRL 93, 082302 (2004); PRC 70, 037901 (2004). Suggested future measurement Measure and ratios in d+Au collisions at all , both backward and forward.

Backward-forward Asymmetry If hadrons at high pT are due to initial transverse broadening of parton, then backward has no broadening forward has more transverse broadening Expects more forward particles at high pT than backward particles RM has B/F>1, since dN/d of soft partons decrease as  increases. Suggested future measurement Measure p and  separately at larger range of , and for different centralities.

STAR (F.Wang, Hard Probes 06) is larger than Au d associated yield in this case x=0.7 x=0.05 Correlation shapes are the same, yields differ by x2. associated yield in that case Degrading of the d valence q? Soft partons -- less in forward, more in backward RM => less particles produced forward, more backward

B. p/ Ratio Success of the recombination model All in recombination/ coalescence model Measure the ratio to higher pT If it disagrees with prediction, it is not a breakdown of the RM. On the contrary the RM can be used to learn about the distributions of partons that recombine.

C. Strange particles 6 4 2 Hwa & CB Yang, nucl-th/0602024 Data from STAR nucl-ex/0601042 40% lower 30% higher This is not a breakdown of the RM. We have not taken into account the different hyperon channels in competition for the s quark in the shower.

 production 130 GeV  production small more suppressed

We need to do more work to understand the upbending of . We have assumed RFs for  &  that may have to be modified. It is significant to note that thermal partons can account for the ratio up to pT=4 GeV/c. QGP: s quarks enhanced & are thermalized.

If  and  are produced mainly by the recombination of thermal s quarks, then no jets are involved. Select events with  or  in the 3<pT<5 region, and treat them as trigger particles. Look for associated particles in the 1<pT<3 region. Predict: no associated particles giving rise to peaks in , near-side or away-side. Suggested future measurement Verify or falsify that prediction

D. Jet Correlations 1. Correlation of partons in jets is negative but not directly measurable D. Jet Correlations 2. Correlation of pions in jets Two-particle distribution k q3 q1 q4 q2 Hwa & Tan, PRC 72, 024908 (2005) This can be measured.

Trigger-normalized fragmentation function 3. D(zT) Trigger-normalized momentum fraction X.-N. Wang, Phys. Lett. B 595, 165 (2004) J. Adams et al., nucl-ex/0604018 STAR claims universal behavior in D(zT) Focus on this region violation of universal behavior due to medium effect ---- thermal-shower recombination fragmentation

Suggested future measurement Study zT ~ 0.5 with pT(trigger) ~ 8-10 GeV/c pT(assoc) ~ 4-5 GeV/c Measure p/ ratio of associated particles. My guess: R(p/) >> 0.1 if so, it can only be explained by recombination. Do this for both near and away sides.

Conical Flow vs Deflected Jets 4. Three-particle correlation Conical Flow vs Deflected Jets Medium away near deflected jets mach cone di-jets π Ulery’s talk at Hard Probes 06

Au+Au Central 0-12% Triggered Signal Strengths Au+Au Central 0-12% Triggered Δ1 Δ2 d+Au Δ1 Δ2 Evaluate signals by calculating average signals in the boxes. Near Side, Away Side, Cone, and Deflected.

More studies are needed. What is the multiplicity distribution (above background) on the away side? If n=2 is much lower than n=1 events (on away side), then the Mach-cone type of events is not the dominant feature on the away side. What is the p/ ratio (above background) on the away side? Evolution with higher trigger momentum should settle the question whether cone events are realistic. Whatever the mechanism is, hadronization would be by recombination for pT<6 GeV/c.

5. Using Factorial Moments to suppress statistical 5. Using Factorial Moments to suppress statistical background event by event. Factorial moment for 1 event Normalized factorial moment Chiu & Hwa, nucl-th/0605054 Event averaged NFM (a) background only (b) bg + 1jet (c) bg + 2jets Try it out, but it is not a way to test recombination.

VII. Two-jet Recombination  and p production at high pT at LHC New feature at LHC: density of hard partons is high. High pT jets may be so dense that neighboring jet cones may overlap. If so, then the shower partons in two nearby jets may recombine. p 2 hard partons  1 shower parton from each

Proton-to-pion ratio at LHC  -- probability of overlap of 2 jet cones If (pT)~pT-7, then we get single jet Hwa & Yang, PRL (to appear), nucl-th/0603053

That is very different from a super-high pT jet. A jet at 30-40 GeV/c would have lots of observable associated particles. GeV/c But they are part of the background of an ocean of hadrons from other jets. The particle detected has some associated partners. There should be no observable jet structure distinguishable from the background.

We predict for 10<pT<20 Gev/c at LHC Large p/ ratio NO associated particles above the background Suggested future measurement Verify or falsify these two predictions

Summary In general, all hadrons produced with pT<6 GeV/c are by recombination. Specifically, many measurements have been suggested. Good signatures: large Rp/ in some regions no particles associated with high pT trigger. After recombination is firmly established, the hadron spectra can be used to probe the distributions of partons that recombine.