Production of Strange Particles at Intermediate p T

Production of Strange Particles at Intermediate p. T at RHIC Rudolph C. Hwa University of Oregon Strangeness in Collisions BNL/RIKEN Workshop February 2006

Work done in collaboration with Chunbin Yang Central China Normal University Wuhan, China

Outline • What’s interesting about the problem • Quick review of recombination • New results on shower partons • Production of by recombination • Implications of the results

Preamble s quarks are enhanced in bulk medium --- low p. T. Strange particles are suppressed in fragmentation functions --- high p. T. At intermediate p. T strange particle production is sensitive to both properties. We find features not present in the non-strange sector, some quite unusual. That’s why it is interesting.

with q w/o q meson baryon # of or or 1 2 1 3 1 0 2 0 There is competition among various channels Formation depends on the densities of all species.

Recombination/Coalescence (Re. Co) Many groups have worked on Recombination/Coalescence. on strangeness no p. T dependence Bialas “linear model” [PLB 442, 449 (98)] Biro et al. (ALCOR) “nonlinear model” [95, 97, 00] Hwa & Yang --- parton model [PRC 66, 064903(02)] Greco, Ko, Levai, PRL 90, 202302 (03); PRC 68, 034904 (03). Fries, Muller, Nonaka, Bass, PRL 90, 202302 (03); PRC 68, 044902 (03). Das, Hwa, PLB 68, 459 (77); Hwa PRD 22, 1593(80). Hwa, Yang, PRC 67, 034902 (03). in the following

A quick review of recombination One-dimensional description of invariant distribution of meson Partons and meson are all collinear. invariant distribution non-invariant wave function in terms of constituents (valons)

Meson wave function Pion: (from ) a=b=0 u 1 Kaon: (from ) a=1, b=2 1 phi: (from phi being a loosely bound state of )

Two-quark distribution thermal suppression factor 0. 07 shower hard scattering in Au. Au: pdf, shadowing, a+b->i+i’(LO) SPD: i->q, s

Logical connections and experimental relevance Fragmentation functions into , K theoretical output Shower parton distributions Parton recombination experimental input Fragmentation functions into p, in agreement with data p. QCD Heavy-ion collisions experimental input Hard parton scattering Soft partons Shower partons in heavy-ion collisions Parton recombination medium effect on jets compare with data p. T distributions

Shower partons Fragmentation functions into , K experimental input theoretical output Parton recombination The shower partons are so important in heavy-ion collisions to account for the medium effect on jets, we review the essence here, and add some new findings. Shower parton distributions

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

Shower parton distributions u d s valence u sea d s g 5 SPDs are determined from 5 FFs. LL KNS L GG L Ls G Gs R RK D Sea D V D G DKSea DK G

Shower Parton Distributions Suppressed Hwa & CB Yang, PRC 70, 024904 (04)

Shower partons Fragmentation functions into , K experimental input Fragmentation functions into p, in agreement with data theoretical output Parton recombination Shower parton distributions The inter-relationships between meson FFs and baryon FFs have never been explored before. p. QCD has focused on the evolution of FFs with Q 2. We study the hadronization processes into M and B.

Gluon pion Using the same G(xi) we can calculate the FF to proton Gluon proton That takes care of the momentum constraint of the 3 quarks. But there must be also an antiproton in the gluon jet.

Joint p-pbar fragmentation function Similarly, for FF into .

Gluon fragmentation function into proton No adjustable parameters Hwa & CB Yang, nucl-th/0601033

Fragmentation function of gluon into also no adjustable parameters Hwa & CB Yang, nucl-th/0601033

Logical connections and experimental relevance Fragmentation functions into , K theoretical output Shower parton distributions Parton recombination experimental input Fragmentation functions into p, in agreement with data p. QCD Heavy-ion collisions experimental input Hard parton scattering Soft partons Shower partons in heavy-ion collisions Parton recombination medium effect on jets compare with data p. T distributions

Central Au+Au collisions production Cq = 23. 2 Ge. V-1, Tq=0. 317 Ge. V, from Cs = 15. 5 Ge. V-1, Ts=0. 323 Ge. V to fit K 0 (comments later) If i=u, d, g, …, Sis is small. If i=s, sbar, fi(k) is small.

mostly Ts. Sq Data from STAR nucl-ex/0601042 Lines from Hwa & CB Yang, nucl-th/0602024

production smaller very small i=q: Sqq can be (a) sea, or (b) valence u uval usea K K ?

sea only Data from STAR nucl-ex/0601042 valence also Hwa & CB Yang, nucl-th/0602024

Ratio R /K Having determined their p. T distributions, we can take their ratio. 40% lower 30% higher 2 4 6

production small Ts = 0. 382 Ge. V Shower partons make negligible contribution Recombination function g = 0. 3 Hwa & CB Yang, nucl-th/0602024 STAR, Phys. Lett. B 612, 181(2005) Suppression of formation in the presence of light quark medium

production Ts = 0. 382 Ge. V as before for even more suppressed Shape of p. T distribution well reproduced. 130 Ge. V Supports the finding that no other component is important besides g = 0. 008 Recombination of sss in the presence of u, d, … is highly suppressed. STAR, PRL 92, 182301 (2004); PHENIX also (05)

• What cannot be changed. i a Hard parton distributions b Shower parton distributions Nonstrange soft parton distribution • What can be adjusted. Strange soft parton distribution , , important for p. T > 4 Gev/c important for p. T < 4 Gev/c , suppressed throughout , dominant throughout

The dominant term is made up from Can the parton momentum be extrapolated to from 1 to 4 Ge. V/c? We need data on and up to 8 Ge. V/c. Bending over of RB/M is a sign of the contribution of the TS component. We expect R not to bend.

A prediction that can be checked now! Since shower partons make insignificant contribution to production for p. T<8 Ge. V/c, no jets are involved. Select events with or in the 3<p. T<6 region, and treat them as trigger particles. Predict: no associated particles giving rise to peaks in , near-side or away-side. Thermal partons are uncorrelated, so all associated particles are in the background. If there are no peaks, there is no need to make background subtraction.

Associated particle distribution (PHENIX)

(1/Ntrig) d. N/d( Signal Au+Au top 5% charged hadrons background trigger (p. T>3 Ge. V/c) in Au+Au ?

Normalization factors in the recombination functions g = 0. 3, g = 0. 008 The rate of recombination is suppressed by the medium environment of light quarks.

Thermal partons , p Cq = 23. 2 Ge. V-1, Tq = 0. 317 Ge. V K, Cs = 15. 5 Ge. V-1, Ts = 0. 323 Ge. V enhanced, but still low compared to q , Cs = 15. 5 Ge. V-1, ~ Tq (2%) Ts = 0. 382 Ge. V ~18% higher Can it be because and hadronize earlier before s & s become too diffuse by expansion?

Conclusion • K, well described by thermal-thermal, and thermal-shower recombination. But R /K is not well reproduced. Need some fine-tuning. • , are due mainly to Ts. Ts, Ts. Ts recombination. Rate of recombination is suppressed due to light quark environment. Inverse slope is higher. • s quark shower partons have no effect in the production of , for p. T<8 Ge. V/c. Jets are not involved. No peaks in associated particle distribution.