Hadronization @ RHIC: Interplay of Fragmentation and Recombination

1. Hadronization @ RHIC: Interplay of Fragmentation and Recombination Steffen A. Bass Duke University & RIKEN-BNL Research Center The Protons Puzzle at RHIC - the demise of pQCD? Recombination + Fragmentation Model Results and Predictions • R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 in print Steffen A. Bass

2. The proton puzzle @ RHIC • where does the large proton over pion ratio at high pt come from? • why do protons not exhibit the same suppression as pions? • fragmentation yields Np/Nπ<<1 • fragmentation starts with a single fast parton: energy loss affects pions and protons in the same way! ratio of KKP fragmentation functions for p and π from u quarks Steffen A. Bass

3. Recombination+Fragmentation Model basic assumptions: • at low pt, quarks and antiquarks recombine into hadrons locally “at an instant”: • hadron momentum P is much larger than average momentum Δp2 of the internal quark wave function of the hadron; • features of the parton spectrum are shifted to higher pt in the hadron spectrum • parton spectrum has thermal part (quarks) and a power law tail (quarks and gluons) from pQCD. Steffen A. Bass

4. Recombination: new life for an old idea High Energy Physics Phenomenology: • K.P. Das & R.C. Hwa, Phys. Lett. B68, 459 (1977) Quark-Antiquark Recombination in the Fragmentation Region • description of leading particle effect • T. Ochiai, Prog. Theo. Phys. 75, 1184 (1986) • E. Braaten, Y. Jia & T. Mehen, Phys. Rev. Lett. 89, 122002 (2002) • R. Rapp & E.V. Shuryak, Phys. Rev. D67, 074036 (2003) Heavy-Ion Phenomenology: • T. S. Biro, P. Levai & J. Zimanyi, Phys. Lett. B347, 6 (1995) ALCOR: a dynamical model for hadronization • yields and ratios via counting of constituent quarks • R.C. Hwa & C.B. Yang, Phys. Rev. C66, 025205 (2002) • R. Fries, B. Mueller, C. Nonaka & S.A. Bass, Phys. Rev. Lett. 90 • V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett. 90 Anisotropic flow: • S. Voloshin, QM2002, nucl-ex/020014 • Z.W. Lin & C.M. Ko, Phys. Rev. Lett 89, 202302 (2002) • D. Molnar & S. Voloshin, nucl-th/0302014 Steffen A. Bass

5. pt range of parton recombination • quark recombination (coalescence) may dominate for all pt < p0 . Combinatorical models (ALCOR, etc.) work well for total particle yields at SPS and RHIC • low pt is not calculable, but calculation at moderate pt (few GeV) may be possible using hadron light-cone formalism • transition from dense medium to dilute medium appears very rapid for fast partons (Δt=Δx/γ), validating sudden approximation • focus on “high” pt evades problems of energy and entropy conservation in recombination: E = (p2+m2)1/2 p Steffen A. Bass

6. Recombination: nonrelativistic formalism use thermal quark spectrum given by: w(p) = exp(-p/T) for a Gaussian meson wave function with momentum width ΛM, the meson spectrum is obtained as: similarly for baryons: Steffen A. Bass

7. Elliptic Flow anisotropic or “elliptic” flow is sensitive to initial geometry low pt domain: high pt domain: more flow in collision plane than perpendicular to it less absorption in collision plane than perpendicular to it total elliptic flow is the sum of both contributions: r(pt): relative weight of the fragmentation contribution in spectra Steffen A. Bass

8. Parton Number Scaling of Elliptic Flow in the recombination regime, meson and baryon v2 can be obtained from the parton v2 in the following way: • neglecting quadratic and cubic terms, one finds a simple scaling law: Steffen A. Bass

9. Input and Model Parameters Input for the model is the momentum distributions of constituent quarks and anti-quarks at the time of hadronization • the quark distribution is assumed to have a low pt thermalcomponent and a high pt pQCD mini-jet component • the thermal component is parameterized as: with a flavor dependent fugacity ga, temperature T, rapidity width Δ and transverse distribution f(ρ,ф) • the pQCD component is parameterized as: with parameters C, B and β taken from a lo pQCD calculation Steffen A. Bass

10. Hadron Spectra Steffen A. Bass

11. Hadron Ratios vs. pt Steffen A. Bass

12. Flavor Dependence of high-pt Suppression R+F model describes different RAA behavior of protons and pions in the fragmentation region all hadron flavors exhibit jet-quenching Steffen A. Bass

13. Parton Number Scaling of v2 in leading order of v2, recombination predicts: P. Soerensen, UCLA & STAR @ SQM2003 • smoking gun for recombination • measurement of partonic v2 ! Steffen A. Bass

14. Elliptic Flow: Recombination vs. Fragmentation • high pt: v2 for all hadrons merge, since v2 from energy-loss is flavor blind • quark number scaling breaks down in the fragmentation domain Steffen A. Bass

15. Summary & Outlook The Recombination + Fragmentation Model: • provides a natural solution to the baryon puzzle at RHIC • describes the intermediate and high pt range of • hadron ratios & spectra • jet-quenching phenomena • elliptic flow • provides a microscopic basis for the Statistical Model issues to be addressed in the future: • entropy production • treatment of gluons • realistic space-time dynamics of parton source • need improved data of identified hadrons at high pt Steffen A. Bass