Dynamics of Hadronization: Interplay of Fragmentation and Recombination

1. Dynamics of Hadronization: Interplay of Fragmentation and Recombination Steffen A. Bass Duke University & RIKEN-BNL Research Center The baryon puzzle at RHIC Recombination + Fragmentation Model Results and Predictions • R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRL 90 202303 (2003) • R.J. Fries, C. Nonaka, B. Mueller & S.A. Bass, PRC 68 044902 (2003) Steffen A. Bass

2. The baryon 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. Species dependent saturation of elliptic flow • hyperon v2 saturates later and higher than kaon v2. • same effect observed for protons and pions. • at low pT the phenomenology seems better described in mT – m0 than pT , indicating hydro scaling, yet scaling breaks down for high pT • what drives the different pT scales for KS and Λ v2? • novel mechanism of baryon formation? Steffen A. Bass

4. Recombination+Fragmentation Model basic assumptions: • at low pt, the quarks and antiquark spectrum is thermal and they recombine into hadrons locally “at an instant”: • features of the parton spectrum are shifted to higher pt in the hadron spectrum • at high pt, the parton spectrum is given by a pQCD power law, partons suffer jet energy loss and hadrons are formed via fragmentation of quarks and gluons Steffen A. Bass

5. Recombination: Pro’s & Con’s Pro’s: • for exponential parton spectrum, recombination is more effective than fragmentation • baryons are shifted to higher pt than mesons, for same quark distribution • understand behavior of protons! Con’s: fragmenting parton: ph = z p, z<1 recombining partons: p1+p2=ph simple recombination violates entropy conservation gluons at hadronization need to be converted Steffen A. Bass

6. 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

7. 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

8. Recombination vs. Fragmentation Fragmentation… …nevercompetes with recombination for a thermal (exponential) spectrum: … but it wins out at large pT, when the spectrum is a power law ~ (pT)-b : Steffen A. Bass

9. Hadron Spectra Steffen A. Bass

10. Hadron Ratios vs. pt Steffen A. Bass

11. 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

12. 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

13. Parton Number Scaling of v2 in leading order of v2, recombination predicts: • smoking gun for recombination • measurement of partonic v2 ! Steffen A. Bass

14. Two-Particle Correlations • Recombination approach allows for two particle correlations, provided they are contained in the parton source distributions • Three distinct types are conceivable: F-F, SH-F and SS-SS • Ansatz for SS-SS: for two mesons, use product of correlated parton distributions: • Which results in a correlated two hadron yield: 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 • leading / next-to-leading particle correlations • 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

16. The End Steffen A. Bass

17. hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization transverse momentum pt ?! time Connecting the dots … jet production fragmentation jet quenching parton recombination HBT radial flow reco/SM? shattered color-glas hydrodynamic evolution Steffen A. Bass

18. 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