1. Steffen A. BassDynamics of Hadronization #1 Steffen A. Bass Duke University & RIKEN-BNL Research Center The baryon puzzle at RHIC Recombination + Fragmentation Model Results and Predictions Dynamics of Hadronization: Interplay of Fragmentation and Recombination  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)

2. Steffen A. BassDynamics of Hadronization #2 The baryon puzzle @ RHIC where does the large proton over pion ratio at high p t come from? why do protons not exhibit the same suppression as pions?  fragmentation yields N p /N π <<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

3. Steffen A. BassDynamics of Hadronization #3 Species dependent saturation of elliptic flow hyperon v 2 saturates later and higher than kaon v 2. same effect observed for protons and pions. at low p T the phenomenology seems better described in m T – m 0 than p T, indicating hydro scaling, yet scaling breaks down for high p T what drives the different p T scales for K S and Λ v 2 ?  novel mechanism of baryon formation?

4. Steffen A. BassDynamics of Hadronization #4 Recombination+Fragmentation Model basic assumptions: at low p t, 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 p t in the hadron spectrum at high p t, 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

5. Steffen A. BassDynamics of Hadronization #5 Recombination: Pro’s & Con’s Pro’s: for exponential parton spectrum, recombination is more effective than fragmentation baryons are shifted to higher p t than mesons, for same quark distribution  understand behavior of protons! Con’s: simple recombination violates entropy conservation gluons at hadronization need to be converted recombining partons: p 1 +p 2 =p h fragmenting parton: p h = z p, z<1

6. Steffen A. BassDynamics of Hadronization #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

7. Steffen A. BassDynamics of Hadronization #7 Recombination: nonrelativistic formalism use thermal quark spectrum given by: w(p) = exp(-p/T) for a Gaussian meson wave function with momentum width Λ M, the meson spectrum is obtained as: similarly for baryons:

8. Steffen A. BassDynamics of Hadronization #8 Recombination vs. Fragmentation Fragmentation… … but it wins out at large p T, when the spectrum is a power law ~ (p T ) -b : … never competes with recombination for a thermal (exponential) spectrum:

9. Steffen A. BassDynamics of Hadronization #9 Hadron Spectra

10. Steffen A. BassDynamics of Hadronization #10 Hadron Ratios vs. p t

11. Steffen A. BassDynamics of Hadronization #11 Flavor Dependence of high-p t Suppression R+F model describes different R AA behavior of protons and pions in the fragmentation region all hadron flavors exhibit jet-quenching

12. Steffen A. BassDynamics of Hadronization #12 anisotropic or “elliptic” flow is sensitive to initial geometry Elliptic Flow more flow in collision plane than perpendicular to it less absorption in collision plane than perpendicular to it low p t domain:high p t domain: total elliptic flow is the sum of both contributions: r(p t ): relative weight of the fragmentation contribution in spectra

13. Steffen A. BassDynamics of Hadronization #13 Parton Number Scaling of v 2  smoking gun for recombination  measurement of partonic v 2 ! in leading order of v 2, recombination predicts:

14. Steffen A. BassDynamics of Hadronization #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:

15. Steffen A. BassDynamics of Hadronization #15 Summary & Outlook The Recombination + Fragmentation Model: provides a natural solution to the baryon puzzle at RHIC describes the intermediate and high p t 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 p t

16. Steffen A. BassDynamics of Hadronization #16 The End

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

18. Steffen A. BassDynamics of Hadronization #18 Parton Number Scaling of Elliptic Flow in the recombination regime, meson and baryon v 2 can be obtained from the parton v 2 in the following way:  neglecting quadratic and cubic terms, one finds a simple scaling law: