1. Recombination for JET Shower MC: Status and Discussion Rainer Fries Texas A&M University JET NLO & MC Meeting Wayne State University, August 23, 2013 On Behalf Of Kyongchol Han Che-Ming Ko

2. Hadronization JET NLO&MC 20132 Rainer Fries Hadronization = difficult, non-perturbative problem Sometimes we can apply one of two extreme limits in which hadronization becomes simpler:  Universality at large momentum  single-particle fragmentation: fragmentation functions can be measured.  Universality at low momenta  thermalization: equation of state, can be calculated on the lattice. In between: universality broken, hadronization system-dependent.

3. Hadrons in Heavy Ion Collisions JET NLO&MC 20133 Rainer Fries Proton/pion ratio R AA Intermediate momentum region in heavy ion collisions (2-8 GeV):  No kinetic equilibrium  Multi-particle dynamics  No microscopic description of parton dynamics.

4. Why Quark Recombination? JET NLO&MC 20134 Rainer Fries Data indicates a dependence of several important observables on the number of valence quarks. Quark coalescence models very successful for hadron production at intermediate P T in HICs.  Large baryon/meson ratios  Elliptic flow scaling with quark number  QGP signature?

5. Quark Recombination Start from a distribution of quarks Instantaneous approximation: 2  1, 3  1 Finite time: recombination rate equations JET NLO&MC 20135 Rainer Fries ?

6. Recombination in Jet Showers JET NLO&MC 20136 Rainer Fries JET goal related to NSAC Performance Measures: Complete realistic calculations of jet production in a high energy density medium for comparison with experiment. (DM7)  This includes chemical composition Well-established hadronization models for vacuum shower Monte-Carlo’s  Lund string fragmentation  Cluster hadronization How to generalize to jets in a medium? Recombination: some early work on vacuum showers. Challenge: get vacuum fragmentation right. Advantage: medium effects are straight forward to implement; does well with heavy ion single particle spectra. [R. Migneron, M. E. Jones, K. E, Lassila, PLB 114, 189 (1983)] [R.C. Hwa and C.B. Yang, PRC 70, 024904 (2004); 024905 (2004)]

7. Formalism: Overview JET NLO&MC 20137 Rainer Fries Challenges:  Calculate parton showers in a controlled way; vacuum or medium modified.  Need event-by-event formalism; momentum and energy conservation in each shower are important.  Want to include space-time information. Established work flow: Here: We use parton and hadron showers from PYTHIA as a testing ground.  No space-time information. Add minimum non- perturbative effects: gluon splitting Perturbative parton shower (PYTHIA, HERWIG, JET MCs) Apply instantaneous quark recombination w/ phenomenological meson and baryon Wigner functions. Sample quarks from thermal medium in which jet is embedded. Recombine into full hadronic resonance spectrum and decay; treat remnant partons.

8. String Fragmentation Extract PYTHIA parton showers evolved to a scale Q 0. Standard PYTHIA Lund string fragmentation: JET NLO&MC 20138 Rainer Fries Lund String String Decay

9. Recombination + Remnant Strings Extract PYTHIA parton showers evolved to a scale Q 0. Standard PYTHIA Lund string fragmentation: Our approach: JET NLO&MC 20139 Rainer Fries Lund String Force gluon decay Recombine String Decay Remnant strings String Decay

10. Recombine Quarks Use instantaneous recombination model by Greco, Ko, Levai: Baryon and meson Wigner functions Here  M = 0.24 GeV,  B = 0.35 GeV JET NLO&MC 201310 Rainer Fries

11. Recombine Quarks In absence of space-time information integrate out spatial coordinates in the Wigner functions. Direct recombination produces hard spectra. Allow recombination into resonances with subsequent decay  Mesons: π, ρ, a 1, K, K *, and K 1  Baryons N, N’, Δ, and Δ’ Reconnect remnant quarks by short strings that fragment. JET NLO&MC 201311 Rainer Fries

12. Results PYTHIA 100 GeV jets: Recombination probability: JET NLO&MC 201312 Rainer Fries

13. Event-By-Event Vacuum Fragmentation JET NLO&MC 201313 Rainer Fries Reproduction of vacuum fragmentation compares favorably to PYTHIA string fragmentation. Lessons learnt:  Resonances important.  Event-by-event calculation important. [K. Han, C.M. Ko, R.J.F., arxiv:1209.1141] 100 GeV light quark jets in e + +e -

14. Adding Medium Partons Sampling thermal partons from a blastwave model (T=170 MeV, = 0.6 (0.65)). Allow recombination of thermal partons JET NLO&MC 201314 Rainer Fries Recombine Remnant strings

15. Adding Shower-Thermal Recombination Pions and protons at RHIC. Thermal-thermal added. Baryon production clearly enhanced by shower-thermal recombination. JET NLO&MC 201315 Rainer Fries

16. Baryon Enhancement Proton/pion ratio is enhanced by shower-thermal recombination. JET NLO&MC 201316 Rainer Fries

17. Baryon Enhancement Very similar picture for LHC. JET NLO&MC 201317 Rainer Fries

18. Plans for the Near Future Additional tests …  E.g. broadening variables  Similar tests done for parton shower MCs?  So far tested against PYTHIA. Next step: new shower MC + reco vs data Protocol for interface with parton shower MCs.  Role of spatial coordinates? Replace blastwave by hydro. JET NLO&MC 201318 Rainer Fries

19. Merging of Modules First step: take vacuum showers from “HT-MC” including space-time information.  Need access to a database of vacuum events.  Hadronization module assumes that full space-time information x  is available.  This will allow us to test recombination with space-time information. List of items to agree on for medium shower:  Shower MC needs to provide identifier of hydro event used.  Hadronization expects full information on space-time point x .  Space-time point = point of last splitting?  Shower medium effects restricted to T < T c.  Partons that “stop” inside QGP will be propagated to the critical hypersurface by the hadronization module. Recombination + remnant fragmentation applied to partons at T = T c and T > T c. JET NLO&MC 201319 Rainer Fries

20. Backup JET NLO&MC 201320 Rainer Fries

21. Recombination in Equilibrium JET NLO&MC 201321 Rainer Fries [He, RJF & Rapp, 1106.6006 [nucl-th]] Realistic hadronization hypersurface  :  Extract equal-time quark phase space distributions f q along  from hydro or kinetic model.  Apply RRM cell-by-cell  meson phase space distribution f M along .  Compute meson current across  a la Cooper-Frye: Result for charm-light system using AZHYDRO: t = const.