Quark Recombination in Heavy Ion Collisions Rainer Fries Texas A&M University & RIKEN BNL Workshop on RHIC Paradigms UT Austin, April 14, 2010

Austin: RHIC Paradigms Overview Introduction Recombination Experimental evidence Recombination Models Connection with Hydro and pQCD Summary Rainer Fries Austin: RHIC Paradigms

ReCo and the Rest of the Pack RHIC Paradigms Where does it fit in? pQCD Minijets Weakly interacting partons Equilibrium sQGP Perfect liquid Recombination Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms How Does QGP Hadronize? Recombination/coalescence of quarks: a simple hadronization model. Coalescence of valence quarks into mesons and baryons Quarks are dressed (constituent quarks), gluons have been split into quark-antiquark pairs. Developed as the “dense” limit of hadronization, as opposed to single parton fragmentation: phase space filled with partons at a critical density Not unlike cluster hadronization models (e.g. HERWIG) Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms How Does QGP Hadronize? Can it be that simple? We learn from kindergarten that Q C D is difficult. But quark recombination seems to work in certain situations: Leading particle effect [Hwa and Das, (1977); many others] Heavy quarks [Rapp, Shuryak (2003)] Close to thermal equilibrium (?) quantum: Is hadronization “probabilistic” or do we need to worry about interference? dynamics: What about the non-abelian nature and gauge invariance? Strong coupling? chromo: How are color singlets formed? Rainer Fries Austin: RHIC Paradigms

Leading Particle Effect Recombination at very forward rapidity No hard scale Recombine beam remanants/spectators. Leading Particle Effect (forward rapidities) D+/D asymmetries clearly not described by pQCD + fragmentation. Explained by recombination with beam remnants [K.P. Das & R.C. Hwa: Phys. Lett. B68, 459 (1977): Quark-Antiquark Recombination in the Fragmentation Region] E791  beam E791 - beam: hard cc production; recombine c with d valence quark from - > reco of c with d [Braaten, Jia & Mehen] Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms What Is it Good For? A solid case for quark recombination could open a direct window to parton dynamics. Hydrodynamics : very useful but limited information about microscopic dynamics. Original claim from recombination: quark number scaling of v2 = hint of collectivity on the parton level. In equilibrated bulk matter: Will present evidence that recombination can be used at low momenta (in equilibrated phase). But even if recombination is the correct microscopic model: hydro + EOS will take care of all observables, no additional dynamics from recombination. Any interesting recombination physics is off-equilibrium! Rainer Fries Austin: RHIC Paradigms

Experimental Evidence Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Jet Quenching RHIC: strong quenching of high-PT pions and kaons. Energy loss of leading parton. Naïve pre-2002 expectation: hadron production from jets above PT ~ 2 GeV. Nuclear modification factor Rainer Fries Austin: RHIC Paradigms

Jet Quenching & Baryon Puzzle RHIC: strong quenching of high-PT pions and kaons. Energy loss of leading parton. No jet quenching for baryons? (RAA , RCP ~ 1) Seen for PT ~ 1.5 … 5 GeV/c. “Baryon Anomaly” at intermediate PT. PHENIX Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Baryon Puzzle Proton/pion ratio > 1 at PT ~ 4 GeV in Au+Au collisions. Expectation from parton fragmentation: p/ ~ 0.1 … 0.3 As measured in p+p and e++e- PHENIX Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Baryon vs Meson General baryon/meson pattern: p, , ,  versus K, , , K*,  Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Elliptic Flow Scaling Scaling first found experimentally n = number of valence quarks Very much unlike (ideal) hydrodynamics Rainer Fries Austin: RHIC Paradigms

Elliptic Flow Scaling(s) In addition at low PT: scaling with kinetic energy Inspired (but not precisely described) by hydrodynamics. Scaling of both KET and n close to perfect up to KET/n ~ 1.0 GeV Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Hydro + Jet Models (2003) Assume hydro valid up to 3-6 GeV/c, interpolate with jet spectra. Baryon vs meson splitting is not a mass effect:  behaves like a pion (m  mp, m >> m) Baryon vs meson universality classes seem to be incompatible with hydro. [Hirano + Nara (2004)] STAR STAR Rainer Fries Austin: RHIC Paradigms

Recombination Models In Heavy Ion Physics Rainer Fries Austin: RHIC Paradigms

Instantaneous Coalescence Model Simplest realization of a recombination model Recombine valence quarks of hadrons Dressed quarks, no gluons Instantaneous projection of quark states (density matrix ) on hadronic states with momentum P: Effectively: 2  1, 3  1 processes Big caveat: projection conserves only 3 components of 4-momentum. Rainer Fries Austin: RHIC Paradigms

Instantaneous Coalescence Hadron spectra can be written as a convolution of Wigner functions W,  Replace Wigner function by classical phase space distribution “Master formula” for all classical instantaneous reco models One further approximation: collinear limit Similar to light cone formalism with kT >> P Production hypersurface Meson Wigner function Quark Wigner function [Greco, Ko & Levai] [RJF, Müller, Nonaka & Bass] [Hwa & Yang] [Rapp & Shuryak] Can be modeled with hard exclusive light cone wave functions Rainer Fries Austin: RHIC Paradigms

Transport Approach (RRM) Boltzmann approach applied to ensemble of quarks and antiquarks Mesons = resonances created through quark-antiquark scattering Breit-Wigner cross sections: In the equilibrium limit: Properties: Conserves energy and momentum, leads to finite hadronization times Maybe able to describe KET scaling. Baryons: difficult, need to implement diquarks. [Ravagli & Rapp PLB 655 (2007)] [Ravagli, van Hees & Rapp, PRC 79 (2009)] Rainer Fries Austin: RHIC Paradigms

Instant. Reco: The Thermal Case Thermal parton spectra yield thermal hadron spectra. For instant. recombination (collinear case): Should also hold in the transport approach. Automatically delivers NB ~ NM if mass effects are suppressed Details of hadron structure do not seem to be relevant for thermal recombination at intermediate and high momentum. Wave function can be integrated out. Important for elliptic flow scaling. Also seen numerically in full 6-D phase space coalescence. Rainer Fries Austin: RHIC Paradigms

Instant. Reco: Exp & Power Laws for mesons Comparison of different scenarios Power law parton spectrum Recombination is suppressed Good: QCD factorization should hold at least for asymptotically large momentum Exponential parton spectrum Recombination more effective Even larger effect for baryons fragmenting parton: ph = z p, z<1 Exponential: recombining partons: p1+p2=ph Rainer Fries Austin: RHIC Paradigms

Inst. Reco: Phenomenology Recombination of thermal partons dominates up to 4 GeV/c for mesons, 6 GeV/c for baryons [Greco, Ko & Levai] [RJF, Müller, Nonaka & Bass] Rainer Fries [RJF, Müller, Nonaka & Bass] Austin: RHIC Paradigms

Austin: RHIC Paradigms Elliptic Flow Scaling Assume universal elliptic flow v2p of the partons before the phase transition Recombination prediction Factorization of momentum and position space (!) Recover scaling law for infinitely narrow wave functions Scaling holds numerically also for less special choices. Momentum shared: fractions x and 1-x Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Elliptic Flow Scaling Data Compilation Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Robustness of Scaling Early critique of quark number scaling: space-momentum correlations can destroy the scaling law. Remember: simple factorization between space and momentum angle assumed to derive analytic scaling: given globally. Other (reasonable!) assumptions about the flow field, including blast wave models lead to scaling violations. Why does KET scaling work better than PT scaling? [Pratt & Pal, NPA 749 (2005)] [Molnar, nucl-th/0408044] Rainer Fries Austin: RHIC Paradigms

Uncertainties on the Scaling Law Scaling law potentially receives uncertainties from: Hadron wave function (higher Fock states, shape) Non-trivial space-momentum correlations Resonance decays, hadronic phase (pions!) Experimentally: small deviations confirmed Rainer Fries Austin: RHIC Paradigms

Elliptic Flow in Transport Approach Kinetic energy scaling for quarks would be preserved going from the quark to the hadron phase. Quark input from Langevin simulation. Quark number scaling holds! Confirmation with baryons still missing. [Ravagli, van Hees, Rapp] Rainer Fries Austin: RHIC Paradigms

Connections with pQCD and Hydro Rainer Fries Austin: RHIC Paradigms

Recombination at High PT Recombination for jets? E.g. shower recombination + mixed processes (soft-hard or soft-shower recombination). Modifications to fragmentation functions. [Hwa, Yang] pT partons Soft (T) Shower (S) Partons from 1 jets soft-soft soft-shower Partons from 2 jets [Majumdar, Wang & Wang (2005)] Rainer Fries Austin: RHIC Paradigms

Recombination & Equilibration Boltzmann implementation: energy conservation + detailed balance + equilibrated quark input should lead to equilibrated hadrons! Numerical tests: compare blast wave hadrons at Tc- to hadrons coalesced from quarks of the same blast wave at Tc+: Excellent agreement of spectra and v2. D   J/ [He, Fries & Rapp (in preparation)] Rainer Fries Austin: RHIC Paradigms

Recombination & Equilibration The resonance recombination model is compatible with equilibration and hydrodynamics. Even can get negative J/ v2 from positive charm quark v2. Will work with any hydrodynamic flow field However, universal hydrodynamic behavior leads to a demise of the predictive power of recombination as a microscopic model in that regime. How can we understand simultaneous KET- and nq-scaling at low PT? Maybe accidental Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms KET-Scaling (Low PT) Mass splitting for v2(pT)  reversed, but small when plotted vs KET. Can force scaling e.g. by introducing sequential freeze-out: large mass particles will reduce their v2. A very reasonable two-group model works for a blast wave: Group I: multi-strange particles freezing out at Tc. Group II: all others including pions freeze out at ~ 110 MeV. Additional criterion: make scaling curve a straight line such that additional quark number scaling becomes trivial. Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms KET-Scaling (Low PT) Easy to find reasonable parameters in the Retiere and Lisa blast wave to achieve KET- and nq-scaling within 10% accuracy. Contours in space of flow asymmetry and fireball eccentricity. Pions prefer slightly lower freeze-out temperatures but are compatible with group II within the 10% accuracy (not changed by resonance decays!). This behavior should qualitatively also hold for a full hydro simulation. [He, Fries & Rapp (in preparation)] Rainer Fries Austin: RHIC Paradigms

KET-Scaling (Low + Intermediate PT) Simultaneous KET- and nq-scaling at low PT does not carry any information about quark recombination, only about the flow field and freeze-out. At intermediate PT: KET ~ PT and thus kinetic energy scaling becomes irrelevant The observed nq-scaling is not compatible with equilibrium. Is recombination the only possibility to explain nq-scaling? We would love to make the case for recombination more robust at intermediate PT. Rainer Fries Austin: RHIC Paradigms

KET-Scaling (Intermediate PT) Alternative scenarios: Hadronic? Viscous hydro? First generation recombination studies: Flow-based, global “v2“ mostly put by hand  non-equilibrium. Clearly need better studies using realistic off-equilibrium phase space distributions of quarks. Example: quark number scaling worked in the Boltzmann implementation ,using non-equilibrated Langevin! More systematic study under way. Rainer Fries Austin: RHIC Paradigms

Other Suggestions for Intermed. PT Prelude: valence quark scaling of hadronic cross sections can lead to v2 scaling in URQMD. But absolute values much too small! What about hadronic phase close to but not at the hydro limit? 2nd order viscous hydro: large effect on v2 from deformed freeze-out distributions. [Bleicher & Stoecker, PLB 526 (2002)] Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Viscous Hydro Assume different equilibration times for baryons and meson. Inspired by constituent scaling of cross sections set This yields reasonably good agreement with data Intermediate pT: meson distributions more deformed than baryons at freeze-out. Caveats: Scaling of  is a (well-motivated) guess so far, cross sections between all measured hadrons have to scale with some accuracy. Jet-like correlations at intermediate PT? Limits of applicability of viscous hydro? [Dusling, Moore & Teaney, arXiv:0909.0754] Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Summary Quark Recombination at RHIC has been successful in describing some aspects of RHIC data could provide a direct window on collective parton dynamics. Low momentum (+equilibration region): Boltzmann formulation of quark recombination applicable, reproduces equilibrium hadrons with arbitrary flow fields. No additional predictive power from recombination. KET and quark number scaling of elliptic flow at low momentum compatible with recombination but only a constraint on hydro + freeze-out conditions. Intermediate PT: True testing ground for recombination models. Clearly off equilibrium, need better description of the physics leading to non-equilibrium quark distributions. Possibly viscous scaling? Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Summary II High PT: Hybrid approaches (“shower+thermal”, “recombination+fragmentation”) successful with data. Connections with other approaches (pQCD, cluster hadronization)? Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Fate of the Gluons? We should not be surprised that valence quarks are the dominant degrees of freedom. Is there any room to accommodate higher Fock states (gluons or sea quarks)? Maybe: no effect on particle yields for thermal spectra! Elliptic flow for hadrons does not obey analytic scaling law anymore For equally shared momenta: But numerically it can still be close to scaling . Systematic difference between baryons and mesons introduced. Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Hadron Correlations Jet like correlations seen deep in the intermediate PT region. Two ways to reconcile with a recombination picture: Correlations induced by soft-hard reco (pick-up reactions) Residual correlations between soft partons are transferred onto hadrons Qualitatively in agreement with data E.g. baryon/meson ratio [Hwa & Yang] [RJF, Bass & Müller] RJF + C. Nonaka frag-frag + reco-reco only central peripheral Away side Rainer Fries Austin: RHIC Paradigms

Austin: RHIC Paradigms Hadron Correlations Baryon/meson ratio seems to be a some measure of equilibration at the time of hadronization. B/M larger in ridge vs single jet B/M larger for longer path length associated with a trigger Rainer Fries Austin: RHIC Paradigms