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

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Experimental Evidence
Rainer Fries
Austin: RHIC Paradigms

9. 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

10. 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

11. 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

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

13. 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

14. 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

15. 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

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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

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

25. 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/ ]
Rainer Fries
Austin: RHIC Paradigms

26. 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

27. 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

28. Connections with pQCD and Hydro
Rainer Fries
Austin: RHIC Paradigms

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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: ]
Rainer Fries
Austin: RHIC Paradigms

38. 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

39. 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

40. 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

41. 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

42. 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