Download - Quark Recombination and Heavy Quarks
Quark Recombination and Heavy Quarks
Rainer FriesTexas A&M University & RIKEN BNL
6th Workshop on High-PT Physics at LHCUtrecht NL, April 6, 2011
High-PT at LHC: Utrecht 2 Rainer Fries
Overview The Case for a Microscopic Hadronization Model
Instantaneous and Resonance Recombination
Recombination and Hydro
Recombination in the Kinetic Regime: Heavy Quarks
Summary
[with Min He and Ralf Rapp]
[with Min He and Ralf Rapp]
High-PT at LHC: Utrecht 3 Rainer Fries
The Case For a Microscopic Hadronization Model
High-PT at LHC: Utrecht 4
How Does QGP Hadronize? Bulk description via hydrodynamics:
local equilibrium assumption + equation of state No microscopic information on the underlying process
Can we construct quark recombination models that preserve local equilibrium? “Traditional” recombination models fail Equilibrium extra features like quark number scaling should
not be visible! Rainer Fries
High-PT at LHC: Utrecht 5
How Does QGP Hadronize? Fragmentation at high-PT: vacuum process for single
partons
True for asymptotically large PT.
D can be approximated by gluon shower + parton-hadron duality
QCD factorization: applicable to partons emerging directly from hard processes: Need hard scale Q to suppress multi-parton processes by 1/Qn. Questionable for partons travelling through an extended
medium. Rainer Fries
00~hu uhhuD
[Collins and Soper, NPB 194 (1982)]
a
D haah
nQ1
High-PT at LHC: Utrecht 6 Rainer Fries
How Does QGP Hadronize? Recombination/coalescence of quarks: a simple
microscopic 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)
qq M qqq B
High-PT at LHC: Utrecht 7 Rainer Fries
Experiment: 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
)()()()(
)(xdxdxdxd
xDD
DD
E791 beam
[Braaten, Jia & Mehen]
[K.P. Das & R.C. Hwa: Phys. Lett. B68, 459 (1977): Quark-Antiquark Recombination in the Fragmentation Region]
),,(),()( 21M2121
21M xxxRxxF
xxdxdxxd
E791 - beam: hard cc production;recombine c with d valence quark from - > reco of c with d
High-PT at LHC: Utrecht 8 Rainer Fries
Experiment: Baryon Puzzle @ RHIC 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
High-PT at LHC: Utrecht 9 Rainer Fries
Experiment: Baryon vs Meson in HI General baryon/meson pattern: p, , , versus
K, , , K*, Incompatible with hydro and fragmentation.
High-PT at LHC: Utrecht 10 Rainer Fries
Elliptic Flow Scaling(s) in HI Quark number scaling first found experimentally
at RHIC n = number of valence quarks Very much unlike (ideal) hydrodynamics
In addition at low PT: scaling with kinetic energy Hydrodynamic feature?
Scaling of both KET and n close to perfect up to KET/n ~ 1.0 GeV
High-PT at LHC: Utrecht 11 Rainer Fries
Fate of Hydro + Jet Models Assume hydro valid up to 3-6 GeV/c at RHIC,
interpolate with jet spectra. Spoiler: behaves like a pion (m mp, m >> m)
Baryon vs meson universality classes seem to be incompatible with hydro.
Intermediate PT: non-standard (hydro, fragmentation) hadronization features?
2v
STARSTAR
[Hirano + Nara (2004)]
High-PT at LHC: Utrecht 12 Rainer Fries
Two Recombination Models
High-PT at LHC: Utrecht 13 Rainer Fries
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.
qq M qqq B
PMPMPdNM ;;)2( 3
3
High-PT at LHC: Utrecht 14 Rainer Fries
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
baMab
M WPdPdNdE
,33
3
2
Quark Wigner function
Meson Wigner functionProduction hypersurface
abbaabab CfffW 1
2
212133
3
233
3
,1;;;2
1;;2
xxPxxRfPxRfPxRfdxdxPdCPdNdE
xPxRfxPRfdxPdCPdNdE
BbacbbaaBB
MbaMM
[Greco, Ko & Levai]
[RJF, Müller, Nonaka & Bass] [Hwa & Yang] [Rapp & Shuryak]
Can be modeled with hard exclusive light conewave functions
High-PT at LHC: Utrecht 15 Rainer Fries
Transport Approach (RRM) Boltzmann approach applied to ensemble of
quarks and antiquarks Mesons = resonances created through quark-
antiquark scattering
Breit-Wigner cross sections: Resonance Recombination
In the long-time limit:
Properties: Conserves energy and momentum, leads to finite
hadronization times Baryons: coming, need to implement diquarks. No confinement: no quark loss terms
pgptfptft M
pM
,,
222
2
2
4mms
mk
Cs M
[Ravagli & Rapp PLB 655 (2007)][Ravagli, van Hees & Rapp, PRC 79 (2009)]
relrelaa
relM pPvspxfpxfpxddEPd
dNE ,,,228 213
33
33
High-PT at LHC: Utrecht 16 Rainer Fries
Instantaneous Recombinaton Describe essential features
of RHIC data at int. PT.
Elliptic flow: 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.
Uses very special flow field, maybe fragile prediction?
2 2 2 2an22 3
d 3p pM tt
B tt
pv p vv
pv p
[Greco, Ko & Levai, (2003)]
[RJF, Müller, Nonaka & Bass, (2003)]
[Pratt & Pal, NPA 749 (2005)][Molnar, nucl-th/0408044]
High-PT at LHC: Utrecht 17 Rainer Fries
Resonance Recombination Kinetic energy scaling for quarks is preserved
going from the quark to the hadron phase.
Quark number scaling holds between mesons and quarks Confirmation with baryons still missing.
[Ravagli, van Hees, Rapp, PRC 79 (2009)]
High-PT at LHC: Utrecht 18 Rainer Fries
Recombination and Hydro
[Work with Min He and Ralf Rapp]
High-PT at LHC: Utrecht 19
Recombination in Equilibrium
Rainer Fries
D
J/
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. Hadronization hypersurface: equal time
[He, RJF & Rapp, PRC (2010)]
High-PT at LHC: Utrecht 20
Recombination in Equilibrium
Rainer Fries
[He, RJF & Rapp, to appear (2011)]
Realistic hadronization hypersurface : Extract equal-time quark phase space
distributions fq along from hydro or kinetic model.
Cell-by-cell apply RRM meson phase space distribution fM along .
Compute meson current across a la Cooper-Frye:
Result for charm-light system using AZHYDRO:
dd
t = const.
High-PT at LHC: Utrecht 21
Recombination in Equilibrium 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 and hadronization
hypersurface.
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?
KET-scaling almost provided by simple hydrodynamic flow: Strong mass dependence vs PT, weak mass dependence vs KET. Can be reduced further by sequential freeze-out from heavier
to lighter hadrons. Rainer Fries
High-PT at LHC: Utrecht 22
KET-Scaling (Low PT) Blastwave + two-stage freeze-out works within exp.
uncertainties. Group I: multi-strange particles freeze-out at Tc. Group II: all others including pions freeze-out at ~ 110 MeV. Can extract quark distributions at Tc from data on multi-
strange hadrons.
v2(KET) tends to be straight line for the parameters at RHIC additional quark number scalingbecomes trivial.
Expectations: KET scaling robust KET+nq scaling maybe accidental (no guiding principle) Rainer Fries
High-PT at LHC: Utrecht 23 Rainer Fries
Recombination in the Kinetic Regime: Heavy Quarks
[Work with Min He and Ralf Rapp]
High-PT at LHC: Utrecht 24
RRM at Intermediate PT
Need: Realistic quark phase-space distributions away from
equilibrium Baryons (for quark number scaling)
Scenarios: Boltzmann (parton cascade) Langevin (for heavy quarks) Viscous hydro (??)
Here: Langevin for heavy quarks in hydrodynamic background.
Rainer Fries
High-PT at LHC: Utrecht 25
Langevin Dynamics Langevin Equations
Transport coefficients: HQ relaxation rates in T-matrix approach
Run Langevin in AZHYDRO background. Test particles in lab frame boost to fluid rest frame
Langevin step boost back to lab frame. Stop at AZHYDRO hadronization hypersurface. Initial distribution: binary collision density pQCD spectrum.
Rainer Fries
[Riek and Rapp, Phys. Rev. C 82, 035201 (2010)]
High-PT at LHC: Utrecht 26
Langevin Dynamics Equilibrium check (artificially large relaxation times)
Realistic coefficients
Rainer Fries
High-PT at LHC: Utrecht 27
Hadronization of Heavy Quarks Calculate recombination probability P(pT) of heavy quarks
for given pT. Light quarks from hydro. Low momentum heavy quarks spend a long time in the QGP
relaxed and close to mass shell fix P(pT) to be unity at pT = 0.
Apply RRM across for fraction P(pT) of test particles.
Apply fragmentation for fraction 1-P(pT) of test particles.
Rainer Fries
High-PT at LHC: Utrecht 28
Heavy Mesons Charm (D)
Bottom (B)
Rainer Fries
Recombination: huge effect on elliptic flow.
High-PT at LHC: Utrecht 29
Semi-Leptonic Decays and Data RAA
Electrons
Rainer Fries
PRELIMINARY
PRELIMINARY
[He, RJF & Rapp, to appear (2011)]
High-PT at LHC: Utrecht 30
Semi-Leptonic Decays and Data What’s missing?
Flow! Have to tune hydro; underestimates flow at Tc.
Diffusion in the hadronic phase. Transport coefficient for D:
Rainer Fries
PRELIMINARY
PRELIMINARY
[He, RJF & Rapp, arXiv:1103.6279]
High-PT at LHC: Utrecht 31
Summary There is need for a microscopic hadronization model in
some situations Hadron production in nuclear collisions at intermediate
momenta. Should be consistent with hydro (soft) hadron production and
high PT fragmentation. Candidate: resonance recombination via Boltzmann dynamics
Low momentum (equilibrated region): Capable of producing equilibrium hadrons. KET and quark number scaling compatible with recombination
but not a consequence of it. Recombination does not add any new predictive power to
hydrodynamics regime. Intermediate PT:
True testing ground for recombination models. Meson-quark v2 scaling for realistic flow fields: baryons to
come. Rainer Fries
High-PT at LHC: Utrecht 32
Summary II Application to heavy quark ensemble prepared with
Langevin dynamics, hydro background, recombination + fragmentation. Data needs tuning of (equilibrium) flow, maybe hadronic
diffusion. Full heavy quark calculation coming soon.
Quark number scaling at intermediate PT with realistic phase space distributions: Works for mesons vs quarks Need check with baryons
Rainer Fries
High-PT at LHC: Utrecht 33 Rainer Fries
Backup: Recombination at High PT
High-PT at LHC: Utrecht 34 Rainer Fries
Recombination at High PT
Recombination for jets? E.g. shower recombination + mixed processes
(soft-hard or soft-shower recombination).
Modifications to fragmentation functions.
'SSSSTSTTw qq
pT
parto
ns Soft (T)
Shower (S)
Partons from 2 jets
Partons from 1 jets
soft-shower
soft-soft
[Hwa, Yang]
[Majumdar, Wang & Wang (2005)]
High-PT at LHC: Utrecht 35 Rainer Fries
Hadronization Module for JET Topical Collaboration on Jet and Electromagnetic
Tomography. Recombination module for jet-shower simulations
in preparation. Goals:
Reproduce vacuum fragmentation. Add medium partons.[Fries, Ko et al., work in progress]
High-PT at LHC: Utrecht 36 Rainer Fries
Backup Slides
High-PT at LHC: Utrecht 37 Rainer Fries
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.
jjiiijiii qqqqbaqqbabaM 210
4/42/2 22
122
02 Tp
iiT
pT
M PvPvPv
TPTP
ii
i
nTPx
i eeei
i //2
1
/2
High-PT at LHC: Utrecht 38 Rainer Fries
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
High-PT at LHC: Utrecht 39 Rainer Fries
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.
TPTPxxTPxTPxB
TPTPxTxPMTp
eeeewwwN
eeewwNew
//)1(//
//)1(/
/
~~
~~~
High-PT at LHC: Utrecht 40 Rainer Fries
Instant. Reco: Exp & Power Laws 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
Exponential: TpTAew /~
DAeDwN TzPT /frag ~
TPTeAwwN /2reco ~
Power law: Tpw ~
TPN ~frag
2reco ~
TPNfor mesons
fragmenting parton:ph = z p, z<1
recombining partons:p1+p2=ph
High-PT at LHC: Utrecht 41
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. Rainer Fries
[He, Fries & Rapp, PRC (2010)]
High-PT at LHC: Utrecht 42
Comparison Flow
Spatial diffusion constant
Rainer Fries
High-PT at LHC: Utrecht 43
Other Suggestions for Intermed. PT
Prelude: valence quark scaling of hadronic cross sections can lead to v2 scaling in URQMD.
But absolute values are 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.
Rainer Fries
32
)()(
NNN
[Bleicher & Stoecker, PLB 526 (2002)]
jiji uppnnppf 1
High-PT at LHC: Utrecht 44
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?
Rainer Fries
23
B
M
[Dusling, Moore & Teaney, arXiv:0909.0754]