TomographyTomography ofof thethe QuarkQuark --GluonGluon -- PlasmaPlasma byby CharmCharm QuarksQuarks
Elena Bratkovskaya In collaboration with Taesoo Song , Hamza Berrehrah , Daniel Cabrera, Juan Torres -Rincon, Laura Tolos , Wolfgang Cassing , Jörg Aichelin and Pol -Bernard Gossiaux
The Heavy Flavor Working Group Meeting, Berkeley Lab., USA, 18-22 January 2016
1 MotivationMotivation
study of the properties of hot and dense nuclear and partonic matter by ‚charm probes ‘:
The advantage s of the ’charm probes ’:
dominantly produced in the very early stages of the reactions in initial binary c c collisions with large energy - momentum transfer
initial charm production is Au + Au well described by pQCD – FONLL
scattering cross sections are small (compared to the light Hope to use ’charm probes ’ for an early Hope to use ’charm probes ’ for an early quarks) not in an equilibrium tomography of the QGP with the su rrounding matter Charm:Charm: experimentalexperimental signalssignals
1. Nuclear modification factor: 2. Elliptic flow v 2:
What is the origin for the “energy loss ” of charm at large pT?
Collision al energy loss (elastic scattering Q+q Q+q ) vs radiative (gluon bremsstrahlung Q+q Q+q+g ) ?
Challenge for theory: simultaneous description of R AA and v 2 !
3 DynamicsDynamics ofof charmcharm quarksquarks inin A+AA+A
1. Production of charm quarks in initial binary collisions
2. Interactions in the QGP : elastic scattering Q+q Q+q collisional energy loss gluon bremsstrahlung Q+q Q+q+g radiative energy loss
3. Hadronization : c/cbar quarks D(D*) -mesons : coalescence vs fragmentation
4. Hadronic interactions : D+baryons; D+mesons
The goal: to model the dynamics of charm quarks/mesons in all phases on a microscopic basis
The tool: PHSD approach
4 BasicBasic ideaidea ofof PHSDPHSD
QGPQGP inin equilibriumequilibrium
fitted to lQCDlQCD Dynamical Quasi Particle Model (DQPM )
controled by lQCD! Quasiparticle properties: ‚resummed ‘ self - energies, propagators Calculation of transport Calculation of cross sections coefficients ηηη, ζ, σζ, σ 000
QGPQGP outout --ofof equilibriumequilibrium HICHIC
Parton -Hadron -String - controled by experimentalexperimental Dynamics ( PHSD ) datadata
Partonic interactions DQPM hadronic interactions hadron physics In -medium hadronic interactions many -body physics: G -matrix FromFrom SISSIS toto LHC:LHC: fromfrom hadronshadrons toto partonspartons
The goal: to study of the phase transition from hadronic to partonic matter and properties of the Quark -Gluon -Plasma on a microscopic level
need a consistent non -equilibrium transport model
with explicit parton -parton interactions (i.e. between quarks and gluons) explicit phase transition from hadronic to partonic degrees of freedom
lQCD EoS for partonic phase ( ‚cross over ‘ at µµµq=0)
Transport theory for strongly interacting systems : off -shell < Kadanoff -Baym equations for the Green -functions S h(x,p) in phase -space representation for the partonic and hadronic phase
PPartonarton --HHadronadron --SStringtring --DDynamicsynamics (( PHSDPHSD ))
QGP phase described by W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; Dynamical Quasi Particle Model W. Cassing, EPJ ST 168 (2009) 3 (DQPM ) A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007 ) 6 DynamicalDynamical QuasiParticleQuasiParticle ModelModel (DQPM)(DQPM) -- BasicBasic ideas:ideas:
DQPM describes QCD properties in terms of ‚resummed ‘ single -particle Green ‘s functions – in the sense of a two -particle irreducible ( 2PI ) approach:
-1 2 Π Π 2 ω Gluon propagator: =P - gluon self -energy: =M g -i2 ΓΓΓΓg
-1 2 Σ Σ 2 ω Quark propagator: Sq = P - q quark self -energy: q=M q -i2 ΓΓΓΓq
the resummed properties are specified by complex self -energies which depend on temperature : Σ Π - the real part of self -energies (Σq, Π) describes a dynamically generated mass (Mq,M g); - the imaginary part describes the interaction width of partons (ΓΓΓq, ΓΓΓg)
space -like part of energy -momentum tensor Tµνµνµν defines the potential energy density and the mean -field potential (1PI) for quarks and gluons (U q, U g)
2PI frame work guarant ies a consistent description of the system in - and out -of f equilibrium on the basis of Kadanoff -Baym equations with proper states in equilibrium
A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 7 TheThe DynamicalDynamical QuasiParticleQuasiParticle ModelModel (DQPM)(DQPM)
Basic idea: interacting quasi -particles: massive quarks and gluons (g, q, q bar ) with Lorentzian spectral functions : 4ωΓΓΓ(T) i i( === g,q,q ) ρi(ωωωT, )=== v 2 2 2 ((()(ω2 −−− p2 −−−M (T))))+++4ω2ΓΓΓ(T) fit to lattice (lQCD) results i i (e.g. entropy density) with 3 parameters
Quasi -particle properties: large width and mass for gluons and quarks
lQCD: pure glue
T =158 MeV •• TC=158 MeV DQPM provides mean -fields (1PI) for gluons and 3 εεεC=0.5 GeV/fm quarks as well as effective 2 -body interactions (2PI) ••DQPM gives transition rates for the formation of hadrons PHSD DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 8 PPartonarton --HHadronadron --SStringtring --DDynamicsynamics (( PHSDPHSD ))
Initial A+A collisions – HSD: N+N string formation decay to pre -hadrons
Formation of QGP stage if εεε > εεεcritical : dissolution of pre -hadrons (DQPM) massive quarks/gluons + mean -field potential Uq Partonic stage – QGP : based on the Dynamical Quasi -Particle Model (DQPM) (quasi -) elastic collisions: inelastic collisions: q +++ q →→→ q +++ q g +++ q →→→ g +++ q q +++ q →→→ g q +++ q →→→ g +++ g q +++ q →→→ q +++ q g +++ q →→→ g +++ q g →→→ q +++ q g →→→ g +++ g q +++ q →→→ q +++ q g +++ g →→→ g +++ g
Hadronization (based on DQPM):
g →→→q+++ ,q q+++q ↔meson or( ' string )' q+++q+++q ↔baryon or( ' string )'
Hadronic phase: hadron -hadron interactions – off -shell HSD
W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009 ) 215; W. Cassing, EPJ ST 168 (2009) 3 9 QGP in equilibrium: Transport properties at finite (T, µµµµq): ηηηη/s
Infinite hot/dense matter = Shear viscosity ηηη/s at finite T PHSD in a box: V. Ozvenchuk et al., PRC 87 (2013) 064903
Shear viscosity ηηη/s at finite (T, µµµq) lQCD:
DQPM QGP in PHSD = strongly - interacting liquid
ηηη/s: µµµq=0 finite µµµq: smooth increase as a function of (T, µµµq)
H. Berrehrah et al. arXiv :1412.1017 10 Non -equilibrium dynamics: description of A+A with PHSD
Important: to be conclusive on charm observables, the light quark dynamics must be well under control!
PHSD: P. Moreau
V. Konchakovski et al., PRC 85 (2012) 011902 ; JPG42 (2015) 055106
PHSD provides a good description of ‚bulk ‘ observables (y -, p T-distributions, flow coeficients v , …) from SPS to LHC n 11 CharmCharm quarkquark productionproduction inin A+AA+A
σσσ cc( ) A+A: charm production in initial NN binary collisions : probability ΡΡΡ === inel σσσ NN
The total cross section for charm The energy distribution of binary NN production in p+p collisions σσσ(cc) collision including Fermi smearing Au+Au, 0 -10%, 200 GeV
Collision e nergy smearing due to the Fermi motion
T. Song etT. al., Song PRC et al., 92 PRC (2015) (2015), 014910, arXiv :1503.03039 arXiv :1503.03039 12 CharmCharm quark/hadronsquark/hadrons productionproduction inin p+pp+p collisionscollisions
1) Momentum distribution of charm quark: use ‚tuned ‘ PYTHIA event generator to reproduce FONLL (fixed -order next -to -leading log) results (R. Vogt et al.)
RHICRHIC
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039
2) Charm hadron production by c -quark fragmentation :
• z : momentum fraction of hadron H in heavy quark Q From C. Peterson et al., PRD27 (1983) 105 • ε From C. Peterson et al., PRD27 (1983) 105 Q=0.01 for Q=charm 13 CharmCharm quark/hadronsquark/hadrons productionproduction inin p+pp+p collisionscollisions
LHCLHC
Momentum distribution of charm quark: use ‚tuned ‘ PYTHIA event generator to reproduce FONLL (fixed -order next -to -leading log) results (R. Vogt et al.)
T. Song et al., arXiv :1512.0089 14 CharmCharm quarkquark scatteringscattering inin thethe QGPQGP (DQPM)(DQPM)
Elastic s cattering with off -shell massive partons Q+q(g) Q+q(g) Non -perturbative QGP!
Elastic cross section uc uc
Distributions of Q+q, Q+g collisions vs s 1/2 in Au+Au, 10% central
H. Berrehrah et al, PRC 89 (2014) 054901; PRC 90 (2014) 051901; PRC90 (2014) 064906 15 CharmCharm quarkquark scatteringscattering inin thethe QGPQGP
½ Differential elastic cross section for uc uc for s =3 and 4 GeV at 1.2T C, 2T C and 3T C
DQPM - anisotropic angular distribution
Note: pQCD - strongly forward peaked Differences between DQPM and pQCD : less forward peaked angular distribution leads to more efficient momentum transfer
N(cc) ~19 pairs, N(Q+q)~130, N(Q+g) ~85 collisions each charm quark makes ~ 6 elastic collisions Smaller number (compared to pQCD ) of elastic scatterings with massive partons leads to a large energy loss
! Note : radiative energy loss is NOT included yet in PHSD (work in progress); expected to be small due to the large gluon mass in the DQPM
H. Berrehrah et al, PRC 89 (2014) 054901; PRC 90 (2014) 051901; PRC90 (2014) 064906 16 Charm spatial diffusion coefficient D s in the hot medium
Ds for heavy quarks as a function of T for µµµq=0 and finite µµµq assuming adiabatic trajectories (constant entropy per net baryon s/n B) for the expansion
Continuous transition at T ! T < T c : hadronic Ds Continuous transition at T C! L. Tolos , J. M. Torres -Rincon, P RD 88 (2013) 074019 V. Ozvenchuk et al., PRC90 (2014) 054909
H. Berrehrah et al, PRC 90 (2014) 051901 , arXiv:1406.5322 H. Berrehrah et al, PRC 90 (2014) 051901 , arXiv:1406.5322 17 ThermalizationThermalization ofof charmcharm quarksquarks inin A+AA+A ??
elastic energy loss s½ =200 GeV flow
Scattering of charm quarks with massive partons softens the p T spectra elastic energy loss Charm quarks are close to thermal equilibrium at low p T < 2 GeV/c
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 18 HadronizationHadronization ofof charmcharm quarksquarks inin A+AA+A
PHSD: if the local energy density εεε < εεεC hadronization of charm quarks to hadrons: 3 1. Dynamical coalescence model εεεC =0.5 GeV/fm Probability for charm quark/antiquark and the light quark/antiquark to for m a meson:
Degeneracy factor: gM = 1 for D D*: g = 3 for D* 0 M D* 0(2400) 0 where D* 1(2420) 0+ D* 2(2460) Width δ from root -mean -square radius of meson:
Hadronization scenarios :
1: only fragmentation 2. coalescence with
Hadronization scenarios :
1: only fragmentation 2: coalescence with
Coalescence probability in Au+Au
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 20 HadronizationHadronization ofof charmcharm quarksquarks inin A+AA+A :: LHCLHC
Dynamical Hadronization scenarios :
4. coalescence with
Coalescence probability in Au+Au
T. Song et al., arXiv :1512.0089 21 ModellingModelling ofof DD --mesonmeson scatteringscattering inin thethe hadronichadronic gasgas
1. D-meson scattering with mesons Model: effective chiral Lagrangian approach with heavy -quark spin symmetry L. M. Abreu , D. Cabrera, F. J. Llanes -Estrada , J. M. Torres -Rincon, Annals Phys. 326, 2737 (2011)
0 + + 0 + + Interaction of D=(D ,D ,D s) and D*=(D* ,D* ,D* s) with octet ( πππ,K,Kbar, ηηη) :
with
2. D-meson scattering with baryons
0 + + 0 + + Model: G-matrix approach: interactions of D=(D ,D ,D s) and D*=(D* ,D* ,D* s) with nucleon octet J P=1/2 + and Delta decuplet J P=3/2 + C. Garcia -Recio , J. Nieves, O. Romanets , L. L. Salcedo , L. Tolos , Phys. Rev. D 87, 074034 (2013 )
Unitarized scattering amplitude from solution of coupled -channel Bethe -Salpeter equations : T === T +++VGT
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 22 DD--mesonmeson scatteringscattering inin thethe hadronhadron gasgas
1. D-meson scattering with mesons 1a) cross sections with m= ρ,ω,φ,Κ∗,... taken as σσσ( D,D* +++m)=== 10 mb
Distribution dN/ds 1/2
2. D-meson scattering with baryons
PHSD
Strong isospin dependence and complicated structure (due to the resonance coupling) of D+m, D+B cross sections!
Hadronic interactions become ineffective for the energy loss of D,D* mesons at high transverse momentum (i.e. large s1/2 ) 23 RRAA atat RHICRHIC -- coalescencecoalescence vsvs fragmentationfragmentation
1. Influence of hadronization scenarios: coalescence vs fragmentation
! Model study: without any rescattering (partonic and hadronic)
coalescence Coalescence probability in Au+Au
fragmentation
Expect: no scattering: R AA =1 Hadronization by fragmentation only (as in pp) RAA =1 Coalescence (not in pp!) shifts R AA to larger p T ‚nuclear matter ‘ effect The hight of the R AA peak depends on the balance: coalescence vs. fragmentation 24 RRAA atat RHIC:RHIC: partonicpartonic scatteringscattering
2. Influence of partonic rescattering ! Model study: by scaling of parton cross sections: σσσ(Q+q(g))* ααα by ααα=0, 0.5, 1, 2 (without hadronic rescattering ) Elliptic flow v 2(p T)
Central Au+Au at s½ =200 GeV : N(cc) ~19 pairs, N(Q+q)~130 collisions Elastic partonic rescattering N(Q+g) ~85 collisions moves R AA to lower p T and suppresses large p T increases v 2 each charm quark makes ~ 6 elastic collisions 25 RRAA atat RHIC:RHIC: hadronichadronic rescatteringrescattering
3. Influence of hadronic rescattering
! Model study: (with partonic rescattering) with / without hadronic rescattering
Central Au+Au at s½ =200 GeV : N(D,D*) ~30 N(D,D*+m) ~56 collisions N(D,D*+B,Bbar) ~10 collisions
each D,D* makes ~ 2 scatterings with hadrons
with hadronic rescattering Hadronic rescattering moves RAA peak to higher p T ! without
T. Song et al., PRC (2015), arXiv :1503.03039 T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 26 DD--mesonmeson ellipticelliptic flowflow vv 2 atat RHICRHIC
with hadronic rescattering
without hadronic rescattering
Hadronic rescattering substantially increases v 2 at larger p T v2 is less sensitive to the hadronization scenarios than R AA
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 27 RRAA atat RHICRHIC
PHSD results: with all rescattering (partonic and hadronic)
4: Dynamical Hadronization scenario (new)
Scenarios 1 -3:
The hight and position of the R AA peak at low p T depends on the hadronization scenario : coalescence/fragmentation!
PHSD: the STAR data are better described within scenario „coalescence with
T. Song et al., PRC 92 (2015) 014910, arXiv :1503.03039 28 ShadowingShadowing effecteffect
Charm production cross section in N*N* in HIC:
1 2 Scale Q = (M T +M T )/2
A A Ri (x 1,Q), R i (x 2,Q) for i=j=gluon are obtained from the EPS09 using that charm production is dominated by gluon fusion : σσσ( g+++ g →→→c+++ /)c σσσq( +++q →→→c+++ )c The (anti -)shadowing effect depend s on the impact parameter in HIC:
based on LO pQCD
T. Song et al., arXiv :1512.0089 29 CharmCharm RR AA atat LHCLHC
in PHSD the energy loss of D -mesons at high p T can be dominantly attributed to partonic scattering
Shadowing effect suppresses the low pT and slightly enhanses the high p T part of R AA
Hadronic rescattering moves R AA peak to higher p T
T. Song et al., arXiv :1512.0089 30 CharmCharm vv 2 atat LHCLHC
Shadowing effect has small impact on v 2
Hadronic rescattering increases v 2
T. Song et al., arXiv :1512.0089 31 OffOff --shellshell effecteffect forfor charmcharm inin QGP:QGP: crosscross sectionssections
Note: the spectral function of c (cbar) quarks cannot be fitted from lattice QCD data due to their small contribution to the entropy
Compare two scenarios for mC (light quarks are off -shell!): 1) mC=1.5 GeV 2) mC = off -shell with the same width of s.f. as for the light quarks
Differential elastic cross section for uc uc: small effect from off -shellness Total elastic cross section for uc uc: big effect : shift of threshold to low s 1/2
T. Song et al., arXiv :1512.0089 32 OffOff --shellshell effecteffect forfor charmcharm inin QGP:QGP: thermalthermal propertiesproperties
Compare two scenarios for mC (light quarks are off -shell!): 1) mC=1.5 GeV 2) mC = off -shell with the same width of s.f. as for the light quarks
Charm collisional energy loss as Spatial diffusion constant D s as a function of the c -quark momentum a function of medium temperature
For the QGP in equilibrium: the off -shellness effect on charm energy loss and Ds is moderate
T. Song et al., arXiv :1512.0089 33 OffOff --shellshell effecteffect forfor charmcharm RR AA andand vv 2 atat LHCLHC
HIC: off -equilibrium potential becomes important due to the large gradients in densit y
Quark spectral function with width
Components: time like & space like
partons potential energy scalar + vector
Scalar potential density increses with T and gives repulsive force on partons in HIC (except nea TC due to hadronization) dominant at HIC
Charm scalar repulsive forces are unknown: Assumpion to investigate – use for charm the same forces as for light quark!
Finding from HIC: PHSD vs exp. data 1) The effect of off -shell charm without repulsive force on R AA and v 2 is small 2) ALICE data favors a weaker repulsive force for off -shell charm quarks compared to light quarks.
T. Song et al., arXiv :1512.0089 34 SummarySummary
PHSD provides a microscopic description of non -equilibrium charm dynamics in the partonic and hadronic phases
Partonic rescattering suppresses the high p T part of R AA , increases v 2 Hadronic rescattering moves R AA peak to higher p T, increases v 2
The structure of R AA at low p T is sensitive to the hadronization scenario , i.e. to the balance between coalescence and fragmentation Shadowing effect supresses R AA
The exp data for the R AA and v 2 at RHIC and LHC are better described in the PHSD: by QGP collisional energy loss due to the elastic scattering of charm quarks with massive quarks and gluons in the QGP phase + by the hadronization scenario „coalescence with
OutlookOutlook the BES RHIC – in progress Influence of radiative energy loss at larger p T ? (expected to be strongly suppressed at lower transverse momenta in the PHSD due to the large mass of gluons for lower relative momenta) 35 ThankThank you!you! EnergyEnergy lossloss
H. Berrehrah et al, PRC 91 (201 5) 05 4902
off on
37 LongitudinalLongitudinal andand tt ransverseransverse momentummomentum changechange
H. Berrehrah et al, PRC 91 (201 5) 05 4902
Drag coeff. off on
38 TransverseTransverse momentummomentum changechange inin DQPMDQPM
H. Berrehrah et al, PRC 91 (201 5) 05 4902 39 DQPM:DQPM: onon --shellshell vsvs offoff --shellshell
H. Berrehrah et al, PRC 89 (2014) 054901; PRC 90 (2014) 051901; PRC90 (2014) 064906 ; PRC 91 (201 5) 05 4902
40