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QGP Formation Signals and Quark Recombination Model. Chunbin Yang Central China Normal University Wuhan. Outline. Heavy ion collisions and QGP formation Anomalies at RHIC Physics ideas in the recombination model Fragmentation in the recombination model Applications to Au+Au collisions
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QGP Formation Signals and Quark Recombination Model Chunbin Yang Central China Normal University Wuhan
Outline • Heavy ion collisions and QGP formation • Anomalies at RHIC • Physics ideas in the recombination model • Fragmentation in the recombination model • Applications to Au+Au collisions • NCQ scaling of flow v2 • Violation of the scaling • Particle species dependence of Cronin effect • Discussions
time Hot and Dense Cooling down freezing out Initial conditions and interactions
QGP formation signals • Strangeness enhancement • Suppression of J/Ψ • Dilepton enhancement • Direct photon • … Parton degree of QGP? QGP signal from the bulk? Experimental probes: 1) Penetrating probes:“jets” energy loss 2) Bulk probes :Elliptic flow, radial flow …
Evidence for the formation of QGP Dihadron Single hadron Jet quenching Energy loss ofjets in medium No suppression for p spectrum
HOW? Hadron production mechanisms • Partons are produced in high energy collisions like e++e-, e+p, p+p, p+A,A+A • Partons in the final stage of evolution are converted into hadrons
Traditional models • String formation and break for low p T • Fragmentation for high p T The string model may not be applicable to heavy ion collisions Fragmentation failed for central Au+Au collisions
Anomalies at intermediate pT • B/M • v2(pT) • Jet structure • Cronin effect p/≈1 v2(baryons) > v2(mesons) not the same as in pp • RCPp > RCP Hard to be understood in traditional models
Hadronization by recombination • The colliding system generates quarks and gluons in the phase space • The quarks get dressed • The dressed quarks recombine into hadrons to the detector
Why Recombination? meson momentum p p q p1+p2 Parton distribution (log scale) (recombine) (fragment) higher yield heavy penalty
Features • quark momenta add, higher yield for high produced pT hadrons • soft parton density depends on medium • more quarks for baryons than for mesons • enhanced dependence on centrality for baryons when thermal partons are involved
No anomalies in recombination • At intermediate pT, aplenty soft quarks are more important for proton production than for pionsp/1 • For baryons, three quarks contribute to the flow, while only two quarks for mesons v2(baryons) > v2(mesons), quark number scaling • Soft and semi-soft recombination Cronin effect • Process dependence of soft partons different jet structure in dA and AA
Recombination models • Use just the lowest Fock state i.e. valence quarks • qqqB q qbarM • Gluons converted to quarks first • The probability for two (three) quarks to form a meson (baryon) is given by a process independent recombination function R
Different implementations • Duke group etc: • 6-dimensional phase space • using Wigner function from density matrix • Oregon group: • one-dimensional momentum space • using phenomenological recombination function
Duke approach • Low pT recombination • high pT fragmentation
Texas/Ohio approach Texas A&M/Budapest (Ko, Greco, Levai, Chen) • Monte Carlo implementation (with spatial overlap) • Soft and hard partons • Soft-hard coalescence allowed Ohio State (Lin, Molnar) • ReCo as a solution to the opacity puzzle
Recombination functions Given by the valon distribution of the hadrons
Determining R • R p was determined from CTEQ • From the parton distributions in proton • a=b=1.755, c=1.05 at Q2=1GeV2 • R was determined from Drell-Yan processes • a=b=0 • See Phys. Rev. C 66, 025204
Fragmentation? Recombination? Answer:NO FRAGMENTATION only RECOMBINATION • Fragmentation is not a description of the hadronization process. It uses phenomenological functions D(z) that give the probability of momentum fraction z of a hadron in a parton jet
Fragmentation D(z) q A A
fragmentation h q recombination Initiating parton (hard) Parton shower (semi-hard) Parton shower
Recombination for fragmentation Recombination function known in the recombination model Fragmentation function known from fitting e+e- annihilation data S V G S K G K Hwa, Phys. Rev. D (1980). Shower parton distributions K, L, G, Ls, Gs BKK KKP etc
Application to Au+Au collisions • Thermalized low pT (soft) partons • Hard partons (semi-hard) shower partons • Three types of recombination for mesons • thermal parton & thermal parton • thermal parton & shower parton • shower parton & shower parton • Joint parton distribution is not factorizable
Parton sources Thermal parton distribution is assumed Hard parton distributions fi(k) can be calculated from • pQCD • nuclear shadowing • nuclear geometry
Parton sources Single shower parton distribution is Joint two (three) shower parton distribution can also be written down
New physics • Thermal-thermal recombination makes p/ increase from very small value to about 1 at pT3GeV/c • Thermal-shower recombination plays an important role • This recombination can be equivalently regarded as modification of the fragmentation functions
NCQ scaling • AMPT model results: • Scaling in v2: partonic dof dominant; • No scaling in v2 : hadronic dof dominant • => • A tool to search for the possible phase boundary! • The beam energy • dependence of the partonic cross sections will not affect the v2 scaling argument. • => • Important for Beam Energy Scan program.
Why NCQ scaling ? Assumptions: F(p1,p2)=F(p1)F(p2) collinear φdependence joint distribution Validity of the assumptions?
Why NCQ scaling violates? • Because of quark interactions, joint distributions are not products of quark distributions • Recombined quarks not necessarily have the same momentum • Fluctuations: large n=1,3 terms appears in quarks distributions. They contribute to v2 • NCQ at RHIC may be coincident
Application to d+Au collisions • Basic formulas the same as for Au+Au collisions • Soft parton distribution the same form, T not temperature but inverse slope • No jet quenching • Nuclear shadowing a little different from that in Au+Au case
Cronin effect Enhancement of hadron spectrum in pA collisions at high pT Traditional explanation: initial interactions Many soft collisions before the last hard one, each gives a kT kick
Cronin effect Shadowing effect is cancelled partially
Puzzles • If Cronin effect is really due to initial interactions, dilepton spectrum should show similar effect. • Experimentally, the effect for dilepton is very small, no definite conclusion • Species dependence of the Cronin effect
From recombination Medium density depends on centrality Medium effects are different in mesonand baryon production
Proton spectrum T different for different centralities
Discussions • QGP signal can be found from the bulk • Hadronization of partons can be described by ReCo for d+Au and Au+Au collisions • ReCo naturally explains species dependence, such as baryon enhancement, v2 scaling... • Cronin effect can be interpreted as from final state interactions
Discussions • Combination with other models, such as hydrodynamics etc, is needed and under development • Recombination formulism from pQCD How to calculate the joint distributions?