ATHIC 2018 Heavy quarkonium dissociation by thermal gluons
ATHIC 2018 Heavy quarkonium dissociation by thermal gluons in the QGP Shile Chen, Min He Tsinghua University, China Nanjing University of Sci. & Tech. , China 2020/9/17 USTC, Hefei, China 1
Contents 1. Introduction: l J/ψ dissociation process in QGP l l Cross section: E 1 vs M 1 Dissociation rate l l Cross section Dissociation rate 2. LO: g + J/Ψ c + cbar 3. NLO: g + J/Ψ g + cbar 4. Summary & Outlook 2020/9/17 2
J/ψ Dissociation in QGP Ø J/ ψ: bound state of charm & anti-charm quark Cornell potential: Ø In QGP, J/ ψ dissociates because of color screening & inelastic scattering with thermal gluons Leading Order 2020/9/17 Next-to-leading Order Ø Experiment data: RAA less than 1, means the yield of J/ψ suppressed in QGP i. e. dissociation 3
Gluo-dissociation: g + J/ψ c + cbar ØEffective Hamiltonian from QCD multipole expansion He� = H 0 + HI Yan 80 perturbation Hamiltonian Chrom-electric dipole term Chrom-magnetic dipole term Where Weyl Gauge 2020/9/17 4
Gluo-dissociation: g + J/ψ c + cbar ØTransition rate from effective Hamiltonian(nonrelativistic quantum mechanical perturbation theory) E 1、M 1 transition matrix element Fermi’s Golden rule ØCross section: E 1: M 1: ØUnder Coulomb approximation E 1: the same result as Peskin’s OPE M 1: 2020/9/17 M 1: a novel contribution 5
J/ψ bound state: Schrodinger Equation ØHeavy quarkonium bound state wave function: Potential function under finite temperature: Satz 88 Stationary Schrodinger Equation: --- higher T, stronger screening --- bound state size grows, binding energy decreases --- Td(J/ψ)~1. 7 Tc , Td(Y)~2. 6 Tc 2020/9/17 6
LO cross section:vacuum S-wave: g + J/ψ c + cbar P-wave: g + χc c + cbar P-wave S-wave ---Cross section of Heavy quarkuniom in vacuum: Coulomb potential differs from full potential result by ~50% ---M 1 overtakes E 1 at low energies ΔL= 0 s-wave isotropic scattering dominant 2020/9/17 7
LO cross section:In medium g + J/ψ c + cbar g + Y b + bbar --- Higher T,bound state size grows E 1 cross section increase --- For J/ψ ,M 1 overtakes E 1 when temperature is low --- For most tightly bound state Y(1 S) , cross section smallest --- Excited state Y(2 S)/ c. B is easier to dissociate 2020/9/17 8 g + Y(2 s)/cb b + bbar
LO dissociation rate l Heavy quarkonium dissociation rate:Degeneracy Gluon Bose distribution Cross section E 1 + M 1 --- For J/ψ , M 1 prominent at low temperature, accounting for 10 -25% of tatal (E 1+M 1) --- At low temperature, εB large, bound state tight gluon sees the bound state as a whole LO gluo-dissociation sensible rate increases with T --- at high T, εB decreases, σ [k 2*fg(k)] shifts toward lower [higher] energy phase space mismatched rate drops off fast calling for NLO 2020/9/17 9
NLO: g + J/ψ g + cbar l. Full calculation of NLO J/Ψ break-up: Four possible situations For given | i > &| f > l s- & u-channel diagrams formed out of VSO & VOO b a analogous to Compton l t-channel diagrams formed out of VSO & V 3 g c 2020/9/17 d 10
NLO: diag. (a) & (b) ØEffective Hamiltonian from QCD multipole expansion Yan 80 Effective Hamiltonian 0 th Hamiltonian VSO: singlet|S> to octet|O> transition vertex Perturbation Hamiltonian ØRelevant transition matrix element VOO: octet|O> to octet|O> transition vertex VSO= Weyl Gauge VOO= 2020/9/17 11
NLO transition matrix: (a)& (b) ØTransition amplitude (NR-QM time-dependent perturbation theory) Each transition vertex contains a gluon creation operator and a gluon annihilation operator Two possible intermediate states 2020/9/17 12
NLO cross section (a)& (b) ØCross section(final state: ccbar CM ~ J/ψ rest frame) flux=c/V 2020/9/17 13 Two amplitudes coherent superposition
NLO: (c) & (d) ØEffective Hamiltonian from QCD multipole expansion Yan 80 Effective Hamiltonian Vertices 0 th Hamiltonian Vso Perturbation Hamiltonian ØRelevant transition matrix elements ØTransition amplitudes(NR-QM time-dependent perturbation theory) 2020/9/17 14 V 3 g
NLO transition amplitudes: (c) & (d) No interference between amplitude (a+b) & amplitude (c+d)! 2020/9/17 15
NLO cross section (c) & (d) ØCross section(final state: ccbar CM ~ J/ψ rest frame) flux=c/V Two amplitudes coherent superposition 2020/9/17 16
NLO cross section: vacuum ---LO, mg=0, NLO, a & b infrared sensitivity, c & d collinear divergence (sensitive to gluon mass): regularized by mg=600 Me. V ; at finite T both regularized by thermal gluon mass ---NLO takes over from LO at high Eg ---NLO a & b increase with Eg; c & d increase with Eg at low gluon energy, leveling off at high Eg 2020/9/17 17
NLO cross section:In medium ØThermal gluon mass NLO quickly takes over from LO; no fall-off --- NLO a & b increases fast with T, due to expanding wave function & decreasing εB, while c & d decreases with T --- Near Td, dipole size blows up > gluon wave-length, dipole transition may not be a good approximation any more --- 2020/9/17 18
NLO dissociation rate ØHeavy quarkonium dissociation rate ------- The artifact of LO dropping off toward high T: replaced by NLO increase Near Td, Γdiss ~ Ge. V: very fast break-up, conceptually consistent with static dissociation by color screening Quantitatively might be questionable, but supported/needed by phenomenological transport study, e. g. Strickland 15, Γdiss > 2 Ge. V needed for T>=Td 2020/9/17 19
Summary and Outlook ØThe cross section and diss. rate of heavy quarkonium dissociation calculated for both LO & NLO ØLO: M 1 diss. rate overtakes. E 1 at low T; LO diss. rate drops off toward high T ØNLO: all four possible intermediate states (Compton + three-gluon vertex) investigated ; NLO diss. rate keeps increasing toward high. T ØOn-going work: generalize this method to light quark situation q/qbar + J/ψ q/qbar + cbar Thank you for attention!! 2020/9/17 20 20
Back-up: HQ & Heavy quarkonium probes t , T , V D J/ψ μ+ μ- • initial prodction t. Q~1/m. Q , p. QCD tψ ~1/ εB, NRQCD • c-quark Brownian diffusion; ψ dissolve vs regenerate • c & cbar • EW decay outside fireball hadronize coal. vs frag. • D & ψ hadronic kinetics various transport coeffi. , e. g. c-diff. coeffi. , Ψ disso. rate, etc. , to be implemented into transport eqs, e. g. Langevin, Boltzmann on top of bulk hydro Micro + Macro physics combined vs quantum effs. 21
Y(1 S) NLO dissociation rate vs quasi-free 22
Peskin: Gluon – quarkonium coupling l Peskin’s OPE analysis Peskin 79 color-octet QQbar can only persist over short space-time range ègluon emissions assemble into small singlet clusters: OPE local operators l E. g. summing up all 2 -gluon emissions, in particular including gluon self-coupling diagrams èarrive at a gauge invariant 2 nd order color-electric dipole transition: 23
QCD multipole expansion: gluon-quarkonium coupling l 2 -PI diagrams Yan 80 --- one iteration Peskin’s result --- full summation effective Lagrangian l Transcription into a NR Hamiltonian via multipole expansion with ---- similar to QED dipoles, albeit with color indices --- inclusion of gluon self-coupling diagrams essential 24
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