Heavy Probes in Heavy-Ion Collisions Theory Part IV

Heavy Probes in Heavy-Ion Collisions Theory Part IV Hendrik van Hees Justus-Liebig Universität Gießen August 31-September 5, 21 Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 1 / 31

Outline 1 Heavy quarkonia in the vacuum Stable charmonium and bottomonium states (M < 2m D ) Non-relativistic potential models 2 Heavy quarkonia in the sqgp J/ψ suppression Heavy-quarkonium dissociation In-medium modification of bound-state potentials Heavy-quarkonia dissociation and regeneration in the QGP Dissociation Cross Sections Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 2 / 31

Charmonium states no flavor-changing neutral currents in weak interactions prediction of fourth quark GIM mechanism (Glashow, Iliopolous, Maiani) CKM-quark-mixing matrix (Cabibbo, Kobayashi, Maskawa) discovered as cc bound state simultaneously by Ting (BNL) and Richter (RHIC) name J/ψ today many charmonia known (only stable states) higher excitations can decay strongly to D + D Name η c J/ψ χ c χ c1 χ c2 ψ mass (GeV) 2.98 3.1 3.42 3.51 3.56 3.69 E B (GeV).75.64.32.22.18.5 state 1S 1S 1P 1P 1P 2S J P C + 1 ++ 1 ++ 2 ++ 1 [L. Kluberg, H. Satz, Landolt-Börnstein 23/I, 6-1 (21)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 3 / 31

Bottomonium states Υ as first bb-bound state discovered by Ledermann (Fermi Lab) 1977 even more stable bottomonium states (due to stronger binding) higher excitations can decay strongly to B + B Name Υ χ b χ b1 χ b2 Υ χ b χ b1 χ b2 Υ mass (GeV) 9.46 9.86 9.89 9.91 1.2 1.23 1.26 1.27 1.36 E B (GeV) 1.1.7.67.64.53.34.3.29.2 state 1S 1P 1P 1P 2S 1P 1P 1P 3S J P C 1 ++ 1 ++ 2 ++ 1 ++ 1 ++ 2 ++ 1 [L. Kluberg, H. Satz, Landolt-Börnstein 23/I, 6-1 (21)] light-quark mesons: mass from strong interaction (confinement) heavy quarkonia: mass due to quark masses can be treated as (quasi-)non-relativistic bound states Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 4 / 31

Non-relativistic potential models use phenomenological static potentials, e.g., Cornell potential V (r) = σr α r long-range scale: confining (non-perturbative QCD), string tension, σ.2 GeV 2 short-range scale: Coulomb-like (pqcd), α π/12 heavy-quarkonium states from non-relativistic Schrödinger equation [ 2m Q 1 ] + V (r) Φ i ( r) = M i φ i (r) m Q fit to spin-averaged heavy-quarkonium spectra m c = 1.25 GeV, m b = 4.65 GeV, σ =.445 GeV, α = π/12 from wave function r 2 i = Φi r Φ i Name J/ψ χ c ψ Υ χ b Υ χ b Υ mass (GeV) 3.1 3.53 3.68 9.46 9.99 1.2 1.26 1.36 E B (GeV).64.2.5 1.1.67.54.31.2 M i (GeV).2 -.3.3.36 -.6 -.6 -.8 -.7 r (fm).5.72.9.28.44.56.68.78 Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 5 / 31

J/ψ suppression as probe for QGP formation heavy quarkonia break up in sqgp dissociation through inelastic scattering with medium particles gluon dissociation, quasi-free knock-out reactions in-medium modification of strong interaction; color screening suppression of heavy quarkonia as signal for QGP formation [T. Matsui, H. Satz, J/ψ PLB 178, 416 (1986)] caveat! already suppression in pa collisions compared to pp absorption, shadowing, Cronin effect as cold-nuclear-matter effects must be taken into account to determine anomalous suppression Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 6 / 31

Heavy-quarkonium dissociation from non-rel. potential models: tightly bound states of small size need hard parton to dissociate heavy quarkonia leading-order process via hard gluon hot hadron gas hadron of high momentum p h distribution of gluons with momentum xp h : g(x) (1 x) 2 average gluon-momentum fraction 1 x = dxxg(x) 1 dx g(x) = 1 5 in hadronic medium with T < T c average momentum p gluon = 3T/5.1 GeV E B.6 GeV deconfined matter (QGP) p gluon 3T for T 1.2T c gluo dissociation of J/ψ possible Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 7 / 31

Heavy-quarkonium dissociation dissociation cross section (similar to photo effect in QED) g + J/ψ c + c [M.E. Peskin, NPB 156, 365 (1979), G. Bhanot, M.E. Peskin, NPB 156, 391 (1979)] σ g+j/ψ c+c 1 m 2 c (k/e B 1) 3/2 (k/e B ) 5 for hadron: convolution with parton-distribution function g(x) g ψ J/ ψ 1e+ π ψ σ [mb] 1e 1 h 1e 2 1 1 [L. Kluberg, H. Satz, Landolt-Börnstein 23/I, 6-1 (21)] k [GeV] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 8 / 31

Potential models in the medium modify Cornell potential by Debye screening confining part: Laplace equation in 1D perturbative part: Laplace equation in 3D Debye-screened Cornell potential V (r, T ) σr 1 exp( µ Dr) µ D r shortcomings of this model α r exp( µ Dr) confining part treated as 1D-gauge theory different in 3D µ D taken in high-energy form µ T lqcd µ D different close to T c (strong interactions sqgp!) [F. Karsch, M.-T. Mehr, H. Satz. ZPC 37, 617 (1988); F. Karsch, H. Satz, ZPC 51, 29 (1991)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 9 / 31

Static heavy-quark potentials from lattice QCD lattice QCD at finite temperature: calculate free energy F = U T S calculate difference between F QQ with Q and Q at distance, r and F average Hamiltonian for static QQ: H T = U = T 2 (F/T )/ T M quarkonium long-distance limit: 2M D (T ) 2m c + U(, T ) can be reinterpreted as medium-modified heavy-quark mass short-distance: polarization zones overlap enhancement of U over T = Cornell potential right potential V = xu + (1 x)f? V lqcd Kaczmarek et al F(r,T=) U(r,T) F(r,T) T S(r,T) r D T > T c r Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 1 / 31

Heavy-quarkonium spectral functions from lqcd lqcd: thermal expectation values of imaginary-time operators Monte Carlo evaluation of path integrals of discreticed QCD action current-correlation function for heavy quarkonia G α (τ, r) = j α (τ, r)j α(, ) connection with spectral function T G α (τ, p; T ) = K(E, τ; T ) = deσ α (E, p; T )K(E, τ; T ) cosh[e(τ β/2)] sinh(βe/2) with inversion problematic on (discretized) imaginary time τ β statistical maximum-entropy method (MEM) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 11 / 31

T-matrix approach for quarkonium-bound-state problem T-matrix Brückner approach for heavy quarkonia as for HQ diffusion consistency between HQ diffusion and QQ suppression! Q c T q k q = V + V T Σ = Σ glu + T 4D Bethe-Salpeter equation 3D Lippmann-Schwinger equation relativistic interaction static heavy-quark potential (lqcd) T α (E; q, q) =V α (q, q) + 2 π {1 n F [ω 1 ( k)] n F [ω 2 (k)]} dk k 2 V α (q, k)g Q Q(E; k)t α (E; k, q) q, q, k relative 3-momentum of initial, final, intermediate QQ state [F. Riek, R. Rapp, arxiv:15.769 [hep-ph]] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 12 / 31

The potential Q Q Q Q non-perturbative static gluon propagator D ( k) = 1/( k 2 + µ 2 D) + m 2 G/( k 2 + m 2 D) 2 finite-t HQ color-singlet-free energy from Polyakov loops exp[ F 1 (r, T )/T ] = Tr[Ω(x)Ω (y)]/n c [ g 2 = exp A,α 2N c T 2 (x)a,α (y) A 2,α(x) ] + O(g 6 ) identify A,α (x)a,α (y) = D (x y) color-singlet free energy F 1 (r, T ) = 4 { } 3 α exp( md r) s + m2 G [exp( m D r) 1] + m D r 2 m D in vacuo m D, m D F 1 (r) = 4 3 [F. Riek, R. Rapp, arxiv:15.769 [hep-ph]] α s r + σr, σ = 2α sm 2 G 3 Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 13 / 31

Heavy quarkonia fit parameters, α s (T ), m D (T ), m D (T ), m G (T ) to lqcd calculate internal energy U(r, T ) = F (r, T ) T T F (r, T ) solve Lippmann-Schwinger equation adjust m Q to get s-wave charmonia/bottomonia masses in vacuum in the following potential 1: N f = 2 + 1 [O. Kaczmarek] potential 2: N f = 3 [P. Petreczky] BbS: Blancenblecler-Sugar reduction scheme Th: Thompson reduction scheme vacuum-mass splittings uncertainty for charmonia 5-1 MeV uncertainty for bottomonia 3-7 MeV overall uncertainty 1% melting temperatures with U and F s-wave (η c, J/ψ): 2-2.5T c, 1.3T c, Υ: > 2T c, 1.7T c, 1T c, 2T c, 1T c, 1T c p-wave (χ c ): 1.2T c, 1T c, χ b : 1.7T c, 1.2T c, all 1T c [F. Riek, R. Rapp, arxiv:15.769 [hep-ph]] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 14 / 31

Quarkonium-spectral functions in the vacuum Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 15 / 31

In-medium charmonium-spectral functions (s states) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 16 / 31

In-medium charmonium-spectral functions (p states) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 17 / 31

J/ψ suppression and regeneration dissociation rate Γ Ψ = i d 3 k (2π) 3 f i(ω k, T )v rel σ (diss) Ψi (s) g + Ψ Q + Q ( gluon dissociation ) σ gψ (k ) = 2π 3 ( 32 3 ) 2 ( ) 1/2 mq 1 E b m 2 Q (k /E B 1) 3/2 (k /E) 5 for decreasing binding energy: cross section sharply peaked at low k gluon dissociation becomes inefficient for loosely bound states additional channel: quasi-free dissociation g + Ψ g + Q + Q [L. Granchamp, R. Rapp, PLB 523, 6 (21); R. Rapp EPC 43, 91 (25)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 18 / 31

Dissociation Cross Sections need dissociation cross sections to evaluate Υ yield Usual mechanism: gluon dissociation (in dipole approximation) Problem: becomes inefficient for loosely bound states σ gυ [mb].5.4.3.2 p 2 thermal-dist (T=3 MeV) gluo-diss. (ε med ) gluo-diss. (ε vac ) τ Υ [fm/c] 1 3 1 2 1 1 1 ε 1s (T) ε 2s (T) ε 1p (T) (1s), m b =5.28.1 1-1 1 2 3 ω [GeV] Γ Y = τ 1 Y =.2.4.6.8 1 T [GeV] d 3 k (2π) 3 f q,g(ω k, T )v rel σy diss (s) m Y = 2m b (T ) ɛ Y (T ) = const ɛ Y (T ) from Schrödinger eq. with screened Cornell potential [Karsch, Mehr, Satz 88] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 19 / 31

Dissociation Cross Sections breakup mechanism for loosely bound states: quasifree dissociation use LO pqcd cross sections for elastic scattering [Combridge 79] g c g c τ Υ [fm/c] 1 3 1 2 1 1 ε 1s (T) ε 2s (T) ε 1p (T) ε 1s =1.1 GeV ε 2s =.54 GeV ε 1p =.66 GeV 1.2.4.6.8 1 T [GeV] Color screening reduces Υ lifetime by factor of 1! Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 2 / 31

J/ψ suppression and regeneration use of in-medium binding energies: need both gluon absorption + quasi-free scattering [L. Granchamp, R. Rapp, PLB 523, 6 (21); R. Rapp EPC 43, 91 (25)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 21 / 31

Quarkonium transport in heavy-ion collisions quarkonium transport in the sqgp p µ p µ f Ψ (x, p) = Γ Ψ (x, p) + β Ψ (x, p) gain/regeneration term (e.g., for Q + Q g + Ψ) β Ψ (x, p) = 1 d 3 k d 3 p Q d 3 p Q 2p (2π) 3 2ω k (2π) 3 2ω Q (2π) 3 2ω Q f Q (x, p Q )f Q(x, gψ p Q)W Q Q (s)θ[t diss T (x)] (2π) 4 δ (4) (p + q p Q p Q) W gψ Q Q = σ Q Q gψ v rel4ω Q ω Q cross section must be the same as for dissociation (up to kinematics) detailed balance Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 22 / 31

Rate equations for quarkonia integrate Boltzmann equation over x, p assume thermalized Q/ Q distributions in the sqgp rate equation dn Ψ = Γ Ψ (N Ψ N (eq) Ψ dτ ) detailed balence ensures correct equilibrium limit conservation of heavy-quark number N Q Q = N Q = N Q over whole evolution of the medium HQ fugacity factors N Q Q = 1 2 N I 1 (N op ) op N op = n (eq) Ψ (T ) I (N op ) + V FBγQ 2 Ψ { V FB γ Q 2n (eq) Q (m Q, T ) for QGP α (T, µ B ) for hadron gas V FB γ Q α n(eq) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 23 / 31

Initial conditions QQ pairs produced in primordial hard collisions only subject to cold-nuclear-matter effects nuclear absorption: dissociation by interaction with surrounding nucleons Cronin effect: broadening of Ψ-p T spectra due to rescattering of gluons before charmonium formation (anti-)shadowing: modification of the parton-distribution functions in nuclei after formation time: assume equilibrium distributions p T distributions direct part: from pp + cold-nuclear-matter effects regenerated part: boosted Boltzmann distribution (blast wave) dn Ψ m T p T dp T R dr r K 1 ( mt cosh y T T ) ( ) pt sinh y t I T Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 24 / 31

Centrality dependence of J/ψ in AA collisions mid rapidity B µµ σ(j/ψ)/σ(dy) 2.9-4.5 35 3 25 2 15 1 5 Pb-Pb (17.3 A GeV) NA5 direct coalescence total Nuc. Abs. 2 4 6 8 1 12 E T (GeV) R AA 1.4 1.2 1.8.6.4.2 Au-Au (2 A GeV) y <.35 PHENIX direct coalescence total Nuc. Abs. 5 1 15 2 25 3 35 N part [X. Zhao, R. Rapp, EPC 62, 19 (29)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 25 / 31

Centrality dependence of J/ψ in AA collisions forward rapidity with and without shadowing 1.4 1.2 1 Au-Au (2 A GeV) y : [1.2,2.2] PHENIX direct coalesence total Nuc. Abs. w/sh. 1.4 1.2 1 Au-Au (2 A GeV) y : [1.2,2.2] PHENIX direct coalesence total Nuc. Abs. R AA.8.6 R AA.8.6.4.4.2.2 1 2 3 4 N part 1 2 3 4 N part [X. Zhao, R. Rapp, EPC 62, 19 (29)] Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 26 / 31

p T dependence of J/ψ R AA mid rapidity 2 1.5 PHENIX coalescence direct total -2% y <.35 2 1.5 PHENIX direct coalescence total 2-4% y <.35 R AA 1 R AA 1.5.5 2 1.5 PHENIX direct coalescence total 4-6% y <.35 2 1.5 6-92% y <.35 PHENIX coalescence direct total R AA 1 R AA 1.5.5 2 4 6 8 p t (GeV) [X. Zhao, R. Rapp, EPC 62, 19 (29)] 2 4 6 8 p t (GeV) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 27 / 31

p T dependence of J/ψ R AA forward rapidity 2 1.5 PHENIX direct coalescence total -2% y : [1.2, 2.2] 2 1.5 PHENIX direct coalescence total 2-4% y : [1.2, 2.2] R AA 1 R AA 1.5.5 2 1.5 PHENIX direct coalescence total 4-6% y : [1.2, 2.2] 2 1.5 6-92% y : [1.2, 2.2] PHENIX direct coalescence total R AA 1 R AA 1.5.5 2 4 6 8 p t (GeV) [X. Zhao, R. Rapp, EPC 62, 19 (29)] 2 4 6 8 p t (GeV) Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 28 / 31

Instead of a summary: questions How are heavy quarkonia in the vacuum theoretically described? What can we learn from that about fundamental properties of QCD? Which cold-nuclear matter (initial state) effects are important for heavy quarkonia? What are the main mechanisms behind heavy-quarkonium suppression in the sqgp? How are the bound-state properties of heavy quarkonia in the medium described? How are the heavy-quarkonium observables in heavy-ion collisions described? Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 29 / 31

Summary Heavy quarkonium states (non-relativistic) bound QQ states potential: color-coulomb (pert.) + confining (non-pert.) part good description of charmonia, J/ψ, χ C,... and bottomonia, Υ, χ b,... tightly bound states with small size Heavy quarkonia in the medium dissociation via scattering with medium particles main mechanism: gluon dissociation, quasi-free break-up reaction J/ψ suppression as signal for QGP formation in HICs cold-nuclear-matter effects (absorption, shadowing Cronin effect) anomalous suppression QGP signal Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 3 / 31

Summary Potential models in the medium heavy quarkonia with lqcd difficult to extract spectral properties (MEM) potential models in the medium use in-medium potentials from the lattice free energy or internal energy? use screened color-coulomb + confining ansatz for potential fit medium dependent parameters to lqcd leads to survival of some quarkonia above T c regeneration important Dissociation/Regeneration of heavy quarkonia in the QGP initial conditions: production cross sections, cold-nuclear matter effects dissociation cross sections for gluon absorption + quasi-free scattering Transport approach to dissociation and regeneration of heavy quarkonia in-medium bound-state properties Hendrik van Hees (JLU Gießen) Heavy Probes in HICs (Theory IV) August 31-September 5, 21 31 / 31