Charmonium ( cc ) mass in hadron-nucleus reactions, how the - PowerPoint PPT Presentation

Charmonium (¯ cc ) mass in hadron-nucleus reactions, how the in-medium gluon condensate can be measured International workshop on “Hadron structure and interaction in dense matter” Tokai, 12.11.2018. Gy. Wolf MTA Wigner RCP • Motivation • Transport • hadron(¯ p, π ,p)A reaction (PANDA, JPARC?) Gy. Wolf, G. Balassa, P. Kov´ acs, M. Z´ et´ enyi, S.H. Lee, Act. Phys. Pol. B10 (2017) 1177, arxiv:1711.10372 Phys. Lett. B780 (2018) 25, arXiv:1712.06537 Act. Phys. Pol. B11 (2018) 531

The QCD vacuum qq > and < α s /πG 2 > condensates: the most important ones: m q < ¯ < ¯ qq > order parameter of the spontaneous chiral symmetry breaking plays fundamental role in the phenomenology of strong interaction How to determine them: Gell-Man-Oakes-Renner relation: f 2 π m 2 π = ( m u + m d ) < ¯ qq > QCD sum rules: fitting many meson masses (gluon condensate can be determined from J/ ψ mass) It gives a consistent picture for meson masses in terms of condensates. In matter: the masses of hadrons made of light quarks changes mainly due to the (partial) restauration of chiral symmetry hadrons made of heavy quarks are sensitive on the changes of gluon condensate measuring the charmonium masses in matter may tell us what is the gluon condensate in matter

Gluon condensate in matter Quark and gluon condensates are known in vacuum, in matter: � d 3 p/p 0 f N ( p, µ ) < N | O | N > < n.m. | O | n.m. > = < 0 | O | 0 > + qq | N > and < N | α s G 2 | N > we need to know < N | ¯ Trace anomaly: = β µν G a µν + m ¯ T QCD µ 2 gG a qq µ Between vacuum states: energy of the vacuum. Between nucleons u ( p ) u ( p ) = < N ( p ) | β µν G a µν + m ¯ 2 gG a m N ¯ qq | N ( p ) > contribution of light quarks ( π N scattering, σ -term): ≈ 50 MeV, gluons contribution to the mass of the proton: ≈ 750 MeV

Why dileptons • without final state interaction • vector mesons decay to dileptons → vector mesons in matter • interesting results for p-nucleus (KEK) and nucleus-nucleus (SPS,RHIC,LHC) collisions almost all direct or indirect indication for in-medium modifica- tion of hadrons are observed in he dileptonic decay channel (some exceptions: TAPS/ELSA: ω → πγ , and mesonic atoms)

KEK E325 12 GeV pA data for φ 150 150 150 counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] βγ <1.25 βγ <1.25 βγ <1.25 βγ <1.25 C Cu C Cu 60 60 60 100 100 100 40 40 40 50 50 50 20 20 20 χ 2 =37 χ 2 =66 χ 2 /ndf=36/50 χ 2 /ndf=83/50 χ 2 =36 χ 2 =74 0 0 0 0 0 0 counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] 1.25< βγ <1.75 1.25< βγ <1.75 1.25< βγ <1.75 1.25< βγ <1.75 C Cu C Cu 150 150 150 100 100 100 100 100 100 50 50 50 50 50 50 χ 2 =66 χ 2 =45 χ 2 /ndf=63/50 χ 2 /ndf=43/50 χ 2 =64 χ 2 =44 0 0 0 0 0 0 counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] counts/[6.7MeV/c 2 ] 1.75< βγ 1.75< βγ 1.75< βγ 1.75< βγ C Cu C Cu 300 300 300 200 200 200 200 200 200 100 100 100 100 100 100 χ 2 =45 χ 2 =58 χ 2 /ndf=46/50 χ 2 /ndf=55/50 χ 2 =46 χ 2 =56 0 0 0 0 0 0 0.9 1 1.1 1.2 0.9 1 1.1 1.2 0.9 1 1.1 1.2 0.9 1 1.1 1.2 [GeV/c 2 ] [GeV/c 2 ] [GeV/c 2 ] [GeV/c 2 ] m ( ρ ) /m (0) = 1 − 0 . 033( ρ/ρ 0 ) Γ( ρ ) / Γ(0) = 3 . 6( ρ/ρ 0 ) R. Muto et al. Phys. Rev. Lett. 98 (2007) 042501

CERES data (d 2 N ee /d η dm ee ) / (dN ch /d η ) (100 MeV/c 2 ) -1 (d 2 N ee /d η dm) / (dN ch /d η ) (50 MeV/c 2 ) -1 σ trig / σ tot ~ 35 % Pb-Au 158 AGeV p-Be 450 GeV 2.1 < η < 2.65 -5 p ⊥ > 50 MeV/c 10 p ⊥ > 200 MeV/c -4 Θ ee > 35 mrad 10 Θ ee > 35 mrad 〈 dN ch /d η〉 = 3.8 2.1 < η < 2.65 〈 N ch 〉 = 220 -5 -6 10 10 η → ee γ -6 10 -7 ω → ee π o 10 ρ/ω → ee ω → ee π o -7 η , → ee γ 10 π 0 → ee γ η , φ → ee -8 → e γ 10 e -8 ρ,ω → ee π o → ee γ 10 η φ → ee → e e γ charm -9 10 -9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 m ee (GeV/c 2 ) m ee (GeV/c 2 ) (d 2 N ee /d η dm) / (dN ch /d η ) (50 MeV/c 2 ) -1 2.1 < η < 2.65 p-Au 450 GeV p ⊥ > 50 MeV/c -4 Θ ee > 35 mrad 10 〈 dN ch /d η〉 = 7.0 -5 10 -6 10 ω → ee π o -7 η , → ee γ 10 π 0 → ee γ -8 ρ,ω → ee 10 η φ → ee → e e γ charm -9 10 0 0.5 1 1.5 m ee (GeV/c 2 ) G. Agakichiev et al. G. Agakichiev et al. Eur. Phys. J. C4 (1998) 231 Phys. Lett. B422 (1998) 405

BUU • ∂F ∂t + ∂H ∂F ∂ x − ∂H ∂F � ( m 0 + U ( p , x )) 2 + p 2 ∂ p = C , H = ∂ p ∂ x • potential: momentum dependent, soft: K=215 MeV � τ + C 2 U nr = A n � d 3 p ′ f N ( x,p ′ ) n n 0 + B � � 2 , (2 π ) 3 n 0 n 0 � p − p ′ 1+ Λ • testparticle method N test i =1 δ (3) ( x − x i ( t )) δ (4) ( p − p i ( t )). F = � Gy. Wolf et al., Phys.Atom.Nucl. 75 (2012) 718-720 Gy. Wolf, M. Zetenyi, Dilepton and φ meson production at the NICA fixed-target experiment, Eur.Phys.J. A52 (2016) 258 Influence of anisotropic Λ / Σ creation on the Ξ multiplicity in sub- threshold proton-nucleus collisions, Phys.Lett. B785 (2018) 226

Collision term • NN ↔ NR, NN ↔ ∆∆ • baryon resonance can decay via 9 channels R ↔ N π , N η , N σ , N ρ , N ω , ∆ π , N(1440) π , KΛ, KΣ • 24 baryon resonances + Λ and Σ baryons π, η, σ, ρ, ω and kaons • ππ ↔ ρ , ππ ↔ σ , πρ ↔ ω • for resonances: energy dependent with • dσ X → NR ∼ A ( M R ) λ 0 . 5 ( s, M 2 R , M 2 N ) dM R Unknown cross sections: Statistical bootstrap: G. Balassa, P. Kov´ acs, Gy. Wolf, Eur. Phys. J. A54 (2018) 25,

Spectral equilibration • medium effects on the spectrum of hadrons (vector mesons) • how they get on-shell (energy-momentum conservation) • Field theoretical method (Kadanoff-Baym equation) B. Schenke, C. Greiner, Phys.Rev.C73:034909,2006 • Off-shell transport W. Cassing, S. Juchem, Nucl.Phys. A672 (2000) 417 S. Leupold, Nucl.Phys. A672 (2000) 475 • Spectral equilibration: Markov or memory effect

Off-shell transport • Kadanoff-Baym equation for retarded Green-function Wigner-transformation, gradient expansion • transport equation for F α = f α ( x, p, t ) A α A ( p ) = − 2 ImG ret = ˆ Γ Γ 2 , 4 ˆ 0 − ReΣ ret ) 2 + 1 ( E 2 − p 2 − m 2 W. Cassing, S. Juchem, Nucl.Phys. A672 (2000) 417 S. Leupold, Nucl.Phys. A672 (2000) 475 • testparticle approximation

Transport equations i − � ǫ 2 P 2 i − M 2 � 0 − Re Σ ret � • d � 2 � P i + � � 1 1 X i ∇ P i Re Σ ret ∇ P i Im Σ ret ( i ) dt = ( i ) + Im Σ ret ( i ) 1 − C ( i ) 2 ǫ i ( i ) i − � ǫ 2 P 2 i − M 2 0 − Re Σ ret � � d � � � P i 1 1 ∇ X i Re Σ ret ∇ X i Im Σ ret ( i ) dt = − + i Im Σ ret ( i ) 1 − C ( i ) 2 ǫ i ( i ) � ∂Re Σ ret i − � ǫ 2 P 2 i − M 2 0 − Re Σ ret ∂Im Σ ret � 1 1 dǫ i ( i ) ( i ) ( i ) dt = + Im Σ ret 1 − C ( i ) 2 ǫ i ∂t ∂t ( i ) • where C ( i ) renormalization factor i − � ǫ 2 P 2 i − M 2 0 − Re Σ ret � � 1 ∂ ∂ ∂ǫ i Re Σ ret ∂ǫ i Im Σ ret ( i ) C ( i ) = ( i ) + Im Σ ret ( i ) 2 ǫ i ( i ) • the last equation for homogenous system can be rewritten as M 2 i − M 2 dRe Σ ret 0 − Re Σ ret dIm Σ ret dM 2 d ( ǫ 2 i − P 2 i ) ( i ) ( i ) ( i ) = = + i Im Σ ret dt dt dt dt ( i )

Evolution of mass distribution in a box the vector meson masses are shifted linearly with density, and change the density linearly from ρ 0 to 0 in 4 fm/c: 80 Breit-Wigner t=300 fm/c 70 t=350 fm/c t=351 fm/c 60 t=352 fm/c t=353 fm/c ω t=354 fm/c 50 Breit-Wigner A (GeV -1 ) 40 30 20 10 0 0.6 0.65 0.7 0.75 0.8 0.85 0.9 m (GeV) 5 Breit-Wigner t=300 fm/c t=350 fm/c ρ 4 t=351 fm/c t=352 fm/c t=353 fm/c t=354 fm/c 3 Breit-Wigner A (GeV -1 ) 2 1 0 0.2 0.4 0.6 0.8 1 1.2 m (GeV)

Charmonium in vacuum and in matter • Charmonium: J/Ψ, Ψ(3686), Ψ(3770): colour dipoles in colour-electric field • ¯ D (¯ cq ) D (¯ qc ) loops contribute to the charmonium selfenergies • in matter the energy of the colour dipole is modified due to the modification of the gluon condensate second order Stark-effect S.H. Lee, C.M. Ko Phys. Rev. C67 (2003) 038202 2 � � ρ N � ∂ψ ( k ) k � α s π E 2 � dk 2 � � ∆ m ψ = − ǫ = 2 m c − m Ψ � � 18 m N ∂k k 2 /m c + ǫ N � � • the effect of the ¯ DD loop modified, because the mass of D mesons also modified due to the change of the quark condensate • The width of the charmonium increases due to the collisional broadening • dilepton branching ratio in matter? due to collisional broadening Γ tot med >> Γ tot vac . What is Γ em med ? Br em med ?

hadron( ¯ p, π ,p) A around charmonium threshold energies Stark-effect+ ¯ Charmonium DD loop J/Ψ -8+3 MeV ρ/ρ 0 Ψ(3686) -100-30 MeV ρ/ρ 0 Ψ(3770) -140+15 MeV ρ/ρ 0 collisional broadening at ρ 0 : 15 MeV, 26 MeV and 26 MeV (cross sections were fitted to charmonium suppression at SPS) background: Drell-Yan: small number of energetic hadron-hadron collisions ¯ ν e and similarly for ¯ DD decay: c quark decays weakly to s quark, D → Ke ¯ D , close to the threshold due to the production of two kaons the available energy for dileptons are strongly reduced up to moderate energies the background is low