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

SLIDE 1

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

SLIDE 2

The QCD vacuum condensates: the most important ones: mq < ¯ qq > and < αs/πG2 > < ¯ 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

πm2 π = (mu + md) < ¯

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

SLIDE 3

Gluon condensate in matter Quark and gluon condensates are known in vacuum, in matter: < n.m.|O|n.m. >=< 0|O|0 > +

• d3p/p0fN(p, µ) < N|O|N >

we need to know < N|¯ qq|N > and < N|αsG2|N > Trace anomaly: T QCD µ

µ

= β 2gGa

µνGa µν + m¯

qq Between vacuum states: energy of the vacuum. Between nucleons mN ¯ u(p)u(p) =< N(p)| β 2gGa

µνGa µν + m¯

qq|N(p) > contribution of light quarks (πN scattering, σ-term):≈ 50 MeV, gluons contribution to the mass of the proton: ≈ 750 MeV

SLIDE 4

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)

SLIDE 5

KEK E325 12 GeV pA data for φ

20 40 60

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

50 100

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

100 200 0.9 1 1.1 1.2

[GeV/c2] counts/[6.7MeV/c2]

100 200 300 0.9 1 1.1 1.2

[GeV/c2] counts/[6.7MeV/c2]

χ2/ndf=46/50 χ2/ndf=55/50 χ2/ndf=63/50 χ2/ndf=43/50 χ2/ndf=36/50 χ2/ndf=83/50

C Cu C Cu C Cu

1.75<βγ 1.75<βγ 1.25<βγ<1.75 1.25<βγ<1.75 βγ<1.25 βγ<1.25

20 40 60

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

50 100

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

100 200

[GeV/c2] counts/[6.7MeV/c2]

100 200 300

[GeV/c2] counts/[6.7MeV/c2]

20 40 60 50 100 150 50 100 50 100 150 100 200 0.9 1 1.1 1.2 100 200 300 0.9 1 1.1 1.2

χ2=46 χ2=56 χ2=64 χ2=44 χ2=36 χ2=74 χ2=45 χ2=58 χ2=66 χ2=45 χ2=37 χ2=66

C Cu C Cu C Cu

1.75<βγ 1.75<βγ 1.25<βγ<1.75 1.25<βγ<1.75 βγ<1.25 βγ<1.25

• R. Muto et al.
• Phys. Rev. Lett. 98 (2007) 042501

m(ρ)/m(0) = 1 − 0.033(ρ/ρ0) Γ(ρ)/Γ(0) = 3.6(ρ/ρ0)

SLIDE 6

CERES data

p-Be 450 GeV

2.1 < η < 2.65 p⊥ > 50 MeV/c Θee > 35 mrad 〈dNch /dη〉 = 3.8 mee (GeV/c2) (d2Nee /dηdm) / (dNch /dη) (50 MeV/c2)-1

charm π0 → eeγ ρ,ω → ee φ → ee η → e e γ η, → eeγ ω → eeπo

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

0.5 1 1.5

p-Au 450 GeV

2.1 < η < 2.65 p⊥ > 50 MeV/c Θee > 35 mrad 〈dNch /dη〉 = 7.0 mee (GeV/c2) (d2Nee /dηdm) / (dNch /dη) (50 MeV/c2)-1

charm π0 → eeγ ρ,ω → ee φ → ee η → e e γ η, → eeγ ω → eeπo

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

0.5 1 1.5

• G. Agakichiev et al.
• Eur. Phys. J. C4 (1998) 231

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

mee (GeV/c2) (d2Nee /dηdmee) / (dNch /dη) (100 MeV/c2)-1

Pb-Au 158 AGeV

σtrig/σtot ~ 35 % p⊥ > 200 MeV/c Θee > 35 mrad 2.1 < η < 2.65 〈Nch〉 = 220 πo → eeγ ρ/ω → ee φ → ee η → eeγ η, → e e γ ω → eeπo

• G. Agakichiev et al.
• Phys. Lett. B422 (1998) 405

SLIDE 7

BUU

• ∂F

∂t + ∂H ∂p ∂F ∂x − ∂H ∂x ∂F ∂p = C, H =

• (m0 + U(p, x))2 + p2
• potential: momentum dependent, soft: K=215 MeV

U nr = A n

n0 + B

• n

n0

τ + C 2

n0

• d3p′

(2π)3 fN(x,p′) 1+

• p−p′

Λ

2,

• testparticle method

F =

Ntest

• i=1 δ(3)(x − xi(t))δ(4)(p − pi(t)).
• 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

SLIDE 8

Collision term

• NN ↔ NR, NN ↔ ∆∆
• baryon resonance can decay via 9 channels

R ↔ Nπ, Nη, Nσ, Nρ, Nω, ∆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
• dσX→NR

dMR

∼ A(MR)λ0.5(s, M 2

R, M 2 N)

Unknown cross sections: Statistical bootstrap:

• G. Balassa, P. Kov´

acs, Gy. Wolf, Eur. Phys. J. A54 (2018) 25,

SLIDE 9

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

SLIDE 10

Off-shell transport

• Kadanoff-Baym equation for retarded Green-function

Wigner-transformation, gradient expansion

• transport equation for Fα = fα(x, p, t)Aα

A(p) = −2ImGret =

ˆ Γ (E2−p2−m2

0−ReΣret)2+ 1 4 ˆ

Γ2,

• W. Cassing, S. Juchem, Nucl.Phys. A672 (2000) 417
• S. Leupold, Nucl.Phys. A672 (2000) 475
• testparticle approximation

SLIDE 11

Transport equations

• d

Xi dt = 1 1−C(i) 1 2ǫi

• 2

Pi + ∇Pi ReΣret

(i) + ǫ2

i −

P 2

i −M2 0 −ReΣret (i)

ImΣret

(i)

• ∇Pi ImΣret

(i)

• d

Pi dt =− 1 1−C(i) 1 2ǫi

• ∇Xi ReΣret

i

+

ǫ2

i −

P 2

i −M2 0 −ReΣret (i)

ImΣret

(i)

• ∇Xi ImΣret

(i)

• dǫi

dt = 1 1−C(i) 1 2ǫi

∂ReΣret

(i)

∂t

+

ǫ2

i −

P 2

i −M2 0 −ReΣret (i)

ImΣret

(i)

∂ImΣret

(i)

∂t

• where C(i) renormalization factor

C(i) =

1 2ǫi

• ∂

∂ǫi ReΣret (i) + ǫ2

i −

P 2

i −M2 0 −ReΣret (i)

ImΣret

(i)

∂ ∂ǫi ImΣret (i)

• the last equation for homogenous system can be rewritten as

dM2

i

dt

=

d(ǫ2

i −P 2 i )

dt

=

dReΣret

(i)

dt

+

M2

i −M2 0 −ReΣret (i)

ImΣret

(i)

dImΣret

(i)

dt

SLIDE 12

Evolution of mass distribution in a box the vector meson masses are shifted linearly with density, and change the density linearly from ρ0 to 0 in 4 fm/c:

10 20 30 40 50 60 70 80 0.6 0.65 0.7 0.75 0.8 0.85 0.9

A (GeV-1) m (GeV)

Breit-Wigner t=300 fm/c t=350 fm/c t=351 fm/c t=352 fm/c t=353 fm/c t=354 fm/c Breit-Wigner 1 2 3 4 5 0.2 0.4 0.6 0.8 1 1.2

A (GeV-1) m (GeV)

Breit-Wigner t=300 fm/c t=350 fm/c t=351 fm/c t=352 fm/c t=353 fm/c t=354 fm/c Breit-Wigner

ω ρ

SLIDE 13

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
• f the gluon condensate second order Stark-effect

S.H. Lee, C.M. Ko Phys. Rev. C67 (2003) 038202 ∆mψ = − ρN 18mN

• dk2
• ∂ψ(k)

∂k

• 2

k k2/mc + ǫ αs π E2

N

ǫ = 2mc − mΨ

• 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 Γtot

med >> Γtot

• vac. What is Γem

med? Brem med?

SLIDE 14

hadron(¯ p, π,p) A around charmonium threshold energies

Charmonium Stark-effect+ ¯ DD loop J/Ψ

• 8+3 MeV ρ/ρ0

Ψ(3686)

• 100-30 MeVρ/ρ0

Ψ(3770)

• 140+15 MeV ρ/ρ0

collisional broadening at ρ0: 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 ¯ DD decay: c quark decays weakly to s quark, D → Ke¯ νe and similarly for ¯ 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

SLIDE 15

Time evolution of masses and pos. of creation in πAu 6.5 GeV

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 5 10 15 20 J/Ψ Ψ(3686)−0.2 Ψ(3770) Mass [GeV] t [fm/c] 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 −10 −8 −6 −4 −2 2 4 surface f(z) z [fm]

The charmonium states are created at the surface of the heavy nucleus, travel through the dense matter (decays with some probability), crosses the thin surface again and reaching the vacuum. Major contribution to the dilepton channel are coming from the dense matter and from the vacuum.

SLIDE 16

Charmonium creation in πAu 6.5 GeV

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.2 0.4 0.6 0.8 1 f(ρ) ρ/ρ0 0.02 0.04 0.06 0.08 0.1 0.12 0.2 0.4 0.6 0.8 1 f(v) v/c

Most of the charmonium are created close to the surface of the nucleus

SLIDE 17

πAu at 6, 7 GeV

10-8 10-7 10-6 10-5 10-4 10-3 3 3.2 3.4 3.6 3.8 dσdilepton/dM [mb/GeV] M [GeV] J/Ψ 100*Ψ(3686) 400*Ψ(3770) 10-8 10-7 10-6 10-5 10-4 10-3 10-2 3 3.2 3.4 3.6 3.8 dσdilepton/dM [mb/GeV] M [GeV] J/Ψ 100*Ψ(3686) 100*Ψ(3770)

SLIDE 18

πBe and πC at 8 GeV

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 3 3.2 3.4 3.6 3.8 dσdilepton/dM [µb/GeV] M [GeV] J/Ψ 10*Ψ(3686) 60*Ψ(3770) 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 3 3.2 3.4 3.6 3.8 dσdilepton/dM [µb/GeV] M [GeV] J/Ψ 10*Ψ(3686) 60*Ψ(3770)

SLIDE 19

¯ pAu at 5, 8 GeV

10-5 10-4 10-3 10-2 10-1 100 101 3 3.2 3.4 3.6 3.8 dσdilepton/dM [µb/GeV] M [GeV] J/Ψ 50*Ψ(3686) 100*Ψ(3770) 10-4 10-3 10-2 10-1 100 101 3 3.2 3.4 3.6 3.8 dσdilepton/dM [µb/GeV] M [GeV] J/Ψ 20*Ψ(3686) 80*Ψ(3770)

SLIDE 20

Ψ(3686) excitation function in ¯ pAu reactions

1×10−10 1×10−9 1×10−8 1×10−7 1×10−6 1×10−5 3.3 3.4 3.5 3.6 3.7 3.8 [mb] E [GeV] in−medium vacuum vacuum shifted

SLIDE 21

Playing with the mass shift

10-8 10-7 10-6 10-5 10-4 10-3 10-2 3 3.2 3.4 3.6 3.8 dσdilepton/dM [µb/GeV] M [GeV] J/Ψ 200*Ψ(3686) 600*Ψ(3770)

pAu E=9 GeV, mass shift 50 MeV

SLIDE 22

Ψ(3686)

• The distance between the peaks corresponds to a mass shift at ρ ≈ 0.9ρ0
• qualitatively the same picture if increase or reduce the mass shift by factor of 2
• measuring the peak distance, we obtain the mass shift at ρ ≈ 0.9ρ0
• measuring the mass shift, we obtain the gluon condensate at ρ ≈ 0.9ρ0
• the same picture in ¯

p, π, p at and above thresholds

• measuring the JP/Ψ, Ψ(3686) states allow to determine their mass shift if it is

> 60 MeV

• key points: cross sections are not, background is several magnitude less than

the signal

• em. width
• absorption cross sections 25 mb (40 mb for p)
• can the error of the experimental mass resolution from the vacuum peak over-

shadow the smaller, in-medium peak?

SLIDE 23

Summary

• Dilepton production in hadron-A provides us the possibility to

study charmonium mass shift in matter. In all systems we found in-medium spikes for Ψ(3686).

• We can measure the gluon condensate in nuclear matter.

SLIDE 24

KEK E325 12 GeV pA data ρ and ω

fit result background φ→e+e- ρ→e+e- ω→e+e- ω→e+e-π0 η→e+e-γ

(a) C

invariant mass

fit result background φ→e+e- ρ→e+e- ω→e+e- ω→e+e-π0 η→e+e-γ

events[/ 10MeV/c2] (b) Cu

invariant mass invariant mass invariant mass invariant mass invariant mass invariant mass [GeV/c2]

events[/10 MeV/c2]

fit result ρ→e+e- ω→e+e-

(a) C

with mass modification

invariant mass invariant mass invariant mass invariant mass invariant mass invariant mass [GeV/c2]

events[/10 MeV/c2]

fit result ρ→e+e- ω→e+e-

(b) Cu

with mass modification

• M. Naruki et al.
• Phys. Rev. Lett. 96 (2006) 092301

m(ρ)/m(0) = 1 − 0.09(ρ/ρ0) no broadening

SLIDE 25

KEK E325 12 GeV pA data for φ

20 40 60

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

50 100

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

100 200 0.9 1 1.1 1.2

[GeV/c2] counts/[6.7MeV/c2]

100 200 300 0.9 1 1.1 1.2

[GeV/c2] counts/[6.7MeV/c2]

χ2/ndf=46/50 χ2/ndf=55/50 χ2/ndf=63/50 χ2/ndf=43/50 χ2/ndf=36/50 χ2/ndf=83/50

C Cu C Cu C Cu

1.75<βγ 1.75<βγ 1.25<βγ<1.75 1.25<βγ<1.75 βγ<1.25 βγ<1.25

20 40 60

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

50 100

counts/[6.7MeV/c2]

50 100 150

counts/[6.7MeV/c2]

100 200

[GeV/c2] counts/[6.7MeV/c2]

100 200 300

[GeV/c2] counts/[6.7MeV/c2]

20 40 60 50 100 150 50 100 50 100 150 100 200 0.9 1 1.1 1.2 100 200 300 0.9 1 1.1 1.2

χ2=46 χ2=56 χ2=64 χ2=44 χ2=36 χ2=74 χ2=45 χ2=58 χ2=66 χ2=45 χ2=37 χ2=66

C Cu C Cu C Cu

1.75<βγ 1.75<βγ 1.25<βγ<1.75 1.25<βγ<1.75 βγ<1.25 βγ<1.25

• R. Muto et al.
• Phys. Rev. Lett. 98 (2007) 042501

m(ρ)/m(0) = 1 − 0.033(ρ/ρ0) Γ(ρ)/Γ(0) = 3.6(ρ/ρ0)

SLIDE 26

TAPS/ELSA data for γA → ωX

100 200 300 400 500 200 400 600 800 5 10 15 20 25 30 540 750 960 counts / [ 12 MeV/c2]

0.2 < | p

→ ω |< 0.4 GeV/c

counts / [ 12 MeV/c2]

0.4 < | p

→ ω |< 0.6 GeV/c

Mπ γ [MeV/c2] counts / [ 12 MeV/c2]

0.6 < | p

→ ω |< 1 GeV/c

x 102 Mπ γ [MeV/c2] counts / [ 12 MeV/c2] 1 < | p

→ ω |< 1.4 GeV/c

x 102 5 10 15 20 25 30 35 40 540 750 960

| p

→ ω | [MeV/c]

Mmean / [ MeV/c2]

Nb LH2

760 780 500 1000 1500

• D. Trnka et al.
• Phys. Rev. Lett. 94 (2005) 192303

m(ρ)/m(0) = 1 − 0.14(ρ/ρ0), ¯ ρ = 0.6ρ/0 Γres = 55MeV

SLIDE 27

NA60 data for ρ

0.2 0.4 0.6 0.8 1 1.2 1.4 500 1000 1500 2000 2500 3000 3500

In-In SemiCentral

T

all p

dN/dM per 20 MeV M (GeV)

• S. Damjanovic et al.

Eur.Phys.J.C49:235-241,2007 thick solid line: ρ-broadening due to hadronic reactions

• R. Rapp, J. Wambach
• Adv. Nucl. Phys. 25, 1

SLIDE 28

CERES data

p-Be 450 GeV

2.1 < η < 2.65 p⊥ > 50 MeV/c Θee > 35 mrad 〈dNch /dη〉 = 3.8 mee (GeV/c2) (d2Nee /dηdm) / (dNch /dη) (50 MeV/c2)-1

charm π0 → eeγ ρ,ω → ee φ → ee η → e e γ η, → eeγ ω → eeπo

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

0.5 1 1.5

p-Au 450 GeV

2.1 < η < 2.65 p⊥ > 50 MeV/c Θee > 35 mrad 〈dNch /dη〉 = 7.0 mee (GeV/c2) (d2Nee /dηdm) / (dNch /dη) (50 MeV/c2)-1

charm π0 → eeγ ρ,ω → ee φ → ee η → e e γ η, → eeγ ω → eeπo

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

0.5 1 1.5

• G. Agakichiev et al.
• Eur. Phys. J. C4 (1998) 231

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

mee (GeV/c2) (d2Nee /dηdmee) / (dNch /dη) (100 MeV/c2)-1

Pb-Au 158 AGeV

σtrig/σtot ~ 35 % p⊥ > 200 MeV/c Θee > 35 mrad 2.1 < η < 2.65 〈Nch〉 = 220 πo → eeγ ρ/ω → ee φ → ee η → eeγ η, → e e γ ω → eeπo

• G. Agakichiev et al.
• Phys. Lett. B422 (1998) 405

SLIDE 29

Statistical Bootstrap approach

• G. Balassa, P. Kov´

acs, Gy. Wolf, Eur. Phys. J. A54 (2018) 25

• Estimate unknown cross sections of different hadronic reactions

up to a few GeV in c.m.s energy.

• Our method incorporate that during the collision a compound

system, a fireball, is formed and, through possible production of subsequent fireballs, this system decays into a specific final state.

• The probability of the resulting final state can be calculated from

the corresponding phase space, the quark content of the final state and from the density of states ρ(m).

SLIDE 30

SLIDE 31

Predictions

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 100 200 300 400 500 600 700 800

R[ppπ0/π+π−] M [GeV]

model data

SLIDE 32

SLIDE 33