Charm and bottom flavored hadrons production from strangeness rich quark gluon plasma hadronization

Inga Kuznetsova and Johann Rafelski

Department of Physics, University of Arizona

Supported by a grant from the U.S. Department of energy, DE-FG02-04ER41318

We study QGP hadronization at given b, c quark content. We

predict the yields of charm and bottom flavored hadrons

within statistical hadronization model. The important new

feature is that we take into account high strangeness and

entropy content of QGP, conserving strangeness yield and

entropy at hadronization.The European Physical Journal C - Particles and Fields. C51, 113-133, (2007) arXiv:hep-ph/0607203

Motivations Probe of QGP properties, confirmation of

deconfinement Information on hadronization temperature of

heavy flavored hadrons Understanding of properties of phase transition

between deconfinement phase and hadronic gas (HG) phase in strangeness rich QGP.

Statistical model Assumed Boltzman distribution for b, c, s, hadrons:

= T ln for all particles γi is phase space occupancy factor

γi =1, ni = nieq is chemical equilibrium for particle i γi

Q is in QGP i=c, b, s, q (q is u or d)

γiH after hadronization, for example for D mesons: γD

H

= γcH γq

H

nT

g W m Ti

eq

i i i

3

22( / ) ,d N

d yn

d V

d yi

i i

eq ,

W x x K x( ) ( ) 2

2where

Main model assumptions We do not assume chemical equilibrium for quark flavors. We work in framework of fast hadronization to final state. Physical

conditions (system volume, temperature) do not change.

Flavor conservation:

fixes statistical parameters (γbH, γc

H, γsH) for quark yield.

Entropy conservation: fixes

In QGP

(The entropy of expanding QGP is conserved: )

d S

d y

d S

d y

Q G P H G

q

H G ( )

d N

d y

d N

d yi

H G

i

Q G P

Td V

d yco n st3 .

1QGPq

;10dy

dN QGPc .1

dy

dN QGPb

For LHC:

Strangeness Strangeness (s) production in thermal gluon fusion follows in time entropy (S)

production Ratio s/S depends on energy of collision, s increases faster with energy then

S. The hot state, where the threshold for s production is exceeded, lives longer

At RHIC energies s/S ~ 0.03, at LHC expect 0.03 ≤ s/S ≤ 0.05

obtained from SHARE 2.1 ``SHARE: Statistical hadronization with resonances,'' G. Torrieri, S. Steinke, W. Broniowski, W.Florkowski, J. Letessier and J. R, Comput. Phys. Commun. 167, 229 (2005) (SHARE 1) [arXiv:nucl-th/0404083];G.Torrieri, S.Jeon, J.Letessier and J. R, Comput. Phys. Commun. 175, 635 (2006) (SHARE 2) [arXiv:nucl-th/0603026]Webpage:http://www.physics.arizona.edu/~torrieri/SHARE/sharev1.html

Effect of strangeness on ratio D/Ds.

D

Df T

s

s

H

q

H

1

( )

D n nc q D

eq

c q D

eq

ii

D n ns c s D s

eq

c s i D s

eq

i

LHC?

Ratio D(B)/Ds(Bs) as a probe of T at measured s/S

Chemical equilibrium

Non-strange to strange charm baryons yields ratios as a function of γs/γq ratio

2

1

)/(/

)/(/

qs

qs

csscqq

cqscqq

LHC?

Double strange charm baryons (Ωc

0) yield as a function of hadronization temperature T

Ωc0 (2700 MeV) decay

modes: Σ+K-K-π+

Ξ0K-π+

Ξ-K-π+ π+

Ω- π+

Ω- π+ π0

Ω- π-π+ π+

Total yield of all hidden charm mesons asa function of T.

J/Ψ yield as a function of γs/γq

Both entropy and strangeness contents enhancement may result to J/Ψ suppression.

More light and\or strange quarks more probability for charm to bound to these quarks than to find anti-charm quark.

Conclusions Phase space occupancy factors of strange and light quarks have

strong influence on heavy flavor hadron production. Significant increase of the yield of strange quark-containing

charm (bottom) mesons and baryons with increase of s/S as compared to the chemical equilibrium yields.

The change in the yield of hadrons without strangeness but with light quark(s) depends on both s/S and γq. The ratio of these hadrons to similar strange hadrons always decreases with increase of s/S.

Yields of hadrons with two heavy quarks, as J/Ψ, decrease compared to chemical equilibrium when γq and\or γs > 1. This may provide a mechanism of J/Ψ suppression.

Entropy after hadronization Because of liberation of

color degree of freedom

The excess of entropy is observed in the multiplicity of particles in final state.

After hadronizaton SQ≈SH , γq

H >1.

When γqH = γq

cr : Bose singularity for pions;

Maximum of possible entropy content after hadronization

Q H 3

Strangeness conservation during hadronization

The equilibrium densities nieq are

sums of all known states densities for given particle i.

sd V

d yn n ns

H

q

H

K

eq

q

H

Y

eq

s

H

q

H eq 2 22

Charm (bottom) hadronization

cd V

d yn n n n

n n n n n n

n n

c

H

o p en

c

c

H

h id

c

q

H

ccq

eq

s

H

ccs

eq

o p en

c

q

H

D

eq

s

H

D s

eq

q

H

q q c

eq

s

H

q

H

sq c

eq

q

H

ssc

eq

h id

c

c

H

c c

eq

2

2 2

2

2 2 ;

;

.

c,b quarks produced in first nn collisions.

c=10, b=1; Flavor conservation equation

γbH >> γc

H >> γsH

Equilibrium case when

γqH = γs

H =1

D(B), Ds(Bs) mesons yield as a function of γs/γq.

γc(b)/Nc(b) is almost independent from Nc(b) .

D B N N

D B N Nc b c b q c b

s s c b c b s c b

( ) / /

( ) / /( ) ( ) ( )

( ) ( ) ( )