Baryon Strangeness correlatons : signals of a

de-confined antecedent

Abhijit Majumder

Nuclear theory group,

Lawrence Berkeley National Lab.

In collaboration with Volker Koch and Jorgen Randrup

Conserved quantities in HIC

Fluctuations of conserved quantities

The BS of QGP

Differentiating the different paradigms: Quasi-particle QGP, Hadron gas, Bound states, Event Generators Conclusions..

OUTLINE

LatticeLattice

The general picture in a Heavy-ion collision What do we know ?

1) Rapid longitudinal expansion…

2) Early thermalization, v2, radial flow…

3) High density matter jet quenching, Bjorken

estimates

4) No first order phase transition !

Imagine a conserved charge carried by a particle in the plasma

++

+ +

+

+

+++

+

+

+

+

+

+

+

+

+

---

-

---

-

- --

- -

----

+ - + -

+ - + -

If nothing drastic happens during hadronization

Net charge conserved in a chosen rapidity interval

++

+

The BS of the QGP!Quantum numbers conserved in Heavy ion collisions:

• Baryon number B (exactly)• Charge Q (exactly)• Strangeness S (almost!) • Combinations are also conserved : BS, QS, BQ etc. • Fluctuations of B,Q,S conserved • Fluctuations of products conserved• Should be conserved in a wide rapidity bin!

• BS is carried by s, s

• Strangeness carriers s, s

Canonical QGP vs. Hadron gas

• BS is carried by • Strangeness carriers

B and S locked together in a QGP, But not in a hadron gas,

Correlation in B & S

Fluctuations of S

x(-3) as quarks have B=1/3, and S=-1

The observable

ii

ii

evtsii

evts

i iii

evtsiii

evts

BS

SSN

SN

SBN

SBN

SS

SSBB

S

SBC

2

2

2

22

11

11

3

3)(

3

Experimentally: measured in the final state, after freezeoutwith only final state hadrons...Theoretically: calculated in the initial state, when fluctuations set in, using prevalent degrees of freedom...

Say the fluctuations are set in by independent mobile species

kk

kflavors

k

SBSBBS n

events

if

species

f

fi

events

BnN

B1

events

i

species

gg

gi

species

ff

fi

events

SnBnN

BS1

Assuming Poisson statistics, n>, G.C. ensemble

events

if

species

f

fi

events

SnN

S1

222k

kflavors

k

SSS n

To calculate replace event average by average over states...Experimentally, have to use method with noApprox.. BSp + K

Simple estimates

• In a QGP phase

nn ssBS 3

nnS ss2

CBS = 1

In hadron gas phase

...9...6

...33

BS

...02 KKKS

At T=170MeV, =0R = 0.66

Almost 50% rise in CBS from hadron gas to QGP

Hadron gas estimate sensitive to chemical potential and temperature. Estimate along the freeze-out line

Increasing the baryon chemical potential, increases baryons. At large S is carried by Kaons and –S by

2

33

K

CBS

Calculated by R.V. Gavai, S. Gupta, Phys.Rev.D66:094510,2002, But in the quenched approximation

Estimates from the Lattice

BSSB

TLogZV

TBS

0

)(

Need off-diagonal susceptibilities …’s in unquenched QCD

222

))((31

333s

ssdu

S

BS

S

SBCBS

At T = 1.5 Tc Off-Diagonal susceptibilities are very small compared to diagonal susceptibilities, CBS = 1+ 0.00(3)/0.53(1)

ss

dsus

ss

ssdsus

1

...30122),(

4

6

2

422

Tc

Tcc

T

T qqq

Full QCD, but with 2 flavors, gives similar insight!F

rom

C.R

. Alt

on e

t. a

l. P

hys

.Rev

.D71

:054

508,

2005

Estimates from a Bound-State-QGP!

..,,,, etcgggqqgqqqqqq

..,,,, etcgggqqgqqqqqq

E. Shuryak, I. Zahed, Phys.Rev.C70:021901,2004; Phys.Rev.D70:054507,2004.

QGP is strongly coupledLarge scattering cross-sectionsMultitude of binary bound states

And heavy quasi-particle states of quarks and gluons, m~gT

Say fluctuations are set in at 1.5Tc

qq is not bound at this temperature

Contributing states:

gqqgqqqq ,,

• Heavy quark, antiquark quasiparticle have C=1

• Quark-antiquark states: 8 like, 24 like (They have no Baryon number) u s + d s + s u + s d These states have C = 0

• Quark gluon states in triplet color representation 36 states, have C = 1

• Quark gluon states in hexaplet color representation considered unbound at T=1.5Tc

All together at T=1.5Tc, CBS = 0.61

Similar to Hadron gas estimate…

Estimate from string fragmentation

• Very strongly interacting system

• Fluctuations set in by string degrees of freedom

• Single string fragmentation: JETSET

• Heavy-ion collision : HIJING

• Study effect of varying acceptance range in rapidity

Final results, from 4 approaches !

At ymax<y<ymin C = 0

All events have B=0

CBS rises and stabilizes at Smaller range of y

Still much smaller than Hadron gas estimate

Hadron gas, SZ plasma smaller than naïve QGPor Lattice estimate

CBS: discerning experimentalobservable

RQMD from S. Huang

Conclusions/problems• Bulk fluctuations of conserved charges can

determine the degrees of freedom• E-by-E measurement of CBS can give insight

into the primordial matter.• Strangeness and baryonic degrees of freedom

are quasi-particulate • No light meson like bound states!

• Experimentally, hard to estimate baryon number: neutrons! • Phase transition causes reshuffling of B & S

• Contamination by weak decays from heavier states

Speculations!

B) Its not hydro-dynamic i) Everything is quasi-particulate, ii) Submerged in a repulsive mean field, iii) Expansion driven by mean field !! ??

A) Its still hydro-dynamic i) The dynamics is driven by gluons ii) Quark quasi-particles go along for the ride iii) Need alternative means to determine the existence of bound states!

A. Peshier, B. Kampfer and G. Soff, Phys.Rev. D66:094003,2002.

J. P. Blaizot, E. Iancu and A. Rebhan, Phys.Rev. D63:065003,2001.