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Heavy-ion collisions in modified AdS spaces

Pozdeeva E.O based on work I.Ya. Aref'eva, E.O.Pozdeeva,T.O.Pozdeeva to be bublished in Theor.Math.Phys. 176(1)(2013)

QFTHEP 2013


Quark Gluon Plasma is the thermally equilibrated state of matter in wich quarks and gluons are deconfined from hadrons Quark Gluon Plasma (QGP) has been discovered in Au+Au collision at energy 100 GeV for nucleon in 2005 @ RHIC


In holographic approch clasical gravity in AdS 5 discribes strong coupling field theory in 4D Minkowski space There is hypothesis that QGP formation in 4D space corresponds to Black Holes creation in dual 5D space.

Gubser, Klebanov, Polyakov, 9802109 Witten, 9802150


The gravitational shock wave in AdS 5 space is dual to ultrarelativistic heavy-ion in 4D space-time. Thus, heavy-ion collisions can be represented such as gravitational shock waves collisions in AdS 5


QGP formation is equivalent to BH creation in AdS
Gubser et al.; 0805.1551, 0902.4062

5


Problem: How to get dependence of experimental multiplicity on energy from holographic model.


Simplest holographic model is related with N=4 SYM
[But QCD is not SYM]



Our goal: to study more complicate models to fit experimental data.


Main conjecture: multiplicity is proportional to entropy

S N
Gubser et al.; 0805.1551

On experiments can be measured only

N

ch

:

N N

ch

B. B. Back et. al., 0210015[nucl-ex].


Accordingly experiment the charged-particles pseudorapidity density depends on colliding energy

dN ch / d s

0.15

for Pb-Pb and Au-Au - collisions
dN ch / d s
E =( 1 / 2 ) s
NN

0.11

pp collision

- colliding energy for nucleon

K. Aamodt et al.[ALICE Collaboration], 1011.3916 [nucl-ex]. DISCREPANCY

The simple holographic model gives

dN c h / d s

2/ 3


The mininal black hole entropy can be estimated by trapped surface area

S S

trapped

=A

trapped

/ 4G

N

The trapped surface is surface whose null normals all propagate inward.
S. W. Hawking and D. Page,Thermodynamics Of Black Holes In Anti-de Sitter Space,Commun.Math.Phys.87(1983)577 C. S. Peёca, J. P. S. Lemos, 9805004 [gr-qc]




N=4 SYM is not QCD
For holographic description of QCD a modified AdS is used to study dependence of entropy on energy
5



Gursoya, Kiritsis et al.,0707.1324, 0707.1349

Early the modification of AdS 5 space-time by introduction of wrapping factor was applied for shock waves with the specialy distributed colliding masses.


Kiritsis, 1111.1931

We consider collisions of walls with averaged mass in modified 5D space-time.



The shock wave with mass spread over transversal surface (shock wall wave) is a simplification of a point source shock wave. We describe heavy-ion collisions by the wall-wall shock wave collisions in AdS 5 (or in its modification)
S. Lin, E. Shuryak, 1011.1918[hep-th] I. Y. Aref'eva, A. A. Bagrov and E. O. Pozdeeva, Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions," JHEP 1205, 117 (2012)


The Einstein equation for particle in dilaton field has the form:

where We consider the shock wave metric
Aref'eva I.Ya. 0912.5482[hep-th] M. Hotta, M. Tanaka, Shock-wave geometry with nonvanishing cosmological constant, Class. Quantum Grav. 10, 307, 1993


Using shock wave ansatz we reduce the Einstein equation to the differential equation for shock wave profile and two equations defining the connection of field and field potential with b-factor:


The most interesting case is the collision of flat objects with mass uniformly distributed The equation corresponding to the domain profile with mass distributed over the domain wall

L

and equation corresponding to the domain profile with mass distributed over the finite region with radius L

coincide up to a constant factor

L

2


The solutions to equations with mass uniformly distributed over finite and infinite surfaces coincide up to constant L 2

We identify the black hole creation with trapped surface formation. The formation conditions are applied to schock wall wave profile at the trapped surface boundary points


The trapped surface area is calculated as follows

where

is the metric determinant of AdS

3

The relative area s dened with the formula


We modify AdS space-time using 4 wrapping factors types

where a>0, R=1 fm, L 4.4 fm


Using the solution to general form of domain equation (for any wrapping factor) and the trapped surface conditions we obtain the relations ;

z

a

z

b

between trapped surface boundary ( z a< z b) points and collision point


For the wrapping factor

we have obtained

following relations between boundary points and collision point ,

For the considered case the collision point is fixed by energy.


The relative area of trapped surface defined by

The maximum entropy value is obtained for approximation

, in this

The dependence of entropy on entropy is linear for the exponential wrapping factor


Power b-factor area of trapped surface

gives following relative

,

The maximal entropy value will at in assumption


For the power wrapping factor the entripy increase as The multiplicity of particles produced in heavy ions (PbPb-and AuAu-collisions) collisions dependents on 3 energy as in the range 10-10 GeV. This model can coinside with experimental data at a 0.47
K. Aamodt et al. [ALICE Collaboration], arXiv:1011.3916 [nucl-ex].


Mixed factor of the form

gives the another

relative area of quasi-trapped surface energy dependence

which has the maximal value at

and roughly is

at

10GeV E <1 TeV


The wrapping factor gives the most complicate relative area of trapped surface energy dependence


Wich has maximal value at

:

The entropy can be roughly estimate at a=1/2 such as

C 1=-0.738 , C 2= 0.393 at 10< E <100

GeV

C 1=-0.073 , C 2= 0.827 at 100< E <1000 GeV


Conclusions
The black holes formation in the domain wall-wall collisions is investigated in the deformed AdS 5 with b-factors. The several b-factor types: power, exponential and mixed are considered. The dependence of the entropy on the energy for different b-factors is analyzed. These results (with the account of AdS/CFT-duality) allow to simulate the dependence of multiplicity on the energy of the colliding heavy-ions ,

a 0.47

,

S E

0. 3

( in agreement with experimental data

).

The additional logarithms appear when considering the mixed factor.