Saturation physics and baryon stopping in the SPS, RHIC, and

LHC energy regions

20100726

冯 笙 琴

13 届全国核结构会议 赤峰

Topics

1. CGC and saturation physics

2. The rapidity distributions of net

baryon in the SPS, RHIC, and LHC

energy regions

3. The results and discussions

Color Glass CondensateHadronic interactions at very high energies are controlled by a new form of matter, a dense condensate of gluon.

Color: gluon are colored

Glass: the fields evolve very slowly with respect to the natural time scale and are disordered.

Condensate: There is a very high density of massless gluons. These gluons can be packed until their phase space density is so high that interactions prevent more gluon occupation.

HERA Data

1.Small x problem

McLerran, hep-ph/0311028

pQCD ok !pQCD ok !

HERA Data

2. Geometric scaling

One expects structure functions

from DIS depend on (in

general) x and Q2/Λ2, but the

function depend only on

at Bjorken x < 0.01

(HERA), i.e. independent of x.

Some kind of scaling at

small x.

Relativistic Heavy Ion Collisions in High Energy Limit

CGC

5. Individual hadrons freeze out

4. Hadron gas cooling with expansion

3. Quark Gluon Plasma thermalization, expansion

2. Pre-equilibrium state collision

1. Nuclei (initial condition)

The picture

Transverse momentum spectra and rapidity distribu

tion of net baryon or final hadrons in Relativistic Hea

vy Ion Collisions.

纵向光锥变量

LC timeLC time

LC longit. coordinateLC longit. coordinate

invariant 4-productinvariant 4-product

LC energyLC energy LC longit. momentumLC longit. momentum

rapidityrapidity

Notation

Feynman, Bjorken x:

)()( xxFD aa

Stochastic Yang-Mills equation

Valence partonsas static random color source

Small x gluons as radiation fieldcreated by (x).

Hadrons at Very High EnergiesHigher energies (smaller x 0)

Valence partons gluon cascade dense gluon state = CGC

Color Glass Condensate

Saturation scale Qs >> QCD

typical transverse size ~ 1/Qs

weak coupling s(Qs) << 1 at high energy

Strong gauge field A ~ Qs /g, E, B ~ Qs2/g

CGC is a weakly-coupled many body system with high non-linearity !

3.03/12 ~),( xAAxQs

Color Glass Condensate theory

hep-ph:0307037

Experiment

So ……

Theory

HERA

Small x problem

Geometric scaling

Saturation physics

pT spectra

dydN hB )(

PRC_80_054905“Baryon stopping as a test of geometric scaling”

Particle production in hadronic collisions

Leading particles (projectile or target ) have rapidity close to original rapidity.

Produced particle populate the region around zero-rapidity.

Feynman scaling of rapiditydistribution of produced particles.

Deep inelastic scattering

Hadron = collections of partons

with momentum distribution

dN/dx

Rapidity: )/1ln( xyy hadron

dx

dNx

dy

dN 强子内部胶子分布图

2. The distribution function of net baryons

The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scatterings.

The fast valence quarks in one nucleus scatter in theother nucleus by exchanging soft gluons, leading to theirRedistribution in rapidity space.

To access the gluon distribution at small x, we use the valence quark distributions at large x

2. The distribution function of net baryons

The distribution of net baryon is proportional to

the valence quark rapidity distribution, by integrating

over PT:

),()()2(

2112

2

2 Tv

T

T pxxqxp

pdC

dy

dN

this is indeed a good approximation at high energy heavy-ion collisions

One important prediction of the color glass

condensate theory is geometric scaling:

the gluon distributions depends on and

only through the scaling variable ,

where

xTP

)(2

2

xQP

s

T

xQAxQs20

3/12 )(

with the changing of variables

1xx yxex 22

yT sexp 222

Thus we rewrite the formula as

1

0

2 )()(2

exxxqx

dxC

dy

dNv

yAQs )1(2ln)/ln( 312

0 where is the scaling variable.

In the NF-model (No Fragmentation) — 220 04.0,2.0 GeVQ

the unintegrated gluon distribution is

)01.0()1(}

)(exp{

)(4

)01.0(

),(4

22

2

2

22 xx

xQ

p

xQ

p

xconst

px

s

T

s

TT

The valence quarks distribution is

)01.0()(

)01.0()(

5.0

xxdxu

xxxxq

vv

v

So the net-baryon distribution originates from the

projectile is

The effective quark mass are considered by substituting

the transverse momentum for i.e. Tp 22)( mesx y

22)( mesxp yT

1

01.0

42

2

2

2

2

)()1(})(

exp{)(

4)(

)(}2

1exp{

regionforwardxxQ

p

xQ

pxdxu

x

dx

regioncentraly

dy

dN

s

T

s

Tvv

m: the mass of effective quark

The results

Rapidity distributions of

net baryon in different

centrality collisions at

SPS energies of

.

GeVs 3.17

Rapidity distributions of

net baryons in different

centralities collisions at

RHIC energies of

. GeVs 200

Rapidity distributions of net baryon in

central Au+Au collisions at RHIC energies

of . GeVs 4.62

The results

The mean rapidity loss is plotted

as a function of the beam

rapidity.

2/

0

part

y

p

N

dydy

dNy

y

yyy

p

3. The results

The effective quark mass is plotted as a function of the beam rapidity, are among 0.25-0.28GeV.m

The ratios of number of baryons which locate in

the central region contributing to the whole

ones.

r

The results

The rapidity distribution of net baryons in central Pb+Pb collisions at LHC energies of with

TeVs 52.522

0 04.02.0 GeVQand .

The discussionsComing to ultrarelativistic heavy ion collisions, as

experimentally realized at RHIC and, in perspective, at

LHC, we note that the CGC should be the appropriate

description of the initial conditions. Indeed, most of the

multiparticle production at central rapidity is from the

small-x. The early stages of a nuclear collision, can

thus be described as the melting of the Colour Glass

Condensates in the two nuclei.

The discussions

The experimental data at SPS 、 RHIC have been analyzed from the perspective of the CGC.

The nuclear stopping have been discussed by saturation model.

LHC results has been predicted