Post on 05-Jan-2016
description
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