Saturation physics and the J/psi productions of CNM in p(d)-A collisions

23/4/24 第九届中国高能物理年会-武汉（华中师大）

Saturation physics and the J/psi productions of CNM in

p(d)-A collisions

冯笙琴三峡大学

[email protected]


Topics

1. CGC and saturation physics

2. The J/psi productions of CNM in p(d)-A collisions

3. The results and discussions

TOPICS


1. CGC and saturation physics


HERA Data

Small x problem

McLerran, NPA750(05)30

pQCD ok !pQCD ok !

HERA DATA


)()( xxFD aa

Stochastic Yang-Mills equation

Valence partonsas static random color source

Small x gluons as radiation fieldcreated by (x).


Color Glass Condensate Hadronic interactions at very high energies are controlled by a new form of matter, a dense condensate of gluon. Color: Gluon are colored Glass: The gluons at small x are generated from gluons at larger values of x. The fields evolve very slowly with respect to the natural time scale and are disordered.Condensate: There is a very high density of mass-less gluons. These gluons can be packed until their phase space density is so high that interactions prevent more gluon occupation.

M. Gyulassy , L. D. McLerran， New forms of QCD matter discovered at RHIC， Nucl.Phys. A750 (2005) 30-63

http://inspirehep.net/author/profile/Gyulassy%2C%20Miklos?recid=649862&ln=en



http://inspirehep.net/author/profile/McLerran%2C%20Larry?recid=649862&ln=en

http://inspirehep.net/record/649862


The two incoming nuclei look as two Lorentz–contracted ‘pancakes’, with a longitudinal extent smaller by a factor 100 (the Lorentz boost factor) than the radial extent in the transverse plane.

Heavy ion collisions at ultra-relativistic energies are visualized as the collision of two sheets of colored glass. The nuclei appear as sheets at ultra-relativistic energies because of Lorentz contraction. The CGC gluons are shown as vectors which represent the polarization of the gluons, and by colors corresponding to the various colors of gluons.


Multi-particle production in a hadronic collision

2/mp

Leading particles (projectile or target ) are shown in real line and are clustered around the projectile and target rapidity.

In the dashed line, the distribution of produced mesons is shown.

Note that y = 0 corresponds to particles with pz = 0 or for which is small, x 1, in the high-energy ≪limit of interest. Thus the multiparticle production at central rapidity reflects properties of the small-x degrees of freedom in the colliding hadron wavefunctions.

smpm

)2(x 1


The rapidity distributions are to a good approximation independent of energy. This is illustrated in right figure, where the rapidity distribution measured at lower energy is shown with a solid line and the rapidity distribution at a different and higher energy is shown with a dotted line.

There is a remarkable feature of rapidity distributions of produced hadrons, generally referred to as either Feynman scaling or Limiting fragmentation. If we plot rapidity distributions of produced hadrons at different energies, then as function of y−yproj


This means that as we go to higher and higher

energies, the new physics is associated with the

additional degrees of freedom at small rapidity in the

center of mass frame (small-x degrees of freedom).

We shall see that in fact these large x degrees of

freedom act as sources for the small x degrees of

freedom.


Some scaling in p-A interactions

Nucl.Phys. A774 (2006) 287



2. The J/psi productions of CNM in p(d)-A collisions

Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC


胶子饱和构架下的 p(d)-A碰撞的 J/psi产生高能碰撞下，此时将一个质子看成一团胶子与核发生碰撞，此时与核子发生碰撞的主要是胶子。

胶子饱和特征质子 -核作用

/ /21 12 2( , )pA J X gA J X

c

d dx G x m

d bdy d b

In order to set normalization for , it is convenient

to compare the gA scattering process in (1) with that of

γA where there is a well developed phenomenology.

State with γ-proton scattering where

bXgA

2/J

dd

2/J

/J

161

dtd

pApA A

(1)

(2)


The S factors are given, in the Mclerran-Venugopalan model, by

]81exp[]

4exp[)( 222

2

rQrQNCrS s

s

c

F

Here Qs is the gluon saturation momentum. The main change of necessary to convert (3) to a cross section for gA→J/Ψ is the way the dipole scatters off nucleus.

(3)

(4)

cc


在 g-A 作用的色共轭表象中，对来自于胶子，对形成J/Ψ ，对应为一个色单态，对是通过偶极子 - 核子的非弹性碰撞而形成色单态的。这非弹性碰撞的点对应纵向坐标为，在位置前，假设偶极子 - 核子碰撞都是弹性碰撞的，非弹碰撞后，维持色单态不变。见下图。

cc

cccc

cc

F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012)Z. F. Jiang, S. Q. Feng, Y. F. Shi, Submitted to PRC


The interaction at , responsible of the transition from a color octet state to

a color singlet state. Under the MV model evaluation employed here, the

interactions probability of occurring before

drr4T(b)

Q2s


Here T(b) is the nuclear profile function. Each of these pieces can be treated as a dipole interaction with the nucleus with dipole separation . This gives the combined factor:

2/- ）（ rr

))(/(-161 22 bTrrQse

）（

where the factor accounts for these interactions being present only the last inelastic interaction at longitudinal coordinate .

)(/ bT


Interactions occurring after the last inelastic interactions preserve the singlet state of the quark-anti-quark system, this gives the combined factor

))(/-1(81 222 bTrrQse

）（

where the factor accounts for these interactions being present only after the last inelastic interaction at longitudinal coordinate , that has to be included to account for the effective length where this kind of Interaction takes place.

)(/-1 bT


引入核相干作用项： 2( )( )( ) T bf e

2 2( ) 2 ( )T b R b R b 核厚度函数：

d-A 碰撞参量：2

22 3/2 2

2

( 2)1

[1 (1 ) ]

partA

B

A

Nb R

RAR


对于夸克偶极子 - 核碰撞的向前弹性散射振幅： )0(22

81

0 1),,(ysQr

F eybrN

Where subscript F indicates the fundamental representation. Evolution of the gluon dipole scattering amplitude (adjoint representation) obeys the equation:

And its initial condition is

)0(2241

0 1),,(ysQr

A eybrN

The relation between them:

),,2/(122

161

ybrNe AsQr

),,(122

81

ybrNe FsQr

),,(),,(2),,( 2 ybrNybrNybrN FFA


We performed numerical calculations of dipole scattering amplitude by using DHJ models. The DHJ model takes into account the change in the anomalous dimension of the gluon distribution function due to the presence of the saturation boundary and takes into account the higher order effect. It successfully describes the single inclusive hadron production in d-A collisions. The dipole scattering amplitude is parameterized as follows:

)(

41exp1),0,( 22

sA QryrN

DHJ model

2/22 )(

81exp1),0,(

sF QryrN


The gluon saturation scale is given by:

collyy

s NeGeVeAQ )13.0( 23/122

GeV6.0 and 3.0

YdQmyQm

s

s

)/ln()/ln(-1 22

22

ss ）（

,628.0s Where )/1ln( xY

smex y /


2 4

2

2 4

(1 ) , ( )( )

( , )(1 ) , ( )

( )

c c ss s

c

s c ss s

S m x m Q xQ

xG x mS Q x m Q xQ

2 21 1/ 21 1 /2 2 0 0

'( , ) ( , ) ' ( ', ') ( , ', )4 4

pA J Xc pA J X

d d r d rx G x m dz r z dz r z T r r bd p dyd B

胶子分布函数为：

根据M-V模型及 DHJ模型，可以得到偶极子与靶核相互作用的截面表达式为：


)})(

1)(22(281

)(2)(2

161{2)

)((

)(0

2

10

210

22

112

)(4

),(4

),(4

),(

bTrrsQbT

rrsQbTbT s

cJpA

eebTrrQd

zrrdzdzrrddzmxGxbdyd

d


3. The results and discussions



4 6 8 10 12 14 16

0.4

0.6

0.8

1

1.2

Npart

RdA

-0.35<y<0.35

4 6 8 10 12 14 160.2

0.4

0.6

0.8

1

1.2

1.4

1.6-2.2<y<-1.2

Npart

RdA

4 6 8 10 12 14 16

0.5

0.6

0.7

0.8

0.9

11.2<y<2.2

NpartR

dA

The nuclear modification factor:

dyd

N

bdyddbd

RJpp

part

JdA

dA

22

F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012)



0 0.5 1 1.5 2 2.50.2

0.4

0.6

0.8

1

RdA

m-DKLMT Model

Gluon Saturation

0 0.5 1 1.5 2 2.50.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.5 1 1.5 2 2.50.6

0.7

0.8

0.9

1

1.1

1.2

y

RdA

中心度： 0-20% 中心度： 0-100% 中心度： 60-88%

F.Dominguez, D.Kharzeev, E.Levin, A.Mueller,K.Tuchin, PLB710,182-187(2012)



1. 用胶子饱和偶极子 - 核作用机制，讨论了冷核对 J/psi 产生的影响。给出的 RdA-Npart 在不同快度区间的关系 , 可以解释实验结果。

2. 同时也讨论了 J/psi 的 RdA- y 在不同中心度的关系。


Thanks

Documents

Saturation physics and the J/psi productions of CNM in p(d)-A collisions