Color Glass Condensate HIM MEETING( 광주 ) Dec. 4, 2004.
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Transcript of Color Glass Condensate HIM MEETING( 광주 ) Dec. 4, 2004.
Color Glass Condensate
HIM MEETING( 광주 )Dec. 4, 2004
0. Introduction
1) What is CGC?
2) Physics related to the CGC
3) Classical Theory(MV)
4) Quantum Theory
5) RGE
<<< HEAVYLY BORROWED >>>From IANCU, LEONIDOV & McLERRAN
(hep-ph/0202270)Try McLerran or A. Mueller for general references
Notation:
Light Cone(LC) coordinate:
Light Cone gauge:
Rapidity:
Pseudorapidity:
Feynman, Bjorken x:
I. What is CGC ?
- Color: colored particles
- Glass: a) disordered
b) Solid in short time scale but
Liquid in long time scale.
- Condensate: highly dense, ~ 1/alpha_s
II. Physics Related to the CGC
A. Total Cross Section of Hadron-Hadron:
1) Intrinsically non-perturbative even though E increase
2) Regge theory in 70s but not so satisfactory
3) Froissart bound:
Unitarity of scattering matrix
4) Why the unitarity saturated.
5) Is this understandable from QCD?
B. Particle Production
1) Can we compute dN/dy even at y=0?
2) Feynman scaling:
Cut the green in half (low energy) and move to red
(high energy) distribution. They match!!! i.e.
independent of energy
As E goes up, the small x degree of freedom fills
in while the large x held fixed
Some kind of RG property shows up.
C. DIS(Electron-Hadron)
1) Electron emits virtual photon
fluctuate into quark-antiquark
interact with partons in hadron
2) The rapidity distribution for gluons of hadron is almost
same as the distribution for produced hadrons after
hadron-hadron collision(or heavy ion collision)
3) However, ZEUS data show sharp increase in rapidity
distribution SMALL-x problem.
4) The saturation must be shown up!!!
the saturation momentum:
5) The saturation momentum increase as E increases
Once
Weak coupling:
Hope gluon, quark distribution can be calculable.
However, it is highly dense so that perturbation
cannot be applicable
D. Geometrical ScalingStructure functions from DIS depend on (in general) (x, Q^2/Lambda^2), but the function depend only on
at x < 0.01 (HERA), i.e. independent of x.
Some kind of scaling at small x.
E. Universality
1) Weak universality:
At sufficient high energy, physics must depend on the specific properties of hadron(nuclei) via saturation scale Q_s(x,A), i.e. With same Q_s, they have to have same properties.
2) Strong universality:
Statistical sense. The behavior of correlation function
is given by universal critical exponents.
III. Classical Theory (MV)
A. Basics
WHAT WE WILL SOLVE:
: Classical soft gluon field
: Color current of fast partons in x^+
direction sitting at x^- = 0
- Softer partons have larger energies(note that )
thus shorter life-times
time-independent color source in view of soft field:
treat the density as a classical random variable
with some probability, weight function, as functional:
Using ,
- The Gluon correlation functions at scale
for example,
- Gluon distributions:
: # of gluons having longitudinal momentum between and and transverse size
The gluon distribution with transverse momenta
per unit rapidity:
To get the readable form:
Consider the equation of motion in light cone gauge without source:
for + component,
therefore,
The quantization:
with the commutation relation,
The gluon density with Fock space operators,
Using that
In coordinate space,
This form is gauge dependent!!!!!
Now inserting WILSON LINES:
where the Wilson line is
We choose the path such that
along the horizontal line,
along the vertical line, (retarded condition)
IN RESULT,
Another interesting quantity: number of gluons per unit rapidity and transverse phase space:
And for homogeneous transverse space,
B. Formal Solution of
가 . Anticipating a solution,
so A^i are pure gauge,
나 . Now choose Covariant gauge:
( 가 ) 항을 이용 ,
다 . Formal Solution
Thus,
라 . Gauge transforming to LC-gauge
Since , we get the equation with solution,
마 . Classical source is dummy and ‘measure’ and ‘weight function’ are gauge invariant so that
C. MV approximation
Independent color sources: A*N_c valence quarks
Consider a tube of transverse area:
The number of valence quarks in the tube:
따라서 ,
한편 , 위의 correlator 들은 ( 마 ) 항을 이용할 때 다음의 weight function 을 사용하면 유도될 수 있다 ,
Linearized Solution:
gluon field 에 대한 운동방정식에서 선형항만 사용하여 풀면 ,
Exact and non-linear solution:이 경우 다음의 correlator 계산이 필수 ,
여기서 기본 propagator 는
위의 correlator 를 전개한 후 위의 propagator 을 이용하여 contraction 을 계산하면 ,
여기서 ,
using
Final Solution:
Quantum Theory and RGE
can be presented by someone
who is an expert on the subject !!
THANKS