MAKING GLUE IN HIGH ENERGY NUCLEAR COLLISIONS Page: 3 of 9
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CLASSICAL MODEL OF GLUON PRODUCTION
At very high energies, the hard valence quark (and gluon) modes are highly
Lorentz contracted, static sources of color charge for the wee parton, Weizsacker-
Williams, modes in the nuclei. The sources are described by the current
J"'a(rt) = JV+pi(rt)6(x-) + 6"-p"(rt)6(x+), (2)
where P1(2) correspond to the color charge densities of the hard modes in nucleus
1 (nucleus 2) respectively. The classical field describing the small x modes in the
EFT is obtained by solving the Yang-Mills equations in the presence of the two
sources. We have then
DNFt " = J" . (3)
The small x glue distribution is simply related to the Fourier transform A?(kt) of
the solution to the above equation by < A(kt)A?(kt) >p.
The above averaging over the classical charge distributions is defined by
( f) = dpidp2 O(pi, p2) exp (- fd2rt .Pt24 (rt)]) (4)
We have assumed identical nuclei with equal Gaussian weights g4p2
Before the nuclei collide (t < 0), a solution of the equations of motion is
A+ = 0; A = (x-)O(-x+)a(rt) + (x+)(-x-)a2(rt), (5)
where ac(rt) (q = 1, 2 denote the labels of the nuclei and i = 1, 2 are the two
transverse Lorentz indices) are pure gauge fields defined through the gauge trans-
formation parameters Aq(7, rt) 
a (rt) = Pe ff, roj dn'A9(2rt)) Vi (Pef*roi dtA(7rt)) . (6)
Here i proj - log(x+/xP oj) is the rapidity of the nucleus moving along the
positive (negative) light cone with the gluon field a0(2). The Aq(q, rt) are determined
by the color charge distributions AiAq = P9 (q=1,2) with AL being the Laplacian
in the perpendicular plane.
For t > 0 the solution is no longer pure gauge. Working in the Schwinger gauge
AT = x+A- + x-A+ = 0, Kovner, McLerran and Weigert  found that with the
A4+ = txa(T, rt) ; A2 = ai(T, rt), (7)
where T = 2x+x-, Eq. 3 could be written more simply in terms of a and Ce Note
that these fields are independent of Ti-the solutions are explicitly boost invariant in
the forward light cone!
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KRASNITZ,A. & VENUGOPALAN,R. MAKING GLUE IN HIGH ENERGY NUCLEAR COLLISIONS, article, November 20, 1998; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc708940/m1/3/: accessed April 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.