Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-06-09
JHEP 0807:074,2008
Physics
High Energy Physics
High Energy Physics - Theory
37 pages, 11 figures; v2: minor typos corrected, references added; v3: addendum included
Scientific paper
10.1088/1126-6708/2008/07/074
We calculate the total cross section for deep inelastic scattering (DIS) on a nucleus at high energy for a strongly coupled N=4 super Yang-Mills theory using AdS/CFT correspondence. In analogy to the small coupling case we argue that at high energy the total DIS cross section is related to the expectation value of the Wilson loop formed by the quark-antiquark dipole. We model the nucleus by a metric of a shock wave in AdS_5. We then calculate the expectation value of the Wilson loop by finding the extrema of the Nambu-Goto action for an open string attached to the quark and antiquark lines of the loop in the background of an AdS_5 shock wave. We find three extrema of the Nambu-Goto action: the string coordinates at the extrema are complex-valued and are given by three different branches of the solution of a cubic equation. The physically meaningful solutions for the total DIS cross section are given either by the only branch with a purely imaginary string coordinate in the bulk or by a superposition of the two other branches. For both solutions we obtain the forward scattering amplitude N for the quark dipole-nucleus scattering. We study the onset of unitarity with increasing center-of-mass energy and transverse size of the dipole: we observe that for both solutions the saturation scale, while energy-dependent at lower energies, at very high energy becomes independent of energy/Bjorken-x. The saturation scale depends very strongly on the atomic number of the nucleus as Q_s ~ A^{1/3}.
Albacete Javier L.
Kovchegov Yuri V.
Taliotis Anastasios
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