DIS on a large nucleus in AdS/CFT

Abstract

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 . While the infinite mass of the "quarks" justifies the recoilless approximation for their interaction with the target, the question arises of applicability of this model to the description of real DIS processes with light quarks, which indeed recoil during the interaction. For instance, while at small coupling in the leading logarithmic α s ln 1/x Bj approximation the recoilless approximation is justified [19,21,17,18], its validity becomes less clear at the subleading logarithmic order (order α 2 s ln 1/x Bj ) [39]. We note that the recoil of the quarks at high energy only affects the impact factors (see e.g. [84]), and not the part of the interaction described by the small-x Bj evolution. Thus the calculation below, when applied to light quarks, should be understood as calculation of the evolution without the impact factors. While the impact factors are likely to be numerically important, we will proceed under the assumption that they will not affect the qualitative features of the obtained scattering amplitude.

Heavy-quark energy loss and thermalization in a strongly coupled supersymmetric Yang-Mills plasma

“…[21,22]. We determine the corrections to the shape of the string up to first order, formulae (32), (35) and (39), and the radiative energy loss of the heavy quark up to second order (73). In this case we only gave the large γ result explicitely, but the exact expression was also found.…”

“…Moreover, the saturation momentum and structure functions of SYM plasma are studied in Ref. [33,34,35,36] and jet fragmentation and energy correlation are investigated in Ref. [37,38,39,40].…”

Azimuthal asymmetries in high-energy collisions of protons with holographic shockwaves

“…where f ( x) describes the energy density distribution of the target in the transverse plane, and µ 2 ∼ A 1/3 [22,23] is the transverse density scale of the shockwave. This non-uniform shockwave at the boundary can be obtained from a source J( x)δ(z − 1/µ) in the bulk convoluted with the Green's function found in [24],…”

“…The explicit factor of A 1/6 arises from the integration over the longitudinal coordinate x − [22,23,32].…”

“…Q s obtained by averaging the Wilson loop in a shockwave background increases very rapidly with the thickness of the nucleus, Q s ∼ A 1/3 [22].…”