Deep Inelastic Scattering from the AdS/CFT correspondence

Abstract

We calculate [1] the cross section of an ultra relativistic nucleus scattering on a qq pair at large coupling in N=4 SUSY gauge theory. We study the problem in the context of the AdS/CFT correspondence [2]. The nucleus is modeled as a gravitational shockwave in an AdS 5 background moving along the light cone. The dipole (qq) is represented by a Wilson loop moving in the opposite direction. Due to the correspondence, calculating the scattering amplitude of the Wilson loop with the nucleus, reduces to calculating the extreme value of the Nambu-Goto action for an open string. Its two end points are attached to the qq respectively and it hangs in an AdS 5 shockwave spacetime. Six solutions are found two of which are physically meaningful. Both solutions predict that the saturation scale Q s at high enough energies becomes energy independent; in particular it behaves as Q s ∝ A 1/3 where A is the atomic number. One solution predicts pomeron intercept α p = 2 and agrees with [3]. However, there is a parameter window of r (dipole size) and s (c.m. energy) where it violates the black disk limit. On the other hand, the other solution respects this limit and corresponds to pomeron intercept α p = 1.5. We conjecture that this is the right value for gauge theories at strong coupling. In this paper we investigate the DIS of a (virtual) photon that splits into a qq pair and scatters on a large nucleus (Fig. 1). The coupling is tuned to be large and is constant throughout the interaction because the β-function of N=4 SUSY theories is zero. We calculate the non-abelian part of the cross section which factors asΦ encodes all the QED effects while N is the forward scattering amplitude of the interaction. Here Q 2 ∝ 1/r 2 (transverse dipole size) and Y = ln1/x B j with x B j the Bjorken-x. The above equation assumes the following approximations: Infinitely large nucleus in the transverse directions and therefore the impact parameter plays an overall (trivial) multiplicative role. This is precisely the meaning of the denominator on the left hand side of the (1). Also we suppose a homogeneous nucleus which implies the problem has no angular dependence as the dipole's orientation is irrelevant. Lastly we ignore time effects by considering a large enough extent of the nucleus along its direction of motion. This last approximation allows us to search for a static string

Multiplicities from black-hole formation in heavy-ion collisions

“…17 It corresponds to the position of the point-like source in the fifth dimension (see discussion above (6.5)). 18 The meaning of the overall coefficient is discussed in subsection 8.2.1. 19 A different value for r Au but close to 8 fm may still fit RHIC data.…”

“…In this description, a heavy-ion collision is described as the process of black hole formation and decay, albeit in a five-dimensional theory of gravity including also other fields, notable a scalar, the dilaton, [1]. In this direction, several attempts have been made to analyse the scattering of high-energy sources, using shock waves in AdS, [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]…”

qq̄potential at finiteT, and weak coupling inN=4SUSY

“…In particular, in [21,46] it was found that at large enough distances the real part of the potential has a power low fall-off extending the results (obtained earlier) in the literature [44,45]. The method of [21,46] involved an analytic continuation of the solution of [44,45] applying the ideas of [47][48][49].…”

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].…”