Polarized deep inelastic and elastic scattering from gauge/string duality

Abstract

In this paper, we investigate deep inelastic and elastic scattering on a polarized spin-1 2 hadron using gauge/string duality. This spin-1 2 hadron corresponds to a supergravity mode of the dilatino. The polarized deep inelastic structure functions are computed in supergravity approximation at large t' Hooft coupling λ and finite x with λ −1/2 ≪ x < 1. Furthermore, we discuss the moments of all structure functions, and propose an interesting sum rule 1 0 dxg 2 x, q 2 = 0 for g 2 structure function which is known as the Burkhardt-Cottingham sum rule in QCD. In the end, the elastic scattering is studied and elastic form factors of the spin-1 2 hadron are calculated within the same framework.

Polarized DIS in 𝒩 = 4 SYM: where is spin at strong coupling?

“…However, the anomalous dimension remains of order unity in the vicinity of j = 2, and thus the twist-two operators give the leading contribution. Similarly, in the polarized case one expects that some protected operator in the J 3 J 3 OPE gives the more important contribution than the double trace operators considered in [23]. We observe that this operator is the R-current itself.…”

“…However, an important point is that in order to obtain a nonzero A (B is in general nonzero), it is necessary to employ models which are dual to the N = 4 theory in the UV, and at the same time contain the massless Nambu-Goldstone modes of spontaneously broken R-symmetry. Otherwise, the current conservation law immediately implies A = 0, as was observed in a 'hardwall' model calculation in [23]. An exemplary model which meets this requirement is the one constructed in [30].…”

“…In the context of gauge/string duality, DIS was first formulated in [16] for the unpolarized case (see, also [17][18][19][20][21][22]), and recently generalized to the polarized case in [23]. The analysis of [23] is focused on the large-x region which corresponds to the supergravity approximation on the string theory side.…”

“…The basic strategy to calculate the structure functions has been laid out in [16] for the unpolarized case and in [23] for the polarized case. Here we briefly recapitulate the essential features at strong coupling and then discuss the extension to the polarized case.…”

“…The analysis of [23] is focused on the large-x region which corresponds to the supergravity approximation on the string theory side. However, the internal degrees of freedom ('partons') of hadrons are visible only at extremely small values of x of order ∼ e − √ λ which in fact is the Regge regime of the theory [16].…”