$1/N$ corrections to $F_1$ and $F_2$ structure functions of vector mesons from holography

The structure functions $F_1$ and $F_2$ of the hadronic tensor of vector mesons are obtained at order $1/N$ and strong coupling using the gauge/gravity duality. We find that the large $N$ limit and the high energy one do not commute. Thus, by considering the high energy limit first, our results of the first moments of $F_1$ for the rho meson agree well with those from lattice QCD, with an important improvement of the accuracy with respect to the holographic dual calculation in the planar limit.

Figure 1

Feynman-Witten diagram associated to the DIS process with two intermediate hadron states. The momentum and the twist of each field are indicated, while the solutions are given in section 2. The incident hadron is represented by a double line, the intermediate spin-one modes are indicated by dashed lines, while the solid line denotes a scalar mode. The vertical dotted line represents the cut of the Cutkosky rule.

Figure 2

$F_1$ as a function of $x$. We display the leading results at low and moderate ($0.1<x\le 1$) values of $x$. Dashed curves represent the $F_1$ computed for $N\to \infty$, while the blue ones correspond to the $1/N$ corrections. The constants $C_1$ and $C_2$ are those which give the moments of $F_1$ shown in Table 2.