Nonminimal coupling contribution to DIS at low $x$ in Holographic QCD

We consider the effect of including a nonminimal coupling between a $U(1)$ vector gauge field and the graviton Regge trajectory in holographic QCD models. This coupling describes the QCD interaction between the quark bilinear electromagnetic current and the Pomeron. We test this new coupling against DIS data at low Bjorken $x$ and obtain an excellent fit with a chi squared of 1.1 over a very large kinematical range in the photon virtuality $Q^2<400{\mathrm{GeV}}^2$ and for $x<{10}^{-2}$. The scale of the new dimension full coupling, which arises from integrating higher spin fields, is of order 1–10 GeV. This value matches precisely the expectations from effective field theory, which indicate that such corrections are controlled by the mass gap between the spin two and spin four glueballs that are described holographically by the graviton and spin four field in the graviton Regge trajectory, respectively.

Figure 1

Tree level Witten diagram representing spin $J$ exchange in a $12\to 34$ scattering.

Figure 2

Structure function $F_2(Q^2,x)$. Experimental points vs prediction of this work with a ${\chi }_{\mathrm{d}.\mathrm{o}.\mathrm{f}}^2=1.1$. Each line corresponds to a given $Q^2({\mathrm{GeV}}^2)$ as indicated.

Figure 3

Regge trajectories compared with glueball masses from lattice simulations [38, 39]. Shown are also the values we obtained for the intercept of each trajectory. Configurations that give the soft Pomeron intercept $j_1=1.09$ were favored in the fitting process.

Figure 4

Hard Pomeron wave function for the best fit found and for its intercept value $J=j_0$. The dotted and dashed line represent the action of the operator ${\tilde{\mathcal{D}}}_{\perp }$ and ${\tilde{\mathcal{D}}}_{\parallel }$ on the hard Pomeron wave function ${\psi }_0(z)$ respectively. In this plot all the functions have been scaled by a factor of 10.

Figure 5

Same as Fig. 4 but for the soft Pomeron and for its intercept value $J=j_1$.