Renormalization of gauge theories on general anisotropic lattices and high-energy scattering in QCD

We study the renormalization of $SU(N_c)$ gauge theories on general anisotropic lattices, to one-loop order in perturbation theory, employing the background field method. The results are then applied in the context of two different approaches to hadronic high-energy scattering. In the context of the Euclidean nonperturbative approach to soft high-energy scattering based on Wilson loops, we refine the nonperturbative justification of the analytic continuation relations of the relevant Wilson-loop correlators, required to obtain physical results. In the context of longitudinally rescaled actions, we study the consequences of one-loop corrections on the relation between the $SU(N_c)$ gauge theory and its effective description in terms of two-dimensional principal chiral models.

Figure 1

The Euclidean Wilson loops ${\mathcal{W}}_1^T$ and ${\mathcal{W}}_2^T$, defined in Eq. (58).

Figure 2

The “tilted” lattice Wilson loops ${\mathcal{W}}_{L1}^{(T_0)}$ and ${\mathcal{W}}_{L2}^{(T_0)}$, Eqs. (64) and (65), projected on the longitudinal plane.

Figure 3

The tilted links of Eq. (69), built from the shortest paths connecting opposite corners of a plaquette.

Figure 4

Analyticity domain of the Wilson-loop correlator with the infrared cutoff removed, ${\mathcal{C}}_E$ [see Eq. (75)]. The solid black lines indicate the boundaries of the domain, and crosses signal the singularities.