Interpolating the 't Hooft model between instant and front forms in the Coulomb gauge*

The 1+1D model of quantum chromodynamics (QCD) in the infinite number of colors, or ‘t Hooft model, is interpolated between the instant form dynamics (IFD) and the light-front dynamics (LFD) using an interpolation parameter δ in the interpolating Coulomb gauge which links the Coulomb gauge (A⁰ = 0) in IFD and the light-front gauge (A⁺ = 0). While calculations such as these were performed [1] in the interpolating axial gauge which links the the spatial or axial gauge (A¹ = 0) in IFD and the light-front gauge (A⁺ = 0), there are several benefits to the Coulomb gauge that cannot be ignored. For example, we involve neither Gribov copies nor ghost fields in the Coulomb gauge. Using this parameter δ, we will solve for the mass gap equation using both Hamiltonian formalism and Feynman diagram analysis, expecting the independence of gauge choice when compared to axial gauge calculations. We then will derive the quark-antiquark bound-state equation in the interpolating dynamics using the dressed fermion propagator and compare with the results obtained in the interpolating axial gauge [1]. We expect meson mass spectra of such mesons that follow Regge trajectories to be independent of δ and gauge choice. We are planning to obtain the bound-state wave functions and compare the results between the interpolating Coulomb gauge and the interpolating axial gauge. Since QCD respects the gauge symmetry, these results should all be independent of the gauge choice. Thus, we expect identical results to [1] for the physical quantities. Using interpolation techniques, we can produce an alternative approach to quasi-PDFs not only with the frame dependence but also with the δ dependence. These interpolating quasi-PDFs can be implemented in the lattice QCD without suffering from the large momentum boost.

1. [1] Ma, Bailing, and Chueng-Ryong Ji. “Interpolating ’t Hooft Model between Instant and Front Forms.” Physical Review D, vol. 104, no. 3, 2021