$N \to Δ$ Transition Form Factors in the Thermal AdS/QCD Soft-Wall Model with Modified Propagators
We investigate electromagnetic (EM) and axial vector (AV) form factors of the nucleon-Delta baryon transition within the thermal AdS/QCD soft-wall model. While the vector bulk-to-boundary propagator admits a well-behaved analytical solution, the transverse axial vector equation of motion involves the vacuum expectation value of the bifundamental scalar (generating chiral symmetry breaking). Due to this, the axial propagator diverges asymptotically, rendering it unsuitable for computing observables in the soft-wall model. To address this problem, we implement a regularization for the axial propagator in the form of a momentum-dependent cut-off, that identifies its correct physical regime. This is achieved via an interior constraint approach to the boundary-value problem, that determines the cut-off point. The consistency of this procedure is verified near the UV limit. As a proof of concept, we test this modified propagator (and also a parametrically deformed version of it) to estimate axial vector form factors of the $N \to Δ$ transition, and find results moderately comparable with form factor profiles from experimental observations, lattice QCD, and other theoretical models. Equipped with this regularization, the thermal soft-wall model becomes a useful tool to probe thermal characteristics of QCD form factors. We demonstrate this for both, the EM and AV sectors of the $N \to Δ$ transition.