Electromagnetic properties of the nucleon and the Roper resonance in soft-wall AdS/QCD at finite temperature

Abstract

We present a study of the nucleon electromagnetic form factors and of the Roper-nucleon transition at finite small temperature $T$, using an extended version of a soft-wall AdS/QCD approach developed by us previously. In the action we introduce the effective potential, which has quadratic dependence on the holographic coordinate $z$ and depends on both the gluon and quark condensates. Choosing the AdS geometry we restrict ourselves to the AdS Poincar\'e metric, because the contribution of the AdS-Schwarzschild geometry starts at next-to-leading order ${\cal O}(T^4)$. Hence, one can neglect the temperature dependence of the AdS geometry at small $T$. This is consistent with the Hawking-Page phase transition at a critical temperature representing the transition between thermal AdS/QCD and AdS-Schwarzschild geometry. In the small temperature regime we base our analysis on the temperature dependence of the effective potential, which starts at order ${\cal O}(T^2)$, due to the leading contribution from the quark condensate. As applications we present the analysis of properties of the nucleon and Roper resonance (masses, form factors, and helicity amplitudes) at low temperatures.