$\Delta$ resonance contributions to QED radiative corrections in neutron and inverse beta decay

Abstract

We incorporate the $\Delta (1232)$ resonance into pion-induced QED radiative corrections to neutron decay and inverse beta decay (IBD). Within the framework of heavy-baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom, we compute additional contributions and study their impact on IBD cross sections and on the renormalization of the nucleon isovector vector and axial-vector charges. $\Delta$ resonance does not renormalize the vector charge. For the axial-vector charge, including the $\Delta$ resonance restores power counting and significantly reduces the QED radiative correction to the experiment-over-lattice-QCD ratio $g_A/\left(g_A^{\mathrm{QCD}}{g}_V\right)$, bringing it to zero within radiative-correction uncertainties. $\Delta$ resonance increases the pion-induced QED radiative corrections to IBD by a factor $1.2$-$1.3$.

Comments: 19 pages, 1 figure