Abstract
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian ${\cal L}^{(1)}_{\pi \Delta}$.
Highlights
The Δð1232Þ resonance is the first and best-established excitation of the nucleon [1]
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme
We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments
Summary
The Δð1232Þ resonance is the first and best-established excitation of the nucleon [1]. While there is a substantial amount of empirical information on the electromagnetic (vector) nucleon-to-delta transition [2,3,4,5,6,7,8,9,10,11,12,13,14,15] [38] that form factors of unstable particles should be determined from the renormalized three-point function at the complex pole [23] to the electromagnetic nucleon-to-Δ resonance transition to third chiral order in manifestly Lorentzinvariant chiral effective field theory.
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