Connection between Second Class Currents and the $\Delta N\gamma$ Form Factors $G_M^*(q^2)$ and $G_E^*(q^2)$

Abstract

An interesting connection between the nucleon weak axial-vector second class current form factor $g_{T}(q^{2})$ present in the matrix element $< {p} | A_{\pi ^{+}}^{\mu}| {n} >$ and the $\Delta N\gamma$ form factors $G_{M}^{\ast}(q^{2})$ and $G_{E}^{\ast}(q^{2})$ is derived. Using a nonperturbative, relativistic sum rule approach in the infinite momentum frame, $G_{M}^{\ast}(q^{2})$ and $G_{E}^{\ast}(q^{2})$ are calculated in terms of $g_{T}(q^{2})$ and the well-known nucleon isovector Sachs form factor $G_{M}^{V}$ as input with no additional model parameters. Reasonable agreement with the data for $G_{M}^{\ast}(q^{2})$ may be achieved with a non-zero $g_{T}(q^{2})$ too large to be accommodated in the Standard Model. We surmise that it is plausible that second class current-associated pion cloud effects are playing a significant role in pion electroproduction processes and perhaps must be taken into account in those methodologies which utilize effective Lagrangians.