While the Lorentz structures of the $N \to \Delta$ transition matrix element of the vector current is well-known, that of the symmetric energy-momentum tensor current is unknown. In this letter, we first reproduce the Lorentz structures of the $\frac{ 1}{ 2}^{ \pm} \to \frac{ 1}{ 2}^{ \pm}$, $\frac{ 1}{ 2}^{ \mp} \to \frac{ 1}{ 2}^{ \pm}$, and $\frac{ 1}{ 2}^{ \mp} \to \frac{ 3}{ 2}^{ \pm}$ transition matrix elements of the vector current. We also repeat the parametrizations of the symmetric energy-momentum tensor current for the $\frac{ 1}{ 2}^{ \pm} \to \frac{ 1}{ 2}^{ \pm}$ and $\frac{ 1}{ 2}^{ \mp} \to \frac{ 1}{ 2}^{ \pm}$ transitions. We then consider both $\frac{ 1}{ 2}^{ \pm} \to \frac{ 3}{ 2}^{ \pm}$ and $\frac{ 1}{ 2}^{ \mp} \to \frac{ 3}{ 2}^{ \pm}$ matrix elements of the symmetric energy-momentum tensor current (say, $N \to \Delta$ transition) for the first time. We found that there are five independent conserved and four independent non-conserved energy-momentum tensor form factors.
Categories: hep-ph