Parametrization of transition energy-momentum tensor form factors

Abstract

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.

Comments: 5 pages