Renormalization constants for scalar, pseudoscalar, and tensor currents

Abstract

We calculate the renormalization constants describing nucleon and pion matrix elements of scalar, pseudoscalar, and tensor ($S, P, T$) current densities. For certain of the constants, expressions can be obtained using standard S${\mathrm{U}}_{3}$ and chiral S${\mathrm{U}}^{3}$\ensuremath{\bigotimes}S${\mathrm{U}}^{3}$ methods. To get the remaining constants, we employ the quark model with spherically symmetric quark wave functions to relate the $S$, $P$, $T$ renormalization constants to known parameters of the usual vector and axial-vector ($V,A$) currents. We also evaluate the renormalization constants using the MIT "bag" model quark wave functions. We summarize our results in tabular form, compare the results of the various calculational methods used, and attempt to estimate the accuracy of our predictions.