Static weak dipole moments of theτlepton via renormalizable scalar leptoquark interactions

Abstract

The weak dipole moments of elementary fermions are calculated at the one-loop level in the framework of a renormalizable scalar leptoquark model that forbids baryon number violating processes and so is free from the strong constraints arising from experimental data. In this model there are two scalar leptoquarks accommodated in a $S{U}_{L}(2)\ifmmode\times\else\texttimes\fi{}{U}_{Y}(1)$ doublet: One of these leptoquarks is nonchiral and has electric charge of $5/3e$, whereas the other one is chiral and has electric charge $2/3e$. In particular, a nonchiral leptoquark contributes to the weak properties of an up fermion via a chirality-flipping term proportional to the mass of the virtual fermion, and can also induce a nonzero weak electric dipole moment provided that the leptoquark couplings are complex. The numerical analysis is focused on the weak properties of the $\ensuremath{\tau}$ lepton since they offer good prospects for experimental study. The constraints on leptoquark couplings are briefly discussed for a nonchiral leptoquark with nondiagonal couplings to the second and third fermion generations, a third-generation nonchiral leptoquark, and a third-generation chiral leptoquark. It is found that although the chirality-flipping term can enhance the weak properties of the $\ensuremath{\tau}$ lepton via the top quark contribution, such an enhancement would be offset by the strong constraints on the leptoquark couplings. So, the contribution of scalar leptoquarks to the weak magnetic dipole moment of the $\ensuremath{\tau}$ lepton are smaller than the standard model (SM) contributions but can be of similar size to those arising in some SM extensions. A nonchiral leptoquark can also give contributions to the weak electric dipole moment larger than the SM one but well below the experimental limit. We also discuss the case of the off-shell weak dipole moments and, for completeness, analyze the behavior of the $\ensuremath{\tau}$ electromagnetic properties.