Symmetry preserving contact interaction treatment of the kaon

A symmetry preserving regularization procedure for dealing with the contact interaction model is proposed in this work. This regularization procedure follows a series of consistency conditions that are necessary to maintain gauge symmetry. Under this regularization, proofs for the preservation of the Ward-Takahashi identities are given and the loop integrals in the contact interaction model are systematically computed. As an application example, the kaon electromagnetic form factor and $K_{l3}$ transition form factor are computed, and self-consistent results are obtained. Since the proposed regularization properly handles the divergence, one is freed from the inconsistencies caused by the regularization and can concentrate more on the physical discussion.

Figure 1

The momentum dependence of kaon electromagnetic form factors $F_{u/s}(t=-Q^2)$.

Figure 2

Results for $f_{+/-}(t)$. In the upper panel, the filled circles and squares are results of the calculation, and the solid and dashed lines are linear fits in Eq. (62). In the lower panel, the solid and dashed lines are the results of the calculation.