$WWV$ $(V=\gamma,Z)$ vertex in the Georgi-Machacek model

Abstract

The CP-even static form factors $\Delta\kappa'_V$ and $\Delta Q_V$ ($V=\gamma,\, Z$) associated with the $WWV$ vertex are studied in the context of the Georgi-Machacek model (GMM), which predicts nine new scalar bosons accommodated in a singlet, a triplet and a fiveplet. General expressions for the one-loop contributions to $\Delta\kappa'_V$ and $\Delta Q_V$ arising from neutral, singly and doubly charged scalar bosons are obtained in terms of both parametric integrals and Passarino-Veltman scalar functions, which can be numerically evaluated. It is found that the GMM yields 15 (28) distinct contributions to $\Delta\kappa'_\gamma$ and $\Delta Q_\gamma$ ($\Delta\kappa'_Z$ and $\Delta Q_Z$), though several of them are naturally suppressed. A numerical analysis is done in the region of parameter space still consistent with current experimental data and it is found that the largest contributions to $\Delta\kappa'_V$ arise from Feynman diagrams with two nondegenerate scalar bosons in the loop, with values of the order of $a=g^2/(96\pi^2)$ reached when there is a large splitting between the masses of these scalar bosons. As for $\Delta Q_V$, it reaches values as large as $10^{-2}a$ for the lightest allowed scalar bosons, but it decreases rapidly as one of the masses of the scalar bosons becomes large. Among the new contributions of the GMM to the $\Delta\kappa'_V$ and $\Delta Q_V$ form factors are those induced by the $H_5^\pm W^\mp Z$ vertex, which arises at the tree-level and is a unique prediction of this model.