Sumino's Cancellation Mechanism in an Anomaly-Free Model

An interesting family gauge boson (FGB) model (Model A) has been proposed by Sumino. The model can give FGBs with a considerably low energy scale in spite of the sever constraints form the observed $K^0$-$\bar{K}^0$ mixing and so on. An essential idea in Model A is in the so-called Sumino cancellation mechanism between QED and FGB diagrams. However, Model A is not anomaly free and, besides, it causes effective interactions with $\Delta N_{\rm family}=2$. In order to avoid these problems, a revised Sumino model with an inverted mass hierarchy (Model B) has proposed, but, in this time, it cannot satisfy the Sumino cancellation mechanism exactly. In this paper, we propose a revised version of Model B, where the model still keeps anomaly free, but it can exactly satisfy the Sumino mechanism. An effect of the revised model will be confirmed by observations $K^+ \rightarrow \pi^+ e^- \mu^+$ and $\mu^- N\rightarrow e^- N$.