Importance of vector leptoquark-scalar box diagrams in Pati-Salam unification with vector-like families

We study lepton flavor violation (LFV) induced by one-loop box diagrams in Pati-Salam (PS) unification with vector-like families. The vector leptoquark (LQ) associated with the PS gauge symmetry breaking generally causes various LFV processes such as K-L -> mu e and mu -> e conversion at the tree-level, thereby driving its mass scale to be higher than PeV scale. The vector-like families are introduced to suppress such tree-level LFV processes, allowing the LQ to have TeV scale mass. In this paper, we point out that there are inevitable one-loop contributions to those LFV processes from the box diagrams mediated by both one LQ and one scalar field, even if the tree-level contributions are suppressed. We consider a concrete model for demonstration, and show that the vector-like fermion masses have an upper bound for a given LQ mass when the one-loop induced processes are consistent with the experimental limits. The vector-like fermion mass should be lighter than 3TeV for 20TeV LQ, if a combination of the couplings does not suppress K-L -> mu e decay. Our findings would illustrate importance of the box diagrams involving both LQ and physical modes of symmetry breaking scalars in TeV scale vector LQ models.

Automated summary

This paper investigates lepton flavor violation (LFV) in Pati-Salam unification and points out the inevitable one-loop contributions to LFV processes from box diagrams mediated by both vector leptoquark and physical modes of symmetry breaking scalars. A concrete model is considered to demonstrate that the vector-like fermion masses have an upper bound for a given leptoquark mass when the one-loop induced processes are consistent with experimental limits.