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

TL;DR

This paper investigates how box diagrams involving vector leptoquarks and scalar fields contribute to lepton flavor violating meson decays in Pati-Salam models with vector-like families, highlighting their significance even when tree-level effects are suppressed.

Contribution

It demonstrates the importance of one-loop box diagrams with both leptoquarks and scalars in constraining Pati-Salam models with vector-like families, a factor often overlooked in previous analyses.

Findings

Vector-like fermion masses must be below 3 TeV for a 20 TeV LQ to satisfy experimental limits.

One-loop box diagrams significantly impact meson decay rates, even with suppressed tree-level contributions.

Constraints on fermion and leptoquark masses inform model building and phenomenology in Pati-Salam theories.

Abstract

We study lepton flavor violating meson decays induced by box diagrams involving a vector leptoquark (LQ) and scalar fields in Pati-Salam (PS) unification with vector-like families. The vector LQ corresponds to the massive gauge boson associated with the PS gauge symmetry breaking and the scalar fields are the physical degrees of freedom of the PS breaking field. The LQ generally causes the rapid flavor violating decays, such as $K_L \to \mu e$, at the tree-level unless its mass scale is higher than PeV scale. The vector-like families are introduced to suppress the tree-level contributions mediated by the LQ and explain the realistic fermion mass matrices. In this paper, we point out that there are inevitable one-loop contributions to those meson decays 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 find that the vector-like fermion masses have an upper bound for a given LQ mass when the one-loop induced meson decays are consistent with the experimental limits. The vector-like fermion mass should be lighter than 3 TeV for 20 TeV LQ, if a combination of the couplings does not suppress $K_L \to \mu e$ decay. Our findings would illustrate importance of the box diagrams involving both LQ and physical modes of symmetry breaking scalars in generic models.