Matter Unification and Lepton Flavour Violation

Abstract

We explore the idea of quark-lepton unification at low energies. In particular, we discuss the minimal framework for matter unification at the multi-TeV scale, in which neutrino masses are necessarily generated via the inverse seesaw mechanism. To assess the testability of this theory for physics beyond the Standard Model, we analyze current experimental constraints and derive the corresponding lower bound on the symmetry breaking scale. We reexamine the impact of existing limits from lepton number violating meson decays, taking into account the freedom associated with unknown quark-lepton mixing angles. Furthermore, we study the correlation between bounds from meson decays and $μ\to e$ conversion. We demonstrate that the upcoming $μ\to e$ conversion experiment at Fermilab can play a crucial role in probing quark-lepton unification at the multi-TeV scale.

Figures (7)

• Figure 1: Feynman graphs for $K_L \to \mu^+ e^-$ decay. In the left-panel we show the contribution to $\bar{K}^0 \to e^- \mu^+$, while in the right-panel we show $K^0 \to e^- \mu^+$.
• Figure 2: The red shaded region is excluded by the experiment bound ${\rm{BR}}(K_L \to e^\pm \mu^\mp) < 4.7 \times 10^{-12}$BNL:1998apv.
• Figure 4: Feynman graph for $\mu \to e$ conversion mediated by the vector leptoquark.
• Figure 5: Predictions for $\mu \to e$ conversion for different scenarios. In a) we show the predictions in Case I, where the colored region is excluded by the experimental bounds on $\mu \to e$ in Gold SINDRUMII:2006dvw. The blue and orange dashed lines show the possible reach of the Mu2e experiment Mu2e:2014fns for run I $( \text{BR}_{\mu \to e} \sim 6 \times 10^{-16} \ )$ and run II $( \text{BR}_{\mu \to e} \sim 10^{-17} \ )$, respectively. In b) we show the predictions for Case II, while the Case III predictions are shown in c). The predictions for Case IV are given in d).
• Figure 6: Limits on the vector leptoquark mass. In a) one has the limits from $K_L$ decays and $\mu \to e$ when $\theta_{13}= \theta_{23}=0$. The red-shaded region is excluded by the $\mu \to e$ conversion in Gold SINDRUMII:2006dvw, and the rare Kaon decay excludes the yellow-shaded region. The dashed lines show the projected limits form the Mu2e experiment for $\mu \to e$ conversion in Al at Fermilab. b) Same as in a) but here we assume $\theta_{13}= \theta_{23}=\pi/4$. The cyan-shaded region is excluded by the $\mu \to e$ conversion in Gold SINDRUMII:2006dvw.