Renormalization group invariant of lepton Yukawa couplings

TL;DR

This paper constructs and analyzes renormalization invariants of lepton Yukawa couplings using quark matrices, revealing conditions under which these invariants are close to unity and exploring their stability against new physics.

Contribution

It introduces a lepton invariant $I^l$ analogous to a quark invariant, and studies its behavior for Dirac and Majorana neutrinos, including conditions for equality with the quark invariant.

Findings

The invariant $I^l$ can be close to unity for certain neutrino mass ranges.

Equality $I^q=I^l$ can occur with specific lightest neutrino masses in inverted hierarchy.

The invariants remain unchanged under generation-independent new physics couplings.

Abstract

By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them $I^q$ is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant $I^l$ for Dirac and Majorana neutrino cases and find that $I^l$ can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality $I^q=I^l$ can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.