Majorana Neutrinos and Clockworked Yukawa Couplings Contribution to Nonobservation of the Rare Leptonic Decay li → ljγ, Clockwork
Abstract
The clockwork is an extra-dimensional setup for generating light particles with exponentially suppressed
or hierarchical couplings of light particles with N massive states having comparable masses near the
threshold scale of the mechanism in theories which contain no small parameters at the fundamental level.
We explore the prospect of charged lepton flavor violation (cLFV) in a clockwork framework which encompasses
Dirac mass terms as well as Majorana mass terms for the new clockwork fermions. We derive
the masses of the nonzero clockwork Majorana masses, and new particles in a clockwork framework and
for their Yukawa couplings to the lepton doublets, in the framework where the clockwork parameters are
universal. When the new clockwork Majorana masses are nonzero, neutrino masses are generated as a
result of the exchange of heavy messenger particles such as right-handed isosinglet neutrinos or isotriplet
scalar bosons known as the seesaw mechanism. In the case of nonzero clockwork Majorana masses, owing
to the sizable effective Yukawa couplings of the higher mass modes, neutrino masses can only be made
tiny by conjecturing a large Majorana mass in the teraelectron volt range for all the clockwork gears. This
is apparent from the constraints on the mass scale of the clockwork fermions due to the nonobservation of
the rare cLFV decay μ → eγ, τ → μγ, τ → eγ. A general description of the clockwork mechanism valid
for fermions, gauge bosons, and gravitons is discussed here. This mechanism can be implemented with a
discrete set of new fields or, in its continuum version, through an extra spatial dimension. In both cases,
the clockwork emerges as a useful tool for model-building applications. Notably, the continuum clockwork
offers a solution to the Higgs naturalness problem, which turns out to be the same as in linear dilaton duals
of Little String Theory.
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