Abstract
The effect of quantum torsion in theories of quantum gravity is usually described by an axionlike field which couples to matter and to gravitation and radiation gauge fields. In perturbation theory, the couplings of this torsion-descent axion field are of derivative type and so preserve a shift symmetry. This shift symmetry may be broken, if the torsion-descent axion field mixes with other axions, which could be related to moduli fields in string-inspired effective theories. In particular, the shift symmetry may break explicitly via nonperturbative effects, when these axions couple to fermions via chirality-changing Yukawa couplings with appropriately suppressed coefficients. We show how in such theories an effective right-handed Majorana neutrino mass can be generated at two loops by gravitational interactions that involve global anomalies related to quantum torsion. We estimate the magnitude of the gravitationally induced Majorana mass and find that it is highly model dependent, ranging from the multi-TeV to keV scale.
Highlights
The recent discovery [1] of the Higgs boson at the CERN Large Hadron Collider (LHC) constitutes an important milestone for the Ultra-Violet (UV) completion of the Standard Model (SM)
In theories of quantum gravity with torsion, an effective right-handed Majorana neutrino mass MR can be generated at two loops by gravitational interactions that involve global anomalies
The global anomalies result, after integrating out a formedvalued pseudoscalar field b, the so-called Kalb-Ramond axion, which describes the effect of quantum torsion
Summary
The recent discovery [1] of the Higgs boson at the CERN Large Hadron Collider (LHC) constitutes an important milestone for the Ultra-Violet (UV) completion of the Standard Model (SM). As was explicitly demonstrated in [6], the fermions f can receive a non-zero mass at the threeloop level, through the anomalous interaction (1) and the chirality-changing Yukawa couplings (2) It was further suggested in [6] that this massgenerating mechanism can be applied to create lowscale fermion masses by pure quantum gravity effects. The role of the U(1) gauge field strength tensor Fμν will be played by the Riemann curvature tensor Rμνρσ, and the role of the gauge fields by the gravitons Such a gravitationally-generating mass mechanism could straightforwardly be applied to fermions without SM quantum charges, such as Majorana righthanded neutrinos, which we restrict our attention here.
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