Abstract
We use the framework of asymptotic safety above the Planck scale to constrain the parameter space of simple models of new physics that can accommodate the measured value of the anomalous magnetic moment of the muon and the relic density of dark matter. We couple parametrically to the trans-Planckian quantum physics a set of SU(2)$\times$U(1) invariant extensions of the Standard Model, each comprising an inert scalar field and one pair of colorless fermions that communicate to the muons through Yukawa-type interactions. The presence of an interactive UV fixed point in the system of gauge and Yukawa couplings imposes a set of boundary conditions at the Planck scale, which allow one to derive unique phenomenological predictions in each case and distinguish the different representations of the gauge group from one another. We apply to the models constraints from the $h\to \mu\mu$ signal strength at ATLAS and CMS, direct LHC searches for electroweak production with leptons and missing energy in the final state, and the dark matter relic density. We find that they further restrict the available parameter space.
Highlights
Safe quantum gravity [1] has emerged in the last few decades as a potentially very predictive framework for a Wilsonian description of the fundamental nature of quantum field theories
For coupling sizes and new physics (NP) mass values appropriate for a solution to δðg − 2Þμ, Σμ can be as large as several tens of MeV, which implies a cancellation between the tree level and one-loop component of the muon mass
The considered models are consistent with the relic density of dark matter (DM) thanks to the presence of a global Abelian symmetry
Summary
Safe quantum gravity [1] has emerged in the last few decades as a potentially very predictive framework for a Wilsonian description of the fundamental nature of quantum field theories. After following the RG flow down to the EWSB scale we determined the size of the leptoquark Yukawa couplings and combined that prediction with the expectations for the Wilson coefficients of the effective field theory (EFT) extracted from global fits to the full set of b → s transition data. By matching those two pieces of information we obtained a fairly precise determination for the mass of the leptoquark, at 4–7 TeV. If only the Yukawa coupling to either the left- or the right-handed component of the muon is allowed by gauge invariance, the model cannot enhance the anomalous magnetic moment via chiral effects. An explicit chirality-flip contribution in the loop of Fig. 1(a) yields a correction to the lepton mass, whose finite part reads
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