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Register a new userOne-Loop Electron Mass and Three-Loop Dirac Neutrino Masses
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Authors
Ernest Ma
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In the context of a left-right extension of the standard model of quarks and leptons with the addition of a gauged $U(1)_D$ dark symmetry, it is shown how the electron may obtain a radiative mass in one loop and two Dirac neutrinos obtain masses in three loops.
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We consider the Peccei-Quinn (PQ) mechanism as the one behind the Dirac neutrino masses when these are generated through the $d=5$ effective operator $bar{L}tilde{H}N_Rphi$ at one loop level, with $phi$ being a Standard Model singlet scalar. In this setup, the PQ symmetry guarantees that the one-loop realization of such an effective operator gives the leading contribution to the Dirac neutrino masses by forbidding the contributions arising from its tree level realizations. All the mediators in the one-loop neutrino mass diagrams can be stabilized by a remnant $Z_N$ symmetry from the PQ symmetry breaking, thus forming a dark sector besides the axion sector and leading to mixed axion/WIMP dark matter scenarios.
We carry out a systematic investigation for the minimal Dirac neutrino mass models emerging from generic one-loop and two-loop topologies that arise from $d=5$ effective operator with a singlet scalar, $sigma$. To ensure that the tree-level Dirac mass, as well as Majorana mass terms at all orders, are absent for the neutrinos, we work in the framework where the Standard Model is supplemented by the well-motivated $U(1)_{B-L}$ gauge symmetry. At the one-loop level, we analyze six possible topologies, out of which two of them have the potential to generate desired Dirac neutrino mass. Adopting a systematic approach to select minimal models, we construct seventeen viable one-loop Dirac neutrino mass models. By embracing a similar methodical approach at the two-loop, we work out twenty-three minimal candidates. Among the forty selected economical models, the majority of the models proposed in this work are new. In our search, we also include the scenarios where the particles in the loop carry charges under the color group. Furthermore, we discuss the possible dark matter candidates within a given model, if any, without extending the minimal particle content.
We propose a model in which the origin of neutrino mass is dependent on the existence of dark matter. Neutrinos acquire mass at the three-loop level and the dark matter is the neutral component of a fermion triplet. We show that experimental constraints are satisfied and that the dark matter can be tested in future direct-detection experiments. Furthermore, the model predicts a charged scalar that can be within reach of collider experiments like the LHC.
We perform a phenomenological study of the scalar sector of two models that generate neutrino mass at the three-loop level and contain viable dark matter candidates. Both models contain a charged singlet scalar and a larger scalar multiplet (triplet or quintuplet). We investigate the effect of the extra scalars on the Higgs mass and analyze the modifications to the triple Higgs coupling. The new scalars can give observable changes to the Higgs decay channel $hrightarrowgamma gamma$ and, furthermore, we find that the electroweak phase transition becomes strongly first-order in large regions of parameter space.
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.
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