Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1{)}_{L_{\mu }-L_{\tau }}$ models

Abstract

Extensions of the standard model with a $U(1)$ gauge symmetry contain gauge invariant kinetic mixing, $\sin \chi$, and gauge non-invariant mass mixing, $\delta M^2$, between the hypercharge and the new gauge boson $Z^{\prime }$. These represent a priori incalculable but phenomenologically important parameters of the theory. They become calculable if there exist spontaneously or softly broken symmetries which forbid them at tree level but allow their generation at the loop level. We discuss various symmetries falling in this category in the context of the gauged $L_{\mu }-L_{\tau }$ models and their interplay with lepton mixing. It is shown that one gets phenomenologically inconsistent lepton mixing parameters if these symmetries are exact. Spontaneous breaking of these symmetries can lead to consistent lepton mixing and also generates finite and calculable values of these parameters at one or two loop order depending on the underlying symmetry. We calculate these parameters in two specific cases: (i) the standard seesaw model with $\mu$-$\tau$ symmetry broken by the masses of the right-handed neutrinos and (ii) in a model containing a pair of vectorlike charged leptons which break $\mu$-$\tau$ symmetry. In case (i), the right-handed neutrinos are the only source of gauge mixing. The kinetic mixing parameters are suppressed and vanish if the right-handed neutrinos decouple from the theory. In contrast, there exists a finite gauge mixing in case (ii) which survives even when the masses of vectorlike leptons are taken to infinity, exhibiting non-decoupling behaviour. The seesaw model discussed here represents a complete framework with practically no kinetic mixing and hence can survive a large number of experimental probes used to rule out specific ranges in the coupling $g^{\prime }$ and mass $M_{Z^{\prime }}$. The model can generate non-universality in tau decays, which can be tested in future experiments.

arXiv comment26 pages; Published version

References in corpus (51)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Neutrino Trident Production: A Powerful Probe of New Physics with Neutrino Beams
• Dressing L_mu - L_tau in Color
• Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations
• Radiatively Induced Neutrino Masses and Large Higgs-Neutrino Couplings in the Standard Model with Majorana Fields
• Hunting All the Hidden Photons
• Cosmology With a Very Light $L_{\mu }-L_{\tau }$ Gauge Boson
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• Leptophobic U(1)'s and the R_b - R_c Crisis
• Muon Anomalous $g-2$ and Gauged $L_{\mu }-L_{\tau }$ Models
• Gauged L_mu - L_tau Symmetry at the Electroweak Scale
• Gauged $L_{\mu }-L_{\tau }$ with Large Muon Anomalous Magnetic Moment and the Bimaximal Mixing of Neutrinos
• Explaining Dark Matter and $B$ Decay Anomalies with an $L_{\mu }-L_{\tau }$ Model
• Limiting two-Higgs-doublet models
• Model for a Light Z' Boson
• Lepton flavor violating Z' explanation of the muon anomalous magnetic moment
• A Flavor Symmetry for quasi-degenerate Neutrinos: L_mu-L_tau
• Coherent Elastic Neutrino Nucleus Scattering (CE$\nu$NS) as a probe of $Z^{\prime }$ through kinetic and mass mixing effects
• Phenomenology of $U(1{)}_{L_{\mu }-L_{\tau }}$ charged dark matter at PAMELA/FERMI and colliders
• Detecting the $L_{\mu }-L_{\tau }$ gauge boson at Belle II
• Physical Parameters and Renormalization of U(1)_a x U(1)_b Models
• Penguin $b\to s{\ell }^{\prime +}{\ell }^{\prime -}$ and $B$-meson anomalies in a gauged $L_{\mu }-L_{\tau }$
• Muon g-2 and LHC phenomenology in the $L_{\mu }-L_{\tau }$ gauge symmetric model
• Leptonic Flavor-changing Z0 Decays in SU(2)xU(1) Theories with Right- handed Neutrinos
• Probing the muon g_μ-2 anomaly, L_μ - L_τ gauge boson and Dark Matter in dark photon experiments
• Non-Standard Neutrino Interactions and Neutral Gauge Bosons
• Minimal Gauged U(1)${}_{L_{\alpha }-L_{\beta }}$ Models Driven into a Corner
• Constraints on flavour-dependent long-range forces from atmospheric neutrino observations at Super-Kamiokande
• Gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ model in light of muon $g-2$ anomaly, neutrino mass and dark matter phenomenology
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• One-loop corrections to the seesaw mechanism in the multi-Higgs-doublet Standard Model
• Gauged L_mu - L_tau and different Muon Neutrino and Anti-Neutrino Oscillations: MINOS and beyond
• On the possibility of search for $L_{\mu }-L_{\tau }$ gauge boson at Belle-II and neutrino beam experiments
• The Dark $L_{\mu }-L_{\tau }$ Rises via Kinetic Mixing
• FIMP and Muon ($g-2$) in a U$(1{)}_{L_{\mu }-L_{\tau }}$ Model
• Universal 2-3 symmetry
• How good is μ-τsymmetry after results on non-zero θ_{13}?
• Constraints on $L_{\mu }-L_{\tau }$ Gauge Interactions from Rare Kaon Decay
• Reconciling dark matter, $R_{K^{(\ast )}}$ anomalies and $(g-2{)}_{\mu }$ in an $L_{\mu }-L_{\tau }$ scenario
• Soft breaking of $L_{\mu }-L_{\tau }$ symmetry: Light neutrino spectrum and Leptogenesis
• Discrete symmetries and models of flavor mixing
• Exploring dark matter, neutrino mass and $R_{K^{(\ast )},\varphi }$ anomalies in $L_{\mu }-L_{\tau }$ model
• Neutrino mass generation with large $SU(2{)}_L$ multiplets under local $U(1{)}_{L_{\mu }-L_{\tau }}$ symmetry
• Leptophilic dark matter in gauged $L_{\mu }-L_{\tau }$ extension of MSSM
• Zee-Babu type model with $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge symmetry
• Supersymmetric gauged U(1)${}_{L_{\mu }-L_{\tau }}$ model for neutrinos and the muon $(g-2)$ anomaly
• Cobimaximal lepton mixing from soft symmetry breaking
• Signatures of supersymmetry and a $L_{\mu }-L_{\tau }$ gauge boson at Belle-II
• Quasi-degenerate neutrinos and leptogenesis from L_mu-L_tau

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• Probing muonic forces with neutron star binaries
• Searching for Heavy Leptophilic $Z^{\prime }$: from Lepton Colliders to Gravitational Waves
• Radiatively generated fermion mass hierarchy from flavour non-universal gauge symmetries
• Light dark matter, rare $B$ decays with missing energy in $L_{\mu }-L_{\tau }$ model with a scalar leptoquark
• Gauged $SU(3{)}_F$ and loop induced quark and lepton masses
• Dark matter, $Z^{\prime }$, vector-like quark at the LHC and $b\to s\mu \mu$ anomaly
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