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Register a new userTeV Scale Resonant Leptogenesis with $L_{mu}-L_{tau}$ Gauge Symmetry in the Light of Muon $(g-2)$
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Motivated by the growing evidence for the possible lepton flavour universality violation after the first results from Fermilabs muon $(g-2)$ measurement, we revisit one of the most widely studied anomaly free extensions of the standard model namely, gauged $L_{mu}-L_{tau}$ model, to find a common explanation for muon $(g-2)$ as well as baryon asymmetry of the universe via leptogenesis. The minimal setup allows TeV scale resonant leptogenesis satisfying light neutrino data while the existence of light $L_{mu}-L_{tau}$ gauge boson affects the scale of leptogenesis as the right handed neutrinos are charged under it. For $L_{mu}-L_{tau}$ gauge boson mass at GeV scale or above, the muon $(g-2)$ favoured parameter space is already ruled out by other experimental data while bringing down its mass to sub-GeV regime leads to vanishing lepton asymmetry due to highly restrictive structures of lepton mass matrices at the scale of leptogenesis. Extending the minimal model with two additional Higgs doublets can lead to a scenario consistent with successful resonant leptogenesis and muon $(g-2)$ while satisfying all relevant experimental data.
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Motivated by the growing evidence for lepton flavour universality violation after the first results from Fermilabs muon $(g-2)$ measurement, we revisit one of the most widely studied anomaly free extensions of the standard model namely, gauged $L_{mu}-L_{tau}$ model, known to be providing a natural explanation for muon $(g-2)$. We also incorporate the presence of dark matter (DM) in this model in order to explain the recently reported electron recoil excess by the XENON1T collaboration. We show that the same neutral gauge boson responsible for generating the required muon $(g-2)$ can also mediate interactions between electron and dark fermions boosted by dark matter annihilation. The required DM annihilation rate into dark fermion require a hybrid setup of thermal and non-thermal mechanisms to generate DM relic density. The tightly constrained parameter space from all requirements remain sensitive to ongoing and near future experiments, keeping the scenario very predictive.
The tightening of the constraints on the standard thermal WIMP scenario has forced physicists to propose alternative dark matter (DM) models. One of the most popular alternate explanations of the origin of DM is the non-thermal production of DM via freeze-in. In this scenario the DM never attains thermal equilibrium with the thermal soup because of its feeble coupling strength ($sim 10^{-12}$) with the other particles in the thermal bath and is generally called the Feebly Interacting Massive Particle (FIMP). In this work, we present a gauged U(1)$_{L_{mu}-L_{tau}}$ extension of the Standard Model (SM) which has a scalar FIMP DM candidate and can consistently explain the DM relic density bound. In addition, the spontaneous breaking of the U(1)$_{L_{mu}-L_{tau}}$ gauge symmetry gives an extra massive neutral gauge boson $Z_{mutau}$ which can explain the muon ($g-2$) data through its additional one-loop contribution to the process. Lastly, presence of three right-handed neutrinos enable the model to successfully explain the small neutrino masses via the Type-I seesaw mechanism. The presence of the spontaneously broken U(1)$_{L_{mu}-L_{tau}}$ gives a particular structure to the light neutrino mass matrix which can explain the peculiar mixing pattern of the light neutrinos.
We discuss the feasibility of detecting the gauge boson of the $U(1)_{L_{mu}-L_{tau}}$ symmetry, which possesses a mass in the range between MeV and GeV, at the Belle-II experiment. The kinetic mixing between the new gauge boson $Z$ and photon is forbidden at the tree level and is radiatively induced. The leptonic force mediated by such a light boson is motivated by the discrepancy in muon anomalous magnetic moment and also the gap in the energy spectrum of cosmic neutrino. Defining the process $e^{+} e^{-} rightarrow gamma Z rightarrow gamma u bar{ u}~(missing~energy)$ to be the signal, we estimate the numbers of the signal and the background events and show the parameter region to which the Belle-II experiment will be sensitive. The signal process in the $L_{mu}-L_{tau}$ model is enhanced with a light $Z$, which is a characteristic feature differing from the dark photon models with a constant kinetic mixing. We find that the Belle-II experiment with the design luminosity will be sensitive to the $Z$ with the mass $M_{Z} lesssim 1 $ GeV and the new gauge coupling $g_{Z} gtrsim 8cdot 10^{-4}$, which covers a half of the unconstrained parameter region that explains the discrepancy in muon anomalous magnetic moment. The possibilities to improve the significance of the detection are also discussed.
We propose an anomaly free unified scenario by invocation of an extra local ${rm U(1)}_{L_{mu}-L_{tau}}$ gauge symmetry. This scenario simultaneously resolves the $R_{K^{(*)}}$ anomalies, the dark matter puzzle and the long-standing discrepancy in muons anomalous magnetic moment. A complex scalar ($eta$) having nonzero ${L_{mu}-L_{tau}}$ charge has been introduced to break this new U(1) symmetry spontaneously. Moreover, for the purpose of studying dark matter phenomenology and $R_{K^{(*)}}$ anomalies in a correlated manner, we introduce an inert ${rm SU(2)}_L$ scalar doublet ($Phi$), a $mathbb{Z}_2$-odd real singlet scalar ($S$) and a $mathbb{Z}_2$-odd coloured fermion ($chi$) which transforms vectorially under the ${rm U(1)}_{L_{mu}-L_{tau}}$ symmetry. This extra gauge symmetry provides a new gauge boson $Z_{mutau}$ which not only gives additional contribution to both $bto s ellell$ transition and $(g-2)_{mu}$ but also provides a crucial annihilation channel for dark matter candidate $rho_1$ of the present scenario. This $rho_1$ is an admixture of CP-even neutral component of $Phi$ and $S$. Our analysis shows that the low mass dark matter regime ($M_{rho_1}lesssim 60$ GeV) is still allowed by the experiments like XENON1T, LHC (via Higgs invisible branching) and Fermi-LAT, making the dark matter phenomenology drastically different from the standard Inert Doublet and the Scalar Singlet models. Furthermore, the present model is also fairly consistent with the observed branching ratio of $Bto X_sgamma$ in $3sigma$ range and is quite capable of explaining neutrino masses and mixings via Type-I seesaw mechanism if we add three right handed neutrinos in the particle spectrum. Finally, we use the latest ATLAS data of non-observation of a resonant $ell^+ell^-$ signal at the 13 TeV LHC to constrain the mass-coupling plane of $Z_{mutau}$.
Very recently, the Fermi-Lab reported the new experimental combined results on the magnetic momentum of muon with a 4.2$sigma$ discrepancy compared with the expectation of the Standard Model cite{Fermi_Lab}. A new light gauge boson $X$ in the $L_{mu}-L_{tau}$ model provides a good explanation for the $g-2$ anomaly. A Dirac fermion dark matter with a large $L_{mu}-L_{tau}$ charge can explain both the $g-2$ anomaly and the dark matter relic density cite{Asai_2021}. In this work, we focus on the case that the mass of the dark matter is larger than the mass of muon (i.e. $m_{Psi} > m_{mu}$) for which the channel $Psi Psi rightarrow mu^- mu^+$ opens. Although the cross section $(sigma v)_{mu^{-}mu^{+}}$ is smaller by a factor of $1/q_{Psi}^2$ ($q_{Psi}$ represents the $L_{mu}-L_{tau}$ charge of the dark matter) compared with the channel $PsiPsi rightarrow XX rightarrow u ubar{ u}bar{ u}$, the resulting secondary electrons and positrons could imprint on their spectra above GeV energies due to the reacceleration effect of cosmic ray propagation. We use the AMS-02 measurements of electrons and positrons to constrain the annihilation cross section of the channel $PsiPsi rightarrow mu^{-}mu^{+}$, which rules out part of the parameter space of the large $L_{mu}-L_{tau}$ charged dark matter model to account for the muon $g-2$ anomaly.
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