In the family grand unification models (fGUTs), we propose that gauge U(1)s beyond the minimal GUT gauge group are family gauge symmetries. For the symmetry $L_mu-L_tau$, i.e. $Q_{2}-Q_{3}$ in our case, to be useful for the LHC anomaly, we discuss an SU(9) fGUT and also present an example in Georgis SU(11) fGUT.
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.
Positron excess upto energies $sim$350 GeV has been observed by AMS-02 result and it is consistent with the positron excess observed by PAMELA upto 100 GeV. There is no observed excess of anti-protons over the expected CR background. We propose a leptophilic dark matter with an $U(1)_{L_{mu}-L_{tau}}$ gauge extension of MSSM. The dark matter is an admixture of the $L_{mu}-L_{tau}$ gaugino and fermionic partners of the extra $SU(2)$ singlet Higgs boson, which break the $L_{mu}-L_{tau}$ symmetry. We construct the SM$otimes U(1)_{ L_{mu}-L_{tau}}$ SUSY model which provides the correct relic density of dark matter and is consistent with constrain on $Z$ from LHC. The large dark matter annihilation cross-section into $mu^{+}mu^{-}$ and $tau^{+}tau^{-}$, needed to explain PAMELA and AMS-02 is achieved by Breit-Wigner resonance.
We investigate Majorana dark matter in a new variant of $U(1)_{L_{mu}-L_{tau}}$ gauge extension of Standard Model, containing three additional neutral fermions $N_{e}, N_{mu}, N_{tau}$, along with a $(bar{3},1,1/3)$ scalar Leptoquark (SLQ) and an inert doublet, to study the phenomenology of dark matter, neutrino mass generation and flavour anomalies on a single platform. The lightest mass eigenstate of the $N_{mu}, N_{tau}$ neutral fermions plays the role of dark matter. We compute the WIMP-nucleon cross section in leptoquark portal and the relic density mediated by inert doublet components, leptoquark and the new $Z^{prime}$ boson. We constrain the parameter space consistent with Planck limit on relic density, PICO-60 and LUX bounds on spin-dependent direct detection cross section. We also discuss about the neutrino mass generation at one-loop level and the viable parameter region to explain current neutrino oscillation data. The $Z^prime$ gauge boson of extended $U(1)$ symmetry and the SLQ play an important role in settling the known issues of flavor sector.
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 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 $Z_{mutau}$.