Gauged $L_{\mu }-L_{\tau }$ symmetry at the electroweak scale

The extension of the standard model by a spontaneously broken abelian gauge group based on the $L_{\mu }-L_{\tau }$ lepton number can resolve the long-standing discrepancy between experimental and theoretical values for the magnetic moment of the muon. It furthermore naturally generates $\mu \mathrm{\text{−}}\tau$ symmetric lepton mixing, introduces neutrino nonstandard interactions, and the associated gauge boson $Z^{\prime }$ serves as a mediator to the right-handed neutrino sector. A detailed fit to electroweak data is performed to identify the allowed values for the mass of $Z^{\prime }$ and its mixing with the standard model $Z$. An economical new scalar sector is constructed that spontaneously breaks $L_{\mu }-L_{\tau }$ and leads to experimental consequences such as lepton flavor violation and collider signatures. Furthermore we discuss the nonabelian extension to an $SU(2{)}^{\prime }$, particularly the neutrino sector.

Figure 1

Detection process for an unmixed $Z^{\prime }$ in electron-positron (LEP) or proton-(anti-)proton (LHC and Tevatron) collisions.

Figure 2

Left: ${\chi }^2$ as a function of $M_2/g^{\prime }$—marginalized over $\sin \xi$—and the 68.27%, 90%, and 99% C.L. limits for one parameter. Right: ${\chi }^2$ contours (68.27%, 90%, and 99% C.L. for two parameters) in the $M_2-\sin \xi$ plane. The cross marks the best-fit values $(g^{\prime }\sin \xi ,M_2/g^{\prime })=(-2.5\times {10}^{-4},219.6\mathrm{GeV})$.

Figure 3

Cross section for the process $pp(p\overline{p})\to Z$, $\gamma \to 2\mu Z^{\prime }\to 4\mu$ with the cuts $p_T>10\mathrm{GeV}$ and $|\eta |<2.5$ for different center-of-mass energies.

Figure 4

Charged-scalar mediated lepton-flavor-changing radiative decay.

Figure 5

Dominating two-loop Barr-Zee-type diagram contributing to $\Delta a_{\mu }$ (left), actual valuges for $\Delta a_{\mu }$ in the approximation $\cos {\beta }^{-}\simeq \cos \beta$, $m_{\sigma }\simeq m_{{\sigma }^{-}}$ (right).