TeV scale resonant leptogenesis with $L_{\mu }-L_{\tau }$ gauge symmetry in light of the muon $g-2$

Motivated by the growing evidence for the possible lepton flavor universality violation after the first results from Fermilab’s 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 $g-2$ favored 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.

Figure 1

Evolution plot of comoving number density of $B-L$ for different benchmark values of $g_{\mu \tau }$ (left panel) and $M_{Z_{\mu \tau }}$ (right panel). The other parameters are set to be $M_1=1.38\mathrm{TeV}$, $\mathrm{\Delta }M=0.001\mathrm{keV}$, and $M_{Z_{\mu \tau }}=100\mathrm{GeV}$ (left panel) and $g_{\mu \tau }={10}^{-2}$ (right panel).

Figure 2

Variation of annihilation cross sections for the processes $N_1{N}_1\to Z_{\mu \tau }{Z}_{\mu \tau }$ (left panel), $N_1{N}_1\to l\overline{l}$ (right panel) with the center of mass energy squared $s$. The relevant benchmark parameters are taken to be $g_{\mu \tau }=0.1$, $M_1=1.2\mathrm{TeV}$, $Y_{De}\sim {10}^{-8}$, $Y_{D\mu }\sim {10}^{-6}$ and $Y_{D\tau }\sim {10}^{-6}$.

Figure 3

Evolution plot of comoving number density of $N_1$ for different benchmark values of $g_{\mu \tau }$ (left panel) and $M_{Z_{\mu \tau }}$ (right panel). The other parameters are set to be $M_1=1.38\mathrm{TeV}$, $\mathrm{\Delta }M=0.001\mathrm{keV}$ and $M_{Z_{\mu \tau }}=200\mathrm{GeV}$ (left panel) and $g_{\mu \tau }={10}^{-2}$ (right panel).

Figure 4

Summary plot showing allowed region of parameter space for $M_{Z_{\mu \tau }}$ above GeV. The blue and green colored bands correspond to the regions where correct baryon asymmetry can be generated for fixed scales of leptogenesis. The pink band represents muon $g-2$ favored region, already ruled out by CCFR exclusion limit [51] shown in yellow colored region. Dashed lines correspond to limits from the LHC [52] and HFAG lepton universality test [53] (see text for details).

Figure 5

Evolution plot of $N_1$ for different benchmark values of mass difference $\mathrm{\Delta }M$ (left panel) and $v_1,\tan \beta$ (right panel). The other relevant parameters are fixed at $g_{\mu \tau }={10}^{-3}$, $M_{Z_{\mu \tau }}=0.3\mathrm{GeV}$, $M_1=1.38\mathrm{TeV}$, $u=2\mathrm{TeV}$ and $x=0.067$. For left panel plot $v_1=200\mathrm{GeV}$ and $\tan \beta =0.50$ while for right panel plot $\mathrm{\Delta }M=10\mathrm{keV}$.

Figure 6

Evolution plot of $B-L$ asymmetry for different possible benchmark combinations of mass difference $\mathrm{\Delta }M$ (left panel) and $v_1,\tan \beta$ (right panel). The other relevant parameters are fixed at $g_{\mu \tau }={10}^{-3}$, $M_{Z_{\mu \tau }}=0.3\mathrm{GeV}$, $M_1=1.38\mathrm{TeV}$, $u=2\mathrm{TeV}$ and $x=0.067$. For left panel plot $v_1=200\mathrm{GeV}$ and $\tan \beta =0.50$ while for right panel plot $\mathrm{\Delta }M=10\mathrm{keV}$.

Figure 7

Summary plot showing the allowed parameter space in $g_{\mu \tau }-M_{Z_{\mu \tau }}$ plane for sub-GeV $M_{Z_{\mu \tau }}$. The region between pink dashed lines represents muon $g-2$ favored region, a small portion of which remain allowed from different exclusion limits shown as shaded regions. The points marked as stars denote benchmark points satisfying the criteria of successful TeV scale resonant leptogenesis (see text for details).