Double beta decay, lepton flavor violation, and collider signatures of left-right symmetric models with spontaneous $D$-parity breaking

We propose a class of left-right symmetric models (LRSMs) with spontaneous $D$-parity breaking, where $SU(2{)}_R$ breaks at the TeV scale while discrete left-right symmetry breaks around $10^9\mathrm{GeV}$. By embedding this framework in a nonsupersymmetric $SO(10)$ grand unified theory (GUT) with Pati-Salam symmetry as the highest intermediate breaking step, we obtain $g_R/g_L\approx 0.6$ between the right- and left-handed gauge couplings at the TeV scale. This leads to a suppression of beyond the Standard Model phenomena induced by the right-handed gauge coupling. Here we focus specifically on the consequences for neutrinoless double beta decay, low-energy lepton flavor violation, and LHC signatures due to the suppressed right handed currents. Interestingly, the reduced $g_R$ allows us to interpret an excess of events observed recently in the range of 1.9 to 2.4 TeV by the CMS group at the LHC as the signature of a right-handed gauge boson in LRSMs with spontaneous $D$-parity breaking. Moreover, the reduced right-handed gauge coupling also strongly suppresses the nonstandard contribution of heavy states to the neutrinoless double beta decay rate as well as the amplitude of low-energy lepton flavor violating processes. In a dominant type-II seesaw mechanism of neutrino mass generation, we find that both sets of observables provide stringent and complimentary bounds which make it challenging to observe the scenario at the LHC.

Figure 1

RG evolution of gauge couplings yielding $g_R/g_L=0.6$ within a non-SUSY $SO(10)$ GUT, where ${\mathcal{G}}_{224}$ and ${\mathcal{G}}_{2213}$ occur as intermediate symmetry breaking steps. The plot shows the running of ${\alpha }_i^{-1}=4\pi /g_i^2$ for the couplings $g_i$ of the relevant gauge groups as a function of the energy scale $\mu$ where $i=2L,2R,4C,1R,BL,3C,Y$. The gauge breaking scales, as denoted by the dashed vertical lines, consistent with gauge coupling unification are $M_Z=91.2\mathrm{GeV}$, $M_{B-L}\approx 4\mathrm{TeV}$, $M_{\mathrm{\Omega }}\approx 6\mathrm{TeV}$, $M_C\approx 10^5\mathrm{GeV}$, $M_P\approx 10^{9.6}\mathrm{GeV}$, and $M_U\approx 10^{16}\mathrm{GeV}$.

Figure 2

Diagrams contributing to neutrinoless double beta decay: Standard LH charged current interaction through the exchange of light Majorana neutrinos (left), RH charged current interaction through the exchange of heavy $W_R$ bosons and heavy neutrinos (middle), doubly charged RH triplet Higgs scalar mediation (right).

Figure 3

Effective $0\nu \beta \beta$ mass (left) and ${}^{76}\mathrm{Ge}$ half-life (right) in the standard mechanism as a function of the lightest neutrino mass. The red (blue) colored bands show the variation due the Majorana phases for a NH (IH) pattern of light neutrinos using the best-fit values of the oscillation parameters while the green and yellow bands correspond to an additional $3\sigma$ variation of the oscillation parameters. The vertical lines represent bounds from Planck and KATRIN while the horizontal lines denote the experimental bounds from GERDA and a combination of the GERDA, Heidelberg-Moscow, and IGEX experiments.

Figure 4

As Fig. 3, but showing the $0\nu \beta \beta$ half-life of ${}^{76}\mathrm{Ge}$ arising in the combined contribution from light neutrino, heavy neutrino and RH Higgs triplet exchange. The heavy mass scales are fixed as $M_N=M_{{\delta }_R}=0.75\mathrm{TeV}$ and $M_{W_R}=2.2\mathrm{TeV}$.

Figure 5

Scatter plot in the common heavy scale $M\equiv M_{W_R}\simeq M_{\mathrm{\Delta }}\simeq M_N$ and the lightest neutrino mass ($m_{\text{lightest}}$), for NH (left) and IH (right) light neutrinos. The light green dots represent parameter points satisfying the current $0\nu \beta \beta$ limit $T_{1/2}>1.9\times 10^{25}\mathrm{yr}$ while the red points are additionally testable in the near future; i.e., they correspond to $3.0\times 10^{26}\mathrm{yr}>T_{1/2}>1.9\times 10^{25}\mathrm{yr}$.

Figure 6

Diagrams contributing to $\mu \to e\gamma$ in the LRSM.

Figure 7

Dominant diagrams contributing to $\mu \to e$ conversion in nuclei (left) and $\mu \to eee$ (right) in the left-right symmetric model. The grey circle represents the effective $\mu -e-$gauge boson vertex with contributions from Fig. 6.

Figure 8

Low-energy LFV process rates as a function of the lightest neutrino mass $m_{\text{lightest}}$ and the common heavy mass $M$, in the case of normal (left) and inverse (right) neutrino mass hierarchy. The oscillation parameters are chosen at their best fit values, and the RH gauge coupling $g_R=0.36$. The solid curves correspond to the respective current limits, whereas the dashed curves give the expected future sensitivities. The shaded area is excluded from current LFV searches.

Figure 9

Random scatter plot in the parameter plane spanned by $M_N$ and $m_{\text{lightest}}$. The oscillation parameters are varied according to their experimental errors for normal (left) and inverse (right) light neutrino masses, and the other heavy masses $M_X$ in the range $0.3M_N<M_X<3M_N$. The light green points satisfy all current LFV limits whereas the dark red boxes additionally yield $R^{\mathrm{Al}}(\mu \to e)>10^{-16}$, i.e., can be probed at COMET or Mu2e.

Figure 10

Production and decay of a heavy RH neutrino with dilepton signature at hadron colliders.

Figure 11

Left: Predicted cross sections $\sigma (pp\to eejj)$ (red curves) and experimental exclusion limits as a function of the $W_R$ mass. The dashed red curve correspond to the LRSM case $g_R=g_L$, $V_{Ne}=1$. The solid (dotted) red curve corresponds to the $D$-parity breaking scenario with $g_R=0.38$ and $|V_{Ne}|=0.82$ ($|V_{N\mu }|=0.56$). The observed (solid black curve) and expected (dashed grey curve and green/yellow bands) 95% exclusion limits are taken from [40]. Right: Discovery potential of the process $pp\to W_R\to l_1^{\pm }{l}_2^{\pm ,\mp }+2$ jets at the LHC as a function of the RH $W_R$ boson mass and heavy neutrino mass $M_N$. The red shaded region is excluded by recent LHC searches. The value of the RH gauge coupling is $g_R=0.38$, and the neutrino oscillation parameters are chosen at the best-fit values.