Probing nonstandard lepton number violating interactions in neutrino oscillations

We discuss lepton number violating processes in the context of long-baseline neutrino oscillations. We summarize and compare neutrino flavor oscillations in quantum mechanics and quantum field theory, both for standard oscillations and for those that violate lepton number. When the active neutrinos are Majorana in nature, the required helicity reversal gives a strong suppression by the neutrino mass over the energy, $(m_{\nu }/E_{\nu }{)}^2$. Instead, the presence of nonstandard lepton number violating interactions incorporating right-handed lepton currents at production or detection alleviate the mass suppression while also factorizing the oscillation probability from the total rate. Such interactions arise from dimension-six operators in the low energy effective field theory of the Standard Model. We derive general and simplified expressions for the lepton number violating oscillation probabilities and use limits from MINOS and KamLAND to place bounds on the interaction strength in interplay with the unknown Majorana phases in neutrino mixing. We compare the bounds with those from neutrinoless double beta decay and other microscopic lepton number violating processes and outline the requirements for future short- and long-baseline neutrino oscillation experiments to improve on the existing bounds.

Figure 1

Generic Feynman diagrams depicting the ${\nu }_{\alpha }\to {\nu }_{\beta }$ process (left) and ${\nu }_{\alpha }\to {\overline{\nu }}_{\beta }$ process (right), which requires a helicity reversal if the interaction vertices are SM-like.

Figure 2

Left: simplified Feynman diagram of the oscillation process under consideration. Shown are the effective interactions at production and detection—a low energy SM CC interaction and LNV NSI, respectively. Right: a possible UV completion in a LR symmetric scenario.

Figure 3

Allowed regions in the $({ϵ}_{\mu \mu },{ϵ}_{\mu \tau })$ parameter space for fixed $L/E_{\mathbf{q}}=735/3\mathrm{km}{\mathrm{GeV}}^{-1}$ and four values of $\eta$ in the $2\nu$ mixing approximation of the ${\nu }_{\mu }-{\nu }_{\tau }$ sector (left). Allowed region in ${ϵ}_{\mu \mu }–{ϵ}_{\mu \tau }$ for fixed $L=735\mathrm{km}$ and again four values of $\eta$, found by integrating over the NuMI beam neutrino energies (right).

Figure 4

Allowed regions in the $({ϵ}_{\mu \mu },{ϵ}_{\mu \tau })$ parameter space for $\eta =0$ (left) and $\eta =\pi /2$ (right) for four different values of the baseline $L$.

Figure 5

Constraints on ${ϵ}_{\mu \mu }$ for ${ϵ}_{\mu \tau }=0$ (left) and ${ϵ}_{\mu \tau }$ for ${ϵ}_{\mu \mu }=0$ (right) and as a function of the baseline $L$ for three values of the Majorana phase $\eta$. The baseline of MINOS is indicated by the dashed line.

Figure 6

Left: allowed regions in the $({ϵ}_{\mu \mu },{ϵ}_{\mu \tau })$ parameter space for ${ϵ}_{\mu e}=0$, $L=735\mathrm{km}$, ${\alpha }_2=0$, and three values of the Majorana phase ${\alpha }_3$. Middle: angle $\mathrm{\Theta }$ from the positive ${ϵ}_{\mu \mu }$ axis to the semimajor axis of the constraint ellipse as a function of the phases. Right: eccentricities of the constraint ellipse also as a function of the phases.

Figure 7

Upper bounds on the NSI coefficients ${ϵ}_{\mu e}$ (left), ${ϵ}_{\mu \mu }$ (center), and ${ϵ}_{\mu \tau }$ (right), as a function of the Majorana phases ${\alpha }_2$ and ${\alpha }_3$, derived from the MINOS limit $S_{\mu \mu }<0.026$. Best fit values for the mixing parameters ${\theta }_{12}$, ${\theta }_{13}$ and ${\theta }_{23}$, $\mathrm{\Delta }{m}_{12}^2$ and $\mathrm{\Delta }{m}_{23}^2$, and ${\delta }_{\mathrm{CP}}$ are taken in the NO.

Figure 8

Other processes capable of probing LNV NSI coefficients. Left: $0\nu \beta \beta$ decay. Middle: ${\mu }^{-}-e^{+}$ conversion. Right: kaon decay $K^{+}\to {\pi }^{-}{\mu }^{+}{\mu }^{+}$.

Figure 9

Upper bounds on the NSI coefficients ${ϵ}_{ee}$ (left), ${ϵ}_{e\mu }$ (center), and ${ϵ}_{e\tau }$ (right) all multiplied by $10^9$ as a function of the Majorana phases ${\alpha }_2$ and ${\alpha }_3$, found from the ${}^{76}\mathrm{Ge}$ $0\nu \beta \beta$ decay limit $T_{1/2}^{0\nu \beta \beta }>5.3\times {10}^{25}\mathrm{y}$. Best fit values for the mixing angles ${\theta }_{12}$, ${\theta }_{13}$, and ${\theta }_{23}$, squared mass splittings $\mathrm{\Delta }{m}_{12}^2$ and $\mathrm{\Delta }{m}_{23}^2$, Dirac $CP$ phase ${\delta }_{\mathrm{CP}}$ are taken in the NO, with a lightest neutrino mass of $m_1=0\mathrm{eV}$.