Impact of flavor changing processes on prospects for majoron discovery at intensity-frontier searches

Abstract

The singlet majoron $J$ is the pseudo-Nambu-Goldstone boson of a global, anomaly-free $U(1)_{B-L}$ symmetry whose spontaneous breaking generates Majorana masses for right-handed neutrinos. At tree level, the only direct coupling of $J$ to Standard Model fields is $Jνν\propto m_ν/f$ (where $m_ν$ denotes the light neutrino mass and $f$ the $B-L$ breaking scale). Couplings to charged fermions and gauge bosons, in contrast, arise only at loop level. Consequently, $J$ can be long-lived over wide regions of parameter space, motivating displaced-decay searches. We study majoron production and displaced decays at proton beam dump experiments, neutrino facilities, and LHC forward detectors (including DUNE, NA62, FASER/FASER2, MATHUSLA, and SHiP), and we quantify the resulting reach in the $(m_J,\,f)$ plane. We show that, for realistic seesaw-induced coupling textures, lepton-flavor-violating (LFV) $τ$ decays $τ\to \ell J$ ($\ell=e,μ$) dominate majoron production at these facilities and can extend sensitivity into the intermediate-mass window $m_J\simeq 0.2\text{-}1.7~\mathrm{GeV}$, complementary to supernova bounds at lower masses and to dedicated LFV searches at higher masses. We also identify physically consistent benchmark textures for the matrix $K=M_D M_D^\dagger/(vf)$ with $M_D$ denoting the Dirac mass matrix and $v$ the electroweak scale (including positive semidefinite ``anarchical'', single-flavor, and CP-violating cases) and map their impact on experimental reach.

Figures (6)

• Figure 1: Functional dependence of the majoron couplings to gauge bosons, which affect the decay widths and production modes of the majoron. We show three examples (indicated by blue, orange, and green lines) of the "anarchical" benchmark defined by Eq. (\ref{['eq:K_anarch']}). A similar dependence holds for the other benchmarks, in particular those given by Eq. (\ref{['eq:K_benchmarks_1']}) and Eq. (\ref{['eq:K_benchmarks_2']}).
• Figure 2: Majoron partial decay widths for $K=K_{\rm anarch}$ benchmarks: $R_J=2/3$ (left), $R_J=1.01$ (center), and $R_J=10$ (right). We fixed $f=1$ GeV, while the general case is obtained by rescaling by $(1\,\mathrm{GeV}/f)^2$.
• Figure 3: Majoron proper decay length $c\tau$ for the anarchical benchmarks: $R_J=2/3$ (red), $R_J=1.01$ (blue), and $R_J=10$ (green). We fixed $f=10^7$ GeV, which corresponds to a typical value that can be probed at IF, see Sec. \ref{['sec:results']}. The general case is obtained by rescaling by $(f/10^7\,\mathrm{GeV})^2$.
• Figure 4: Results for the "anarchical" benchmark (see Eq. (\ref{['eq:K_anarch']})), shown in the $m_J$ vs. $1/f$ plane. Sensitivity curves correspond to $N_{\rm sig}=3$ expected displaced-decay events; majorons are produced primarily via $\tau\to\ell\,J$ from forward $D_s/D\to\tau\nu_\tau$ decays and are detected through all visible decay channels into charged-lepton pairs (both flavor-conserving and flavor-violating). The gray-shaded region denotes the combined exclusion from past beam-dump experiments (CHARM, BEBC, NuCal). Hatched and shaded regions show existing astrophysical constraints from supernova cooling (SN-$ee$, SN-$\mu\mu$, SN-$e\mu$) and terrestrial LFV searches ($\mu\to e\,J_{\rm inv.}$, $\tau\to\mu\,J_{\rm inv.}$, $\tau$ lifetime), as labeled. Colored solid curves show projected reaches for the listed future facilities (see legend); dashed lines indicate projected sensitivities of Belle II and MEG-II. The hierarchy between off-diagonal and diagonal elements is controlled by three values of $R_J$: $R_J=2/3$ (left), $R_J=1.01$ (center), and $R_J=10$ (right). In the right panel, we additionally show the reach from $\mu\to e\,J$ production using the high-energy muon flux traversing FASER2 (dotted), as well as limits from excess muon decays $\mu^\pm\to J\,e^\pm$ (orange shading) and from prompt majoron decays following muon decay (red shading); these limits are weaker for the other benchmarks and are omitted there. Note that the $R_J=2/3$ benchmark does not yield a positive-semi-definite $K$ matrix and is shown for comparison only (see text).
• Figure 5: Same as Fig. \ref{['fig:sensitivity_plot_1']}, but for the maximally CP-violating texture defined in Eq. (\ref{['eq:K_benchmarks_2']}), with $\kappa=0.01$ (left) and $\kappa=0.577$ (right). The diagonal entries are fixed at $K^d = 8\pi^2 v/f$, while $\kappa$ controls the magnitude of all off-diagonal (purely imaginary) LFV entries and hence the branching fractions $\mathrm{BR}(\tau\to\ell\,J)$. These benchmarks are motivated by leptogenesis scenarios requiring large CP-violating phases in the seesaw sector.