$L_μ-L_τ$ gauge bosons in beam dumps and supernovae

TL;DR

This work analyzes a sub-GeV $L_\mu-L_\tau$ gauge boson, emphasizing its neutrino-rich couplings and loop-induced kinetic mixing to photons which suppress visible decays. Using first-principles production modeling at SHiP, it revises the projected reach, showing neutral and charged meson decays and proton bremsstrahlung as dominant channels, while muon bremsstrahlung remains subdominant and electromagnetic cascades can contribute flux below detection thresholds. It then re-evaluates core-collapse SN constraints with improved microphysics, including ballistic and diffusive energy transport, high-energy neutrino signals from SN1987A, and low-energy SN heating constraints across two progenitor models, finding high-energy neutrino bounds to be the strongest probe in much of the parameter space. The results establish a complementary, robust set of laboratory and astrophysical constraints on the muon-philic gauge boson, underscoring the need for careful treatment of kinetic mixing and SN transport effects in these models.

Abstract

We study the phenomenology of a sub-GeV $L_μ-L_τ$ gauge boson. We find discrepancies with existing literature in sensitivity projections for the upcoming SHiP experiment and in the treatment of supernovae cooling constraints. We present a quantitative analysis of different production modes in beam dumps and compare our results to previous work. In the context of supernovae, we re-evaluate the standard supernova cooling bounds from SN1987A and analyze additional supernova-based probes: diffusive cooling, constraints from the existence of low-energy supernovae, and the absence of a high-energy neutrino signal from SN1987A.

Figures (6)

• Figure 1: Constraints and experimental projections in the mass-coupling plane for the $L_\mu - L_\tau$ gauge boson. We derive new reach estimates for the SHiP beam-dump experiment, assuming that $6\times 10^{20}$ protons on target will be collected (green solid lines). We also show an updated combination of supernovae constraints (shaded gray region with dashed and solid green lines corresponding to large/small progenitor masses, respectively). Previous constraints from early-universe measurements of $\Delta N_{\rm eff}$Escudero:2019gzq, neutrino-electron scattering in Borexino Altmannshofer:2019zhyKelly:2024tvh, from NA64$\mu$NA64:2024klw are shown for comparison.
• Figure 2: Flux of $L_{\mu}-L_\tau$ dark vectors pointed at the SHiP spectrometer prior to their decay. We have chosen the mass $m_V=10~{\rm MeV}$ for illustration, since many of the flux components contribute. The dashed vertical line at $E_V = 200$ MeV represents the energy cut that we assume for LLP reconstruction in the SHiP spectrometer. For proton bremsstrahlung (green), we shade the region between the expected flux obtained for different choices of a proton form factor parameter $\Lambda_p$, with $\Lambda_p = 1$ GeV (dashed) and $\Lambda_p\to \infty$ (solid); see text and \ref{['sec:beamdump_appendix']} for further discussion.
• Figure 3: Sensitivity of SHiP with $2\times 10^{20}$ (solid) or $6\times 10^{20}$ (dashed) protons on target. In the parameter space that SHiP is able to test, and that is unconstrained by cosmology, production is dominated by neutral mesons produced by the primary proton beam and/or proton bremsstrahlung (above the dimuon threshold). For proton bremsstrahlung, we take $\Lambda_p \to \infty$ for demonstration. Comparisons with past literature results and the impact of $\Lambda_p$ are discussed in \ref{['sec:beamdump_appendix']}.
• Figure 4: Supernova bounds on the $L_{\mu}-L_\tau$ gauge boson. We show bounds arising from observed neutrino spectra (gray shading) of SN1987A, cooling constraints computed in the single production/absorption limit (solid black lines) and the diffusive limit (dashed blue lines) and limits on SN progenitor heating (green dotted lines). In each case there are two sets of bounds derived from two SN models, s18.8-SFHo-MUONS and s20.0-SFHo-MUONS. The diffusive cooling curves terminate at couplings where the diffusion approximation breaks down (the region of validity of this approximation is indicated by the light blue shaded region); these curves exclude parameter space below them. The energy deposition bounds exclude parameter space to the left of dotted lines down to $m_V \approx 2m_\mu$ (below this mass, the visible branching fraction of $V$ is negligible).
• Figure 5: Left: Comparison with previous literature -- for consistency, our results include $V$-production solely from neutral meson decays and proton bremsstrahlung. BFJ (purple) Bauer:2018onh rescales between models in a different approach, and the DarkCast (gold) Ilten:2018crwIlten:2022lfq approach fails when event rates are not substantially large. Right: Illustration of scaling with beam intensity and/or live-time.