Muonic Boson Limits: Supernova Redux

Abstract

We derive supernova (SN) bounds on muon-philic bosons, taking advantage of the recent emergence of muonic SN models. Our main innovations are to consider scalars $φ$ in addition to pseudoscalars $a$ and to include systematically the generic two-photon coupling $G_{γγ}$ implied by a muon triangle loop. This interaction allows for Primakoff scattering and radiative boson decays. The globular-cluster bound $G_{γγ}<0.67\times10^{-10}~{\rm GeV}^{-1}$ derived for axion-like particles carries over to the muonic Yukawa couplings as $g_a<3.1\times10^{-9}$ and $g_φ< 4.6\times10^{-9}$ for $m_{a,φ}\lesssim 100$ keV, so SN arguments become interesting mainly for larger masses. If bosons escape freely from the SN core the main constraints originate from SN1987A $γ$ rays and the diffuse cosmic $γ$-ray background. The latter allows at most $10^{-4}$ of a typical total SN energy of $E_{\rm SN}\simeq3\times10^{53}$erg to show up as $γ$ rays, for $m_{a,φ}\gtrsim 100$keV implying $g_a \lesssim 0.9\times10^{-10}$ and $g_φ\lesssim 0.4\times10^{-10}$. In the trapping regime the bosons emerge as quasi-thermal radiation from a region near the neutrino sphere and match $L_ν$ for $g_{a,φ}\simeq 10^{-4}$. However, the $2γ$ decay is so fast that all the energy is dumped into the surrounding progenitor-star matter, whereas at most $10^{-2}E_{\rm SN}$ may show up in the explosion. To suppress boson emission below this level we need yet larger couplings, $g_{a}\gtrsim 2\times10^{-3}$ and $g_φ\gtrsim 4\times10^{-3}$. Muonic scalars can explain the muon magnetic-moment anomaly for $g_φ\simeq 0.4\times10^{-3}$, a value hard to reconcile with SN physics despite the uncertainty of the explosion-energy bound. For generic axion-like particles, this argument covers the "cosmological triangle" in the $G_{aγγ}$--$m_a$ parameter space.

Figures (12)

• Figure 1: Profile of the Garching muonic SN model SFHo-18.8 at $t_{\rm pb}=1$ s Bollig:2020xdr that we will use as our "cold reference model." Top: Chemical potentials, temperature, plasma frequency $\omega_{\rm p}$, and Debye screening scale $k_{\rm s}$. Bottom: Number densities $n_i$, normalized to $n_0 = 0.181~{\rm fm}^{-3}$, corresponding to nuclear density of $3\times10^{14}~{\rm g}~{\rm cm}^{-3}$.
• Figure 2: Constraints on the muonic Yukawa coupling $g_a$ of pseudoscalars (left panel) and $g_\phi$ of scalars (right panel) as a function of boson mass. We also show the constraint where the muon $g_\mu{-}2$ discrepancy would get worse (pseudoscalars) or could be explained (scalars). The shading or double arrows indicate the excluded range, except for the scalar range ruled in by $g_\mu{-}2$. The SN bounds are derived in this paper and summarized in Table \ref{['tab:allconstraints']} using both a hot and a cold SN reference model. We here show conservative limits (the larger number in the free-streaming case and the smaller one in the trapping regime). The HB-star bounds are taken from Ref. Carenza:2020zil, the cosmological $N_{\rm eff}$ constraint from Ref. Depta:2020zbh.
• Figure 3: Cross section for the muonic Compton process with a final-state vector (solid), scalar (dashed) or pseudoscalar (dotted). The vector case requires a factor of 2 for the final-state polarizations. The energy $\omega$ is considered in the muon rest frame. For $\omega \gtrsim m_\mu$ the scalar and pseudoscalar cross sections quickly approach each other, while asymptotic agreement with the vector case requires very large energies.
• Figure 4: Top: Charged-particle abundances in our reference model shown in Fig. \ref{['fig:SNProfile']}. The difference between $Y_e+Y_\mu$ and $Y_p$ highlights the appearance of light nuclei or nuclear clusters in the decoupling region. Bottom: Average screening factor $f_{\rm s}$ for Primakoff scattering defined in Eq. \ref{['eq:ScreeningFactor']}. The red line is the Rosseland average, the blue line a thermal average for boson emission as explained in the text.
• Figure 5: Time and radial evolution of the temperature (top panel), baryon number density normalized to nuclear density $n_0 = 0.181\, {\rm fm}^{-3}$ (central panel), and muon abundance $Y_\mu$ for the SN model SFHo-18.8 Bollig:2020xdr that was also used in Fig. \ref{['fig:SNProfile']}.