Nucleon-nucleon bremsstrahlung of dark gauge bosons and revised supernova constraints

We calculate the rate of production of hypothetical light vector bosons (LVBs) from nucleon-nucleon bremsstrahlung reactions in hot and dense matter. We use the soft-radiation approximation and express the rates directly in terms of the measured nucleon-nucleon elastic differential cross sections. These results are combined with the observation of neutrinos from supernova SN1987a to deduce constraints on the couplings of vector bosons with masses $\lesssim 200$ MeV to either electric charge (dark photons) or to baryon number. We establish for the first time strong constraints on LVB that couple only to baryon number and revise earlier constraints on the dark photon. For the latter, we find that the excluded region of parameter space is diminished by about a factor of 10.

Figure 1

Diagrams in which radiation, denoted by the wavy line, attaches to the external nucleon legs (solid lines) dominate in the low-energy limit. The gray blobs represent the antisymmetrized nucleon-nucleon potential and contain both the direct and the exchange contributions.

Figure 2

Neglected diagrams $\left(e\right)$ and $\left(f\right)$, in which radiation attaches to internal nucleon lines, and $\left(g\right)$, in which it couples to short-distance two-body currents represented by the gray blob.

Figure 3

The $np$ scattering cross section reconstructed from the phase shifts is compared with data and the predictions of the OPEP. The change in the total cross section as more partial waves are included is shown and is in accordance with the expectation about its rapid convergence. In contrast, the Born cross sections in the OPEP fail to reproduce both the qualitative and quantitative features seen in the data.

Figure 4

Dipole (left) and quadrupole (right) contributions to the emissivity integral defined in Eqs. (18) and (19), respectively. The solid lines were obtained using experimentally measured differential cross sections and the dotted lines are obtained from the OPEP model. Fiducial values $T=30$ MeV and $m=0$ are used in these plots.

Figure 5

Cooling and trapping constraints in the parameter space of the LVB that couples to baryon number. The solid blue line is the lower limit set by cooling, and the dashed blue line is the upper limit set by trapping. Experimental constraints derived from neutron scattering from Ref. [30] (black dot-dashed curve) and from neutron optics from Ref. [31] (red dashed curve) are also shown.

Figure 6

The temperature dependence of the thermally averaged nuclear cross sections needed for the calculation of the bremsstrahlung absorption contributions to the mean free path of LVBs.

Figure 7

The revised excluded region in the dark-photon parameter space. Blue curves show results obtained using the bremsstrahlung rates calculating in the SRA, while the red curves are taken from [7] and are based on rates calculated using the OPEP (see text for details).