SN1987A cooling due to Plasmon-Plasmon scattering in the Randall-Sundrum Model

The light braneworld radion, stabilized via the Goldberger-Wise mechanism in the Randall-Sundrum model, can be produced copiously inside the supernova core due to plasmon-plasmon annihilations. The radion, thus produced, subsequently decays to a neutrino-antineutrino pair and takes away the energy released in the SN1987A explosion. Assuming that the supernovae cooling rate for any new physics channel(Raffelt's criterion) $\dot{\varepsilon}(\gamma_P\gamma_P \stackrel{\phi}{\longrightarrow} \nu_{\tau} \overline{\nu}_{\tau}) \leq 7.288\times 10^{-27} \rm{GeV}$, we find the lower bound on the radion vacuum expectation value $\langle\phi\rangle \sim 3$~TeV for $m_\phi = 30$ MeV corresponding to the deformation parameter $q=1.17$ in the Tsallis statistics formalism. In the scenario with $q=1$, we find $\langle\phi\rangle = 178$ GeV for $m_\phi = 30$ MeV.