TSALLIS STATISTICS AND THE ROLE OF A STABILIZED RADION IN THE SUPERNOVAE SN1987A COOLING

Abstract

The radion in the two-brane Randall–Sundrum model is required to stabilize the size of the fifth (extra) spatial dimension. It can be copiously produced inside the supernova core due to electron–positron annihilation (e+e-→ϕ), plasmon–plasmon annihilation (γP+γP→ϕ) and nucleon–nucleon bremsstrahlung and can take away the energy released in SN1987A explosion. Working within the q-deformed statistics (Tsallis statistics) and using the "Raffelt criterion" on the supernovae cooling rate [Formula: see text], we find that in Case I (cooling due to e+e-→ϕ channel): for q = 1.22, as the radion mass mϕ changes from 20 GeV to 150 GeV, the lower bound 〈ϕ〉 changes from 7 TeV to ~1.5 TeV and in Case II (cooling due to γP+γP→ϕ channel): for q = 1.11, as mϕ ranges from 20 GeV to 150 GeV, the lower bound 〈ϕ〉 changes from 201 TeV to 3.3 TeV. We investigate the dependence of 〈ϕ〉 on q and found that in Case I: mϕ = 50(100) GeV , 〈ϕ〉 changes from 0.5(0.2) TeV (for q = 1.18) to 5.5(4.8) TeV (for q = 1.30) and in Case II: for mϕ = 50(100) GeV , 〈ϕ〉 changes from 0.8(~0.1) TeV (for q = 1.09) to 569(216) TeV (for q = 1.13). We also verified that the normal Fermi–Dirac and Bose–Einstein statistics get recovered from the Tsallis statistics in the q→1 limit.