Magnetic field effect on charged scalar pair creation at finite temperature

In this work we explore the effects of a weak magnetic field and a thermal bath on the decay process of a neutral scalar boson into two charged scalar bosons. Our findings indicate that a magnetic field inhibits pair production, while temperature enhances it. The employed formalism allows us to isolate the contribution of magnetic fields in vacuum, leading to a separate analysis of the effects of different ingredients. This is essential since the analytical computation of the decay width requires some approximation and the results that can be found in the literature are not always coincident. We perform the calculation in vacuum by two different weak-field approximations. The particle pair production in vacuum is found to coincide with finite-temperature behavior, which is opposite the results obtained by other authors in scenarios that involve neutral particles decaying into a pair of charged fermions. Among other differences between these scenarios, we find out that the analytical structure of the self-energy imposed by the spin of particles involved in the process is determinant in the behavior of the decay rate with the magnetic field.

Figure 1

Leading-order contribution to the neutral scalar $\mathrm{\Phi }$ boson self-energy in a magnetic field background. ${\varphi }^{\prime }s$ are light charged scalar bosons and the double dashed lines represent their propagators dressed with the magnetic field.

Figure 2

Feynman representation for the imaginary scalar self-energy (indicated by the vertical line).

Figure 3

Magnetic field effect on the heavy boson decay rate at $T=0$, for a fixed value of $p_0/m=3$.

Figure 4

Magnetic field effect on the heavy boson decay width for different temperatures and a fixed value of $p_0/m=3$.

Figure 5

Decay width as a function of $eB/m^2$ in the regions (a) $\lambda \ll 1$ and (b) $\lambda \gg 1$, both for several values of $p_{\perp }$ and a fixed value of $p/m=3$.

Figure 6

Panel (a) shows the imaginary part of the self-energy and panel (b) shows the decay width, both as a function of $eB/m^2$ for three different transverse momentum values: $p_{\perp }/m=0$ (continuous line), $p_{\perp }/m=0.5$ (dashed line), and $p_{\perp }/m=1$ (dotted line), all with the fixed value $p/m=3$.