Response to an external magnetic field of the decay rate of a neutral scalar field into a charged fermion pair

In this work, we explore the effects of a weak magnetic field on the decay process of a neutral scalar boson into a pair of charged fermions in vacuum. Since the analytical computation of the decay width needs some approximation, following two different approaches, we study the low and high transverse momentum limits. Our findings indicate that the magnetic field effect depends on the kinematics of the scalar particle.

Figure 1

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

Figure 2

Schematic representation of the imaginary part of the self-energy, obtained by cutting the one-loop Feynman diagram.

Figure 3

Decay width (in units of energy) as a function of the magnetic field for different values of the transverse momentum, for the high momentum approximation, taking $p/m=5$.

Figure 4

Decay response to the external magnetic field as a function of the magnetic field strength, for different values of the transverse momentum, in the high momentum approximation, taking $p/m=5$.

Figure 5

Ratio of the decay responses to the external magnetic field for two different channels, $\varphi \to \overline{\psi }+\psi$ and $\varphi \to \phi +\phi$, where $\psi$ and $\phi$ are charged fermions and scalars, respectively. We plot this ratio as a function of the magnetic field in the high momentum approximation, for $p_{\perp }/m={10}^3$, and, as usual, we take $p/m=5$.