Dark photon manifestation in the triplet-like QED processes $\gamma + \ell_i \to \ell^+_j \ell^-_j + \ell_i$, $i\neq j,$ $i=e, \mu,$ $j=e, \mu,\tau$

TL;DR

This paper investigates the potential to detect dark photons in specific QED processes involving lepton pairs, focusing on resonance effects and the kinetic mixing parameter to identify experimental signatures.

Contribution

It introduces a method to search for dark photons via triplet-like QED processes, emphasizing the resonance contribution in Compton-type diagrams and estimating the kinetic mixing parameter.

Findings

Resonance effects can enhance dark photon signals in certain kinematic regions.

The contribution of dark photons is significant near the resonance, unlike in Borsellino diagrams.

A method to estimate the kinetic mixing parameter as a function of dark photon mass is proposed.

Abstract

The triplet-like QED processes $\gamma + \ell_i \to \ell^+_j \ell^-_j + \ell_i$ with $i\neq j,$ and $i=e, \mu,$ $j=e, \mu,\tau$ has been investigated as the reactions where a dark photon, $A'$, is produced as a virtual state with subsequent decay into a $\ell^+_j \ell^-_j-$-pair. This effect arises due to the so-called kinetic mixing and is characterized by the small parameter $\epsilon$ describing the coupling strength relative to the electric charge $e$. The main advantage of searching $A'$ in these processes is that the background to the $A'$ signal is pure QED. Concerning $A'$, we consider its contribution in the Compton-type diagrams only since, in this case, the virtual dark photon has time-like nature and its propagator has the Breit-Wigner form. So, near the resonance, $A'$ can manifest itself. The contribution of $A'$ in the Borsellino diagrams is negligible since, in this case, the virtual dark photon is space-like, the $A'$ propagator does not peak and the effect is proportional, at least, to $\epsilon^2$. We calculate the distributions over the invariant mass of the produced $\ell^+_j \ell^-_j-$ pair and search for the kinematical region where the Compton-type diagrams contribution is not suppressed with respect to the Borsellino ones. The value of the parameter $\epsilon$ is estimated as a function of the dark photon mass for a given number of events.