The triplet photoproduction on a free electron as a possible way to search for a dark photon

Abstract

The process of the triplet production on a free electron, $\gamma e^{-}\to e^{+}{e}^{-}{e}^{-}$, has been investigated as a reaction where a dark photon, $A^{\prime }$, is produced as a virtual state with subsequent decay into a $e^{+}{e}^{-}$-pair. This effect arises due to the so-called kinetic mixing and is characterized by the small parameter $ϵ$ describing the coupling strength relative to the electric charge e. The search of $A^{\prime }$ in this process has advantage because the background to the $A^{\prime }$ signal is pure QED. This QED background is described by eight Feynman diagrams taking into account the identity of final electrons. As concern $A^{\prime }$, we leave its contribution in Compton-like diagrams only since, in this case, the virtual dark photon is time-like and its propagator has the Breit-Wigner form. So, near the resonance $A^{\prime }$ can manifest itself. The contribution of $A^{\prime }$ in Borsellino diagrams is negligible since, in this case, the virtual dark photon is space-like, the $A^{\prime }$ propagator does not peak and effect is proportional at least to ${ϵ}^2$. We calculate the distributions over the invariant masses of the both produced $e^{+}{e}^{-}$ pairs and search for the kinematical region where the Compton-like diagrams contribution is not suppressed as compared with the Borsellino one. We estimate what value of the parameter $ϵ$, as a function of the dark photon mass, can be obtained at given number of the measured events.

Comments: 24 pages, 7 figures