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

Abstract

The triplet-like QED processes $\gamma +{\ell }_i\to {\ell }_j^{+}{\ell }_j^{-}+{\ell }_i$ with $i\ne j,$ and $i=e,\mu ,$ $j=e,\mu ,\tau$ has been investigated as the reactions where a dark photon, $A^{\prime }$, 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 $ϵ$ describing the coupling strength relative to the electric charge $e$. The main advantage of searching $A^{\prime }$ in these processes is that the background to the $A^{\prime }$ signal is pure QED. Concerning $A^{\prime }$, 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, $A^{\prime }$ can manifest itself. The contribution of $A^{\prime }$ in the Borsellino diagrams is negligible since, in this case, the virtual dark photon is space-like, the $A^{\prime }$ propagator does not peak and the effect is proportional, at least, to ${ϵ}^2$. 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 $ϵ$ is estimated as a function of the dark photon mass for a given number of events.

Comments: 27 pages, 13 figures, accepted for publication in Phys Rev D