Phase dependent current statistics in short-arm Andreev interferometer

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $\varphi$ across the junction, approaching the normal-state value at $\varphi =\pi$. At T=0 and at the applied voltage much smaller than the proximity gap ${\mathrm{\Delta }}_{\varphi }$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger with respect to their values in the normal state; at $eV\gg {\mathrm{\Delta }}_{\varphi }$ they acquire large excess components. At the gap edge, $eV={\mathrm{\Delta }}_{\varphi }$, the effective transferred charge defined through $d{P}_I\mathrm{/}dI$ and $d{P}_I\mathrm{/}dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T\mathrm{\ne }0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV={\mathrm{\Delta }}_{\varphi }$.