Abstract
We demonstrate that in sufficiently long diffusive superconducting-normal-superconducting ($\mathit{SNS}$) junctions dc Josephson current is exponentially suppressed by electron-electron interactions down to zero temperature. This suppression is caused by the effect of Cooper pair dephasing which occurs in the normal metal and defines a new fundamental length scale ${L}_{\ensuremath{\varphi}}$ in the problem. This length is fully consistent with that derived earlier from the analysis of dissipative electron transport across $\mathit{NS}$ interfaces at subgap energies. Provided the temperature length exceeds ${L}_{\ensuremath{\varphi}}$ this dephasing length can be conveniently extracted from equilibrium measurements of the Josephson current.
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