The potential of the Weil-Petersson metric on Torelli space

It is proved that the function $12\pi\log(Z^\prime(1)/\det\operatorname{Im}\tau)$, where $Z(s)$ is Sel'berg zeta function and $\tau$ is the matrix of the periods of a distinguished Riemann surface, is a potential of the Weil-Petersson metric on the Torelli space.