Detection strategies for scalar gravitational waves with interferometers and resonant spheres

We compute the response and the angular pattern function of an interferometer for a scalar component of gravitational radiation in Brans-Dicke theory. We examine the problem of detecting a stochastic background of scalar GWs and compute the scalar overlap reduction function in the correlation between an interferometer and the monopole mode of a resonant sphere. While the correlation between two interferometers is maximized taking them as close as possible, the interferometer-sphere correlation is maximized at a finite value of $f\times d,$ where f is the resonance frequency of the sphere and d the distance between the detectors. This defines an optimal resonance frequency of the sphere as a function of the distance. For the correlation between the VIRGO interferometer located near Pisa and a sphere located in Frascati, near Rome, we find an optimal resonance frequency $f\simeq 590\mathrm{Hz}.$ We also briefly discuss the difficulties in applying this analysis to the dilaton and moduli fields predicted by string theory.