Decay of massive scalar field in a Schwarzschild background

The decay of massive scalar field in the Schwarzschild black hole background is investigated here by consideration its quasinormal spectrum. It has been proved that the so-called $quasi-resonant$ modes, which are arbitrary long living (purely real) modes, can exist only if the effective potential is not zero at least at one of the boundaries of the $R$-region. We have observed that the quasinormal spectrum exists for all field masses and proved both analytically and numerically that when $n\to \mathrm{\infty }$ the real part of the frequencies approaches the same asymptotical value ($\ln 3\mathrm{/}(8\pi M)$) as in the case of the massless field.