On the metastability of the Standard Model vacuum

If the Higgs mass $m_H$ is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on $m_H$ imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for $m_H=115$ GeV, the Higgs potential develops an instability below the Planck scale for $m_t>(166\pm 2) \GeV$, but the electroweak vacuum is sufficiently long-lived for $m_t > (175\pm 2) \GeV$.