Vacuum stability, wormholes, cosmic rays and the cosmological bounds on mt and mH

Abstract

In the standard model, if the top quark mass m t is larger than some critical value depending on the Higgs mass m H, then we live in an unstable vacuum state corresponding to a local minimum of the effective potential. An experimental discovery of the top quark with m t above this critical value would invalidate the standard version of the wormhole theory, according to which the vacuum energy should be zero at the absolute minimum of the effective potential. However, unless the top quark is much heavier than this, the lifetime is much heavier than this, the lifetime of the unstable vacuum state is greater than the age of our part of the universe. In this paper we develop a stochastic approach to tunneling and apply it to examine the possibility that cosmic ray collisions may trigger vacuum decay and derive improved cosmological bounds on m H and m t.