Direct anthropic bound on the weak scale from supernovæ explosions

Core-collapse supernovæ presumably explode because trapped neutrinos push the material out of the stellar envelope. This process is directly controlled by the weak scale v: we argue that supernova explosions happen only if fundamental constants are tuned within a factor of few as v∼ΛQCD3/4MPl1/4, such that neutrinos are trapped in supernovæ for a time comparable to the gravitational timescale. We provide analytic arguments and simulations in spherical approximation, that need to be validated by more comprehensive simulations. The above result can be important for fundamental physics, because core-collapse supernova explosions seem anthropically needed, as they spread intermediate-mass nuclei presumably necessary for "life." We also study stellar burning, finding that it does not provide anthropic boundaries on v.