Abstract
Core-collapse supernovae 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 $v \sim \Lambda_{\rm QCD}^{3/4} M_{\rm Pl}^{1/4}$, such that neutrinos are trapped in supernovae for a time comparable to the gravitational time-scale. 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 $v$.
Highlights
Nature contains two relative mass scales: the vacuum energy density V ∼ ð10−30MPlÞ4 and the weak scale v2 ∼ ð10−17MPlÞ2 where v is the Higgs vacuum expectation value
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 ∼ Λ3Q=C4DM1P=l 4, such that neutrinos are trapped in supernovæ for a time comparable to the gravitational timescale
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 study stellar burning, finding that it does not provide anthropic boundaries on v
Summary
Nature contains two relative mass scales: the vacuum energy density V ∼ ð10−30MPlÞ4 and the weak scale v2 ∼ ð10−17MPlÞ2 where v is the Higgs vacuum expectation value Their smallness with respect to the Planck scale MPl 1⁄4 1.21019 GeV is not understood and is considered as “unnatural” in relativistic quantum field theory, because it seems to require precise cancellations among much larger contributions. On the Higgs side, it has been noticed that light quark and lepton masses me, mu, md are anthropically restricted in a significant way: a nontrivial nuclear physics with more nuclei than just H and/or He (and thereby chemistry, and life) exists because me=ΛQCD, mu=ΛQCD, md=ΛQCD have appropriate values which allow for the existence of a hundred of nuclear species [9,10,11,12] Such anthropic boundaries in me, mu, md give extra indicative support to the possibility that physics is described by a theory where fundamental constants have different values in different local minima. There are two main classes of less tuned vacua, leading to two aspects of the paradox: (a) Natural theories: extensions of the SM where v is naturally small compared to MPl. (b) Less unnatural theories: SM-like theories with smaller yf and bigger v=MPl
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