Andi Ross, Koushik Dutta, Max Tegmark and I recently put our paper on the likely values of the Higs vev on the web – here is a link. This touches on the issue that maybe the constraints on the existence of atoms may be related to the unnaturally small value of the Higgs vacuum expectation value (vev). This idea was first suggested in my paper with Steve Barr, Dave Seckel and V Agrawal. We had been inspired by Weinberg’s anthropic discussion of the cosmological constant and realized that the constraint that atoms exist could explain the key puzzle – called the fine tuning problem – of why the Higgs mass scale was so low. In this work we considered the variation of the vev with all other parameters of the Standard Model held fixed.
In the present work with Andi, Koushik and Max we address what would happen if the other parameters of the Standard Model were also variable. We argue that the most relevant ones are the Yukawa couplings that are related to quark and lepton masses. For these, we use the experimentally observed mass distribution, found in previous work..
Since the Yukawa couplings vary, there is not just an allowed window for the vev, but rather a liklihood distribution. It is this that we describe in the paper. The result works in the sense that there is a modest spread about the most likely value, and the observed value is pretty typical of the allowed values. While this observation certainly does not show that the atomic constraints are responsible for the low value of the vev, nevertheless the results support the possibility that atomic constraints are at play in this hep puzzle.