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Direct anthropic bound on the weak scale from supernovæ explosions – or how I learned to stop worrying and love the Higgs

Guest blog by Prof Alessandro Strumia, not only a famous misogynist but also a physicist ;-)

I thank Luboš for hosting this post, where I present a strangelove-like idea that might be the long-sought explanation of the most puzzling aspect of the Standard Model (SM) of the Fundamental Interactions: the existence of two vastly different mass scales. The electro-weak Fermi scale (set by the Higgs mass, that controls the mass of all other elementary Standard Model particles) is 17 orders of magnitude smaller than the gravitational Planck scale (the mass above which any elementary particle is a black hole, according to Einstein Relativity and Quantum Mechanics).

The puzzle is that, according to many theorists, the Standard Model Higgs is unnatural because its squared mass receives Planck-scale quantum corrections, so that cancellations tuned by one part in \(10^{34}\) are needed to get the small Fermi scale. This naturalness argument lead theorists to expect that the Higgs cannot be alone, that it must exist together with new physics that protects its lightness. Theorists proposed concrete examples of new physics that makes the Higgs natural: supersymmetry, technicolor, extra dimensions... Dozens of thousands of research publications studied these ideas and supersymmetry seemed to work so beautifully that most theorists expected that the Fermi scale is the scale of supersymmetry breaking.

The physics of the fundamental interactions enjoyed a decennium of great interest, returning to be a data-driven field, when in 2010 the Large Hadron Collider (LHC) started to explore physics above the Fermi scale. Experiments could finally answer the biggest question identified in decades of theoretical speculations: the origin of the Fermi scale.

The dominant expectation, based on naturalness, was that the LHC would have opened a golden age for high-energy physics, discovering the Higgs boson together with the new physics that protects its lightness. Some theorists worried that too much new physics could be a background to itself.

This is no longer a worry: LHC discovered the Higgs and no new physics. Data agree with the Standardissimo Model. The lack of supersymmetry and of any other new physics that makes the Fermi scale “natural” is now considered as a serious issue.

Unnaturalness is so important that, before accepting such conclusion, one would like to check that it persists at higher energies. But LHC already reached 13 TeV and most of its discovery potential has been exploited. No higher-energy collider is in construction. Getting funds for reaching higher energies and possibly finding more nothing is difficult: a new 100 TeV collider seem to cost 29 billions of dollars. It's a lot of money. We're gonna have to earn it. A paper on arXiv today includes gender as motivation for giving it to CERN. Supersymmetry would have been a better motivation: that's why before LHC physicists dubbed the present situation as “nightmare scenario”. Waiting for 100 TeV data at my 100th birthday, I provisionally assume that present negative results from LHC mean that the Fermi scale is unnatural.

Crisis can lead to progress. It is maybe not exaggerated to see a parallel between the present negative results from LHC and the negative results of the Michelson-Morley experiment, that in 1887 shacked the strong belief in the ugly aether theory, opening a crisis later beautifully resolved by relativity. Today we are confused about naturalness. Nature is surely following some logic. Marx said that «history repeats itself, first as tragedy, then as farce». So maybe this time nature follows a ugly logic missed by physicists who seek something beautiful.

The unnatural smallness of the Fermi scale could be due to anthropic selection. The A-word is not politically correct among physicists, but anthropic selection is like the horseshoe of Bohr: it works even when physicists don't believe in it.

Anthropic selection might sound science fiction, but it easily follows from our present theoretical understanding of physics. All what is needed is a theory (possibly string theory) that admits as minima of its potential a “landscape” of many vacua (say, \(10^{500}\)) with different values of their vacuum energy and of their Fermi scale (more in general with different particle physics, as particles are excitations around the vacuum). Thanks to enough diversity, rare vacua have “good” physical laws that allow for complex nuclei, chemistry, stars... and life and observers. Thanks to cosmological inflation, different vacua are realised in different regions of space-time, separated by deserts and walls (known as “cosmological horizons” and “potential barriers”). Thanks to diversity plus separation, our universe can be a region in one “good” vacuum immersed in a bigger “multiverse” of shi**ole regions. As “life” can only form in rare regions with “good” physics, observers worry about naturalness because they measure fundamental constant that seem tuned for their existence, but not more tuned than that.

Weinberg in 1987 proposed an anthropic argument for the smallness of the cosmological constant. Agrawal, Barr, Donoghue and Seckel in 1997 noticed that light fermion masses \(m_f\) have special values that allow for the possible existence of many nuclei, rather than just Hydrogen and/or Helium. More complex chemistry seems needed for “life”. However this anthropic boundary does not explain the smallness of the Fermi scale \(v\), because fermion masses are obtained in the Standard Model as \(m_f=y_f v\) (dimension-less Yukawa couplings \(y_f\) times Fermi scale \(v\)): a SM-like vacuum with the same “good” fermion masses obtained from bigger Fermi scale \(v\) times smaller Yukawas \(y_f\) needs less tuning, and would thereby be more likely in a multiverse. So far the Standard Model seems uselessly unnatural even if fermion masses are anthropically selected.

An anthropic explanation of the smallness of the Fermi scale needs an anthropic boundary that directly restricts the Fermi scale. In order to search for such extra boundary, we look at events where weak interactions play a key role. There are two events where non-trivial physics happens thanks to the same numerical coincidence\[

v\sim M_{\rm Planck}^{1/4} \Lambda_{\rm QCD}^{3/4}

\] that involves the Fermi scale, the Planck mass and the naturally small QCD scale (or proton mass).

The first event is Big Bang Nucleosynthesis: Hall, Pinner and Ruderman showed in 2014 that BBN produces comparable Hydrogen and Helium abundances because neutrinos decouple at a temperature comparable to the proton/neutron mass difference, and because BBN happens when the age of the Universe is 3 minutes, comparable to the neutron life-time. This is puzzling, but it does not seem to lead to an anthropic boundary.

The second event is core-collapse supernova explosions. According to their standard theoretical understanding (partially validated by the 1987 observation of supernova neutrinos), explosions happen because weak interactions of outflowing neutrinos push the material outwards. This pushing is effective because neutrinos are trapped for a few seconds, a time comparable to the gravitational time-scale of a supernova. We argued that explosions disappear if the Fermi scale \(v\) is changed by a factor of few in either direction. If \(v\) is too small, neutrinos are too much trapped and exit too late when the collapse is over. If \(v\) is too large, neutrinos are not trapped and immediately fly away with negligible weak interactions.

Core-collapse supernova explosions spread intermediate-mass elements that seem needed by “life”, such as Oxygen. This is illustrated by the following periodic table, where elements are colored according to what produces them, and primary and secondary elements that seem needed by the chemistry of “life” are highlighted.

Core-collapse supernova explosions (in green) seem anthropically relevant.

In conclusion, we might observe an unnaturally small value of the Fermi scale because of anthropic selection: no observers exist in universes where the Fermi scale has larger, more natural, values.

I over-simplified: scientific details and doubts can be found in this talk and in this arXiv preprint in collaboration with D'Amico, Urbano and Xue. We are high-energy physicists, not experts of supernova explosions nor of astro-biology. I hope that experts can better test the idea: it's important because it might explain the smallness of the Fermi scale, and this is a major topic in fundamental physics since decades.

Actually (despite my jokes) this is a deadly serious topic. Fundamental physics now risks abandoning the high-energy frontier. But our scientific job is seeking the correct understanding, even if it means losing our job.

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