# A world with no weak forces

Gravity, electromagnetism, strong, and weak — these are the beating hearts of the universe, the four fundamental forces. But do we really need the last one for us to exist?

Harnik, Kribs and Perez went about building a world without weak interactions and showed that, indeed, life as we know it could emerge there. This was a counter-proof by example to a famous anthropic argument by Agrawal, Barr, Donoghue and Seckel for the puzzling tininess of the weak scale, i.e. the electroweak hierarchy problem.

Let’s ask first: would the Sun be there in a weakless universe? Sunshine is the product of proton fusion, and that’s the strong force. However, the reaction chain is ignited by the weak force!

So would no stars shine in a weakless world? Amazingly, there’s another route to trigger stellar burning: deuteron-proton fusion via the strong force! In our world, gas clouds collapsing into stars do not take this option because deuterons are very rare, with protons outnumbering them by 50,000. But we need not carry this, er, weakness into our gedanken universe. We can tune the baryon-to-photon ratio — whose origin is unknown — so that we end up with roughly as many deuterons as protons from the primordial synthesis of nuclei. Harnik et al. go on to show that, as in our universe, elements up to iron can be cooked in weakless stars, that they live for billions of years, and may explode in supernovae that disperse heavy elements into the interstellar medium.

A “weakless” universe is arranged by elevating the electroweak scale or the Higgs vacuum expectation value ($\approx$ 246 GeV) to, say, the Planck scale ($\approx 10^{19}$ GeV). To get the desired nucleosynthesis, care must be taken to keep the u, d, s quarks and the electron at their usual mass by tuning the Yukawa couplings, which are technically natural.

And let’s not forget dark matter. To make stars, one needs galaxy-like structures. And to make those, density perturbations must be gravitationally condensed by a large population of matter. In the weakless world of Harnik et al., hyperons make up some of the dark matter, but you would also need much other dark stuff such as your favourite non-WIMP.

If you believe in the string landscape, a weakless world isn’t just a hypothetical. Someone somewhere might be speculating about a habitable universe with a fourth fundamental force, explaining to their bemused colleagues: “It’s kinda like the strong force, only weak…”

Bibliography

Viable range of the mass scale of the standard model
V. Agrawal, S. M. Barr, J. F. Donoghue, D. Seckel, Phys.Rev.D 57 (1998) 5480-5492.

A Universe without weak interactions
R. Harnik, G. D. Kribs, G. Perez, Phys.Rev.D 74 (2006) 035006

Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking
C. Quigg, R. Shrock, Phys.Rev.D 79 (2009) 096002

The Multiverse and Particle Physics
J. F. Donoghue, Ann.Rev.Nucl.Part.Sci. 66 (2016)

The eighteen arbitrary parameters of the standard model in your everyday life
R. N. Cahn, Rev. Mod. Phys. 68, 951 (1996)

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#### Nirmal Raj

Nirmal Raj is a postdoc at TRIUMF National Lab whose research is centered beyond the Standard Model, mostly on dark matter and new physics at the electroweak scale, and occasionally within the Standard Model in the form of supernova neutrinos. His favorite things include neutron stars, underground experiments, and particle colliders. Also, cryptic crosswords, writing short stories, and hiking in the Pacific Northwest.