# A New Solution to the Hierarchy Problem?

Hello particle Chompers,

Today I want to discuss a slightly more advanced topic which I will not be able to explain in much detail, but goes by the name of the gauge Hierarchy problem or just the the Hierarchy Problem‘. My main motivation is to simply make you curious enough that you will feel inspired to investigate it further for yourself since it is one of the outstanding problems in particle physics and one of the main motivations for the construction of the LHC. A second motivation is to bring to your attention a recent and exciting paper which proposes a potentially new solution to the hierarchy problem.

The hierarchy problem can roughly be stated as the problem of why the vacuum expectation value (VEV) of the Higgs boson, which determines the masses of the electroweak W and Z bosons, is so small compared to the highest energy scales thought to exist in the Universe. More specifically, the masses of the W and Z bosons (which define the weak scale) are roughly $\sim 10^{2}$ GeV (see Figure 1) in particle physics units (remember in these units mass = energy!).

On the other hand the highest energy scale thought to exist in the Universe is the planck scale at $\sim 10^{19}$ GeV which is associated with the physics of gravity. Quantum field theory tells us that the Higgs VEV should get contributions from all energy scales (see Figure 2) so the question is why is the Higgs VEV, and thus the W and Z boson masses, a factor of roughly $\sim 10^{17}$ smaller than it should be?

In the Standard Model (SM) there is no solution to this problem. Instead one must rely on a spectacularly miraculous numerical cancellation among the parameters of the SM Lagrangian. Miraculous numerical coincidences’ like this make us physicists feel uncomfortable to the point that we give it the special name of fine tuning’. The hierarchy problem is thus also known as the fine tuning problem.

A search for a solution to this problem has been at the forefront of particle physics for close to 40 years. It is the aversion to fine tuning which leads most physicist to believe there must be new physics beyond the SM whose dynamics are responsible for keeping the Higgs VEV small. Proposals include supersymmetrycomposite Higgs models, extra dimensions, as well as invoking the anthropic principle in the context of a multiverse. In many cases, these solutions require a variety of new particles at energies close to the weak scale ($\sim 100-1000$ GeV) and thus should be observable at the LHC. However the lack of evidence at the LHC for any physics beyond the SM is already bringing tension to many of these solutions. A solution which does not require new particles at the weak scale would thus be very attractive.

Recently a novel mechanism, which goes by the name of $\emph{cosmological relaxation of the electroweak scale}$, has been proposed which potentially offers such a solution. The details (which physicists are currently still digesting) are well beyond the scope of this blog. I will just mention that the mechanism incorporates two previously proposed mechanisms known as inflation$^1$ and the QCD axion$^2$ which solve other known problems. These are combined with the SM in a novel way such that the weak scale can arise naturally in our universe without any fine tuning and without new particles at the weak scale (or multiple universes)! And as a bonus, the axion in this mechanism (referred to as the relaxion’) makes a good dark matter candidate!

Whether or not this mechanism turns out to be a solution to the hierarchy problem will of course require experimental tests and further theoretical scrutiny, but its a fascinating idea which combines aspects of quantum field theory and general relativity so I hope it will serve as motivation for you to begin learning more about these subjects!

$\bf{Footnotes:}$

1. Inflation is a theorized period of exponential accelerated expansion of our Universe in the moments just after the big bang. It was proposed as a solution to the problems of why our Universe is so flat and (mostly) homogenous while also explaining the structure we see throughout the Universe and in the cosmic microwave background.

2. Axions are particles proposed to explain why the amount of CP violation in the QCD sector in the SM is so small, which is known as the `strong CP problem‘.

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#### Roberto Vega-Morales

Roberto Vega-Morales is currently a post-doctoral researcher in high energy theory at the University of Granada in Spain. Previously he was at the Laboratoire de Physique Thèorique in Paris France. He conducted his Ph.D studies at Northwestern University as well as Fermilab and was awarded the 2014 J.J. and Noriko Sakurai Dissertation Award in Theoretical Particle Physics. His research focuses on the phenomenology of the Higgs boson at the LHC as well as models of Supersymmetry and extended Higgs sectors. He struggled mightily with French and is happy to be speaking Spanish nowadays.