The hierarchy problem can roughly be stated as the problem of why the vacuum expectation value<\/a> (VEV) of\u00a0the Higgs boson<\/a>, which determines the masses of the electroweak\u00a0W and Z bosons<\/a>, is so small compared to the highest energy scales thought to exist in the Universe. More specifically, the masses of the W and Z\u00a0bosons (which define the weak scale)\u00a0are roughly $latex \\sim 10^{2}$ GeV (see Figure 1)\u00a0in particle physics units (remember in these units mass = energy!).<\/p>\n On the other hand the highest energy scale thought to exist in the Universe is the planck scale at $latex \\sim 10^{19}$ GeV which is associated with the physics of gravity. Quantum field theory tells us that the Higgs VEV\u00a0should get contributions from all energy scales (see Figure 2)\u00a0so the question is why is\u00a0the Higgs VEV, and thus the W and Z boson masses,\u00a0a factor of roughly $latex \\sim 10^{17}$ smaller than it should be?<\/p>\n In the Standard Model<\/a> (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.<\/p>\n 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\u00a0VEV\u00a0small. Proposals\u00a0include\u00a0supersymmetry<\/a>,\u00a0composite Higgs models<\/a>, extra dimensions<\/a>, as well as invoking the anthropic principle<\/a> in the context of a multiverse<\/a>.\u00a0In many cases, these solutions require a variety of new particles\u00a0at energies close to the weak scale ($latex \\sim 100-1000$ 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\u00a0bringing tension to many of these solutions. A\u00a0solution which does not require new particles at the weak scale would thus be very attractive.<\/p>\n Recently a novel mechanism<\/a>,\u00a0which goes by the name of $latex \\emph{cosmological relaxation of the electroweak scale}$, has been proposed which potentially offers such a\u00a0solution. 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\u00a0known as\u00a0inflation<\/a>$latex ^1$ and the QCD axion<\/a>$latex ^2$ 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!<\/p>\n 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\u00a0idea which\u00a0combines aspects of\u00a0quantum field theory and general relativity so\u00a0I hope it will serve as motivation for you to begin learning more about these subjects!<\/p>\n $latex \\bf{Footnotes:}$<\/p>\n 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\u00a0explaining the structure<\/a> we see throughout the Universe and in the cosmic microwave background<\/a>.<\/p>\n 2. Axions are particles proposed\u00a0to explain why the amount of CP violation<\/a> in\u00a0the QCD sector in the SM is so small, which is known as the `strong CP problem<\/a>‘.<\/p>\n","protected":false},"excerpt":{"rendered":" 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 … <\/p>\n![\"The](\"http:\/\/www.particlebites.com\/wp-content\/uploads\/2015\/06\/Wmass-300x286.jpg\")
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