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In theoretical physics, a hierarchy problem is a confusing observation that two fundamental quantities with the same units have vastly different values, and therefore the na´ve calculation based on dimensional analysis can lead to incorrect results. In other words, it is an apparent paradox begging for an explanation. While all the numbers originating from a fundamental theory should na´vely be comparable to 1, there are numbers in Nature that are much smaller (or much greater) and these are called hierarchy problems.
More specifically, in particle physics, the hierarchy problem is the big question why the typical energy scale associated with the electroweak symmetry breaking - roughly, the typical size of all masses of elementary particles - is so much (1015 times) smaller than the Planck energy. More technically, the question is why the Higgs boson is so much lighter than the Planck mass, although one would expect that the large (quadratically divergent) quantum contributions to the Higgs boson mass squared would inevitably make the mass huge, comparable to the Planck mass.
Given this hierarchy problem with the Higgs boson mass, it is expected that new physics should make an appearance at energy scales not much higher than the scale of energy required to produce the Higgs boson, and thereby provide an explanation for its small mass.
The most popular theory - but not the only proposed theory - to solve the hierarchy problem (i.e. to answer the question) is supersymmetry. But this only explains how a tiny Higgs mass can be protected from quantum corrections , but not why it is small but still nonzero in the first place. Put another way, why are we so close to a second order phase transition?
While the Higgs boson mass has been the most commonly considered hierarchy problem, there are others in theoretical physics. For example the masses of the neutrinos (see also Solar neutrino problem) are much less than the masses of all of the other standard model particles. One proposed explanation for the light neutrino mass scale is the seesaw mechanism. Even the matter fermions differ in mass amongst themselves by a factor of more than 105. However, these problems may not be as severe as the Higgs boson mass problem since the masses of the fermions (the neutrinos and matter) are not nearly as sensitive as the Higgs boson mass to quantum effects.
In cosmology, current observations in favor of an accelerating universe imply the existence of a tiny, but nonzero cosmological constant. This is a hierarchy problem very similar to that of the Higgs boson mass problem, since the cosmological constant is also very sensitive to quantum corrections. It is complicated, however, by the necessary involvement of General Relativity in the problem and may be a clue that we don't understand gravity on long distance scales (such as the size of the universe today). While quintessence has been proposed as an explanation of the acceleration of the Universe, it does not actually address the cosmological constant hierarchy problem in the technical sense of addressing the large quantum corrections.
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