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==Technical definition==
A hierarchy problem occurs when the fundamental value of some physical parameter, such as a [[coupling constant]] or a mass, in some [[Lagrangian mechanics|Lagrangian]] is vastly different from its effective value, which is the value that gets measured in an experiment. This happens because the effective value is related to the fundamental value by a prescription known as [[renormalization]], which applies corrections to it. Typically the renormalized value of parameters are close to their fundamental values, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections. Hierarchy problems are related to [[
Studying [[renormalization]] in hierarchy problems is difficult, because such quantum corrections are usually power-law divergent, which means that the shortest-distance physics are most important. Because we do not know the precise details of the [[quantum gravity|shortest-distance theory of physics]], we cannot even address how this delicate cancellation between two large terms occurs. Therefore, researchers are led to postulate new physical phenomena that resolve hierarchy problems without fine-tuning.
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[[File:Hqmc-vector.svg|thumb|300px|right|Cancellation of the [[Higgs boson]] quadratic [[mass renormalization]] between [[fermion]]ic [[top quark]] loop and [[scalar field|scalar]] stop [[squark]] tadpole [[Feynman diagram]]s in a [[supersymmetry|supersymmetric]] extension of the [[Standard Model]]]]
More technically, the question is why the [[Higgs boson]] is so much lighter than the [[Planck mass]] (or the [[grand unification energy]], or a heavy neutrino mass scale): one would expect that the large quantum contributions to the square of the Higgs boson mass would inevitably make the mass huge, comparable to the scale at which new physics appears unless there is an incredible [[Fine-tuning (physics)|fine-tuning]] cancellation between the quadratic radiative corrections and the bare mass.
The problem cannot even be formulated in the strict context of the Standard Model, for the Higgs mass cannot be calculated. In a sense, the problem amounts to the worry that a future theory of fundamental particles, in which the Higgs boson mass will be calculable, should not have excessive fine-tunings.
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