Everything about Hierarchy Problem totally explained
In
theoretical physics, a
hierarchy problem occurs when the fundamental parameters (
couplings or masses) of some
Lagrangian are vastly different (usually larger) than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as
renormalization. Typically the renormalized parameters are closely related to the fundamental parameters, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections to it. Hierarchy problems are related to
fine-tuning problems and problems of naturalness.
Studying the 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 don't know the precise details of the shortest-distance theory of physics (
quantum gravity), we can't even address how this delicate cancellation between two large terms occurs. Therefore, researchers postulate new physical phenomena that resolve hierarchy problems without fine tuning.
The Higgs Mass
In
particle physics,
the hierarchy problem is the question why the
weak force is 10
32 times stronger than
gravity. Both of these forces involve constants of nature,
Fermi's constant for the weak force and
Newton's constant for gravity. Furthermore if the
Standard Model is used to calculate the quantum corrections to Fermi's constant, it appears that Fermi's constant is unnaturally large and should be closer to Newton's constant unless there's a delicate cancellation between the bare value of Fermi's constant and the quantum corrections to it.
More technically, the question is why the
Higgs boson is so much lighter than the
Planck mass (or a
GUT scale, 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's an incredible
fine-tuning cancellation between the quadratic radiative corrections and the bare mass.
It should be remarked that the problem can't be even formulated in the strict context of the Standard Model, for the Higgs mass can't 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, shouldn't have excessive fine-tunings.
Accepting the physical reality of the hierarchy problem, it's 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 is
supersymmetry. This explains how a tiny Higgs mass can be protected from quantum corrections. Supersymmetry removes the power-law divergences of the radiative corrections to the Higgs mass; however, there's no understanding of why the Higgs mass is so small in the first place which is known as the
mu problem.
The Cosmological Constant
In
physical 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 doesn't actually address the cosmological constant hierarchy problem in the technical sense of addressing the large quantum corrections. Supersymmetry doesn't permit to address the cosmological constant problem, since supersymmetry cancels the M
4Planck contribution but not the M2Planck one (quadratically diverging).
Further Information
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