Hierarchy problem

The hierarchy problem is a term of high energy physics, which is often used specifically in reference to the value of the Higgs mass. It refers to the deficit explanation of a theory regarding a significant difference between a fundamental parameter of the theory ( coupling constant or mass) and its experimentally determined (or expected ) value. It is related to the naturalness problem and the fine-tuning problem ( fine tuning ).

Higgs mass

The most prominent hierarchy problem of particle physics is the question of why gravity is much weaker than the electro- weak interaction. Technically, this is expressed in the size of the Higgs mass, which the energy scale of the electroweak interaction of the masses of the gauge bosons sets ( Higgs mechanism ). In a quantum field theory of radiation and loop corrections ( Feynman graphs of higher order ) are to note the mass of a particle ( effective mass, see also self-energy ). These corrections can the "actual " bare ground (bare mass ) of the particle significantly exceed, so that the effective mass is different. While the masses of the gauge bosons are protected by chiral symmetry by local gauge symmetries and the fermion against such corrections, this is the scalar ( spin 0 ) Higgs boson is not possible.

Scalars can not be preserved by a symmetry face immense radiative corrections by coupling to other particles their mass diverges due to such corrections square with the highest energy scale of the theory. One expects therefore a natural mass of the order of this scale for scalars. In a quantum field, which also includes the gravity, it is the Planck scale. However, the Planck scale ( 1019 GeV scale ) is 16 orders of magnitude above the electroweak scale ( 103 GeV scale ). The effective (ie experimentally accessible ) Higgs mass whose value you need for the Higgs mechanism in the electroweak scale and which has now been experimentally determined to be about 125 GeV, that is not in its natural value near the Planck mass ( naturalness problem ).

Although this quadratic divergence can wegrenormiert and the Higgs mass are brought to its desired value near the electroweak scale, but this requires technically demanding and unnatural fine-tuning. In addition, the origin of the Higgs mass remains so misunderstood easily.

In addition, one obtains, in addition to calculate the mass of the Higgs Feynman higher order finite correction that depends on the masses and the coupling constants of the remaining particles of the theory. For the particles of the Standard Model, the resulting corrections are negligible, however, they are great for very heavy particles might exist, even if the Higgs couples only very indirectly to them. Even if the Higgs boson is a central component of the Standard Model of elementary particle physics, the hierarchy problem is not a problem of the standard model itself, since it contains none of these heavy particles. Strictly speaking, the hierarchy problem within the Standard Model not even be formulated as a calculation of the Higgs mass is not possible there. The problem is rather that the Higgs mass is very sensitive to new physics ( "beyond the standard model " ) is.

Thus, the explosive nature of the hierarchy problem is due to the fact that the Standard Model of elementary particle physics is indeed a self-consistent theory and very good agreement with the existing experimental data, but there are some reasons mainly from a theoretical point of view, to assume that it is not the standard model is the ultimate theory and one expects new physics at higher energy ranges.

So the standard model contradicts Although currently no experimental findings ( however contradict the evidence of minimal but non-zero neutrino masses of the adoption of the standard model ), but it has been tested only in the energy range below the TeV scale in a big way. Furthermore, although the electromagnetic and weak interactions are combined within the standard model for electroweak interactions, however, a union is not possible with the strong interaction (GUT ) or even of gravitation in the standard model. Also with regard to the number of parameters ( 20 ), the standard model, from a theoretical point of view, unsatisfactory. In addition, evidence of dark matter or dark energy does not seem to be explainable within the framework of the standard models of particle physics and cosmology and on new physics "beyond the standard model " (eg, the mentioned new heavy particles ) to interpret.

Solutions

Supersymmetry

A solution to the hierarchy problem is supersymmetry ( SUSY ). Since bosons and fermions contribute with different signs to the corrections, it's obvious ( though not the historical motivation ) to resolve the hierarchy problem introduce a boson - fermion symmetry. In the case of exact supersymmetry, the problematic terms then lift automatically on each other, a fine tuning is therefore not necessary. Even if supersymmetry is broken (which must be the case, in fact, if it exists ) if it is not so is accurate, the maximum logarithmically divergent terms which are not a problem arise. In order for these divergences and therefore the Higgs mass does not become too large, SUSY is restricted to an energy range of a few TeV.

String theory

Another solution is the string theory, in which up to ten kompaktifizierte extra dimensions exist, which may have a radius of up to one tenth of a millimeter and in the can only advance to the gravity. In these extra dimensions the gravitational force would be significantly weakened. The real power would be in reality so much bigger and would approach the other three fundamental forces.

Randall - Sundrum model

A third approach to the problem has Lisa Randall. The Randall - Sundrum model tries to solve the hierarchy problem by introducing a single additional dimension - that distinguishes the model of the string theories.