Hierarchy problem
Hierarchy problem is a term used in high energy physics , which is often used specifically in relation to the value of Higgs mass . In particular, it denotes the deficit of a theory with regard to a clear difference between a fundamental parameter of the theory ( coupling constant or mass) and its experimentally determined (or also expected) value. It is related to the naturalness problem and the fine-tuning problem ( fine tuning ).
Higgsmasse
The most prominent hierarchy problem in elementary particle physics is the question of why gravity is significantly weaker than the electroweak interaction . Technically, this is expressed in the size of the Higgs mass, which determines the energy scale of the electroweak interaction over the masses of the gauge bosons ( Higgs mechanism ). In the context of a quantum field theory , radiation and loop corrections ( Feynman graphs of higher order) of the mass of a particle must be taken into account ( effective mass , see also self-energy ). These corrections can significantly exceed the “actual” bare mass of the particle, so that the effective mass deviates. While the masses of the gauge bosons are protected from such corrections by local gauge symmetries and the fermions by chiral symmetry , this is not possible with the scalar ( spin 0) Higgs boson.
Scalars cannot be protected from immense radiation corrections by coupling to other particles by a symmetry, their mass diverges quadratically with the highest energy scale of the theory due to such corrections. One therefore expects a natural mass of the order of magnitude of this scale for scalars. In a quantum field theory that also includes gravity, this is the Planck scale . However, the Planck scale (order of magnitude 10 19 GeV) is 16 orders of magnitude above the electroweak scale (order of magnitude 10 3 GeV). The effective (i.e. experimentally accessible) Higgs mass, the value of which is required for the Higgs mechanism in the range of the electroweak scale and which has now been experimentally determined to be around 125 GeV, is therefore not at its natural value in the vicinity of the Planck mass (naturalness problem ).
Although this quadratic divergence can be normalized and the Higgs mass can be brought to its desired value in the vicinity of the electroweak scale, this requires technically demanding and unnatural fine-tuning . In addition, the origin of the Higgs mass is easily misunderstood.
In addition, when calculating the Higgs mass from the higher order Feynman graphs, a finite correction is obtained that depends on the masses and coupling constants of the other particles in the theory. The corrections resulting from this are negligible for the particles of the Standard Model , but they become large for possibly existing very heavy particles, even if the Higgs only couples them very indirectly. Even if the Higgs boson is a central component of the Standard Model of elementary particle physics, the hierarchy problem is therefore not a problem of the Standard Model itself, since it does not contain any of these heavy particles. Strictly speaking, the hierarchy problem cannot even be formulated within the standard model, since 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”).
The explosive nature of the hierarchy problem can be traced back to the fact that the standard model of elementary particle physics is a consistent theory and agrees very well with the previous experimental data, but there are some reasons, especially from a theoretical point of view, to assume that the standard model is not is the final theory and one expects new physics in higher energy ranges.
The standard model does not currently contradict any experimental findings (however, the references to minimal but not vanishing neutrino masses contradict the assumption of the standard model), but it has only been tested on a large scale in an energy range below the TeV scale. Furthermore, although the electromagnetic and the weak interaction are combined within the standard model to form the electroweak interaction, a combination with the strong interaction ( GUT ) or even with gravity is not possible in the standard model. The standard model is also unsatisfactory from a theoretical point of view with regard to the number of parameters (around 20). In addition, references to dark matter or dark energy do not seem to be explainable within the framework of the standard models of particle physics and cosmology and to point to new physics “beyond the standard model” (e.g. the new heavy particles mentioned).
- "Based only on a proper respect for the power of nature to surprise us, it seems nearly as obvious that new physics exists in the 16 orders of magnitude in energy between the presently explored territory near the electroweak scale and the Planck scale." - Stephen P. Martin: A Supersymmetry Primer
- ( "To surprise us solely on the basis of an appropriate respect for the power of nature, it seems almost self-evident that new physics exist in the 16 energy magnitudes between the previously explored area close to the electroweak scale and the Planck scale." )
Suggested solutions
Supersymmetry
One way out of the hierarchy problem is supersymmetry (SUSY). Since bosons and fermions with different signs contribute to the corrections, it is obvious (if not the historical motivation) to introduce a boson-fermion symmetry to solve the hierarchy problem. In the case of exact supersymmetry, the problematic terms automatically cancel each other out, so fine tuning is not necessary. Even if supersymmetry is broken (which must indeed be the case if it exists), i.e. if it is not exact, there are maximally logarithmically divergent terms, which are unproblematic. So that these divergences and thus the Higgs mass do not become too large, SUSY is restricted to an energy range of a few TeV.
String theory
A further solution is offered by string theory , in which there are up to ten compactified extra dimensions that can have a radius of up to a tenth of a millimeter and into which only gravity can penetrate. In these extra dimensions the gravitational force would be considerably weakened. The actual force would in reality be much greater and would approach the other three basic forces .
Randall-Sundrum model
The Randall-Sundrum model offers a third solution to the problem . This tries to solve the hierarchy problem by introducing a single additional dimension - this is what distinguishes the model from string theories.
literature
- Lisa Randall - Warped Passages. Unraveling the Mysteries of the Universe's Hidden Dimensions , New York 2005; ISBN 0-06-053108-8 (published in German in October 2006 under the title: Verborgene Universen. A journey into extradimensional space , S. Fischer Verlag, ISBN 3-10-062805-5 )
- GF Giudice , Odyssey in the Zeptoraum: A Journey into the Physics of the LHC , Springer-Verlag, Berlin Heidelberg 2012, ISBN 978-3-642-22394-5 .