Supersymmetry

The Super symmetry (SUSY) is a hypothetical symmetry of the particle , the bosons (particles with integer spin ) and fermions converts (particles with half-integer spin) into each other. Particles that transform into one another under a SUSY transformation are called super partners .

Because of their potential to answer open questions in particle and astrophysics , supersymmetric theories are very popular, especially in theoretical physics . Most of the great unified theories and superstring theories are supersymmetric. The minimally possible extension of the Standard Model of Particle Physics (SM), the Minimal Supersymmetric Standard Model (MSSM), which is compatible with previous findings , is the most experimentally examined candidate for physics beyond the Standard Model (BSM Physics).

However, despite promising theoretical arguments, no experimental evidence has been found to date that supersymmetry actually exists in nature - in particular, no superpartners of known particles have been observed. This means that if this symmetry exists, it is broken . The breaking mechanism and the energy at which the symmetry would apply are unknown.

Formulation history: Wess-Zumino-Modell and MSSM

Supersymmetry (in four-dimensional space-time ) was introduced in 1971 by Juri A. Golfand and his student Evgeni Lichtman (Evgeni Likhtman) (in Moscow ) and independently in 1972 by DV Volkov and Wladimir Akulow (in Charkiw / Charkow , Ukraine), as well as in the context of string theories (initially only on the two-dimensional string world surface ) by Jean-Loup Gervais , Bunji Sakita , André Neveu , John Schwarz and Pierre Ramond . Earlier work by Hironari Miyazawa from the 1960s on a baryon - meson symmetry was then ignored.

As a model of elementary particle physics, the theory only received greater attention in 1974 through the independent work of Julius Wess and Bruno Zumino . This model, known today as the Wess-Zumino model, describes two scalar bosons that interact with themselves and with a chiral fermion . Although unrealistic, the Wess-Zumino model is a popular example because of its simplicity and which shows important properties of supersymmetric field theories.

The first supersymmetric model compatible with previous experimental observations, the Minimal Supersymmetric Standard Model (MSSM), was proposed in 1981 by Howard Georgi and Savas Dimopoulos . According to their predictions, the masses of the previously unobserved super partners are in the range of 100 GeV / c² to 1 TeV / c², which is accessible for the Large Hadron Collider (LHC), which went into operation in 2009 . These masses are consistent with the finding that no superpartners were previously observed and suggest that superpartners of known elementary particles could be detected at the LHC. However, this has not yet been achieved (as of March 2019).

General properties

Supersymmetry algebra

The supersymmetry transformations that convert fermions and bosons into each other expand space-time symmetry, the Poincaré group .

Sidney Coleman and Jeffrey Mandula showed in 1967, under what seemed to be generally valid conditions, that - apart from the generators of the Poincaré group - all generators of physically relevant symmetries under Poincaré transformations must be invariant, i.e. every major symmetry of a physical model Product group of the Poincaré group with a group that has nothing to do with spacetime ( Coleman-Mandula theorem ).

But after Wess and Zumino had shown in 1974 that there can also be fermionic generators of symmetries that change like particles with spin  1/2 during rotations and that Coleman and Mandula did not take into account, Rudolf Haag , Jan Łopuszański and in 1975 classified Martin Sohnius the possible symmetry algebras with bosonic and fermionic generators ( Haag-Łopuszański-Sohnius theorem ).

The simplest supersymmetrical extension of the Poincaré group is realized in the Wess-Zumino model and extends it by two Weyl spinors . The relevant commutator and anti- commutator relations are ${\displaystyle Q,{\bar {Q}}}$

${\displaystyle \{Q_{\alpha },{\bar {Q}}_{\dot {\beta }}\}=2({\sigma ^{m}})_{\alpha {\dot {\beta }}}P_{m}\,,\ \ \{Q,Q\}=\{{\bar {Q}},{\bar {Q}}\}=[Q,P]=[{\bar {Q}},P]=0\,.}$

The Pauli matrices and denote the four-pulse . ${\displaystyle \sigma ^{m}}$ ${\displaystyle P_{m}}$

Loop fixes

Correction contributions to the Higgs mass. The quadratic divergence of the fermion loop in the upper diagram is compensated by the lower diagram of a scalar super partner.

The existence of additional elementary particles makes additional contributions to the loop corrections for observable physical parameters. If super partners have exactly the same quantum numbers apart from the spin, then the loop corrections are identical in amount, but differ in sign (due to the different spin): the corrections add up to zero.

In broken, in particular spontaneously broken, SUSY models, the corrections do not necessarily add up to zero, but often produce comparatively smaller effects.

The (partial) compensation of the loop corrections by super partners has two interesting effects:

• Supersymmetry offers a possibility to solve the naturalness problem (English naturalness problem or fine-tuning problem ). This problem consists in the fact that loop diagrams divergent to the square of the energy scale lead to disturbingly large correction contributions to the renormalized mass of the Higgs boson . For each quadratically divergent correction term, there could now be an equivalent term of the respective super partner with the opposite sign; the problematic corrections would add up to zero.
• In spontaneous or unbroken SUSY theories, in contrast to the standard model, the expected value of the energy density in field-free space is finite. So it seems easier to include gravity , for whose field the energy density is the source, in a quantum theoretical model (see below supergravity ).

Dark matter

→ Main article : Dark matter

In order not to contradict experimental results, one must assume that the decay processes of super partners in standard model particles (without another super partner as a decay product) are strongly suppressed or impossible ( R-parity conservation ). As a result, the lightest supersymmetrical partner particle (LSP) is practically stable. Since, according to current cosmological models, particles of any mass could be generated in the early phases of the universe, an electrically neutral LSP - such as the lightest neutralino - is a candidate for the explanation of dark matter.

Selected aspects

MSSM: Minimum Supersymmetrical Standard Model

→ Main article : MSSM

The MSSM is the smallest possibility in terms of the number of particles to build a realistic supersymmetric particle physics model. The MSSM extends the standard model with an additional Higgs doublet and SUSY partner particles for all particles in the model. No explicit mechanism is given that explains why the new particles have different masses than their standard model partners. Instead, all super -symmetry-breaking terms that are renormalizable , gauge invariant and R-parity-preserving are explicitly included in the model with initially unknown coupling constants .

Unified theories

→ Main article : Great Unified Theory

Coupling constants of the basic forces (s: strong, w: weak, em: electromagnetic interaction) as a function of energy , they only "almost" meet in the standard model. Gravitation is denoted by g. ${\displaystyle \alpha }$ ${\displaystyle E}$

The existence of the new particles from a mass of 100 to 1000 GeV influences the running , i.e. H. the energy dependence of the parameters (“coupling constants”) that characterize the strength of the three interactions occurring in the standard model, so that they  approach a common value at extremely high energies of GeV. In the Standard Model, they only meet at almost one point, while supersymmetric theories provide a much more precise “point of union”. This is sometimes interpreted as an indication of unified theories in which the three interactions of the Standard Model are just different effects of a single superordinate interaction, analogous to the electrical and magnetic interaction. ${\displaystyle 10^{16}}$

Super gravity

→ Main article : Supergravity

As in the standard model, the spacetime symmetries extended by the SUSY generators are initially global symmetries. However, if SUSY is declared as local symmetry, then this forces two new particles: the graviton with spin 2, which is expected to be the interaction particle of gravitation , and the gravitino with spin 3/2. Therefore, local SUSY theories are also called supergravity (SUGRA).

Compared to local space-time symmetry within the Standard Model , which cannot be renormalized, this has two potential advantages, which, especially in the initial phase of supersymmetrical approaches, nourished the hope that SUSY would provide a possible mechanism for a theory of quantum gravity :

• The different spin of Graviton and Gravitino could lead to non-renormalizable terms being compensated and the theory as a whole becoming renormalizable.
• The vacuum energy density of space, a source term for gravity according to the theory of relativity , is finite for SUGRA, in the case of unbroken supersymmetry even exactly zero. In contrast, in the standard model, the expected value of the energy density is already infinite in a vacuum , s. o. loop corrections .

To date, however - with the potential exception of superstring approaches that go beyond simple supersymmetry - it has not been possible to set up a consistent theory of supergravity. SUGRA, however, could be an effective theory below the Planck scale : it is a possible mechanism for spontaneous breaking of supersymmetry.

In some models, it is conceivable that the Gravitino could be detected in accelerator experiments such as the LHC .

Supersymmetry in other areas of physics

As dynamic symmetry, supersymmetry was used, for example, in nuclear physics ( Interacting Boson Model ) and in solid-state physics and in disordered systems, for example by Konstantin Efetov .

The integrated optics was developed in 2013 as a new field of application of supersymmetric concepts. This makes it possible to research selected properties of supersymmetrical configurations in easily accessible laboratory arrangements with the help of optical model systems. This approach uses the analogous mathematical structure of the quantum mechanical Schrödinger equation and the wave equation , which describes the propagation of light in one-dimensional systems. The spatial distribution of the refractive index corresponds to a potential landscape in which optical wave packets propagate. In addition to aspects of basic research, supersymmetric optical systems for applications in the areas of phase matching , mode conversion and spatial multiplexing are of interest.

See also

• Hierarchy problem

literature

• Ian J. Aitchison: Supersymmetry in particle physics - an elementary introduction. Cambridge Univ. Pr., Cambridge 2007, ISBN 978-0-521-88023-7
• Harald JW Müller-Kirsten, Armin Wiedemann: Introduction to Supersymmetry . 2nd ed. World Scientific, Singapore 2010, ISBN 978-981-4293-41-9 (revised ed. Of 1st ed. Of 1987)
• Sergio Ferrara, Rudolf M. Mössbauer: Searching for the superworld. World Scientific, Singapore 2007, ISBN 978-981-270-018-6
• Michael Dine: Supersymmetry and string theory - beyond the standard model. Cambridge Univ. Press, Cambridge 2007, ISBN 0-521-85841-0
• John Terning: Modern supersymmetry - dynamics and duality. Clarendon Press, Oxford 2007, ISBN 978-0-19-856763-9
• Jonathan A. Bagger: Supersymmetry, supergravity and supercolliders. World Scientific, Singapore 1999, ISBN 981-02-3816-9
• Luisa Cifarelli et al .: Properties of SUSY particles. World Scientific, Singapore 1993, ISBN 981-02-1424-3

Web links

• SP Martin: A Supersymmetry Primer . (PDF) Very popular English language source on the subject. Based on well-known quantum field theory, the MSSM is motivated and justified by the Wess-Zumino model. Phenomenological aspects of the MSSM and possible extensions are briefly discussed.

Individual evidence

1. ^ J. Wess, B. Zumino: Supergauge transformations in four dimensions. in: Nuclear physics. B. Amsterdam 70.1974, 39-50. ISSN  0550-3213
2. ↑ https://home.cern/news/news/physics/highlights-2019-moriond-conference-electroweak-physics Highlights from the 2019 Moriond conference (electroweak physics) - The latest experimental data provide more stringent tests of the Standard Model and of rare phenomena of the microworld ; March 29, 2019; accessed on April 28, 2019
3. ^ Sidney Coleman, Jeffrey Mandula: All possible symmetries of the S-matrix. , Physical Review, Vol. 159, 1967, pp. 1251-1256. ISSN  0031-899X
4. ↑ Hague, Lopuszanki, Sohnius: All possible generator of super symmetries of the S-matrix. in: Nuclear physics. B. Amsterdam 88.1975, 257. ISSN  0550-3213
5. ↑ See e.g. BD Hooper, T. Plehn: Supersymmetric Dark Matter - How light can the LSP be? in: Physics letters. B. Amsterdam 562.2003, 18-27. ISSN  0031-9163
6. ↑ U. Amaldi, W. de Boer, H. Fürstenau, Comparison of Grand Unified Theories with electroweak and strong coupling constants measured at LEP , Physics Letters Vol. 260, 1991, p. 447
7. ^ Takeo Moroi: Effects of the Gravitino on the Inflationary Universe.
8. ↑ Nanopoulos u. a .: Light-Gravitino Production at Hadron Colliders. in: Physical review. D. Melville 57.1998, 373-382. ISSN  0556-2821
9. ^ Mohammad-Ali Miri, Matthias Heinrich, Ramy El-Ganainy, Demetrios N. Christodoulides: Supersymmetric optical structures . In: APS (Ed.): Physical Review Letters . 110, No. 23, 2013, p. 233902. doi : 10.1103 / PhysRevLett.110.233902 . Accessed April 2014.
10. ^ Matthias Heinrich, Mohammad-Ali Miri, Simon Stützer, Ramy El-Ganainy, Stefan Nolte, Alexander Szameit, Demetrios N. Christodoulides: Supersymmetric mode converters . In: NPG (Ed.): Nature Communications . 5, 2014, p. 3698. doi : 10.1038 / ncomms4698 . Accessed April 2014.