Standard model extension

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In the standard model extension (Engl. Standard Model Extension , SME) is a theory to extend the Standard Model of particle physics. It is an effective model to theoretically evaluate any experimentally ascertainable Lorentz and CPT symmetry breaking . Despite its name, the SME is just one of many theories that try to explain / model physics beyond the Standard Model . The SME was developed by Alan Kostelecky and others from the 1990s after he found a possible violation of Lorentz symmetry in string theories with Stuart Samuel in 1989 .

The SME includes the theories of electroweak and strong interaction as well as general relativity . In addition, it contains operators that violate Lorentz symmetry and at the same time are compatible with fundamental principles of physics. About half of these operators also break the CPT invariance . This is immediately understandable, since a possible CPT symmetry breaking must generally also represent a violation of the Lorentz symmetry. The SME is used for modern experimental and theoretical investigations of the Lorentz and CPT invariance.

Motivation and historical development

One of the most important and at the same time most difficult questions in today's physical research is aimed at a quantum mechanical description of gravity . To do this, it is generally necessary to set up theoretical models that go beyond established physics and contain new phenomena. Examples of such physical models are string theory , loop quantum gravity , supersymmetric models , non-commutative field theories, etc. To distinguish between this multitude of models, it would be necessary to measure their various theoretically predicted phenomena. Now, one of the major difficulties in this research area is that most of these new phenomena are e.g. Z. are immeasurably small.

One would typically expect, however, that in a quantum mechanical description of gravity, the microscopic structure of space-time would show major differences compared to the known macroscopic structure. One of the new phenomena could be, for example, that the microscopic and the macroscopic spacetime structure differ in their symmetry. In fact, it has been shown in several works that have been done in Alan Kostelecký's group since 1989 that certain string theories can spontaneously break the Lorentz and CPT symmetry . In later studies it turned out that the other theoretical quantum gravity models mentioned above can also violate the Lorentz symmetry. This is interesting because the predicted phenomenon of Lorentz and CPT symmetry breaking can be determined experimentally so precisely that the above-mentioned measurability problem can be solved in many situations.

These theoretical considerations have led to the creation of the SME test model. It is designed to describe only the Lorentz and CPT symmetry violations among the multitude of possible quantum gravity effects (and only in energy ranges that are sufficiently small compared to the Planck scale ). This means that the SME test model itself is not one of the quantum gravity models; rather, it enables the identification and interpretation of experiments on Lorentz and CPT invariance . The SME is an effective field theory. It is constructed so generally that it contains practically all forms of Lorentz and CPT symmetry breaking (at low energies) regardless of the specific quantum gravity model.

The first step in setting up the SME test model took place in 1995 with the introduction of effective interactions that describe deviations from the Lorentz and CPT invariance . The size and type of these deviations were parameterized by so-called SME coefficients, which can be measured or limited in experiments. The first such test used data from the interferometry of neutral mesons , since such experiments are particularly sensitive to deviations from CPT symmetry . Don Colladay and Alan Kostelecký then set up the minimal SME in 1997 and 1998 in the flat Minkowski room. This work forms the basis for phenomenological investigations into the Lorentz and CPT invariance in physical systems in which gravitation is negligible. In 2004, the minimal SME was then completed by including gravitational effects. Sidney Coleman and Sheldon Glashow published the isotropic borderline case of the SME model in 1999. Higher order terms have also been studied since then.

Lorentz transformations: observer vs. Particle transformations

Violations of the Lorentz invariance only lead to observable differences in physical systems of the same type if these are connected to one another by a so-called “particle transformation”. The distinction between “observer” and “particle transformation” is the key to understanding the breaking of Lorentz symmetry.

Observer transformations refer to rotations or Lorentz boosts from external observers. The physical system under consideration remains unchanged. This is simply equivalent to changing the coordinate system. On the other hand, one can also leave the coordinate system unchanged and consider rotations or Lorentz boosts of the physical system. One then speaks of particle transformations. In the special theory of relativity, these two types of transformations are equivalent and are also referred to as "passive" or "active".

In the SME model, this equivalence is lost. Inertial systems are still connected to one another by the usual Lorentz transformations , so that the symmetry is preserved under observer transformations. This ultimately ensures that the physics remains independent of the choice of coordinate system. This principle is more fundamental than Lorentz symmetry and should be guaranteed in any reasonable theory. It is different with the particle transformations. Similar physical systems that move relative to one another or have a different orientation in space are no longer equivalent in the SME model. There are generally measurable differences between such systems. This results from the fact that the marked spacetime directions in the SME, which parameterize the deviations from Lorentz symmetry, do not transform themselves with a rotation or with a Lorentz boost of a local experiment. They are assumed to be fixed in space-time.

Construction of the SME

The formalism of effective field theory forms the basis for the construction of the SME. Effective field theories have proven to be an extremely flexible tool in a wide variety of areas of physics. In solid-state physics, for example, such field theories can be used to successfully describe non-relativistic systems - even on a discrete background (at least at low energies). The SME model is therefore formulated as a field-theoretical Lagrange density . In order to integrate the entirety of conventional physical knowledge into the SME, the SME model contains the Lagrange density of the standard model of particle physics and that of Einstein's theory of gravity .

In order to describe the violation of Lorentz and CPT invariance , no new degrees of freedom (particles) are introduced, but the existing ones are modified. This is achieved by introducing additional corrections into the Lagrangian density of the SME with the following properties (see above). The correction terms must behave as a scalar (more precisely: as a scalar tensor density) under observer transformations, so that physics remains independent of the choice of the coordinate system. For this purpose, these terms are formed from the covariant multiplication of ordinary field operators with non-dynamic vectors or tensors . These background vectors and tensors determine distinct directions in spacetime and thereby violate Lorentz symmetry and in some cases also CPT symmetry under particle transformations.

The non-dynamic vectors or tensors represent the coefficients that describe the deviation from Lorentz and CPT symmetry. Experimental investigations are aimed at measuring these coefficients or at least limiting their possible size. Since no violations of the Lorentz and CPT invariance have been measured so far, the SME coefficients must be very small. This would also be expected from a theoretical point of view, since quantum gravity effects are most likely determined by the extremely small Planck length . Some SME coefficients could also be significantly larger because, due to their specific properties, they would still only provide minimal phenomenological effects.

A variety of theoretical investigations, such as B. causality and positivity have so far not provided any indications of possible internal contradictions in the SME.

Spontaneous breaking of the Lorentz symmetry

In quantum field theory, there are two ways to break a symmetry, namely spontaneously or explicitly. An important finding in the theory of the violation of Lorentz symmetry is that an explicit break generally leads to an incompatibility between the Bianchi identities and various covariant continuity equations (for the energy-momentum tensor and for the spin tensor). A spontaneous violation of Lorentz symmetry generally avoids such problems. This insight favors dynamic mechanisms for violating the Lorentz invariance.

With spontaneous symmetry breaking , so-called Nambu – Goldstone bosons typically occur . In the case of Lorentz symmetry, theoretical investigations in various models have shown that these Nambu-Goldstone particles can be identified with the photon , the graviton , spin-dependent interactions or spin-independent interactions.

Experimental investigations based on the SME

The SME enables the prediction of potential phenomenological indicators for deviations from Lorentz and CPT symmetry in practically all currently feasible experiments. This test model has therefore established itself as a universal and powerful tool for many areas of experimental physics.

At the present time, no violations of the Lorentz or CPT invariance have been measured. Therefore, experimental results currently only take the form of upper bounds for SME coefficients. Since all SME coefficients represent components of vectors or tensors , their numerical value depends on the choice of the reference system. In order to facilitate comparisons between different experimental results, all measurements are normally related to standardized coordinates: the heliocentric equatorial reference system at rest. This coordinate system is appropriate because it can be assumed to be inertial and the transformation into the laboratory system is manageable.

Experimental studies mostly look for interactions between the properties of a physical system (such as momentum , spin or quantization axis) and the vectorial or tensorial SME coefficients. One of the main effects results from the fact that terrestrial experiments change their orientation and speed due to the rotation and the orbital movement of the earth relative to the standardized inertial system . This results in predicted readings that vary with the sidereal day and year. Since the movement of the earth around the sun is not relativistic, the predictions for the annual variations are comparatively small (reduction factor 10 −4 ). The most important time-dependent effect remains the variation with the sidereal day, which results from the earth's rotation.

Measurements of SME coefficients have or can be made in a variety of physical systems. Such measurements include:

The results of all measurements of SME coefficients carried out so far are listed in the Data Tables for Lorentz and CPT Violation.

See also

literature

  • Don Colloday, Alan Kostelecky: CPT Violation and the Standard Model, Phys. Rev. D, Vol. 55, 1997, pp. 6760-6774, Arxiv
  • Don Colloday, Alan Kostelecky: Lorentz-Violating Extension of the Standard Model, Phys. Rev. D, Volume 58, 1998, p. 116002, Arxiv
  • Alan Kostelecky: Search for relativity violations, Scientific American, January 2006, online
  • Maxim Pospelov, Michael Romalis: Lorentz invariance on trial, Physics Today, Volume 57, Issue 7, 2004, pp. 40-46

Web links

credentials

  1. ^ A b D. Colladay, VA Kostelecky: CPT Violation and the Standard Model . In: Physical review D 55, 6760 . 1997. arxiv : hep-ph / 9703464 .
  2. ^ A b D. Colladay, VA Kostelecky: Lorentz-Violating Extension of the Standard Model . In: Physical review D 58, 116002 . 1998. arxiv : hep-ph / 9809521 .
  3. ↑ a b c d V.A. Kostelecky: Lorentz Violation, and the Standard Model . In: Physical review D 69, 105009 (2004) . 2004. arxiv : hep-th / 0312310 .
  4. ^ Adrian Cho: Special Relativity Reconsidered In: Science. Vol. 307. no.5711, p. 866, February 11, 2005.
  5. ^ Kostelecky, Samuel, Spontaneous breaking of Lorentz symmetry in string theory , Physical Review D, Volume 39, 1989, pp. 683-685
  6. ^ Kostelecky, Background Information on Lorentz and CPT violation , Indiana University
  7. ^ O. Greenberg: CPT Violation Implies Violation of Lorentz Invariance . In: Physical review Lett. 89, 231602 . 2002. arxiv : hep-ph / 0201258 .
  8. ^ V. Alan Kostelecký: The Search for Relativity Violations . In: Scientific American Magazine.
  9. ^ Neil Russell: Fabric of the final frontier . In: New Scientist Magazine. No. 2408, August 16, 2003.
  10. ↑ Elizabeth Quill: Time Slows When You're on the Fly . In: Science. November 13, 2007.
  11. ^ V. Alan Kostelecký, S. Samuel: Spontaneous Breaking of Lorentz Symmetry in String Theory . In: Physical review D 39, 683 . 1989.
  12. ^ V. Alan Kostelecký, R. Potting: CPT and strings . In: Nuclear physics. B 359, 545 . 1991.
  13. ^ A b V. Alan Kostelecký, R. Potting: CPT, Strings, and Meson Factories . In: Physical review D 51, 3923 . 1995. arxiv : hep-ph / 9501341 .
  14. ^ S. Coleman, SL Glashow: High-energy tests of Lorentz invariance . In: Physical review D 59, 116008 . 1999. arxiv : hep-ph / 9812418 .
  15. ^ V. Alan Kostelecký, M. Mewes: Electrodynamics with Lorentz-Violating Operators of Arbitrary Dimension . In: Physical review D 80, 015020 . 2009. arxiv : 0905.0031 .
  16. ^ A b V. Alan Kostelecký, J. Tasson: Prospects for Large Relativity Violations in Matter-Gravity Couplings . In: Physical review Lett. 102, 010402 . 2008. arxiv : 0810.1459 .
  17. ^ V. Alan Kostelecký, R. Lehnert: Stability, Causality, and Lorentz and CPT Violation . In: Physical review D 63, 065008 . 2001. arxiv : hep-th / 0012060 .
  18. ^ R. Bluhm, V. Alan Kostelecký: Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity . In: High Energy Physics . 2005. arxiv : hep-th / 0412320 .
  19. ^ V. Alan Kostelecký, R. Potting: Gravity from Spontaneous Lorentz Violation . In: Physical review D 79, 065018 . 2009. arxiv : 0901.0662 .
  20. ^ V. Alan Kostelecký, R. Potting: Gravity from Local Lorentz Violation . In: General Relativity and Quantum Cosmology 37, 1675 . 2005. arxiv : gr-qc / 0510124 .
  21. ↑ N. Arkani-Hamed, HC Cheng, M. Luty, J. Thaler: Universal dynamics of spontaneous Lorentz violation and a new spin-dependent inverse-square law force . In: JHEP 0507, 029 . 2005. arxiv : hep-ph / 0407034 .
  22. ↑ C. Lämmerzahl: The special theory of relativity on the test stand In: Physik Journal. 3, 77 (2005).
  23. ^ V. Alan Kostelecký, N. Russell: Data Tables for Lorentz and CPT Violation . In: High Energy Physics . 2010. arxiv : 0801.0287 .