Standard-Model Extension

The standard model extension (English Standard Model Extension, SME) is an effective model to evaluate possible to experimentally observable Lorentz and CPT symmetry breaking theory can.

The SME includes the theories of the electroweak and strong interactions as well as the general theory of relativity. In addition, it contains operators that violate Lorentz symmetry and at the same time are compatible with basic principles of physics. About half of these operators also breaks the CPT invariance. This is immediately understandable as a possible CPT- symmetry breaking in general at the same time must also constitute a violation of Lorentz symmetry. The SME is used to modern experimental and theoretical investigations of Lorentz and CPT invariance.

Motivation and historical development

One of the most important and also most difficult issues in today's physics research aims at a quantum mechanical description of gravity. For this purpose, it is generally necessary to establish theoretical models that go beyond the established physics and include new phenomena. Examples of such physical models are the string theory, loop quantum gravity, supersymmetric models, noncommutative field theories, etc. In order to distinguish between these various models, it would be necessary to measure their various theoretically predicted phenomena. One of the main difficulties in this area of ​​research consists in the fact that most of these new phenomena currently are immeasurably small.

However, one would typically expect at a quantum mechanical description of gravity the microscopic structure of spacetime has significant differences compared to the known macroscopic structure. One of the new phenomena could be, for example, that the microscopic and the macroscopic space-time structure is different in its symmetry structure. Indeed, in several works, in Alan Kosteleckýs working group have been created since 1989, been shown that it can lead to a spontaneous breaking of Lorentz and CPT symmetry in certain string theories. Has been found in later studies that may lead to a violation of Lorentz symmetry in the other above-mentioned theoretical quantum gravity models. This is interesting because the predicted phenomenon of Lorentz and CPT symmetry breaking can be determined experimentally so accurate that the above Messbarkeitsproblem can be solved in many situations.

These theoretical considerations have led to the establishment of the SME test model. It is designed keeping the number of possible quantum gravity effects only the Lorentz and CPT symmetry violations (and only in fields of energy compared to the Planck scale are sufficiently small ) to describe. This means that the SME test model does not count himself to the quantum gravity models; rather, it allows for the identification and interpretation of experiments to Lorentz and CPT invariance. The SME is an effective field theory. She is so generally designed to ( at low energies ) includes virtually all forms of Lorentz and CPT symmetry breaking independently of the specific quantum gravity model.

The first step in the preparation of the SME test model was carried out in 1995 with the introduction of effective interactions that describe the deviations from the Lorentz and CPT invariance. The size and type of these deviations were doing parameterized by the so-called SME coefficients that 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 the CPT symmetry. Don Colladay and Alan Kostelecký then have the minimal SME situated in the flat Minkowski space in 1997 and 1998. These works form the basis for phenomenological studies on Lorentz and CPT invariance in physical systems in which gravity is negligible. In 2004, the minimum SME was then completed by the inclusion of gravitational effects. Sidney Coleman and Sheldon Glashow have published the isotropic limiting case of the SME model 1999. Higher order terms have since been also studied.

Lorentz transformations: Observer - vs. Teilchentransformationen

Violations of Lorentz invariance only lead to observable differences in similar physical systems if they are by a so-called " Teilchentransformation " with each other. The distinction between " observer " and " Teilchentransformation " is the key to understanding the breaking of Lorentz symmetry.

Observer transformations refer to rotations or Lorentz boosts by external observers. The physical system under consideration remains unchanged. This simply corresponds to a change of the coordinate system. On the other hand, you can also leave the coordinate system unchanged and consider rotations or Lorentz boosts of the physical system. One then speaks of Teilchentransformationen. 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. Intertialsysteme are still connected by the usual Lorentz transformation to each other so that the symmetry is maintained under observer transformations. This ultimately ensures that the physics is independent of the choice of coordinate system. This principle is more fundamental than the Lorentz symmetry and should be guaranteed in any reasonable theory. The situation is different with the Teilchentransformationen. Similar physical systems, which move relative to each other or have a different orientation in space, are no longer equivalent in the SME model. It is generally to be measured in principle differences between such systems. The results from the fact that the excellent space-time directions in the SME, which parameterize the deviations from the Lorentz symmetry, not mittransformieren at a rotation or a Lorentz boost of a local experiment. They are adopted set in space-time as fixed.

Construction of the SME

The basis for the construction of the SME is the formalism of effective field theory. Effective field theories have proven in the most diverse branches of physics as an extremely flexible tool. In solid-state physics can be with such field theories, for example, nonrelativistic systems - also on discreet background - successfully describe ( at least at low energies). The SME model is therefore formulated as a field theory Lagrangian density. In order to integrate the totality of the conventional physical knowledge in the SME, the SME model involves the Lagrangian of the Standard Model of particle physics and Einstein's theory of gravitation.

To describe now a violation of Lorentz and CPT- invariance, no new degrees of freedom ( particles ) to be introduced, but the modified current. This is accomplished by introducing additional corrections to the Lagrangian of the SME with the following properties (see above). The correction terms have to be a scalar (or more precisely as a scalar tensor ) behave under observer transformations, so that physics is independent of the choice of coordinate system. For this purpose, these terms are formed from the multiplication of ordinary covariant field operators with non-dynamic vectors or tensors. This background vectors and tensors determine excellent directions in space-time and thus violate the Lorentz symmetry and in some cases, the CPT symmetry under Teilchentransformationen.

The non-dynamic vectors or tensors represent the coefficients that describe the deviation from the Lorentz and CPT symmetry. Experimental studies aimed to measure these coefficients, or at least to limit their potential size. As no violations of Lorentz and CPT invariance were measured, the SME coefficients must be very small. This would 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 be significantly larger because they would deliver by their specific properties still minimal phenomenological effects.

A plurality of theoretical investigations, such as Causality and positivity have been delivered no evidence for any internal contradictions in the SME.

Spontaneous breaking of 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 Lorentz symmetry violation of is that an explicit breaking in general to an incompatibility between the Bianchi identities and different covariant continuity equations leads (for the energy -momentum tensor and the spin tensor ). A spontaneous violation of Lorentz symmetry is in principle such problems out of the way. So this insight favors dynamic mechanisms for the violation of Lorentz invariance.

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

Based on the SME experimental investigations

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

At the present time, no violations of Lorentz invariance or CPT have yet been measured. Therefore, experimental results currently take only the form of upper limits for SME coefficients. Since all SME coefficients components of vectors or tensors represent its numerical value depends on the choice of the reference system. In order to facilitate comparisons between different experimental results, all measurements are usually based on standardized coordinates: the Heliocentric dormant equatorial reference system. This coordinate system is appropriately because it can be assumed to be the inertial and the transformation in the laboratory system is manageable.

Experimental studies usually look for interactions between the properties of a physical system (such as pulse, spin or quantization ) and the vectorial or tensorial SME coefficients. One of the main effects due to the fact that the terrestrial experiments rotation and the orbital motion of the planet to the standardized inertial change their relative orientation and velocity. This results in the predicted measurement values ​​which vary with the sidereal day and the year. Since the movement of the earth around the sun is nonrelativistic, are the predictions for the annual variations comparatively small ( reduction factor of 10-4). As the most important time-dependent effect remains the variation with the sidereal day, which results from the rotation of the earth.

Measurements of SME coefficients or may have been carried out in a variety of physical systems. Such measurements include:

• Astrophysical observations of high-energy particles
• Double refraction and dispersion of light from cosmological sources
• Gauge bosons and Higgs
• Electromagnetic cavity resonators
• Equivalence principle
• Experiments at particle accelerators
• Gravity tests in the laboratory and in space
• Interferometry with matter waves
• Watch comparison experiments
• Neutrino oscillations
• Oscillations and decomposition of K-, B- and D- mesons
• Polarization of the cosmic background radiation
• Spectroscopy of hydrogen and antihydrogen
• Spin-polarized material
• The second and third generation particles
• Comparisons of particles with antiparticles

The results of all previously performed measurements of SME coefficients are listed Violation in the Data Tables for Lorentz and CPT.