Data tables for Lorentz and CPT violation

Recent years have seen a renewed interest in experimental tests of Lorentz and CPT symmetry. Observable signals of Lorentz and CPT violation can be described in a modelindependent way using effective field theory (Kostelecký and Potting, 1995). The general realistic effective field theory for Lorentz violation is called the standard-model extension (SME) (Colladay and Kostelecký, 1997; 1998; Kostelecký, 2004). It includes the standard model coupled to general relativity along with all possible operators for Lorentz violation. Both global and local Lorentz violation are incorporated. Since CPT violation in realistic field theories is accompanied by Lorentz violation (Greenberg, 2002), the SME also describes general CPT violation. Reviews of the SME can be found in Kostelecký (1999), (2002), (2005), Bluhm (2006), Kostelecký (2008), (2011). Each Lorentz-violating term in the Lagrange density of the SME is constructed as the coordinate-independent product of a coefficient for Lorentz violation with a Lorentz-violating operator. The Lorentz-violating physics associated with any operator is therefore controlled by the corresponding coefficient, and so any experimental signal for Lorentz violation can be expressed in terms of one or more of these coefficients. The Lorentz-violating operators in the SME are systematically classified according to their mass dimension, and operators of arbitrarily large dimension can appear. At any fixed dimension, the operators are finite in number and can in principle be enumerated. A limiting case of particular interest is the minimal SME, which can be viewed as the restriction of the SME to include only Lorentz-violating operators of mass dimension 4 or less. The corresponding coefficients for Lorentz violation are dimensionless or have positive mass dimension. The results summarized here concern primarily but not exclusively the coefficients for Lorentz violation in the minimal SME. We compile data tables for these SME coefficients, including both existing experimental measurements and some theory-derived limits. Each of these data tables provides information about the results of searches for Lorentz violation for a specific sector of the SME. For each measurement or constraint, we list the relevant coefficient or combination of coefficients, the result as presented in the literature, the context in which the search was performed, and the source citation. The tables include results available from the literature up to 31 July 2010, with updates provided by Kostelecký and Russell (2011). The scope of the searches for Lorentz violation listed in the data tables can be characterized roughly in terms of depth, breadth, and refinement. Deep searches yield great sensitivity to a small number of SME coefficients. Broad searches cover substantial portions of the coefficient space, usually at a lesser sensitivity. Searches with high refinement disentangle combinations of coefficients. In the absence of a compelling signal for Lorentz violation, all types of searches are necessary to obtain complete coverage of the possibilities. As a guide to the scope of the existing searches, we extract from the data tables three summary tables covering the sectors for matter (electrons, protons, neutrons, and their antiparticles), photons, and gravity. These summary tables list our best estimates for the maximal attained sensitivities to the relevant SME coefficients in the corresponding sectors. Each entry in the summary tables is obtained under the assumption that only one coefficient is nonzero. The summary tables therefore provide information about the overall search depth and breadth, at the cost of masking the search refinement. In addition to the data tables and the summary tables, we also provide properties tables listing some features and definitions of the SME and the coefficients for Lorentz violation. The Lagrange densities for the minimal QED extension in Riemann spacetime, the minimal SME in Riemann-Cartan spacetime, and the nonminimal photon sector in Minkowski REVIEW OF MODERN PHYSICS, VOLUME 83, JANUARY–MARCH 2011