Disentangling Forms of Lorentz Violation With Complementary Clock Comparison Experiments

Atomic clock comparisons provide some of the most precise tests of Lorentz and CPT symmetries in the laboratory. With data from multiple such experiments using different nuclei, it is possible to constrain new regions of the parameter space for Lorentz violation. Relativistic effects in the nuclei allow us to disentangle forms of Lorentz violation which could not be separately measured in purely nonrelativistic experiments. The disentangled bounds in the neutron sectors are at the 10 GeV level, far better than could be obtained with any other current technique. [email protected] There is a great deal of current interest in the possibility that Lorentz and CPT invariances may not be exact in nature. Violations of these symmetries could be tied to quantum gravity, and if any such violation were observed experimentally, it would be a discovery of profound importance. Modern tests of Lorentz and CPT symmetry have included studies of matter-antimatter asymmetries for trapped charged particles [1, 2, 3] and bound state systems [4, 5], determinations of muon properties [6, 7, 8], analyses of the behavior of spin-polarized matter [9, 10], Michelson-Morley experiments [11, 12, 13], measurements of neutral meson oscillations [14, 15, 16, 17, 18, 19], polarization measurements on the light from distant galaxies [20, 21, 22, 23], high-energy astrophysical tests [24, 25, 26, 27], and others. So far, no significant evidence of Lorentz violation has been found. There is a parameterization of Lorentz and CPT violations in low-energy effective field theory, known as the standard model extension (SME). The SME contains possible Lorentzand CPT-violating corrections to the standard model [28, 29] and general relativity [30]. The SME provides a useful framework for interpreting experimental tests of these symmetries. Many of the coefficients that characterized the SME have been constrained very tightly. However, many others have not. (Up-to-date information about bounds on SME coefficients may be found in [31].) Moreover, in many cases, only specific combinations of coefficients can be bounded, rather than the individual coefficients themselves. Some of the most precise laboratory tests of Lorentz symmetry are clock comparison experiments [32, 33, 34, 35, 36, 37]. The results of these experiments are usually interpreted in the context of the Schmidt model [38], which assigns all of a nucleus’s angular momentum to a single unpaired nucleon. Since these atomic clock experiments are so powerful, there has been a great deal of interest in devising methods to expand the scope of the bounds they provide. For example, the suggestion that atomic clock experiments on orbiting satellites could add sensitivity to previously unconstrained SME parameters [39] attracted a great deal of interest. In this paper, we shall show that with multiple complementary clock comparison experiments using different isotopes, there is unexpected sensitivity to new areas of the SME parameter space. (A somewhat similar technique, using complementary experiments with different materials, was used in [40] to place improved bounds on an entirely different collection of SME coefficients.) The minimal SME Lagrange density for a single species of fermion is Lf = ψ̄(iΓ ∂μ −M)ψ, (1)