Abstract
Clock-comparison experiments are among the sharpest existing tests of Lorentz symmetry in matter. We characterize signals in these experiments arising from modifications to electron or nucleon propagators and involving Lorentz- and CPT-violating operators of arbitrary mass dimension. The spectral frequencies of the atoms or ions used as clocks exhibit perturbative shifts that can depend on the constituent-particle properties and can display sidereal and annual variations in time. Adopting an independent-particle model for the electronic structure and the Schmidt model for the nucleus, we determine observables for a variety of clock-comparison experiments involving fountain clocks, comagnetometers, ion traps, lattice clocks, entangled states, and antimatter. The treatment demonstrates the complementarity of sensitivities to Lorentz and CPT violation among these different experimental techniques. It also permits the interpretation of some prior results in terms of bounds on nonminimal coefficients for Lorentz violation, including first constraints on nonminimal coefficients in the neutron sector. Estimates of attainable sensitivities in future analyses are provided. Two technical appendices collect relationships between spherical and cartesian coefficients for Lorentz violation and provide explicit transformations converting cartesian coefficients in a laboratory frame to the canonical Sun-centered frame.
Highlights
Among the best laboratory tests of rotation invariance are experiments measuring the ticking rate of a clock as its orientation changes, often as it rotates with the Earth
Tests of this symmetry have experienced a revival in recent years, stimulated by the possibility that minuscule violations could arise from a unification of quantum physics with gravity such as string theory [2]
The general Lagrange density (1) for a fermion propagating in the presence of arbitrary Lorentz and CPT violation implies the perturbative result (2) for the corresponding nonrelativistic oneparticle Hamiltonian
Summary
Among the best laboratory tests of rotation invariance are experiments measuring the ticking rate of a clock as its orientation changes, often as it rotates with the Earth. We extend the existing theoretical treatment of Lorentz and CPT violation in clock-comparison experiments to include SME operators of nonminimal mass dimension d > 4 that modify the Dirac propagators of the constituent electrons, protons, and neutrons in atoms and ions. At an arbitrary given value of d, all Lorentz- and CPT-violating operators affecting the propagation have been identified and classified [35], which in the present context permits a perturbative analysis of the effects of general Lorentz and CPT violation on the spectra of the atoms or ions used in clock-comparison experiments. Note that natural units with c 1⁄4 ħ 1⁄4 1 are adopted throughout
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