Radiatively induced Lorentz and gauge symmetry violation in electrodynamics with varyingα

Abstract

A time-varying fine structure constant ðtÞ could give rise to Lorentz-and CPT-violating changes to the vacuum polarization, which would affect photon propagation. Such changes to the effective action can violate gauge invariance, but they are otherwise permitted. However, in the minimal theory of varying , no such terms are generated at lowest order. At second order, vacuum polarization can generate an instability-a Lorentz-violating analogue of a negative photon mass squared Àm 2 / ð _ 2 Þ 2 logðà 2 Þ, where à is the cutoff for the low-energy effective theory.Two exotic forms of physics beyond the standard model that have recently gotten a lot of attention are Lorentz symmetry violations [1] and time-dependent fundamental constants. If these two phenomena exist, they are likely to be closely related. For example, if the fine structure constant ¼ e 2 4 is actually a function of time ðtÞ, there is naturally a preferred spacetime direction, @ , which violates boost invariance. We shall investigate this potential connection, which may also be related to violations of electrodynamical gauge invariance.The most common theory with varying constants that has been studied is one with a time-dependent . Other possibilities have included changes in the quantum chromodynamics scale à QCD and therefore the electron-proton mass ratio. However, these possibilities are usually approached phenomenalistically, without reference to a full underlying quantum field theory. Lorentz violation has been treated somewhat differently in recent years. Although there is a long history of searches for deviations from special relativity-also frequently handled in purely phenomenalistic fashion-the standard approach now is to use effective field theory. The effective field theory containing all possible local, Lorentz-violating operators built from standard model fields is called the standard model extension (SME) [2]. The SME Lagrange density contains new operators, involving tensor objects constructed from quantum fields, contracted with constant background tensors. An example of such an operator is Àa " c c . For parameterizing the results of experimental tests, a restricted subset of the theory, the minimal SME, is typically used. The minimal SME contains only operators that are gauge invariant and power counting renormalizable.Lorentz violation and varying constants have both been tightly constrained experimentally, and many of the most stringent tests are in quantum electrodynamics (QED). In most cases, it is conventional to consider only the leading order effects of Lorentz violation or a varying ; since _ must be small, Oð _ 2 Þ terms may be of negligible importance. In this paper, we shall begin by following this convention; however, the higher order terms are interesting when they can produce qualitatively different effects than those possible at leading order. For this reason, after discussing Oð _ Þ radiative corrections, we shall consider additional effects that are Oð _ 2 Þ and Oð € Þ. Measurements of _ may be made in a number of...

Lorentz andCPTviolation in scalar-mediated potentials

“…However, because of the spin reversal present in Às , the matrix element y Às j Às 0 is equal to À y s 0 j s . Note that present in (9) [and (11)] are almost all the possible vector structures that can be constructed at first order in the momenta. There are three independent threevector operators that may be constructed: the total momenta along the incoming and outgoing lines from a vertex (p þp 0 ), the momentum transfer (q ¼p Àp 0 ), and the spin operator ().…”

“…While there is thus far no compelling experimental reason to believe that Lorentz or CPT invariances are not exact, many candidate theories of quantum gravity suggest the possibility of such symmetry violations, at least in certain regimes. The possibilities for symmetry breaking include spontaneous breaking in string theory [1,2] and elsewhere [3], mechanisms in loop quantum gravity [4,5] and noncommutative geometry [6,7], Lorentz violation through spacetime-varying couplings [8,9], and anomalous breaking of Lorentz and CPT symmetries [10].…”

Neutrino beam constraints on flavor-diagonal Lorentz violation

“…Many prospective theories of quantum gravity may involve the breaking of these symmetries, at least in certain regimes. The mechanisms for the symmetry breaking include spontaneous breaking in string theory [2,3] and theories of vector fields [4], effects in loop quantum gravity [5,6] and non-commutative geometry [7,8], Lorentz violation through spacetime-varying couplings [9,10], and anomalous breaking of Lorentz and CPT symmetries [11].…”

One-loop nonbirefringent effects on the electromagnetic vertex in the Standard Model Extension

“…Interesting works involving radiative corrections produced by the SME exist [11][12][13][14][15][16][17][18][19]. An important result that has been established [15] is renormalizability of the one-loop contributions from the most general quantum electrodynamics sector of the minimal SME.…”