Gauge field theories with Lorentz-violating operators of arbitrary dimension

Abstract

The classification of Lorentz-and CPT-violating operators in nonabelian gauge field theories is performed. We construct all gauge-invariant terms describing propagation and interaction in the action for fermions and gauge fields. Restrictions to the abelian, Lorentz-invariant, and isotropic limits are presented. We provide two illustrative applications of the results to quantum electrodynamics and quantum chromodynamics. First constraints on nonlinear Lorentz-violating effects in electrodynamics are obtained using data from experiments on photon-photon scattering, and corrections from nonminimal Lorentz and CPT violation to the cross section for deep inelastic scattering are derived.

Lorentz and CPT violation in partons

“…Other terms in Table I of Ref. [32] involving coefficients of the a type include a µ f at d = 3 and a (5)λµν Ff at d = 5, but none of these contribute at leading order to the processes studied here. The field redefinitions insure that the coefficients c µν f and a (5)λµν f of interest can be taken to be symmetric in any pair of indices and to have vanishing traces, implying 9 independent observable components of the c type and 16 independent observable components of the a (5) type [36,69].…”

“…For simplicity, we disregard possible flavor-changing couplings and limit attention to spin-independent effects. For a single massless Dirac fermion, the corresponding gauge-invariant Lorentz-and CPT-violating Lagrange density L ψ can be written in the form [32,54]…”

“…The explicit form of L ψ for d ≤ 6 relevant for our purposes is contained in Table I of Ref. [32]. The corresponding coefficients for Lorentz violation may be assumed perturbatively small based on current experimental results [11] and the restriction to observer concordant frames [63].…”

“…In the context of unpolarized DIS, the effects of nonzero flavor-diagonal quark coefficients a (5)µαβ f controlling CPT-odd operators with mass dimension five have recently been studied [32]. These coefficients stem from the nonminimal SME term L SME ⊃ −(a (5)…”

“…Our efforts here to explore spin-independent SME effects in the quark sector extend those in the literature, including studies of single and pair production of t quarks at Fermi National Accelerator Laboratory (Fermilab) and at the LHC [22][23][24], applications of chiral perturbation theory [25][26][27][28][29], estimates of attainable sensitivities from DIS [30][31][32], and related investigations [33,34]. Spin-independent SME coefficients for CPT violation in the quark sector can also be constrained using neutral-meson interferometry [35,36] via oscillations of kaons [37][38][39][40][41] and of D, B d , and B s mesons [42][43][44][45][46][47][48].…”