Evaluating matrix elements relevant to some Lorentz violating operators

Abstract

Carlson, Carone and Lebed have derived the Feynman rules for a consistent formulation of noncommutative QCD. The results they obtained were used to constrain the noncommutativity parameter in Lorentz violating noncommutative field theories. However, their constraint depended upon an estimate of the matrix element of the quark level operator ( p − m) in a nucleon. In this paper we calculate the matrix element of ( p − m), using a variety of confinement potential models. Our results are within an order of magnitude agreement with the estimate made by Carlson et al. The constraints placed on the noncommutativity parameter were very strong, and are still quite severe even if weakened by an order of magnitude.

Phenomenology of Lorentz-conserving noncommutative QED

“…Theories involving noncommutative spacetime structure based on algebras with c-number θ µν suffer from Lorentz-violating effects. Such effects are severely constrained [9,10,11,12,13,14,15,16,17] by a variety of low energy experiments [28]. Lorentz-violating effects appear in field theories as a consequence of θ 0i and ǫ ijk θ ij defining preferred direction in a given Lorentz frame.…”

“…In one of the most popular scenarios position four-vectors are promoted to operators that do not commute at short distance scales [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. There has been a lot of work on field theories with an underlying noncommutative space-time structure.…”