Noncommutative QED and γγ scattering

We study γγ scattering in noncommutative QED (NCQED) where the gauge field has Yang-Mills type coupling, giving new contributions to the scattering process and making it possible for it to occur at tree level. The process takes place at one loop level in the Standard Model (SM) and could be an important signal for physics beyond SM. But it is found that the Standard Model contribution far exceeds the tree level contribution of the noncommutative case. Introduction Noncommutativity of a pair of conjugate variables forms the central theme of quantum mechanics in terms of the Uncertainty Principle. We are quite familiar with the noncommutativity of rotations in ordinary Euclidean space. The idea of noncommutative (NC) space-time can be traced back to the work of Snyder [1]. But more recently, string theory arguments have motivated an extensive study of Quantum Field Theory (QFT) on NC spaces [2]. The noncommutativity of space-time is realised by the coordinate operators, xμ, satisfying [xμ, xν ] = ιΘμν (1) with Θμν = θǫμν . θ is the noncommutativity parameter with dimensions (mass) −2 and ǫμν is the standard Levi-Civeta tensor. The field theories formulated on such spaces are nonlocal and violate Lorentz symmetry. The deviation from the standard theory manifests as violation of Lorentz invariance. We can still expect manifest Lorentz invariance for energies satisfying Eθ << 1. In the limit θ → 0, we recover the standard theory. The theory of electrons in a strong magnetic field, projected to the lowest Landau level, is a classic example of NC field theory. Various attempts, both theoretical and phenomenological, have been made to study QFT on NC spaces. The study of perturbative behaviour and divergence structure [3], C, P and T properties and renormalisability [4] of such theories has been undertaken. It has been shown that quantum theories with time-like noncommuatativities are not ∗E–mail : [email protected], [email protected]