Inferring the covariant Θ-exact noncommutative coupling in the top quark pair production at linear colliders

Abstract

Abstract A novel non-minimal interaction of neutral right-handed fermion and abelian gauge field in the covariant Θ-exact noncommutative standard model (NCSM) which is invariant under Very Special Relativity (VSR) Lorentz subgroup, opens an avenue to study the top quark pair production at linear colliders. Here the non-minimal coupling is denoted as κ and the noncommutative (NC) scale Λ. In this work, we consider two types of analysis, one is without considering helicity basis technique and another, considering helicity of the initial and final state particles. Further, the realistic electron and positron beam polarization are taken into account to measure the NC parameters. In the first case, when κ is positive and certain values of Λ, we found that a specific threshold value of machine energy (optimal energy in the units of GeV) $$ \sqrt{s_0}\left(\simeq 2.52\ \varLambda +39\right) $$ s 0 ≃ 2.52 Λ + 39 may be quite useful to look for the signature of the spacetime noncommutativity with unpolarized beam. The statistical χ 2 analysis of the azimuthal anisotropy which is due to broken rotational invariance about the beam axis, is quite possible when κ takes negative value 0 > κ > −0.596 which persuade a lower limit on NC scale Λ (1.0 to 2.4 TeV) at κ max = −0.296 with 95% C.L according to luminosity ranging from 100 fb−1 to 1000 fb−1 at machine energy $$ \sqrt{s}=1.4 $$ s = 1.4 TeV and 3.0 TeV. In another case, we perform detailed analysis for the polarized and unpolarized electron-positron beam to probe spacetime noncommutativity in light of following observables like azimuthal anisotropy, helicity correlation, and top quark helicity left-right asymmetry. The polarization of the initial beam {P e − , P e + } = {−0.8, 0.3}({−0.8, 0.6}) enhances the ranges of lower limit on Λ, i.e. 1.13 to 2.80 TeV at κ max alongside the κ max enhanced into −0.5445 (−0.607) 95%C.L accord with luminosity and machine energy. Finally, we studied the intriguing mixing of the UV and the IR by invoking a specific structure of noncommutative anti-symmetric tensor Θ μν which is invariant under translational T (2) VSR Lorentz subgroup.