Top-quark pair production in electron-positron collisions within the minimal noncommutative Standard Model

We study top-quark pair production in electron-positron collisions within the framework of the minimal noncommutative Standard Model. Noncommutative effects are incorporated using the Seiberg-Witten map, and the scattering squared amplitude for the process $e^+e^-\to t\bar{t}$ is computed consistently up to second order in the noncommutativity parameter $\Theta^{\mu\nu}$. We derive the total cross-section, the polar and azimuthal angular distributions, and the forward-backward asymmetry, all of which exhibit sensitivity to space-time noncommutativity. Numerical results are evaluated for center-of-mass energies relevant to future linear colliders, such as the ILC and CLIC. Our analysis demonstrates that noncommutative geometry can induce significant characteristic deviations from the Standard Model predictions, offering a potential indirect probe of space-time noncommutativity at high-energy $e^+e^-$ collisions.