Transverse momentum and rapidity distributions of top quarks in pair and single top quark production within the non-commutative standard model at the LHC

This paper presents a comprehensive study of top quark phenomenology within the Non-Commutative Standard Model. We calculate non-commutative corrections to the squared amplitudes for top quark pair production, as well as for single top quark production via the $t$-channel and $tW$-channel, while noting that the $s$-channel remains unaffected by non-commutative geometry. Utilizing MadGraph5_aMC@NLO, we determine total cross-sections at various center-of-mass energies and examine differential distributions in transverse momentum and rapidity at leading order in both the strong coupling $\alpha_S$ and the non-commutative parameter $\Theta$. For single top production in the $t$-channel, a matching technique is employed to extend the validity of the distribution to low $p_t^{top}$ values through resummation. We also compare the non-commutative corrections with higher-order QCD corrections obtained at NLO using MCFM and at NNLO from existing literature. Our findings reveal significant deviations arising from non-commutative geometry at high energies, providing insights into potential new physics at energy scales accessible by current and future colliders.