Constraining non-commutative geometry with W/Z+jet production at the LHC

We present a comprehensive calculation of the squared matrix elements for all partonic channels contributing to [Formula: see text]+jet production at hadron colliders within the framework of the non-commutative Standard Model (NCSM), including leptonic decays [Formula: see text] and [Formula: see text]. Our computation incorporates both [Formula: see text] corrections to the Standard Model vertices and additional interaction terms inherent to the NCSM. A key finding is that the production amplitudes receive first-order corrections at [Formula: see text], a distinctive feature compared to many other processes where non-commutative effects enter only at [Formula: see text]. The leptonic decay widths, in contrast, are modified solely at [Formula: see text]. This [Formula: see text] enhancement provides improved sensitivity to non-commutative geometry, allowing us to probe for and constrain the non-commutative energy scale in the multi-TeV range. We provide numerical predictions for angular (azimuthal and rapidity) distributions and the forward–backward asymmetry, and compare them to state-of-the-art Standard Model predictions at leading and next-to-leading order from the MCFM Monte Carlo program. Finally, we test the NCSM with experimental data by analyzing an unbinned, particle-level [Formula: see text]+jet dataset from the ATLAS experiment. From this data, we calculate the azimuthal spectrum and forward-backward asymmetry, which are then used to derive stringent lower bounds on the non-commutative scale [Formula: see text]. Our analysis accounts for Earth rotation effects by treating the non-commutative tensor as fixed in a celestial frame and deriving time-averaged observables in the rotating detector frame.