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 $W^\pm/Z$+jet production at hadron colliders within the framework of the non-commutative Standard Model (NCSM), including leptonic decays $W\to e\nu$ and $Z\to {\mu^+\mu^-}$. Our computation incorporates both $\mathcal{O}(\Theta)$ 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 $\mathcal{O}(\Theta)$, a distinctive feature compared to many other processes where non-commutative effects enter only at $\mathcal{O}(\Theta^2)$. The leptonic decay widths, in contrast, are modified solely at $\mathcal{O}(\Theta^2)$. This $\mathcal{O}(\Theta)$ 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 \texttt{MCFM} Monte Carlo program. Finally, we test the NCSM with experimental data by analyzing an unbinned, particle-level $Z$+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 $\Lambda$. 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.