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

TL;DR

This work investigates spacetime non-commutativity using W/Z plus jet production at the LHC within the non-commutative SM. By deriving leading-order squared amplitudes for all relevant partonic channels and implementing a narrow-width approximation, the authors show that NC effects enter production at $O(\Theta)$, while leptonic decays are only $O(\Theta^2)$. They perform a MC reweighting analysis to compare NC predictions with SM predictions (including NLO) and ATLAS $Z+$jet data, finding that angular observables—particularly azimuthal distributions and forward–backward asymmetries—provide strong NC sensitivity, constraining the NC scale to the multi-TeV range. The results demonstrate that vector-boson plus jet channels are powerful probes of non-commutative geometry at collider energies, with current data yielding bounds of roughly $\Lambda \gtrsim 1.7$–$3$ TeV (conservative) and potentially higher under aggressive interpretations, and future HL-LHC data promising even greater reach. Overall, the paper provides a concrete, experimentally testable framework for constraining non-commutative spacetime structure at accessible energies.

Abstract

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 $W\to eν$ and $Z\to e^+e^-$. Our computation incorporates both $\mathcal{O}(Θ)$ 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 $\mathcal{O}(Θ)$, a distinctive feature compared to many other processes where non-commutative effects enter only at $\mathcal{O}(Θ^2)$. The leptonic decay widths, in contrast, are modified solely at $\mathcal{O}(Θ^2)$. This $\mathcal{O}(Θ)$ 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 $Λ$.

Figures (8)

• Figure 1: Feynman diagrams for the leading-order contributions to $W/Z+$jet production in the NCSM at the LHC.
• Figure 2: Normalized differential rapidity (top) and azimuthal (bottom) distributions for various NC scales. Left column: electron from $W$ decay. Right column: $Z$ boson.
• Figure 3: Normalized differential rapidity (left) and azimuthal (right) distributions for the three principal directions of the NC tensor, $(\beta_x, \beta_y, \beta_z) = (1,0,0)$, $(0,1,0)$, and $(0,0,1)$, at a fixed NC scale $\Lambda$.
• Figure 4: Impact of the four-point interaction on the angular distributions. The parameter $\xi$ controls the inclusion ($\xi=1$) or exclusion ($\xi=0$) of the four-point vertex contribution. The left panel shows the rapidity distribution, the right panel the azimuthal distribution.
• Figure 5: SM angular distributions obtained with MCFM at LO and NLO, compared to predictions from the NCSM. The bands represent theoretical uncertainties from renormalization and factorization scale variations.