Measurement of the forward $Z$ boson production cross-section in $pp$ collisions at $\sqrt{s}$ = 7 TeV

Abstract: A measurement of the production cross-section for $Z$ bosons that decay to muons is presented. The data were recorded by the LHCb detector during $pp$ collisions at a centre-of-mass energy of 7 TeV, and correspond to an integrated luminosity of 1.0 fb$^{-1}$. The cross-section is measured for muons in the pseudorapidity range $2.0 < \eta < 4.5$ with transverse momenta $p_{T} > 20$ GeV/c. The dimuon mass is restricted to $60 < M_{\mu^{+}\mu^{-}} < 120$ GeV/c$^{2}$. The measured cross-section is $$\sigma_{Z\rightarrow\mu^{+}\mu^{-}} = (76.0 \pm 0.3 \pm 0.5 \pm 1.0 \pm 1.3) \, \text{pb}$$ where the uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. This result is in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. The cross-section is also measured differentially as a function of kinematic variables of the $Z$ boson. Ratios of the production cross-sections of electroweak bosons are presented using updated LHCb measurements of $W$ boson production. A precise test of the Standard Model is provided by the measurement of the ratio $$\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}} + \sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}{\mu}}}{\sigma{Z\rightarrow\mu^{+}\mu^{-}}} = 20.63\pm0.09\pm0.12\pm0.05,$$ where the uncertainty due to luminosity cancels.

Measurement of Forward $Z$ Boson Production at 7 TeV in $pp$ Collisions

This paper presents a meticulous analysis of the forward production cross-section of $Z$ bosons in proton-proton ($pp$) collisions at a center-of-mass energy of 7 TeV. The data were collected using the LHCb detector at CERN, corresponding to an integrated luminosity of 1.0 fb$^{-1}$. The $Z$ bosons are identified through their decay into muon pairs, a clean channel highly favored due to its distinct signature and reduced background noise.

Highlights and Findings

• Cross-section Measurement: The production cross-section for the $Z \rightarrow \mu^+ \mu^-$ process is quantified at $$\sigma_{Z\rightarrow\mu^{+}\mu^{-}} = (76.0 \pm 0.3 \pm 0.5 \pm 1.0 \pm 1.3)$$ pb. The quoted uncertainties cover statistical, systematic, beam energy, and luminosity errors. This measurement aligns well with predictions from NNLO perturbative QCD calculations, confirming the robustness of the Standard Model (SM) under the experimental conditions.
• Kinematic Range and Differential Cross-sections: Measurements focus on muons within the pseudorapidity range $2.0 < \eta < 4.5$ and transverse momenta $p_T > 20$ GeV/c. The dimuon invariant mass is required to be within $60 < M_{\mu^{+}\mu^{-}} < 120$ GeV/c$^2$. Additionally, differential cross-sections are reported as functions of the $Z$ boson's rapidity ($y_Z$), transverse momentum ($p_{T,Z}$), and $\phi^*_Z$. These differential measurements provide valuable insights into parton distribution functions (PDFs) and the dynamics of electroweak interactions.
• Electroweak Boson Ratios: The analysis extends to the ratio of $W$ to $Z$ boson production cross-sections, delivering stringent tests for the consistency of SM predictions. The ratio $$\left( \frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}} + \sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}} \right)$$ is experimentally determined with a high degree of precision, $R_{W/Z} = 20.63 \pm 0.09 \pm 0.12 \pm 0.05$.
• Improved Precision: By revisiting the $W$ boson production analyses using enhanced trigger efficiency data, previously measured cross-section values for $W^+$ and $W^-$ bosons are updated, achieving significantly reduced uncertainties.

Implications and Future Developments

The results provide critical inputs for refining PDF models by testing their validity at non-central rapidities and expanding the constraints on fundamental parameters of the SM. The ongoing precision of such measurements will enhance the understanding of QCD interactions, particularly in the forward region, invaluable for future explorations at higher energies and luminosities, including those at the High-Luminosity LHC (HL-LHC).

Given these findings, subsequent research may explore the subtleties of QCD corrections and potential beyond-the-Standard-Model effects observable at high-energy colliders. Moreover, the techniques developed and refined through this analysis could aid in the precision measurements of other processes involving electroweak bosons. The meticulous focus on systematic uncertainties, alongside statistical precision, sets a benchmark for similar measurements across experimental platforms.