A precision measurement of the $Z$ boson production cross-section at $\sqrt{s} = 13$ TeV in the forward region is presented, using $pp$ collision data collected by the LHCb detector, corresponding to an integrated luminosity of 5.1 fb$^{-1}$. The production cross-section is measured using $Z\rightarrow\mu^+\mu^-$ events within the fiducial region defined as pseudorapidity $2.0<\eta<4.5$ and transverse momentum $p_{T}>20$ GeV/$c$ for both muons and dimuon invariant mass $60<M_{\mu\mu}<120$ GeV/$c^2$. The integrated cross-section is determined to be $\sigma (Z \rightarrow \mu^+ \mu^-)$ = 196.4 $\pm$ 0.2 $\pm$ 1.6 $\pm$ 3.9~pb, where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measured results are in agreement with theoretical predictions within uncertainties.
Relative uncertainty for the integrated $Z -> \mu^{+} \mu^{-}$ cross-section measurement. The total uncertainty is the quadratic sum of uncertainties from statistical, systematic and luminosity contributions.
Final state radiation correction used in the $y^{Z}$ cross-section measurement. The first uncertainty is statistical and the second is systematic.
Final state radiation correction used in the $p_{T}^{Z}$ cross-section measurement. The first uncertainty is statistical and the second is systematic.
The interaction of virtual photons is investigated using the reaction e+e- -> e+e- hadrons based on data taken by the OPAL experiment at e+e- centre-of-mass energies sqrt(s_ee)=189-209 GeV, for W>5 GeV and at an average Q^2 of 17.9 GeV^2. The measured cross-sections are compared to predictions of the Quark Parton Model (QPM), to the Leading Order QCD Monte Carlo model PHOJET to the NLO prediction for the reaction e+e- -> e+e-qqbar, and to BFKL calculations. PHOJET, NLO e+e- -> e+e-qqbar, and QPM describe the data reasonably well, whereas the cross-section predicted by a Leading Order BFKL calculation is too large.
Total cross section in the given phase space and assuming ALPHA = 1/137.
Differential cross section as a function of X where X is the maximum value of X1 or X2, the upper and lower vertex values.
Differential cross section as a function of Q**2 where Q**2 is the maximum value of Q1**2 or Q2**2, the upper and lower vertex values.