QCD analysis of the CMS inclusive differential $Z$ production data at $\sqrt{s}=8\mathrm{TeV}$

The parton distribution functions (PDFs) of the proton are one of the essential ingredients to describe physics processes at hadron colliders. The $Z$ boson production data at the LHC have a potential to constrain PDFs, especially the gluon distribution. In this study the CMS measurement of the inclusive double differential $Z$ boson production cross section in terms of transverse momentum and rapidity is compared to the next-to-leading order theory predictions at the center-of-mass energy, $\sqrt{s}=8\mathrm{TeV}$ with an integrated luminosity of $19.71{\mathrm{fb}}^{-1}$. In addition, the sensitivity of this measurement to PDFs is studied within the framework of the HERAFitter. A moderate improvement to the gluon distribution is observed at the Bjorken $x\approx 0.1$ region. However, in order to obtain further improvement to the gluon distribution in the global fits, the higher-order theory calculations accessible via fast techniques are necessary.

Figure 1

The comparison of $Z$ boson CMS data to the theory predictions obtained from the MCFM [39] in different $Z$ rapidity [$Y(Z)$] bins.

Figure 2

Correlation coefficients (${\mathrm{Q}}_i$; $i=g$, $u$, $d$, $s$) between the gluon (top left), the up quark (top right), the down quark (bottom left) and the strange quark (bottom right) PDFs and the inclusive $Z$ boson production cross section for the $p_T(Z)>40\mathrm{GeV}$ range.

Figure 3

Distribution of the gluon for $Q^2=10{\mathrm{GeV}}^2$. The bands correspond to experimental PDF uncertainties of the fit to HERA data only (red) and both HERA and the CMS data (blue and green).

Figure 4

Same as in Fig. 3, but for $u$ (left) and $d$ (right) valence quarks.

Figure 5

Constrained parton density functions for the gluon (top), and $u$ (middle) and $d$ valence (bottom) quarks from the QCD analysis of CMS $Z$ boson data at the scales $Q^2=10{\mathrm{GeV}}^2$ (left panel) and $M_Z^2$ (right panel). The uncertainties include those due to the experimental (red), the model (yellow) and the parametrization variations (green). All uncertainties are added in quadrature.