Measurement of the weak mixing angle with the Drell-Yan process in proton-proton collisions at the LHC

A multivariate likelihood method to measure electroweak couplings with the Drell–Yan process at the LHC is presented. The process is described by the dilepton rapidity, invariant mass, and decay angle distributions. The decay angle ambiguity due to the unknown assignment of the scattered constituent quark and antiquark to the two protons in a collision is resolved statistically using correlations between the observables. The method is applied to a sample of dimuon events from proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of $1.1{\mathrm{fb}}^{-1}$. From the dominant $u\overline{u}$, $d\overline{d}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process, the effective weak mixing angle parameter is measured to be ${sin}^2{\theta }_{\mathrm{eff}}=0.2287\pm 0.0020(\mathrm{stat}.)\pm 0.0025(\mathrm{syst}.)$. This result is consistent with measurements from other processes, as expected within the standard model.

Figure 1

Top: diagram describing the SM process $q\overline{q}\to {\gamma }^{*}/Z\to {\ell }^{-}{\ell }^{+}$. Bottom: definition of the angle ${\theta }^{*}$ in the production and decay of an intermediate state $X$, such as $gg$ or $q\overline{q}\to X\to {\ell }^{-}{\ell }^{+}$.

Figure 2

Analytical parameterization of the parton distribution functions $x{f}_a(x,Q^2)$ at $Q=100\mathrm{GeV}$ using the cteq6 [19] numerical computation for the various quarks, antiquarks, and the gluon. The gluon distribution is scaled by a factor of 0.1.

Figure 3

Distribution of the effective cross section factor $2m{F}_{q\overline{q}}(m^2,Y=0)$ defined in Eq. (8) for five quark flavors (from top to bottom $q=u$, $d$, $s$, $c$, $b$) for proton-proton collision energies of 7 TeV as a function of the dilepton mass $m$. An equivalent factor for gluon-fusion production is shown for comparison and is scaled by a factor of 0.1.

Figure 4

The dilution factor $D_{q\overline{q}}(\widehat{s}=m_Z^2,Y)$ for $u\overline{u}$ (top, red boxes) and $d\overline{d}$ (bottom, blue crosses) production as a function of the dilepton rapidity $Y$. The prediction from the Pythia simulation (boxes and crosses) of the $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process and the analytical distributions (solid curves) from Eq. (9) are shown.

Figure 5

Distributions of $Y$ (top), $m$ (middle), and $\cos {\theta }^{*}$ (bottom), from Pythia simulation (points) of the $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process and analytical distributions from Eq. (7). Distributions for five quark flavors are shown combined $\Sigma q\overline{q}$ (black circles) and separately, in order of decreasing contribution: $u\overline{u}$ (red boxes), $d\overline{d}$ (blue crosses), $s\overline{s}$ (green diamonds), $c\overline{c}$ (magenta triangles), and $b\overline{b}$ (cyan stars). Distributions are normalized to unit area and are shown as fractions of events per bin.

Figure 6

Accepted $\cos {\theta }^{*}$ range as a function of $Y$ for $\widehat{s}=m_Z^2$ and for the kinematic selection used in this analysis. The outer boundary corresponds to Eq. (14) and the horizontal lines near $\cos {\theta }^{*}=\pm 0.92$ correspond to Eq. (15).

Figure 7

Distributions of $Y$ (top), $m$ (middle), and $\cos {\theta }^{*}$ (bottom), from Pythia simulation (points) of the $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process and its analytical parameterization (smooth curve). Combined distributions from Fig. 5 appear in red at the top of each plot (red circles for an “ideal” simulation), while distributions after acceptance and resolution effects, including photon FSR, appear in blue below (blue squares for a simplified “detector” simulation). Distributions are normalized to unit area and are shown as fractions of events per bin.

Figure 8

Distribution of $\cos {\theta }^{*}$ for data (points) and Powheg-based detector simulation with ${sin}^2{\theta }_W=0.2311$ (histogram) of the $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process for $|Y|<1$ (top) and $|Y|>1$ (bottom).

Figure 9

Distributions of $Y$ (top), $m$ (middle), and $\cos {\theta }^{*}$ (bottom) from the Powheg-based detector simulation with ${sin}^2{\theta }_W=0.2311$ of the $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ process (points). The MC sample corresponds to an integrated luminosity of $16{\mathrm{fb}}^{-1}$. The lines show the projections of the probability density functions.

Figure 10

Distributions of $Y$ (top), $m$ (middle), and $\cos {\theta }^{*}$ (bottom) in the analysis of $q\overline{q}\to {\gamma }^{*}/Z\to {\mu }^{-}{\mu }^{+}$ events from CMS (points). The lines show the projections of the probability density functions.