Measurement of the muon charge asymmetry in inclusive $pp\to W+X$ production at $\sqrt{s}=7\mathrm{TeV}$ and an improved determination of light parton distribution functions

Measurements of the muon charge asymmetry in inclusive $pp\to W+X$ production at $\sqrt{s}=7\mathrm{TeV}$ are presented. The data sample corresponds to an integrated luminosity of $4.7{\mathrm{fb}}^{-1}$ recorded with the CMS detector at the LHC. With a sample of more than 20 million $W\to \mu \nu$ events, the statistical precision is greatly improved in comparison to previous measurements. These new results provide additional constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable $x$ from ${10}^{-3}$ to ${10}^{-1}$. These measurements and the recent CMS measurement of associated $W+\text{charm}$ production are used together with the cross sections for inclusive deep inelastic $e^{\pm }p$ scattering at HERA in a next-to-leading-order QCD analysis. The determination of the valence quark distributions is improved, and the strange-quark distribution is probed directly through the leading-order process $g+s\to W+c$ in proton-proton collisions at the LHC.

Figure 1

The dimuon mass profile as a function of muon $\eta$ for ${\mu }^{-}$ (a), (c) and ${\mu }^{+}$ (b), (d), where (a) and (b) are before the correction and (c) and (d) are after the correction. The generated muon $p_{\mathrm{T}}$ varied by reconstruction resolution in data is used to obtain the dimuon invariant mass of the reference.

Figure 2

The $\eta$ distribution of the leading ${\mu }^{+}$ (a) and ${\mu }^{-}$ (b) in the $Z/{\gamma }^{*}\to {\mu }^{+}{\mu }^{-}$ sample. The dimuon invariant mass is within $60<m_{\mu \mu }<120\mathrm{GeV}$. The MC simulation is normalized to the data. The light shaded band is the total uncertainty in predicting the $Z/{\gamma }^{*}\to {\mu }^{+}{\mu }^{-}$ event yields using MC simulation, as described in Sec. 6.

Figure 3

Data to simulation comparison for ${\cancel{E}}_{\mathrm{T}}$ (a) and $\varphi$ distribution of ${\overrightarrow{\cancel{E}}}_{\mathrm{T}}$ (b) in the Drell-Yan control sample. Here, the hadronic recoil derived from the data was used to correct the MC simulation. The $Z/{\gamma }^{*}\to {\tau }^{+}{\tau }^{-}+t\overline{t}$ contribution (dark shaded region) in data is normalized to the integrated luminosity of the data sample using a MC simulation, and the normalization of the $Z/{\gamma }^{*}\to {\mu }^{+}{\mu }^{-}$ MC simulation (light shaded region) is taken as the difference between the data and the estimated $Z/{\gamma }^{*}\to {\tau }^{+}{\tau }^{-}+t\overline{t}$ contribution. In this data sample, the $Z/{\gamma }^{*}\to {\tau }^{+}{\tau }^{-}+t\overline{t}$ contribution is negligible.

Figure 4

The ${\cancel{E}}_{\mathrm{T}}$ distribution for ${\mu }^{+}$ (a) and ${\mu }^{-}$ (b) in the data sample dominated by the QCD background. The hadronic recoil derived from data has been used to correct the MC simulation. The $W\to \mu \nu$ contribution (light shaded region) is normalized to the integrated luminosity of the data sample using a MC simulation, and the normalization of the QCD simulation (dark shaded region) is taken as the difference between the data and the estimated $W\to \mu \nu$ contribution. The $W\to \mu \nu$ contribution in this data sample is negligible. The dark shaded band in each ratio plot shows the statistical uncertainty in the QCD MC ${\cancel{E}}_{\mathrm{T}}$ shape, and the light shaded band shows the total uncertainty, including the systematic uncertainties due to QCD ${\cancel{E}}_{\mathrm{T}}$ modeling as discussed in Sec. 6.

Figure 5

Muon $p_{\mathrm{T}}>25\mathrm{GeV}$ data sample. Examples of the extraction of the $W\to \mu \nu$ signal from fits to ${\cancel{E}}_{\mathrm{T}}$ distributions of $W\to \mu \nu$ candidates in data: $0.0\le |\eta |<0.2$ (a), (b), $1.0\le |\eta |<1.2$ (c), (d), and $2.1\le |\eta |<2.4$ (e), (f). The fits to $W^{+}\to {\mu }^{+}\nu$ and $W^{-}\to {\mu }^{-}\overline{\nu }$ candidates are in panels (a), (c), (e) and (b), (d), (f), respectively. The ratios between the data points and the final fits are shown at the bottom of each panel. The dark shaded band in each ratio plot shows the statistical uncertainty in the shape of the MC ${\cancel{E}}_{\mathrm{T}}$ distribution, and the light shaded band shows the total uncertainty, including all systematic uncertainties as discussed in Sec. 6.

Figure 6

Comparison of the final muon charge asymmetry ($\mathcal{A}$) extracted for the positive pseudorapidity ($\eta >0$) and negative pseudorapidity ($\eta <0$) regions with muon $p_{\mathrm{T}}>25\mathrm{GeV}$ (a) and muon $p_{\mathrm{T}}>35\mathrm{GeV}$ (b) samples. The uncertainties include only the statistical uncertainty from the signal extraction and uncertainty in the determination of the efficiencies for positive and negative muons.

Figure 7

Comparison of the measured muon charge asymmetries to the NLO predictions calculated using the fewz 3.1 [38] MC tool interfaced with the NLO CT10 [3], NNPDF2.3 [45], HERAPDF1.5 [46], MSTW2008 [2], and MSTW2008CPdeut [15] PDF sets. No EW corrections have been considered in these predictions. Results for muon $p_{\mathrm{T}}>25$ and $>35\mathrm{GeV}$ are shown in panels (a) and (b), respectively. The vertical error bars on data points include both statistical and systematic uncertainties. The data points are shown at the center of each $|\eta |$ bin. The theoretical predictions are calculated using the fewz 3.1 [38] MC tool. The PDF uncertainty for each PDF set is shown by the shaded (or hatched) band and corresponds to 68% C.L.

Figure 8

Comparison of the measured muon charge asymmetries to the NNLO predictions for muon $p_{\mathrm{T}}>25$ (a) and muon $p_{\mathrm{T}}>35\mathrm{GeV}$ (b). The NNLO HERAPDF1.5 [46] PDF has been used in the NNLO calculations. The calculations are performed using both the fewz 3.1 [38] and dynnlo 1.0 [47, 48] MC tools. The NLO prediction based on fewz 3.1 is also shown here. The HERAPDF1.5 PDF uncertainties are shown by the shaded (NLO) and hatched (NNLO) bands.

Figure 9

Comparison of this measurement to the previous CMS electron charge asymmetry result [12]. Results are shown for lepton $p_{\mathrm{T}}>35\mathrm{GeV}$.

Figure 10

Comparison of the measured muon charge asymmetry to theoretical predictions based on the fewz 3.1 [38] and resbos [49, 50, 51, 52] tools. The NLO CT10 PDF is used in both predictions. Results are shown for muon $p_{\mathrm{T}}>25$ (a) and muon $p_{\mathrm{T}}>35\mathrm{GeV}$ (b). The CT10 PDF uncertainty is shown by the shaded bands.

Figure 11

Distributions of $u$ valence (top) and $d$ valence (bottom) quarks as functions of $x$ at the scale $Q^2=m_W^2$. The results of the 13-parameter fixed-$s$ fit to the HERA data and muon asymmetry measurements (light shaded band), and to HERA only (dark hatched band) are compared. The total PDF uncertainties are shown. In the bottom panels the distributions are normalized to one for a direct comparison of the uncertainties. The change of the PDFs with respect to the HERA-only fit is represented by a solid line.

Figure 12

Parton distribution functions, shown as functions of $x$, obtained by using HERA DIS data and CMS measurements of $W$-boson production in the free-$s$ NLO QCD analysis. Gluon, valence, and sea distributions are presented at the starting scale $Q_0^2=1.9{\mathrm{GeV}}^2$ of the PDF evolution (top) and the mass squared of the $W$ boson (bottom). The sea distribution is defined as $\mathrm{\Sigma }=2·(\overline{u}+\overline{d}+\overline{s})$. The full band represents the total uncertainty. The individual contributions from the experimental, model, and parametrization uncertainties are represented by the bands of different shades. The gluon and sea distributions are scaled down by a factor of 20.

Figure 13

Antistrange-quark distribution $\overline{s}(x,Q)$ and the ratio $R_s(x,Q)$, obtained in the QCD analysis of HERA and CMS data, shown as functions of $x$ at the scale $Q^2=1.9{\mathrm{GeV}}^2$ (top) and $Q^2=m_W^2$ (bottom). The full band represents the total uncertainty. The individual contributions from the experimental, model, and parametrization uncertainties are represented by the bands of different shades.