Measurements of $W$ and $Z/{\gamma }^{*}$ cross sections and their ratios in $p+p$ collisions at RHIC

We report on the $W$ and $Z/{\gamma }^{*}$ differential and total cross sections as well as the $W^{+}/W^{-}$ and $(W^{+}+W^{-})/(Z/{\gamma }^{*})$ cross section ratios measured by the STAR experiment at RHIC in $p+p$ collisions at $\sqrt{s}=500\mathrm{GeV}$ and 510 GeV. The cross sections and their ratios are sensitive to quark and antiquark parton distribution functions. In particular, at leading order, the $W$ cross section ratio is sensitive to the $\overline{d}/\overline{u}$ ratio. These measurements were taken at high $Q^2\sim M_W^2,M_Z^2$ and can serve as input into global analyses to provide constraints on the sea quark distributions. The results presented here combine three STAR datasets from 2011, 2012, and 2013, accumulating an integrated luminosity of $350{\mathrm{pb}}^{-1}$. We also assess the expected impact that our $W^{+}/W^{-}$ cross section ratios will have on various quark distributions, and find sensitivity to the $\overline{u}-\overline{d}$ and $\overline{d}/\overline{u}$ distributions.

Figure 1

Signal and background $E_T^e$ distributions for positron (a) and electron (b) candidates in the BEMC. The background contributions are shown as stacked histograms, where the solid blue and brown diagonal histograms correspond to the electroweak residual backgrounds from $Z\to ee$ and $W\to \tau \nu$ decay channels, respectively. The vertical cyan and diagonal green histograms correspond to the residual QCD contributions estimated from the data driven and second EEMC methods, respectively. The red dashed histogram shows the $W\to e\nu$ signal along with all estimated background contributions and is compared to the data, the black markers. The vertical error bar on the data represents the statistical uncertainty and the horizontal bar shows the bin width.

Figure 2

Signal and background signed-$p_T$ balance distributions for positron (a) and electron (b) candidates in the EEMC. The background contributions are shown as stacked histograms, where the solid blue and brown diagonal histograms correspond to the electroweak residual backgrounds from $Z\to ee$ and $W\to \tau \nu$ decay channels, respectively. The vertical cyan histograms correspond to the residual QCD contributions estimated from the data driven method. The red dashed histogram shows the $W\to e\nu$ signal along with all estimated background contributions and is compared to the data, the black markers. The vertical error bar on the data represents the statistical uncertainty and the horizontal bar shows the bin width.

Figure 3

Panel (a) shows the distribution of the reconstructed invariant mass from $Z$ decay candidates compared to $Z/{\gamma }^{*}\to e^{+}{e}^{-}$ MC distribution. Panel (b) shows the number of $Z$ candidate events plotted against the reconstructed rapidity and compared to the MC distribution. The red dashed histogram shows the $Z\to e^{+}{e}^{-}$ MC signal and is compared to the data, the black markers. The vertical error bar on the data represents the statistical uncertainty and the horizontal bar shows the bin width. The asymmetry in the MC between negative and positive $y_Z$ in (b) can be attributed to the rapidity asymmetry in the efficiencies, seen in Fig. 6, since these events have not yet been corrected for detector and cut efficiencies.

Figure 4

A four-Gaussian function fit to measured $0.0<{\eta }_e<0.25$ BEMC $Q_e·E_T^e/p_T$ distribution using the log-likelihood method. The colored lines show individual $e^{+}$ (red dashed) and $e^{-}$ (solid blue) double-Gaussian distributions resulting from the four-Gaussian fit.

Figure 5

Double Gaussian fit to measured EEMC $Q_e·E_T^e/p_T$ distribution using the log-likelihood method. The colored lines show individual $e^{+}$(red dashed) and $e^{-}$(solid blue) Gaussian distributions resulting from the double-Gaussian fit.

Figure 6

Individual dataset efficiencies for: positron (a) and electron (b) $W^{\pm }$ decay candidates plotted as a function of pseudorapidity. Panel (c) shows the $e^{-}/e^{+}$ efficiency ratio vs pseudorapidity. Panel (d) shows the efficiency for $Z$ decay candidates vs rapidity.

Figure 7

The measured $d{\sigma }_{W^{+}}^{\mathrm{fid}}/d{\eta }_{e^{+}}$ (closed circle markers) and $d{\sigma }_{W^{-}}^{\mathrm{fid}}/d{\eta }_{e^{-}}$ (closed triangle markers) for the combined datasets (2011–2013) are plotted as a function of ${\eta }_e$. The bottom panel shows $d{\sigma }_{W^{-}}^{\mathrm{fid}}/d{\eta }_{e^{-}}$ when zooming in on the vertical axis. FEWZ [47] was used to compare various NLO PDF sets (CT14MC2nlo [56], CJ15 [57], MMHT14 [58], nnpdf3.1 [59], and JAM19 [60]) to the measured differential cross sections.

Figure 8

The measured $d{\sigma }_Z^{\mathrm{fid}}/d{y}_Z$ for the combined datasets (2011–2013) is plotted against the $Z$ rapidity, and compared to theory calculations done using FEWZ [47] for several different NLO PDF sets (CT14MC2nlo [56], CJ15 [57], MMHT14 [58], nnpdf3.1 [59], and JAM19 [60]).

Figure 9

The measured total $W^{\pm }$ and $Z$ cross sections for the combined STAR datasets (2011–2013). For clarity the PHENIX measurements are plotted at -5 GeV from $\sqrt{s}=510\mathrm{GeV}$ ($W\to \mu$) and 500 GeV ($W\to e$), respectively. The inset plot in the upper panel highlights the STAR and PHENIX results ($\sqrt{s}\sim 500\mathrm{GeV}$). For the $Z$ cross section, the STAR data uses a mass window of $70\mathrm{GeV}<m_{e^{+}{e}^{-}}<110\mathrm{GeV}$, CT14MC2nlo and CMS use $60\mathrm{GeV}<m_{e^{+}{e}^{-}}<120\mathrm{GeV}$, and ATLAS uses $66\mathrm{GeV}<m_{e^{+}{e}^{-}}<116\mathrm{GeV}$. The dashed lines in the figure show the respective $W^{\pm }$ and $Z$ cross section curves computed using FEWZ and the CT14MC2nlo [56] PDF.

Figure 10

Ratio of the STAR calculated total cross sections to the total cross sections found using the CT14MC2nlo PDF set [48] versus the decay boson’s charge. These comparisons place a mass window of $70\mathrm{GeV}<m_{e^{+}{e}^{-}}<110\mathrm{GeV}$ on the $Z$ cross section. The error bars shown here are the total uncertainties including contributions from the efficiency, luminosity, and PDF uncertainties.

Figure 11

Ratio of fiducial cross sections for production of $W^{+}$ and $W^{-}$ bosons plotted against the decay charged lepton pseudorapidity, ${\eta }_e$, for each of the three datasets: 2011 (black circle), 2012 (blue square), and 2013 (red triangle). For clarity, positions of the data points for the 2011, 2012, and 2013 datasets within each bin are offset by -0.03, 0.0, and 0.03. The error bars correspond to the statistical uncertainty associated with the cross section ratio.

Figure 12

The combined (2011, 2012, and 2013) results for the ratio of the fiducial cross sections for the production of $W^{+}$ and $W^{-}$ bosons plotted against the decay charged letpon pseudorapidity, ${\eta }_e$. The error bars represent the statistical uncertainty, whereas the rectangular boxes represent the systematic uncertainty for the respective data point. These measurements are compared to various theory predictions displayed in the legend.

Figure 13

The combined results for the ratio of the fiducial cross sections for the production of $W^{+}$ and $W^{-}$ bosons compared to the predictions from the original and reweighted CT14MC2nlo PDF [56] predictions. The error bars on the STAR data represent the quadrature sum of the statistical and systematic uncertainties. The blue hatched band represents the CT14MC2nlo PDF uncertainty, while the red band shows the reweighted CT14MC2nlo PDF uncertainty after fitting the STAR data.

Figure 14

The impact of STAR $W^{+}/W^{-}$ data on $\overline{u}-\overline{d}$, $\overline{d}/\overline{u}$, $\overline{d}$, and $\overline{u}$ PDF distributions at $Q=100\mathrm{GeV}$. The solid blue line shows the difference between the reweighted and nominal CT14MC2nlo PDF central value, normalized by the nominal PDF uncertainty. The hatched bands represent the ratio between the reweighted and nominal PDF uncertainties. The black lines represent the nominal PDF uncertainties from the solid blue line.

Figure 15

The measured $(W^{+}+W^{-})/Z$ (red circle marker) for the combined datasets (2011–2013). Compared to this measurement is the $(W^{+}+W^{-})/Z$ computed from the STAR 2009 dataset [31](black square marker), and evaluations using the FEWZ framework [47] and several input NLO PDF sets (MMHT14 [58], CT14MC2nlo [56], nnpdf3.1 [59], CJ15 [57], and JAM19 [60]).