Cross Section and Parity-Violating Spin Asymmetries of $W^{\pm }$ Boson Production in Polarized $p+p$ Collisions at $\sqrt{s}=500\mathrm{GeV}$

Large parity-violating longitudinal single-spin asymmetries $A_L^{e^{+}}=-{0.86}_{-0.14}^{+0.30}$ and $A_L^{e^{-}}={0.88}_{-0.71}^{+0.12}$ are observed for inclusive high transverse momentum electrons and positrons in polarized $p+p$ collisions at a center-of-mass energy of $\sqrt{s}=500\mathrm{GeV}$ with the PHENIX detector at RHIC. These $e^{\pm }$ come mainly from the decay of $W^{\pm }$ and $Z^0$ bosons, and their asymmetries directly demonstrate parity violation in the couplings of the $W^{\pm }$ to the light quarks. The observed electron and positron yields were used to estimate $W^{\pm }$ boson production cross sections for the $e^{\pm }$ channels of $\sigma (pp\to W^{+}X)\times \mathrm{BR}(W^{+}\to e^{+}{\nu }_e)=144.1\pm 21.2(\mathrm{stat}{)}_{-10.3}^{+3.4}(\mathrm{syst})\pm 21.6(\mathrm{norm})\mathrm{pb}$, and $\sigma (pp\to W^{-}X)\times \mathrm{BR}(W^{-}\to e^{-}{\overline{\nu }}_e)=31.7\pm 12.1(\mathrm{stat}{)}_{-8.2}^{+10.1}(\mathrm{syst})\pm 4.8(\mathrm{norm})\mathrm{pb}$.

Figure 1

The spectra of positron (upper panel) and electron (lower panel) candidates before (solid histogram) and after (dashed histogram) an isolation cut. The bands reflect the uncertainty of the background.

Figure 2

Background subtracted spectra of positron (upper panel) and electron (lower panel) candidates before the isolation cut compared to the spectrum of $W$ and $Z$ decays from an NLO calculation [12, 13]. The gray bands reflect the uncertainty of the background.

Figure 3

Inclusive cross sections for $W$ leptonic decay channel of this measurement and $\overline{p}p$ measurements [23, 24, 25, 26]. Statistical and systematic uncertainties were added here in quadrature. The curves are theory calculations [20].

Figure 4

Longitudinal single-spin asymmetries for electrons and positrons from $W$ and $Z$ decays. The error bars represent 68% C.L. The theoretical curves are calculated using NLO with different polarized PDFs [12].