Measurement of the Polarization of $W$ Bosons with Large Transverse Momenta in $W+\mathbf{\text{jets}}$ Events at the LHC

A first measurement of the polarization of $W$ bosons with large transverse momenta in $pp$ collisions is presented. The measurement is based on $36{\mathrm{pb}}^{-1}$ of data recorded at $\sqrt{s}=7\mathrm{TeV}$ by the CMS detector at the LHC. The left-handed, right-handed, and longitudinal polarization fractions ($f_L$, $f_R$, and $f_0$, respectively) of $W$ bosons with transverse momenta larger than 50 GeV are determined by using decays to both electrons and muons. The muon final state yields the most precise measurement: $(f_L-f_R{)}^{-}=0.240\pm 0.036(\mathrm{stat})\pm 0.031(\mathrm{syst})$ and $f_0^{-}=0.183\pm 0.087(\mathrm{stat})\pm 0.123(\mathrm{syst})$ for negatively charged $W$ bosons and $(f_L-f_R{)}^{+}=0.310\pm 0.036(\mathrm{stat})\pm 0.017(\mathrm{syst})$ and $f_0^{+}=0.171\pm 0.085(\mathrm{stat})\pm 0.099(\mathrm{syst})$ for positively charged $W$ bosons. This establishes, for the first time, that $W$ bosons produced in $pp$ collisions with large transverse momenta are predominantly left-handed, as expected in the standard model.

Figure 1

Fit results using $36{\mathrm{pb}}^{-1}$ of collision data for the $L_P(e^{-})$ (top) and $L_P(e^{+})$ (bottom) distributions. The left-handed, right-handed, and longitudinal $W$ components, with normalization as determined by the fit, are represented by the dashed, dotted, and dash-dotted lines, respectively. The shaded distributions show the QCD and electroweak (EWK) backgrounds. The solid line represents the sum of all individual components and can be directly compared with the data distribution (circles).

Figure 2

Fit results using $36{\mathrm{pb}}^{-1}$ of collision data for the $L_P({\mu }^{-})$ (top) and $L_P({\mu }^{+})$ (bottom) distributions. The left-handed, right-handed, and longitudinal $W$ components, with normalization as determined by the fit, are represented by the dashed, dotted, and dash-dotted lines, respectively. The shaded distribution shows the EWK backgrounds. The solid line represents the sum of all individual components and can be directly compared with the data distribution (circles).

Figure 3

The muon fit result (black dot) in the $[(f_L-f_R),f_0]$ plane for negatively charged (top) and positively charged (bottom) leptons. The 68% confidence level contours for the statistical and total uncertainties are shown by the green shaded region and the black contour, respectively. The disallowed region is hatched.