Indirect measurement of $\sin^2 θ_W$ (or $M_W$) using $μ^+μ^-$ pairs from $γ^*/Z$ bosons produced in $p\bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV

TL;DR

This paper presents a precise indirect measurement of the electroweak mixing parameters by analyzing the forward-backward asymmetry of μ+μ− pairs from Drell–Yan processes in p p̄ collisions at 1.96 TeV. By modeling the angular distribution in the Collins–Soper frame and incorporating electroweak radiative corrections through zfitter into NLO QCD predictions, the authors extract sin^2 θ_eff and infer sin^2 θ_W and M_W using an on-shell renormalization framework. The analysis combines a rigorously calibrated muon system, data-driven background corrections, and resolution unfolding, yielding sin^2 θ_eff = 0.2315(9)(4) and sin^2 θ_W = 0.2233(8)(4), corresponding to M_W = 80.365(43)(19) GeV/c^2, consistent with LEP-1/SLD and previous Tevatron results. This work demonstrates a robust methodology for indirect electroweak parameter extraction using hadron-collider data with state-of-the-art EW/QCD corrections and detailed systematics treatment.

Abstract

Drell-Yan lepton pairs are produced in the process $p\bar{p} \rightarrow μ^+μ^- + X$ through an intermediate $γ^*/Z$ boson. The forward-backward asymmetry in the polar-angle distribution of the $μ^-$ as a function of the invariant mass of the $μ^+μ^-$ pair is used to obtain the effective leptonic determination $\sin^2 θ^{lept}_{eff}$ of the electroweak-mixing parameter $\sin^2 θ_W$, from which the value of $\sin^2 θ_W$ is derived assuming the standard model. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.2 fb-1 of integrated luminosity from $p\bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of $\sin^2 θ^{lept}_{eff}$ is found to be 0.2315 +- 0.0010, where statistical and systematic uncertainties are combined in quadrature. When interpreted within the context of the standard model using the on-shell renormalization scheme, where $\sin^2 θ_W = 1 - M_W^2/M_Z^2$, the measurement yields $\sin^2 θ_W$ = 0.2233 +- 0.0009, or equivalently a W-boson mass of 80.365 +- 0.047 GeV/c^2. The value of the W-boson mass is in agreement with previous determinations in electron-positron collisions and at the Tevatron collider.

Figures (18)

• Figure 1: Collins-Soper coordinate axes $(x,z)$ in the lepton-pair rest frame, along with the laboratory $z$ axis ($z_{lab}$). The three axes are in the plane formed by the proton ($\vec{P}_{\rm A}$) and antiproton ($\vec{P}_{\rm B}$) momentum vectors within the rest frame. Relative to the laboratory $z$ axis, the transverse component of $-(\vec{P}_{\rm A}+\vec{P}_{\rm B})$ is the same as the transverse-momentum vector of the lepton pair in the laboratory ($\vec{P}_{\rm T}$).
• Figure 2: Muon-pair invariant mass distributions. The upper set of crosses is the background-subtracted data, the middle set of crosses is the EWK background, and the lower set of crosses is the QCD background (same-charge muon pairs). The EWK background is derived from simulation.
• Figure 3: Typical dependence of $A_{\rm fb}$ as a function of the lepton-pair invariant mass. The curve is an analytic calculation. The vertical line is at $M = M_Z$.
• Figure 4: Distribution of $C^+$ for SS pairs in the central $\eta$ region of $(-0.3,0)$. The crosses are the data, and the solid histogram is the generator-level distribution normalized to the data.
• Figure 5: Distribution of $C^+$ for OS pairs in the central $\eta$ region of $(-0.3,0)$. The crosses are the data, and the solid histogram is the generator-level distribution normalized to the data.