[Paper Review] Precision Measurements of Electroweak Parameters with Z Bosons at the Tevatron

A. Bodek|arXiv (Cornell University)|Dec 27, 2015

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents precision measurements of the effective electroweak mixing angle, $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z)$, and an indirect determination of the W boson mass using dilepton events from proton-antiproton collisions at the Tevatron. By applying advanced calibration, event weighting, and PDF constraint techniques, the CDF and D0 collaborations achieve sub-0.0005 uncertainty, yielding $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z) = 0.23222 \pm 0.00046$ (CDF) and $0.23146 \pm 0.00047$ (D0), with an indirect $M_W = 80.327 \pm 0.023$ GeV, consistent with the Standard Model but highlighting persistent tension with direct $M_W$ measurements.

ABSTRACT

We report on the extraction of $\\sin^2\ heta^{\ m lept}_{\ m eff}(M_Z)$ and an indirect measurement of the mass of the W boson from the forward-backward asymmetry of dilepton events in the $Z$ boson mass region at the Tevatron. The data samples of $e^+e^-$ and $\\mu^+\\mu^-$ events collected by the CDF detector correspond to the full 9.4 fb$^{-1}$ run II sample and yield an effective electroweak mixing angle $\\sin^2\ heta^{\ m lept}_{\ m eff}(M_Z) = 0.23222 \\pm 0.00046$. The corresponding result reported by the D0 collaboration with the full 9.4 fb$^{-1}$ $e^+e-$ sample is $\\sin^2\ heta^{\ m lept}_{\ m eff}(M_Z) = 0.23146 \\pm 0.00047$. The CDF collaboration also extracts the on-shell electroweak mixing angle $ \\sin^2 \ heta_W = 0.22401 \\pm 0.00044$ which corresponds to an indirect measurement of the W boson mass $M_W ({\ m indirect}) = 80.327 \\pm 0.023 \\;{\ m GeV}$. The quoted uncertainties include both statistical and systematic contributions.

Motivation & Objective

• To resolve the 3.2σ tension between high-precision LEP-1 and SLD measurements of $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z)$ by obtaining new, competitive measurements at the Tevatron.
• To improve the precision of the indirect W boson mass measurement using forward-backward asymmetry in dilepton events near the Z pole.
• To reduce systematic uncertainties in electroweak parameter extraction by implementing advanced calibration, event weighting, and PDF constraint techniques.
• To test the consistency of the Standard Model with the known Higgs boson mass by comparing indirect $M_W$ predictions with direct measurements.
• To provide a robust, PDF-uncertainty-suppressed measurement of $\sin^2\theta_{W}$ using $A_{\rm fb}$-constrained PDF replicas.

Proposed method

• A new detector energy scale calibration technique was applied to muons and electrons, varying with pseudorapidity $\eta$, azimuthal angle $\phi$, and charge, reducing systematic uncertainties.
• An event weighting method was used to cancel acceptance and efficiency uncertainties by measuring the $\cos\theta$ coefficient $A_4$, with additional weights for antiquark dilution to eliminate rapidity dependence.
• The Z fitter Effective Born Approximation (EBA) electroweak radiative corrections were implemented in POWHEG and RESBOS simulations to enable simultaneous extraction of $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z)$ and $\sin^2\theta_W = 1 - M_W^2/M_Z^2$.
• A $\chi^2$-weighting technique was applied to PDF replicas (nnpdf3.0 nnlo), reducing PDF uncertainty in $\sin^2\theta_W$ by 20% by down-weighting replicas inconsistent with the $A_{\rm fb}(M)$ data.
• The forward-backward asymmetry $A_{\rm fb}(M)$ was extracted from dilepton events in the Z boson mass region, with $A_{\rm fb} = 3A_4/8$, and used to constrain $\sin^2\theta_{W}$.
• The analysis used the full 9.4 fb$^{-1}$ Tevatron Run II data sample from CDF and D0, with combined statistical and systematic uncertainties.

Experimental results

Research questions

• RQ1 Can the Tevatron achieve sub-0.0005 precision in $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z)$ to resolve the tension between LEP-1 and SLD measurements?
• RQ2 To what extent can $A_{\rm fb}$-constrained PDF replicas reduce PDF-related uncertainties in $\sin^2\theta_W$ and $M_W$?
• RQ3 How do the indirect $M_W$ measurements from dilepton asymmetries compare with direct $M_W$ measurements and SM predictions given $M_H = 125.6$ GeV?
• RQ4 Can advanced calibration and weighting techniques suppress systematic uncertainties to the level of SLD and LEP-1 experiments?
• RQ5 Does the combination of Tevatron $M_W^{\rm indirect}$ with updated $M_t$ values from LHC experiments increase the tension with the SM prediction?

Key findings

• The CDF collaboration measured $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z) = 0.23222 \pm 0.00046$, with uncertainties including both statistical and systematic contributions.
• The D0 collaboration measured $\sin^2\theta^{\rm lept}_{\rm eff}(M_Z) = 0.23146 \pm 0.00047$ using the full 9.4 fb$^{-1}$ $e^+e^-$ sample.
• The CDF collaboration extracted the on-shell $\sin^2\theta_W = 0.22401 \pm 0.00044$, corresponding to an indirect $M_W = 80.327 \pm 0.023$ GeV.
• The $\chi^2$-weighting technique reduced the PDF uncertainty in $\sin^2\theta_W$ by 20% compared to standard PDF sets.
• The indirect $M_W$ measurement is consistent with the Standard Model prediction of $M_W \approx 80.327$ GeV, but lies 1.5σ above the SM prediction when combined with the world average $M_t$.
• The results show a 2σ tension between the 2015 CMS $M_t$ measurement and earlier Tevatron $M_t$ values, which would further increase the discrepancy in $M_W$ if confirmed.