Measurement of the effective leptonic weak mixing angle

Abstract: Using $pp$ collision data at $\sqrt{s}=13$ TeV, recorded by the LHCb experiment between 2016 and 2018 and corresponding to an integrated luminosity of $5.4$ fb$^{-1}$, the forward-backward asymmetry in the $pp \to Z/\gamma^{*} \to \mu^+\mu^-$ process is measured. The measurement is carried out in ten intervals of the difference between the muon pseudorapidities, within a fiducial region covering dimuon masses between $66$ and $116$ GeV, muon pseudorapidities between $2.0$ and $4.5$ and muon transverse momenta above $20$ GeV. These forward-backward asymmetries are compared with predictions, at next-to-leading order in the strong and electroweak couplings. The measured effective leptonic weak mixing angle is $\sin^2\theta_{\rm eff}^\ell = 0.23147 \pm 0.00044 \pm 0.00005 \pm 0.00023$, where the first uncertainty is statistical, the second arises from systematic uncertainties associated with the asymmetry measurement, and the third arises from uncertainties in the fit model used to extract $\sin^2\theta_{\rm eff}^\ell$ from the asymmetry measurement. This result is based on an arithmetic average of results using the CT18, MSHT20, and NNPDF31 parameterisations of the proton internal structure, and is consistent with previous measurements and with predictions from the global electroweak fit.

• The paper presents a detailed measurement of the effective leptonic weak mixing angle with a reported value of sin²θₑffˡ = 0.23147, including a thorough uncertainty breakdown.
• It utilizes forward-backward asymmetry in Z/γ* → μ⁺μ⁻ events across muon pseudorapidity intervals, comparing results with next-to-leading order predictions.
• The study computes an average using three proton structure models, aligning the results with global electroweak fits and prior measurements.

The paper presents a detailed measurement of the effective leptonic weak mixing angle, an important parameter in the electroweak sector of the Standard Model of particle physics. The study uses data from proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV. This data was collected by the LHCb experiment between 2016 and 2018, with an integrated luminosity of $5.4$ fb$^{-1}$.

The focus of the measurement is on the forward-backward asymmetry in the process $pp \to Z/\gamma^{*} \to \mu^+\mu^-$, which is analyzed across ten intervals of muon pseudorapidity differences. The fiducial region for the analysis includes dimuon masses from 66 to 116 GeV, muon pseudorapidities between 2.0 and 4.5, and muon transverse momenta above 20 GeV.

The results of the asymmetry measurements are compared with next-to-leading order predictions in both strong and electroweak interactions. The effective leptonic weak mixing angle is determined to be $$\sin^2\theta_{\rm eff}^\ell = 0.23147 \pm 0.00044 \pm 0.00005 \pm 0.00023$$, with the uncertainties broken down as follows:

• The first uncertainty is statistical, reflecting the inherent variability in the data.
• The second is due to systematic uncertainties from the asymmetry measurement process.
• The third arises from uncertainties in the fit model used to determine the mixing angle from the measured asymmetries.

This result is derived as an arithmetic average using three different parameterizations for the proton's internal structure: CT18, MSHT20, and NNPDF31. The finding aligns with previous measurements and the predictions from the global electroweak fit, providing further validation of the existing theoretical framework.