Determination of W-boson Properties at Hadron Colliders

TL;DR

The paper tackles the challenge of precisely determining W-boson properties at hadron colliders amid sizable QCD and QED uncertainties. It introduces a ratio-based method that uses measured $Z$-boson observables and perturbative QCD calculations of the W/Z ratio for key leptonic observables, enabling predictions of the W distributions through $A_W=R_O\,A_Z$ with scaled variables $X_O^V={\cal O}^V/M_V$ and $R_O(X_O)$. Across the transverse momentum, transverse mass, and leptonic transverse energy observables, the ratio cancels much of the radiative corrections, yielding small theoretical uncertainties (often sub-percent to a few percent) in the relevant regions, while trading some statistical precision for reduced systematics. The approach is particularly advantageous for high-luminosity runs, offering a robust, perturbatively grounded alternative or supplement to traditional W-property measurements, with potential NNLO enhancements required for some observables. Overall, the method provides a principled framework to constrain W-boson mass and width with improved control over systematic uncertainties using existing Z-boson data.

Abstract

Methods for measuring the W-boson properties at hadron colliders are discussed. It is demonstrated that the ratio between the W- and Z-boson observables can be reliably calculated using perturbative QCD, even when the individual W- and Z-boson observables are not. Hence, by using a measured Z-boson observable and the perturbative calculation of the ratio of the W- over Z-boson observable, we can accurately predict the W-boson observable. The use of the ratio reduces both the experimental and theoretical systematic uncertainties substantially. Compared to the currently used methods it might, at high luminosity, result in a smaller overall uncertainty on the measured W-boson mass and width.

Figures (5)

• Figure 1: a) The ratio $R_{P_T}$ as a function of the scaled vector boson transverse momentum, $X_{P_T}=P_T^V/M_V$, at different orders in $\alpha_S$. The arrow on the left side represent the LO value of the ratio. The solid line and the dashed lines are the result of fits to the order $\alpha_S$ and $\alpha_S^2$ Monte-Carlo calculations. The dotted lines represent the one sigma uncertainty due to the Monte-Carlo integration for the order $\alpha_S^2$ calculation. The uncertainty for the order $\alpha_S$ is smaller and not shown. b) The $K$-factor, $K_{P_T}=R_{P_T}^{(2)}/R_{P_T}^{(1)}$, as a function of $X_{P_T}$ together with the uncertainty range associated with the Monte-Carlo integration.
• Figure 2: a) The $P_T^Z$-distributions for both the CDF CDFZPt and D0 D0ZPt data. The solid line represent the fit to the D0-data as given in ref. D0ZPt. The dotted lines represent a fit to the D0-data uncertainties. b) The $W$-boson CDF-data, along with the perturbative order $\alpha_S$ and $\alpha_S^2$ calculation and the order $\alpha_S^2$ prediction using the ratio method with the D0 $Z$-boson data. The dotted lines represent the uncertainties stemming from the D0-data.
• Figure 3: a) The LO (solid line) and NLO (dashed line) ratio $R_{M_T}$ as a function of the scaled transverse mass $X_{M_T}=M_T^V/M_V$. The leptonic branching fractions are not included. b) The $K$-factor $K_{M_T}=R_{M_T}^{(1)}/R_{M_T}^{(0)}$ as a function of $X_{M_T}$ (solid line), and the K-factor for the $W$ transverse mass (dashed line), normalized to 1 at $X_{MT}=1$. In both case we have included the one sigma uncertainty range associated with the Monte-Carlo integration.
• Figure 4: a) The $K$-factor of the lepton transverse energy distribution for both the $W$-boson (solid line) and $Z$-boson (dashed line). b) The $K$-factor (NLO/LO) for the ratio $\left(d\,\sigma^W/d\,X_{E_T}(\Gamma_W)\right) /\left(d\,\sigma^W/d\,X_{E_T}(\Gamma_W = 5\ \hbox{GeV})\right)$ for different $\Gamma_W$ in the numerator.
• Figure 5: a) The LO (solid line) and NLO (dashed line) ratio $R_{E_T}$ as a function of the lepton scaled transverse energy $X_{E_T}=2\times E_T^V/M_V$. b) The $K$-factor $K_{E_T}=R_{E_T}^{(1)}/R_{E_T}^{(0)}$ as a function of $X_{E_T}$. The dotted lines represent the one sigma uncertainty associated with the Monte Carlo integration.