The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC

TL;DR

The paper performs a global electroweak fit of the Standard Model after the LHC discovery of a new boson, treating it as the SM Higgs and overconstraining the theory with precision EW data. It uses state-of-the-art theoretical calculations (NNLO QCD, two-loop EW, updated $R^0_b$, and modern fermion couplings) and incorporates direct Higgs mass measurements to constrain the model. The results yield a p-value of $0.07$ for the SM fit, an indirect Higgs mass of $M_H=94^{+25}_{-22}$ GeV, and precise predictions for $M_W$ and $\sin^2\theta^{\ell}_{\rm eff}$ that agree with direct measurements, while also obtaining an indirect top mass of $m_t=175.8^{+2.7}_{-2.4}$ GeV. The analysis confirms the SM's consistency with electroweak data at the current level, though small tensions persist and future data will further test the model.

Abstract

In view of the discovery of a new boson by the ATLAS and CMS Collaborations at the LHC, we present an update of the global Standard Model (SM) fit to electroweak precision data. Assuming the new particle to be the SM Higgs boson, all fundamental parameters of the SM are known allowing, for the first time, to overconstrain the SM at the electroweak scale and assert its validity. Including the effects of radiative corrections and the experimental and theoretical uncertainties, the global fit exhibits a p-value of 0.07. The mass measurements by ATLAS and CMS agree within 1.3sigma with the indirect determination M_H=(94 +25 -22) GeV. Within the SM the W boson mass and the effective weak mixing angle can be accurately predicted to be M_W=(80.359 +- 0.011) GeV and sin^2(theta_eff^ell)=(0.23150 +- 0.00010) from the global fit. These results are compatible with, and exceed in precision, the direct measurements. For the indirect determination of the top quark mass we find m_t=(175.8 +2.7 -2.4) GeV, in agreement with the kinematic and cross-section based measurements.

Figures (5)

• Figure 1: Result of a pseudo MC analysis of the complete electroweak fit. Shown are distributions of the $\chi^2_{{\rm min}}$ test statistics obtained from a pseudo MC simulation with varying (hatched histogram) and fixed theoretical uncertainty parameters ($\delta_{\rm th}\xspace$) in the fit (shaded/green histogram). The $\chi^2_{{\rm min}}$ obtained in the complete fit to data is indicted by the arrow together with the $p$-values found for these two cases. Also shown is an idealised $\chi^2$ function assuming a Gaussian case with 14 degrees of freedom (solid black line).
• Figure 2: Left: pull comparison of the fit results with the direct measurements in units of the experimental uncertainty. Right: determination of $M_H$ excluding the direct $M_H$ measurements and all the sensitive observables from the fit, except the one given. Note that the fit results shown are not independent.
• Figure 3: $\Delta\chi^2\xspace$ profiles as a function of the Higgs mass (top left), the top quark mass (top right), the $W$ boson mass (bottom left) and the effective weak mixing angle (bottom right). The data points placed along $\Delta\chi^2\xspace=1$ represent direct measurements of the respective observable and their $\pm 1\sigma$ uncertainties. The grey (blue) bands show the results when excluding (including) the new $M_H$ measurements from (in) the fits. For the blue bands as a function of $m_t$, $M_W$ and $\sin\!^2\theta^{\ell}_{{\rm eff}}$ the direct measurements of the observable have been excluded from the fit in addition (indirect determination). The solid black curves in the lower plots represent the SM prediction for $\sin\!^2\theta^{\ell}_{{\rm eff}}$ and $M_W$ derived from the minimal set of input measurements, as described in the text. In all figures the solid (dotted) lines illustrate the fit results including (ignoring) theoretical uncertainties in the fit.
• Figure 4: Contours of 68% and 95% CL obtained from scans of fixed $M_W$ and $m_t$. The blue (grey) areas illustrate the fit results when including (excluding) the new $M_H$ measurements. The direct measurements of $M_W$ and $m_t$ are always excluded in the fit. The vertical and horizontal bands (green) indicate the 1$\sigma$ regions of the direct measurements.
• Figure 5: Experimental constraints on the $S$ and $T$ parameters with respect to the SM reference ($M_{H,\rm ref}=126$ GeV and $m_{t,\rm ref}=173$ GeV). Shown are the 68%, 95% and 99% CL allowed regions, where the third parameter $U$ is left unconstrained (orange, left) or fixed to 0 (blue, right). The prediction in the SM is given by the black (grey) area when including (excluding) the new $M_H$ measurements.