Electroweak Precision Observables, New Physics and the Nature of a 126 GeV Higgs Boson

TL;DR

This work updates the electroweak precision observable fit in light of a $m_h\approx125$–GeV Higgs, using a Bayesian framework to constrain New Physics through oblique parameters $(S,T,U)$, the $\epsilon_{1,2,3,b}$ set, nonuniversal $Zb\bar b$ vertex corrections, and a nonstandard Higgs–vector coupling. It also translates EWPO into bounds on a complete set of dimension-six operators, finding that NP scales are typically in the $10$–$15$ TeV range and that the data strongly favor either an elementary Higgs or a composite Higgs complemented by additional states to maintain agreement with EWPO. The results underscore the continued power of EWPO to probe the mechanism of electroweak symmetry breaking and to constrain models addressing the hierarchy problem, even after direct NP searches have so far found no signals. The analysis also emphasizes the need for independent cross-checks of recently computed two-loop fermionic corrections to $Zf\bar f$ vertices to solidify NP constraints.

Abstract

We perform the fit of electroweak precision observables within the Standard Model with a 126 GeV Higgs boson, compare the results with the theoretical predictions and discuss the impact of recent experimental and theoretical improvements. We introduce New Physics contributions in a model-independent way and fit for the S, T and U parameters, for the $ε_{1,2,3,b}$ ones, for modified $Zb\bar{b}$ couplings and for a modified Higgs coupling to vector bosons. We point out that composite Higgs models are very strongly constrained. Finally, we compute the bounds on dimension-six operators relevant for the electroweak fit.

Figures (12)

• Figure 1: Comparisons between the direct measurement and the posterior probability distributions for the input parameters in the SM fit, together with their indirect determinations from the EWPO measurements, obtained by assuming a flat prior for the single parameter under consideration. Using the results of ref. Freitas:2012syfreitasprivate and introducing the parameters $\delta \rho_Z^{\nu,\ell,b}$, the subleading two-loop fermionic EW corrections to $\rho_Z^f$ have been taken into account in the plots, except for the bottom-centre and bottom-right plots, in which the corrections have been omitted. Here and in the following, the dark (light) regions correspond to $68\%$ ($95\%$) probability. In the bottom-right plot, we report the indirect determinations of the Higgs mass excluding the observables $M_W$, $\Gamma_Z$, $P_\tau^{\rm pol}$, $\mathcal{A}_l$ and $A_{\rm FB}^{0,b}$, except for the one specified in each row. The vertical blue (red) band represents the one obtained from the the fit with all the observables (from the direct measurement). We assume a flat prior for the Higgs mass ranging from 10 MeV to 1 TeV.
• Figure 2: Compatibility plots of $M_W$, $\mathcal{A}_\ell$ and $A_{\rm FB}^{0,b}$. Any direct measurement corresponds to a point in the (central value, experimental error) plane, and its compatibility with the indirect determination is given in numbers of standard deviations by the color coding. The present experimental result is indicated by a star.
• Figure 3: Compatibility plot of $R_b^0$ computed using the results of ref. Freitas:2012sy (left) or the large $m_t$ expansion for the two-loop fermionic EW corrections to $\rho_Z^f$ (right).
• Figure 4: Left: Two-dimensional probability distribution for the oblique parameters $S$ and $T$ obtained from the fit with $S$, $T$, $U$ and the SM parameters, with the large-$m_t$ expansion for the two-loop fermionic EW corrections to $\rho_Z^f$. Center: Two-dimensional probability distribution for the oblique parameters $S$ and $T$ obtained from the fit with $S$, $T$ and the SM parameters with $U=0$, with the large-$m_t$ expansion for the two-loop fermionic EW corrections to $\rho_Z^f$. The individual constraints from $M_W$, the asymmetry parameters $\sin^2\theta_{\rm eff}^{\rm lept}$, $P_\tau^{\rm pol}$, $A_f$ and $A_{\rm FB}^{0,f}$ with $f=\ell,c,b$, and $\Gamma_Z$ are also presented, corresponding to the combinations of parameters $A$, $B$ and $C$ in eq. (\ref{['eq:abc']}). Right: Same as center, but using the results of ref. Freitas:2012syfreitasprivate. In this case, the constraint from $\Gamma_Z$ cannot be used.
• Figure 5: Two-dimensional probability distributions for $\epsilon_1$ and $\epsilon_3$ in the fit, with floating $\epsilon_{1,2,3,b}$ (left), or with assuming $\epsilon_2=\epsilon_2^{\rm SM}$ and $\epsilon_b=\epsilon_b^{\rm SM}$ (right). In the left plot, the effect of non-universal vertex corrections is presented. In the right plot, we also show the impact of different constraints. The SM prediction at 95% is denoted by a point with an error bar.