The Effective Standard Model after LHC Run I

TL;DR

The paper treats the Standard Model as the low-energy limit of an EFT with dimension-6 operators, encoded by coefficients $\bar{c}_i$, and combines electroweak precision tests with Higgs data, associated-Higgs production kinematics, and triple-gauge couplings to derive model-independent limits after LHC Run I. It develops an expansion formalism that goes beyond $S$ and $T$ to map the full operator basis into observables, and demonstrates the complementarity of LEP EWPTs, Tevatron/Higgs measurements, and LHC TGC data. The authors quantify constraints on a broad set of operators, showing that some coefficients are best constrained by TGCs while others by Higgs data, and they provide first complete bounds on $\bar{c}_{3W}$; they also illustrate the approach with a 2HDM UV completion. The analysis emphasizes that the SM remains an effective theory with multi-TeV sensitivity to many dimension-6 operators, and it outlines how Run II data will further sharpen these constraints while probing the EFT's validity in higher-energy regimes.

Abstract

We treat the Standard Model as the low-energy limit of an effective field theory that incorporates higher-dimensional operators to capture the effects of decoupled new physics. We consider the constraints imposed on the coefficients of dimension-6 operators by electroweak precision tests (EWPTs), applying a framework for the effects of dimension-6 operators on electroweak precision tests that is more general than the standard $S,T$ formalism, and use measurements of Higgs couplings and the kinematics of associated Higgs production at the Tevatron and LHC, as well as triple-gauge couplings at the LHC. We highlight the complementarity between EWPTs, Tevatron and LHC measurements in obtaining model-independent limits on the effective Standard Model after LHC Run~1. We illustrate the combined constraints with the example of the two-Higgs doublet model.

Figures (10)

• Figure 1: Results of a $\chi^2$ analysis of $ST$ parameters in EWPTs using the expansion formalism of wellsandzhang. The dotted, dashed and solid contours denote the regions allowed at the $68\%, 95\%,$ and $99\%$ CL, respectively, which may be compared with those of 1209.2716.
• Figure 2: The 95% CL ranges found in analyses of the leptonic observables (left panel) and including also the hadronic observables (right panel). In each case, the upper (green) bars denote single-coefficient fits, and the lower (red) bars denote multi-coefficient fits. The upper-axis should be read $\times \frac{m_W}{v}\sim 1/3$ for $\bar{c}_W + \bar{c}_B$.
• Figure 3: The same-flavour $p_T$ distribution of the leading lepton after the TGC analysis cuts for ATLAS at 8 TeV. The Standard Model distribution is shown in blue with solid lines, and the effect of $\bar{c}_{HW} = 0.1$ is superimposed in green with dashed lines.
• Figure 4: Comparisons between the $\chi^2$ functions from fits to the same-flavour ATLAS distribution including only linear (solid lines) and also quadratic (dashed lines) dependences on the dimension-6 coefficients $\bar{c}_{HW}$ (left panel) and $\bar{c}_{3W}$ (right panel).
• Figure 5: Comparisons of the constraints on the dimension-6 coefficients $\bar{c}_{W}$, $\bar{c}_{HW}$ and $\bar{c}_{HB}$ (top row), $\bar{c}_{g}$, $\bar{c}_{\gamma}$ and $\bar{c}_{3W}$ (middle row), and $\bar{c}_{b}$, $\bar{c}_{t}$ and $\bar{c}_{H}$ (bottom row) provided by the LHC signal-strength data together with the ATLAS 8-TeV (purple lines), the CMS 7- and 8-TeV TGC measurements (blue lines) and their combination (red lines).