Decoupling theoretical uncertainties from measurements of the Higgs boson

We develop a technique to present Higgs coupling measurements, which decouple the poorly defined theoretical uncertainties associated to inclusive and exclusive cross section predictions. The technique simplifies the combination of multiple measurements and can be used in a more general setting. We illustrate the approach with toy LHC Higgs coupling measurements and a collection of new physics models.

Figure 1

Likelihood contours for three different Higgs decays: (a) with (solid) and without (dashed) theoretical uncertainties; (b) without theoretical uncertainties for the nominal gluon-fusion cross section (solid) and a shifted value (dashed) estimated from QCD scale variations.

Figure 2

Visualization of $\partial {\mathit{\mu }}^{\mathrm{fix}}/\partial {\alpha }_i$ for the (a) $H\to \gamma \gamma$, (b) $H\to ZZ\to 4\ell$, and (c) $H\to WW\to \ell \nu \ell \nu$ likelihoods.

Figure 3

Comparison of the effective model using different templates with the same local covariance.

Figure 4

Various comparisons of the combined $\gamma \gamma ,ZZ,WW$ likelihoods in the $({\kappa }_V,{\kappa }_F)$ (left) and $({\kappa }_{\gamma },{\kappa }_g)$ (right) planes. Top: comparison of the full combined likelihood, a naive combination with inconsistent profiling and double-counted constraint terms, and the combination of recoupled likelihoods with consistent profiling and without double-counted constraint terms. Bottom: comparison of the full combined likelihood and the combination of recoupled likelihoods using the nominal uncertainties and modified constraint terms with uncertainties inflated by 30%.

Figure 5

Decay-diagonal correlations of signal strengths ${\mu }_{\mathrm{GF},d}$ vs ${\mu }_{\mathrm{VBF},d}$ for $d=\gamma \gamma ,VV,\tau \tau$ in different models. The coupling variation is limited to $\xi <0.4$ and the value $\xi =0.2$ is singled out. The slight deviations from a complete decoupling are discussed in the text.

Figure 6

The sensitivity heuristic $R_i(\xi )$ evaluated for various new physics models and the theoretical uncertainties $i$ associated to the gluon-fusion cross section for $\ge 0$ jets and $\ge 2$ jets.

Figure 7

Comparison of full likelihood (solid) and recouped (dashed) likelihood for scenarios A, B, and C. Scenario C illustrates the impact of using three templates aligned (red), by hand (green), and learning (blue) as described in the text. The top row is based on the nominal Gaussian constraint, and the bottom row shows the result of replacing it with an alternative Rfit constraint term. The effective likelihood with $\alpha =0$ is shown as a dotted line.

Figure 8

Dark singlet: correlated Higgs signal strengths for the decay-diagonal channels (left) and nondiagonal channels (right). The first of the two signal strengths in the notation ${\mu }_{p_1,d_1}-{\mu }_{p_2,d_2}$ is shown on the vertical axis, the second on the horizontal axis. In the lower panels, we give the different signal strengths as a function of ${\mathrm{\Gamma }}_{\mathrm{inv}}/{\mathrm{\Gamma }}_{\mathrm{SM}}={\xi }^2$.

Figure 9

Singlet mixing: correlated Higgs signal strengths for the decay-diagonal channels (left) and nondiagonal channels (right). The first of the two signal strengths in the notation ${\mu }_{p_1,d_1}-{\mu }_{p_2,d_2}$ is shown on the vertical axis, the second on the horizontal axis. In the lower panels, we give the different signal strengths as a function of $\cos \theta =\sqrt{1-{\xi }^2}$.

Figure 10

Composite Higgs: correlated Higgs signal strengths for the decay-diagonal channels (left) and nondiagonal channels (right). The first of the two signal strengths in the notation ${\mu }_{p_1,d_1}-{\mu }_{p_2,d_2}$ is shown on the vertical axis, the second on the horizontal axis. In the lower panels, we give the different signal strengths as a function of $f=v/\xi$.

Figure 11

2HDM: correlated Higgs signal strengths for decay-diagonal channels (left two panels) and nondiagonal channels (right two panels), each for type-I and type-II setups. The first of the two signal strengths in the notation ${\mu }_{p_1,d_1}-{\mu }_{p_2,d_2}$ is shown on the vertical axis, the second on the horizontal axis. In the lower panels, we give the different signal strengths as a function of $\cos (\beta -\alpha )=\xi$.

Figure 12

MSSM: correlated Higgs signal strengths for decay-diagonal channels (left two panels) and nondiagonal channels (right two panels), each for two MSSM benchmark spectra. The first of the two signal strengths in the notation ${\mu }_{p_1,d_1}-{\mu }_{p_2,d_2}$ is shown on the vertical axis, the second on the horizontal axis. In the lower panels, we give the different signal strengths as a function of $m_A$, linked to $\xi$ via Eq. (38).