We ask for explanations for

• unification of Standard Model and general relativity,
• dark matter and dark energy,
• large matter antimatter asymmetry,
• cosmic inflation,
• …

Can the Higgs boson provide a glimpse on, or direction to these problems?

Higgs boson is an essential (residual) particle from EWSB in the SM. It unitarizes longitudinal WW boson scattering. Its mass, as a scalar particle, is sensitive to UV physics.

• Is the SM Higgs boson solely responsible for EWSB?

• We need precise predictions to interpret data: test SM-only hypothesis, constrain BSM models.
  • Methods to quantify deviations
• We should focus on the most promising kinematical regions.
  • High Higgs transverse momenta (\(p_T\))

• modify SM couplings (rescale parameters and couplings)
• effective field theory (new Lorentz structures)
• simplified models, UV complete theories

Parametrize Higgs-gluon coupling by dim.-7 operators (Gracey '02; Neill '09; Germer '07)

\[\begin{multline*} \mathcal{L}_{eff}=\frac{\color{black}{C_{1}}}{\color{red}{\Lambda}}HF_{\mu\nu}^{a}F^{a\,\mu\nu} +\frac{\color{black}{C_{2}}}{\color{red}{\Lambda^{3}}}HD_{\alpha}F_{\mu\nu}^{a}D^{\alpha}F^{a\,\mu\nu}+\frac{\color{black}{C_{3}}}{\color{red}{\Lambda^{3}}}HF_{\nu}^{a\,\mu}F_{\sigma}^{b\,\nu}F_{\mu}^{c\,\sigma}f^{abc}\\ +\frac{\color{black}{C_{4}}}{\color{red}{\Lambda^{3}}}HD^{\alpha}F_{\alpha\nu}^{a}D_{\beta}F^{a\,\beta\nu}+\frac{\color{black}{C_{5}}}{\color{red}{\Lambda^{3}}}HF_{\alpha\nu}^{a}D^{\nu}D^{\beta}F_{\beta}^{a\,\alpha} \\ \equiv \frac{\color{black}{C_{1}}}{\color{red}{\Lambda}} \mathcal{O}_1 + \frac{\color{black}{C_{2}}}{\color{red}{\Lambda^3}} \mathcal{O}_2 + \frac{\color{black}{C_{3}}}{\color{red}{\Lambda^3}} \mathcal{O}_3 + \frac{\color{black}{C_{4}}}{\color{red}{\Lambda^3}} \mathcal{O}_4 + \frac{\color{black}{C_{5}}}{\color{red}{\Lambda^3}} \mathcal{O}_5 \end{multline*} \]

• Compute kinematical distributions

Normalization to corresponding part of cross-section: only shape matters here; coefficients \(C_i\) a priori unknown. (Harlander, Neumann '13)

• About 1% error for total inclusive cross-section (NNLO):
  • asymptotic expansions (Harlander, Ozeren '09; Pak, Rogal, Steinhauser '09)
  • exact high energy limit (Marzani, Ball, Del Duca, Forte, Vincini '08 '09; Harlander, Mantler, Marzani, Ozeren '10; Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld '03)

\[ F(\Gamma) \to \sum_\gamma \mathcal{T} F(\gamma) \star F(\Gamma\backslash\gamma) \]

• Two loop diagram (\(\hat{s}, m_H^2, m_t^2\)) reduces to tadpole integrals with vanishing external momenta and massless integrals
• Automatized setup expq2e (Harlander, Seidensticker, Steinhauser '98; Steinhauser '01)

• LO studies (Ellis, Hinchliffe, Soldate '88; Baur, Glover '90; Del Duca, Kilgore, Oleari, Schmidt, Zeppenfeld '01; Alwall, Li, Maltoni '12; Bagnaschi, Degrassi, Slavich, Vicini '12)

• Our goal was to estimate effects and assess the validty of the HTL
  (Harlander, TN, Ozeren, Wiesemann '12; TN, Wiesemann '14)
  

• We can improve the prediction, if the asymptotic expansion "converges"
  

• just asymptotic expansion in two loop virtual corrections

• massive one loop real emission contributions exactly (H + 4 partons)

• Unitarity cuts pioneered in the mid 90's (Bern, Dixon, Dunbar, Kosower '94)
• Generalized unitarity: multiple cuts, complex momenta, D dimensions
  (Britto, Cachazo, Feng '05; Anastasiou, Britto, Feng, Kunszt, Mastrolia '06; Forde '07;)
• lead to the NLO one-loop revolution: i.e. BlackHat, GoSam, HelacNLO, MadLoop, OpenLoops, Rocket, …

• Generalized unitarity: multiple cuts, complex momenta, D dimensions
  (Britto, Cachazo, Feng '05; Anastasiou, Britto, Feng, Kunszt, Mastrolia '06; Forde '07;)
  

• lead to the NLO one-loop revolution: i.e. BlackHat, GoSam, HelacNLO, MadLoop, OpenLoops, Rocket, …

• Our setup: S@M (Maître, Mastrolia '07) + boxes, triangles (rat pieces) via D-dim gen. unitarity (Badger '09), bubbles via Stokes' Theorem spinor-integration (Mastrolia '09)

• similar recent study "green curve with parton showers": Frederix, Frixione, Vryonidou, Wiesemann '16

(Neumann, Williams 1605.XXXXX)

• "fix" LO virt interference, check scale dependence
• consider other observables (jet \(p_T\), jet inclusive, Higgs \(p_T\) inclusive, etc.)
• take into account NNLO K-factor (or similar)
• consider improvements for BSM searches (?)