Higgs phenomenology at hadron colliders

1. Decays of the Higgs boson

• A light SM Higgs boson mostly decays into $b\bar b$. Compute the decay rate for $H\rightarrow b\bar b$.
• For a Higgs mass of around 160 !GeV, the main decay mode is $H\rightarrow WW$. Compute the decay rate.

The Higgs branching ratios can be found here​.

You may also have a look at the following Mathematica ​notebook.

2. Gluon fusion and Higgs effective field theory

The computation of the leading order cross-section of a Higgs boson via gluon fusion involves the computation of a top quark loop. In the large top mass limit, the gluon fusion production of a Higgs boson can be described by an effective field theory where the Higgs couples directly to the gluons,

%$\begin{cal}L\end{cal}=C_H\, H\, G_{\mu\nu}^{a\, G_a}{\mu\nu}$,

where $C_H$ is an effective (dimensionful) coupling constant and $G_{\mu\nu}^{a$ denotes the gluon field strength tensor.}

For details on the calculation of the top loop and the effective theory, see the notes and/or check the following Mathematica notebooks (which actually contain much more information):

1. pp>H at LO (1-loop): details of the calculation (Mathematica Notebook) HiggsGG-LO-mtfinite.nb​
2. pp>H at NLO: details of the calculation (Mathematica Notebook) higgsGG-NLO.nb​
3. pp>H at NLO: cross section evaluation for the LHC (Mathematica Notebook+PDF libraries to be compiled) phenHiggs.tar.gz​.

Exercise (DIFFICULT but interesting!!): Use the all the material above to derive the EFT description of a pseudo-scalar Higgs, A,

%$\begin{cal}L\end{cal}=C_A\, A\, G_{\mu\nu}^{a\, {\tilde G}_a}{\mu\nu}$,

where $C_A$ is an effective (dimensionful) coupling constant and $G_{\mu\nu}^{a$ denotes the gluon field strength tensor and %${\tilde G}a}{\mu\nu}=\frac12 \epsilon^{{\mu\nu\rho\sigma} Ga}{\rho\sigma}$ is its dual. Compute the loop amplitude, derive the Feynman rules in the large top mass limit and calculate the LO and NLO cross sections at the LHC.

3. Discover the SM Higgs at the LHC

• Find the best prediction for Higgs production at the LHC ​here.

Choose a channel and investigate signal and background:

1. The 4 lepton final state: $pp \to H\to Z Z \to e^+e- \mu^{+ \mu}-$
   • Signal
     • Events: Parton Level​ Detector Level​
     • Plots: Parton Level​ Detector Level​
   • Background
     • Events: Parton Level​ Detector Level​
     • Plots: Parton Level​ Detector Level​

1. The 2 lepton + missing Et final state: $pp \to H\to W^{+ W}- \to e^{- \bar \nu_e \mu}+ \nu_\mu $
   • Signal
     • Events: Parton Level​ Detector Level​
     • Plots: Parton Level​ Detector Level​
   • Background
     • Events: Parton Level​ Detector Level​
     • Plots: Parton Level​ Detector Level​
2. Top associated production $pp \to t\bar tH$ with $H \to b \bar b$
   • Signal + Background samples:
     • Events: Parton Level​ Detector Level​
     • Plots: Parton Level​ Detector Level​

4. Gluon fusion vs. weak boson fusion

• Use the web interface of MadGraph/MadEvent to generate the cross-sections for H+2jets at the LHC via gluon fusion and weak boson fusion. Hint: For the gluon fusion, you need to use the Higgs efective field theory (heft) in MadGraph/MadEvent.
• Plot the rapidities of the two jets for boson production channels.
• What do you observe? What do you conclude?
• What happens to this picture when a third jet is added?

-- Main.FabioMaltoni - 28 Aug 2008