== 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 [attachment:h-br.pdf here].

You may also have a look at the following Mathematica [attachment:HDecay.nb 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) [attachment:HiggsGG-LO-mtfinite.nb HiggsGG-LO-mtfinite.nb]
   1. pp>H at NLO: details of the calculation (Mathematica Notebook) [attachment:HiggsGG-NLO.nb higgsGG-NLO.nb]
   1. pp>H at NLO: cross section evaluation for the LHC (Mathematica Notebook+PDF libraries to be compiled) [attachment:phenHiggs.tar.gz 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 
${\tilde G}''a^{\mu\nu}=\frac12 \epsilon^{\mu\nu\rho\sigma} G''a^{\rho\sigma}$  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 [http://maltoni.web.cern.ch/maltoni/TeV4LHC/index.html 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:  [attachment:h4l-signal.lhe.gz Parton Level] [attachment:h4l-signal.lhco.gz Detector Level]    
         * Plots: [attachment:h4l-signal-lhe.pdf Parton Level] [attachment:h4l-signal-lhco.pdf Detector Level] 
      * Background 
         * Events:  [attachment:h4l.lhe.gz Parton Level] [attachment:h4l.lhco.gz Detector Level] 
         * Plots: [attachment:h4l-lhe.pdf Parton Level] [attachment:h4l-lhco.pdf 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:  [attachment:hww-signal.lhe.gz Parton Level] [attachment:hww-signal.lhco.gz Detector Level] 
         * Plots: [attachment:hww-signal-lhe.pdf Parton Level] [attachment:hww-signal-lhco.pdf Detector Level]  
      * Background 
         * Events:  [attachment:hww-background.lhe.gz Parton Level] [attachment:hww-background.lhco.gz Detector Level] 
         * Plots: [attachment:hww-background-lhe.pdf Parton Level] [attachment:hww-background-lhco.pdf Detector Level] 
   1. Top associated production $pp \to t\bar tH$ with $H \to b \bar b$
      *  Signal + Background samples:
         * Events:  [attachment:ttbb.lhe.gz Parton Level] [attachment:ttbb.lhco.gz Detector Level] 
         * Plots: [attachment:ttbb-lhe.pdf Parton Level] [attachment:ttbb-lhco.pdf 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