CalcHEP tutorial

In order to get on with CalcHEP, we'll see two examples one sightly more complicated than the other. Hopefully, by the end of this tutorial, you'll be able to use pretty every function of CalcHEP.

This is not however a reference manual. One is available here.

A simple leptonic process

Let's start with a simple process and try to compute matrix elements using CalcHEP. In this section, we'll study:

ee → μμττ

The process will be studied in the standard model framework.

Preparing HEPMDB

First, connect to HEPMDB and go in the Calculate section. In the left panel, in the CalcHEP section, check whether the Standard Model (CKM=1) line appears. If not, in the CalcHEP menu, choose Import model. When you find the line Standard Model (CKM=1) for CalcHEP (it should be the model 43), select it and click Select. The model should now be accessible in your environment.

This model is the complete standard model without CKM matrix. As a consequence, it is lighter and in situation where quarks' flavours don't matter, it gives the same results as the standard model.

A template batch file

Select the model and select Edit Full Batch File in the CalcHEP menu. A new window will appear. You will be able to edit the batch file which is the file describing the process of interest. Click on the button Load batch template.

You now have a template file with nearly every possible field already offered. You also have help in the comments. The comments are lines beginning with a #. They are ignored by CalcHEP and thanks to them, you can add any information you want for any body reading the batch file.

Model information

The first three fields are information about the model.

1. The first line gives the model to use. You shouldn't touch it as this is a relique of CalcHEP local batch mode.
2. The second option is Model changed. This tells CalcHEP that model files have been changed.
3. Finally, Gauge tells what gauge to use, Feynmann or unitary. Many model are built implictly assuming that the gauge is Feynmann's. So you shouldn't change this field either.

Defining the process

We have several lines to define our process. Remove every Process, Decay and Composite field. You can now write:

Process: e,E -> m,M,l,L

In the standard model of CalcHEP, e refers to electron, m to muons, l to taus and the capital letters to their anti-particle. The particle list with their names for the model is available at the View particles entry of the CalcHEP menu. You can't access it while editing the batch file however.

So we set up an electron-positron scattering with a pair of muons and a pair of taus outgoing. No further information is needed to describe the process itself.

Beams configuration

We now have to configure the beams. The next field is about the pdfs. While this is useful for proton or any composite particle scattering, we don't need it for electron-positron scattering. We can write:

pdf1: OFF

And the same thing for the second pdf.

Concerning the energy of the beam, let's set 100 GeV beams.

p1: 100 p2: 100

Changing model parameters

We now have the possibility to change some model parameters. Let's say you want to change the strength of the electromagnetic force. You'll write:

Parameter: EE=0.31

with 0.31 being the new value of the electrical charge of the electron in natural unit. Some model are more flexible than others on that kind of point. But for our tutorial, we're not going to change weel known parameters.

Instead, we're going to scan the possible Higgs masses. For this, you can write:

Run parameter: Mh Run begin: 100 Run step size: 10 Run n steps: 6

This means we're going to scan the following values for Mh: 100 Gev, 110 GeV, 120 GeV, 130 GeV, 140 GeV, 150 GeV. This is of course a pretty useful possibility when studying a new model.

We then have the possibility to set some parameters about QCD but this will be studied in the next example.

Cuts

Various cuts are possible. For our simple tutorial, we're not going to study them. Please refer to the reference manual if you're interested in them.

Kinematics and regularization

To tell CalcHEP how to handle the phase space, you should fill the kinematic information. Using this information, a nice parametrisation of the phase space is used.

In our case, the txo ingoing particles will will give two bosons, each of them decaying in a lepton pair. A nice chocice would be:

Kinematics : 12 -> 34, 56 Kinematics : 34 -> 3 , 4 Kinematics : 56 -> 5 , 6

It is also important to tell CalcHEP where the resonances are to have better precision for computation. In our case, we have resonance on the dimuon and ditau masses for the Z boson and for the Higgs. So we'll write:

Regularization momentum: 34 Regularization mass: MZ Regularization width: wZ Regularization power: 2 Regularization momentum: 34 Regularization mass: Mh Regularization width: wh Regularization power: 2 Regularization momentum: 56 Regularization mass: MZ Regularization width: wZ Regularization power: 2 Regularization momentum: 56 Regularization mass: Mh Regularization width: wh Regularization power: 2

Plots

CalcHEP has automated plot capacities. However, with HEPMDB, they are of little use. We're just going to ignore them.

Event generation

For event generation, we really have two main parameters:

1. The number of events. We'll write: Number of events (per run step): 100000
2. The output file name. Filename: tutorial_ee_mmll

Parallelization

When using the template file of HEPMDB, all parallelization parameters are good. It is possible though, to set the maximum number of CPU to 24.

Vegas session

Finally, the Vegas session has some parameters. It will be used to compute the cross-section and to prepare the grid for event generation. Two sessions with 5 calls of 100,000 points is a good deal.

nSess_1: 5 nCalls_1: 100000 nSess_2: 5 nCalls_2: 100000

Final words

And here is our final batch file, ready for run. I recommand plotting the number of events as a function of the tau pair invariant mass.