CalcHEP tutorial
In order to familiarise yourself with CalcHEP, we will study two examples, one sightly more complicated than the other. Hopefully, by the end of this tutorial, you will be able to use majority of the functions of CalcHEP.
Please note that this is not a reference manual. If you wish to look at the reference manual, it is available here.
A simple leptonic process
Let's start with a simple process and try to compute the matrix elements using CalcHEP. In this section, we will study:
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 anybody reading the batch file.
Model information
The first three fields are information about the model.
- The first line gives the model to use. You should not touch it as this specifies the model in the CalcHEP local batch mode. There is no default for this setting so this line must be included.
- The second option is Model changed. This tells CalcHEP that model files have been changed.
- Finally, Gauge specifies which gauge is used, Feynman or unitary. Many models are built implicitly assuming that the gauge is Feynman's, so you should not 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:
In the standard model of CalcHEP, e refers to electrons, m to muons, l to taus and the capital letters to their anti-particle. The list of particle names and symbols to use can be viewed by selecting View Particles in the CalcHEP drop-down menu. You cannot access it while editing the batch file however.
So we have 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 do not need it for electron-positron scattering. We can write:
And the same thing for the second pdf.
Concerning the energy of the beam, let's set 100 GeV beams.
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 would write:
with 0.31 being the new value of the electrical charge of the electron in natural units. Some models are more flexible than others on that kind of point. But for our tutorial, we are not going to change the well known parameters.
Instead, we're going to scan the possible Higgs masses. For this, you can write:
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 are not going to study them. Please refer to the reference manual if you are 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 two ingoing particles will give two bosons, each of them decaying in a lepton pair. Hence, our kinematics are written as:
where the numbers refer to the particle in the process, in this case, 12 are the electron and positron, 3 and 4 are the muons etc.
To improve the precision of the computation, it is important to tell CalcHEP where the resonances are. In our case, we have resonance on the dimuon and ditau masses for the Z boson and for the Higgs. So we will write:
Plots
CalcHEP has automated plot capacities. However, with HEPMDB, they are of little use. We will ignore them.
Event generation
For event generation, we really have two main parameters:
- The number of events. We'll write: Number of events (per run step): 100000
- 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 usually sufficient. With the number of calls there is a trade-off; the higher the number of calls means it will take longer to run the batch file on HEPMDB but reducing the number of calls leads to a decrease in accuracy of the cross sections. It is therefore worth experimenting with a couple of points in the batch interface of CalcHEP to see what optimization can be made.
Final words
The batch file is now complete and ready to run. Click Save and return to the CalcHEP drop-down menu, where you should select Run Full Batch File.
Involving partons
For a more complex interaction involving partons, we study the collision of protons to create a specified final state. To make this easier to understand, we will look at the example given in the template batch file, and explain each section and its relevance. Hence we study:
This investigates the interaction of two protons on the parton level to create a W boson (without specifying positive or negative charge), a bottom quark and its anti-quark. Again this process is in the Standard Model framework.
Model Information
The batch file should be loaded according to the instructions in the previous example. Again the gauge should be set to Feynman, and Model Changed set to False. This tells the batch file that the model files have not been altered.
Defining the process
For this process, all of the definitions available in this section of the batch file need to be included. First, specify the main process.
As the W boson is a gauge boson, we need to include a decay mode of this particle. We will look at its decay to an unspecified charged lepton and its corresponding neutrino. To do this, new variable names need to be input, we will us le for any charged lepton, and n for any neutrino. The decay is written as follows:
Almost all of the particles we have introduced are composites, i.e they represent several particles that can be involved in this particular type of interaction. When the batch file is run it calculates all possible processes for every combination of these particles, so it is important to include all composites. We write:
