Short description of the tool

The aim is to build an event generator for quarkonium physics. Production rates are computed within the NRQCD theory (Non-Relativistic QCD, Bodwin, Braaten and Lepage, see hep-ph/9407339), where cross sections are expanded in $\alpha_s$ and $\normalsize v$, the relative velocity in the heavy quarkonium state. As a result, cross sections read

where the creation of a heavy-quark pair is described by the short-distance coefficients $\hat \sigma(Q\bar Q(n))$, whereas the non-perturbative evolution of this heavy-quark pair into a quarkonium state is encoded into the long-distance matrix elements $<O^{{\mathcal Q}(n)>$. The label $\normalsize n $ stands for the intermediate state of the heavy quark pair, which is usually expressed in the spectroscopic notation:}

with $\normalsize S $ the spin of the heavy quark pair, $ \normalsize L $ its orbital angular momentum, $ \normalsize J $ its total angular momentum, and $ \normalsize c $ its color state. MadOnia automatically generates any tree-level amplitude for an arbitrary transition $\normalsize n$ (up to P-wave state) required for the computation of the short-distance coefficients. The amplitude generator is interfaced with MadEvent to produce unweighted events. These events are written in the same format in the lhe format and can be passed through Pythia for the showering and hadronization.

How to use the code

Edit the proc_card.dat and generate the process

• Enter the processus name in the proc_card.dat in the following format:

pp>jcc~[3P18to443]

This corresponds to the production of a $\normalsize J/\psi$ (PID=443) via an intermediate state $\normalsize 2S+1=3$, $\normalsize L=P$, $\normalsize J=1$, $\normalsize c=8$, i.e. a spin-1, P-wave, color-octet intermediate state. As another example:

pp>jbb~[1S01to551]

corresponds to the production of an $\normalsize \eta_b$ via a color-singlet transition.

Pay attention

the heavy-quark pair must be placed in that order, and at the end! For example,

pp>jc~c[3P18to443]

or

pp>cc~[3P18to443]j

will not work!

For the model, select sm_onium.

• Then type

./bin/newprocess

to generate the process

Edit the param_card.dat

If you edit the file param_card.dat, you will see that in addition to the sm parameters, you have a block called LDME. The parameters in this block correspond to the long distance matrix element, expressed in the BBL normalization (see hep-ph/9407339). You can specify the value of the LDME's for each transition. The transition $\normalsize n$ is indicated at the end of the line as a comment. For example, the line

        3.      1.16E+00         # 3S11

sets

Note that only one LDME parameter is assigned to each transition $^{2S+1}L_J{[c]}$. For example, for all the following processes

pp >j cc~[3S18to443]	color-octet $\normalsize J/\psi$ production
pp > jcc~[3S18to10441]	color-octet $\normalsize \chi_{c0}$ production
pp > jbb~[3S18to100553]	color-octet $\normalsize \Upsilon(2S)$ production

the same LDME parameter will be used in the param_card.dat.

For the rest…

Just proceed as for a usual generation of events:

./bin/generate_events to generate events

Note that you can put cuts on the quarkonium state via the run_card.dat.

Once your events have been generated, you can use the tool MadAnalysis to draw distributions of events.

-- Main.PierreArtoisenet - 02 Mar 2009