Fabrizio and Glen's contribution for Durham Workshop

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Our contribution to the Durham WorkShop was a study on the possibility to separate continuum (uds and ccbar) and bbbar events by using event shape variables, i.e. exploiting the different shapes of the events.

We set up PYTHIA in order to simulate both uds+ccbar and bbbar events and begin a study at generator level.

The aim is to search for event variables that could be used to train a neural network, and use the output of the net as a test statistic to sepatare between signal and bkgnd events.

We generate a sample of 600K events of each type (uds, ccbar and bbbar).
In the analysis performed in order to define the tag bit for the D*a1 the only cut on shape variables is the cut on r2 . The idea is to try to improve the rejection exploiting the fact that continuum events are "jet-like", while signal events are spherical. What we have noticed is that, if we divide the event in two hemispheres according the the thrust axis and compute the invariant masses of the two, after having applied a cut on r2 there are still lots of continuum events with high hemisphere masses, situation that otherwise we expect to have for the signal events.

The r2 cut is supposed to reject events in the 2-jet-like configuration, but if there's one or more radiated gluon (as it is likely to happen in the continuum case), this cut is not efficient. However, since the hemispheres masses are as large as 2 to 3 GeV, in this situation non-perturbative QCD still applies and it is possible to compute the QCD matrix element squared of the event, when the event is "clustered" in 4 jets. Therefore the idea is to cluster the events in 3 or 4 jets and exploit the variables called in literature y3 and y4, the QCD matrix element and all possible variables related to the jet structure of the event to further reject continuum.

The clusterization of the event proceeds in the following way (Durham (or kt) algorithm):

for each particles i,j in the event define the "distance" y(i,j):

y(i,j) = (2 * min( Ei^2, Ej^2) * (1 - cosTheta(i,j))) / Evis^2 ;

replace particles i,j with minimum y(i,j) with a "pseudo-particle" with 4-momentum P(mu) = P(mu)i + P(mu)j;

the clustering procedure continues until the total number of "jets" reconstructed is 3 or 4 and y3 and y4 are the minimum y(i,j) in the case of 3 or 4 final jets.

Once the event is clustered in 4 jets, it is possible to compute the QCD matrix element, following the prescriptions found in literature (LEP papers). In the plot, the distribution of ln(QCD matrix element) and of the thrust for signal and bkgnd are presented.

With the event clustered in 4 jets, also the angles between the 4-jets can be defined;

the angle between the highest and second highest energy jets (BZ-angle) and the angle between the lowest and second lowest energy jets (KS-angle);

the angle between the plane defined by the highest and lowest energy jets and that defined by the othe two jets (NR-angle) and the angle between the plane defined by the highest and second highest jets and that define by the other two (34-angle).

All this variables have been combined in a Neural Network (JETNET 3.51); for this first study the configuration of the NN is the following:

3 input layers with 8 input nodes (the variables defined above);

1 hidden layer with 12 nodes;

1 output node.

To train the network we've used 100K events bbbar events and 100k events for each bkgnd source. After the training, the network has been applied to a different sample of 500K events of each type of events. The distribution of the output is shown here.

In order to compare the result obtained with NN analysis to that obtained in the analysis to define the D*a1 tag bit, we have applied a cut on the NN output to obtain the same efficiency on bbbar events that we have with the cut: r2 < 0.35. These are the results:

Output > 0.3 => eff(bbbar) = 90%; eff(uds) = 14%; eff(ccbar) = 18%

r2 < 0.350 => eff(bbbar) = 90%; eff(uds) = 44%; eff(ccbar) = 47%

Our next step will be to repeat the same exercise using the official BaBar MC samples and study the outcome.

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Last Update: 27/09/2000 9:30 GMT