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Matrix Element Method
The Matrix Element Method consist in minimizing a likelihood.
The likelihood for N events is defined as
The best estimate of the parameter is obtained through a maximisation of the likelihood. It is common practice to minimize with respect to ,
In general, the probability that an event is accepted depends on the characteristics of the measured event, and not on the process that produced it. The measured probability density can be related to the produced probability density : $\bar{P}(x,\alpha){{{ Acc(x) P(x,\alpha) Acc(x) x -ln (\tilde{L}) }}}-\sum_{i=1}^{{N} ln(P(x_i;\alpha)) + N \int Acc(x) P(x,\alpha)dx-\sum_{i=1}}N ln(Acc(x_i))\alpha$.
Definition of the Weight
The Matrix Element Method associates a weight to each experimental event where
- is the set of information describing the events in the detector (momenta,tag,...)
- describe a theoretical hyppothesis
- is the cross section of this theoretical hyppothesis
- is the aplitude linked to this theoretical framework
- is the parton distribution function associate to the initial parton
- is the TransferFunction
Computation of those elements
The MadWeight has created a series of tool to compute the transfer function, the weight, the cross-section, the likelihood,... Some of these tools have their own specific page/
-- Main.OlivierMattelaer - 22 May 2009
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