Version 2 (modified by trac, 7 years ago) (diff)

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## Matrix Element Method

The Matrix Element Method consist in minimizing a likelihood.

The likelihood for N events is defined as %$L(\alpha)=e{-N \int \bar{P}(x,\alpha)dx} \prod_{i=1}{N} \bar{P}(x_i;\alpha)$%

The best estimate of the parameter is obtained through a maximisation of the likelihood. It is common practice to minimize with respect to , %$-ln (L)=-\sum_{i=1}{N} ln(\bar{P}(x_i;\alpha)) + N \int \bar{P}(x,\alpha)dx$%

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 %%: %$\bar{P}(x,\alpha){{{ Acc(x) P(x,\alpha)$% where %% is the detector acceptance, which depends only on %%. So the quantity that we have to minimize is %$-ln (\tilde{L}) }}}-\sum_{i=1}{N} ln(P(x_i;\alpha)) + N \int Acc(x) P(x,\alpha)dx$% where the term has been omitted since it does not depend on .

## Definition of the Weight

The Matrix Element Method associates a weight to each experimental event %$P( x  \alpha)=\frac{1}{\sigma_{ \alpha}} \int d \phi( y) M_{ \alpha} 2 ( y) dw_1 dw_2 f_1(w_1) f_2(w_2) W(x, y)$% where
1. is the set of information describing the events in the detector (momenta,tag,...)
2. describe a theoretical hyppothesis
3. is the cross section of this theoretical hyppothesis
4. is the aplitude linked to this theoretical framework
5. is the parton distribution function associate to the initial parton
6. 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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