Version 2 (modified by trac, 7 years ago) (diff) |
---|
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 } |
- 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
Attachments (17)
- latex6a5f0a64b4e0ab39f10fc25a90c23c2e.png (414 bytes) - added by anonymous 7 years ago.
- latex01b40e9a19e56933190c06f199a84f74.png (224 bytes) - added by anonymous 7 years ago.
- latexc044175accbd59a10c36458f084e225c.png (382 bytes) - added by anonymous 7 years ago.
- latexbc56cda5df7d1f46f5056b663ba53dc4.png (275 bytes) - added by anonymous 7 years ago.
- latexafae0bdaadeb336150bfa1ae82517193.png (421 bytes) - added by anonymous 7 years ago.
- latexb0c8e35dc265861e8273af0f1e4bb55b.png (795 bytes) - added by anonymous 7 years ago.
- latexcc63ab5ee3df799e60050201d1424eb2.png (380 bytes) - added by anonymous 7 years ago.
- latex950f0c917f688170fcf3e3592aafd1c1.png (444 bytes) - added by anonymous 7 years ago.
- latex4b4f584ab45c970551ed62ac4774c9e6.png (2.0 KB) - added by anonymous 7 years ago.
- latex001d55f21998fc785413074f9e01e5fc.png (485 bytes) - added by anonymous 7 years ago.
- latexef7422b088d700b475a9afcc3c491911.png (1.8 KB) - added by anonymous 7 years ago.
- latex206585effd5dc22ff981d5595aa6cc8f.png (189 bytes) - added by anonymous 7 years ago.
- latexd973d438b62816891e2770a75702f74c.png (191 bytes) - added by anonymous 7 years ago.
- latex5a874c98f8509cee1ff53cca04bb8ffe.png (723 bytes) - added by anonymous 7 years ago.
- latexcc09f3058de66dad9bb3f1c081bc1156.png (191 bytes) - added by anonymous 7 years ago.
- latex549538b28acd804900a6e1ec2ee043f4.png (1.6 KB) - added by anonymous 7 years ago.
- latex159e70796754351432813d1199b172b5.png (1.3 KB) - added by anonymous 7 years ago.
Download all attachments as: .zip