# ms limit: the Likelihood

- Likelihood = L( ms , gi )
  - ms = only free parameter
  - gi = “external” (fixed) parameters ( fs , fd, md, , bckg., )
- (Log) Likelihood difference:
  DLL= ln(L( ms )) - ln(Lmin)
- 95 % lower limit :
  intersection of DLL
  with 95 % C.L. curve
- Ideal (symmetric ) case :
  DLL = 1.92
- Fast MC. For several ms values :
  - generate (~1000) samples with same statistics as the data
  - in each sample vary gi within errors (include systematics)
  - find value of ln(L) below which lie 95 % of the sample
  How to combine limits ?

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