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Error Analysis

Error Analysis. Monte Carlo Technique 02 October 2013. Statistical Errors. Statistical Error – No Background. Calculate the yield Allow for statistical fluctuations: Unfold cross section Repeat for 1000 tries. y i = gRandom->Gaus( y i , Sqrt ( y i ) ).

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Error Analysis

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  1. Error Analysis Monte Carlo Technique 02 October 2013

  2. Statistical Errors

  3. Statistical Error – No Background • Calculate the yield • Allow for statistical fluctuations: • Unfold cross section • Repeat for 1000 tries yi= gRandom->Gaus( yi, Sqrt(yi) )

  4. Statistical Error – With Background • Calculate the yield • Calculate the background yield from 18O • Allow for statistical fluctuations: • Unfold cross section • Repeat for 1000 tries yi= gRandom->Gaus( yi, Sqrt(yi+2yibg) )

  5. Absolute Systematic Errors

  6. Absolute Beam Energy • Calculate the Nij for each nominal beam energy, Ei (since we will use GEANT4) • Allow for absolute beam energy to change by: • Calculate the yield • Unfold cross section • Repeat for 1000 tries Ei= Ei* gRandom->Gaus(1, 0.001 )

  7. Other Absolute Systematic Errors • Calculate the Nij for each nominal beam energy, Ei (since we will use GEANT4) • Allow for absolute beam energy to change by: • Calculate the yield • Include other absolute systematic errors: • Unfold cross section • Repeat for 1000 tries Ei= Ei* gRandom->Gaus(1, 0.001 ) Nij= Nij* gRandom->Gaus(1, δφ/φ ) yi= yi* gRandom->Gaus(1, Sqrt( (δI/I)2+ (δR/R)2+ (δT/T)2+ ε2 )

  8. Relative Systematic Errors

  9. Relative Beam Energy • Calculate the Nij for each nominal beam energy, Ei (since we will use GEANT4) • Allow for absolute beam energy 7.8 MeV to change by: • Higher energies has samerelative error, • Calculate the yield • Unfold cross section • Repeat for 1000 tries E0 = 7.8 * gRandom->Gaus(1, 0.001 ) Ei= E0 + iΔ Now, we have to worry about beam stability (RF stability). Need injector FFB system to maintain relative beam stability

  10. Other Relative Systematic Errors • Calculate the Nij for each nominal beam energy, Ei (since we will use GEANT4) • Allow for absolute beam energy 7.8 MeV to change by: • Higher energies has samerelative error, • Calculate the yield • Include other relative systematic errors: • Unfold cross section • Repeat for 1000 tries E0 = 7.8 * gRandom->Gaus(1, 0.001 ) Ei= E0 + iΔ N= N* gRandom->Gaus(1, δφ/φ ) y = y * gRandom->Gaus(1, Sqrt( (δI/I)2+ (δR/R)2+ (δT/T)2+ ε2 )

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