Difference: ConnorsAnalysis-AnalysisTimeline (16 vs. 17)

Revision 172018-04-03 - ConnorGraham

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 The overall aim of NA62 if to measure the branching fraction (using BR as the canonical shorthand from here) of the decay K⁺→π⁺νν. In order to do so, we must account for errors both statistical and systematic. Therefore, if we measure the BR and normalise the number of events we observe by dividing it by one of the primary kaon decays (μ⁺ν or π⁺π⁰) we can cancel many of the major systematics. If we use both primary decays for a normalisation sample and compare the value, we can check if we are properly accounting for all systematics, as both should provide the same result. First we use the number of observed events of decay i:
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+N_i = f_K ⋅ t ⋅ [BR(K→i)] ⋅ A_i
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+N_i = f_K ⋅ t ⋅ [BR(K→i)] ⋅ A^total_i
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+where f_K is the frequency of kaons in the beam, t is the time period of data taking and A_i is the total "acceptance" or number of decays in the detector's fiducial region (this should cover all contributions, even things like the possibility of events being incorrectly tagged as the decay you are measuring).
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+where f_K is the frequency of kaons in the beam, t is the total time period of data taking and A^total_i is the total "acceptance" or fraction of decays in the detector's fiducial region that pass all processing and cuts (this should cover all contributions, even things like the possibility of events being incorrectly tagged as the decay you are measuring, pileup, matter interactions etc...).

We can define the total acceptance as the product of three contributions:

A^total_i=A^geo_i ⋅ A^cuts_i ⋅ A^cor_i

where A^geo_i is the Geometric acceptance (number of events that can be reconstructed by the detector equipment), A^cuts_i is the acceptance due to the selection cuts (calculated from MC) and A^cor_i is the correction to the acceptance due to elements not modeled in the MC (such as the trigger efficiency).

From here we define A_i = A^cuts_i
 From this we can construct an equation for:
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+BR(K⁺→π⁺νν) = BR(K⁺→μ⁺ν) ⋅ ^N_π⁺νν/_{N_μ⁺ν} ⋅ ^A_μ⁺ν/_{A_π⁺νν}
 where the f_K and t terms cancel, along with many of the efficiencies included in the acceptance and BR(K⁺→μ⁺ν) can be taken from the PDG listings as it has been thoroughly measured by previous experiments.
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+BR(K⁺→π⁺νν) = BR(K⁺→μ⁺ν) ⋅ ^N_π⁺νν/_{N_μ⁺ν} ⋅ ^A_μ⁺ν/_{A_π⁺νν}
 where the f_K and t terms cancel, along with the geometric acceptance and many of the correction efficiencies included in the total acceptance, and BR(K⁺→μ⁺ν) can be taken from the PDG listings, as it has been thoroughly measured by previous experiments.
 Step 1: Generate a K_μ2 normalisation sample. [done] 
 Start by generating a sample of K_μ2 data with Pnn like cuts from one burst (current file) and organise some output histograms
 Step 3: Run on as much 2016 data as possible with HTCondor to calculate a value for "N_μ⁺ν". [done] 
 Run selection on run number 6431 (large, good quality run) to start with
  Run on Giuseppe's list of all good runs of 2016
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+Step 4: Start looking at the efficiencies that don't cancel in the acceptances fraction "ε_r". 
 Pion ID efficiency: where the efficiency of pion ID in Pnn data "ε_π^data(π⁺νν)" can be described by: [being studied by others]
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+Step 4: Start looking at the efficiencies that don't cancel in the acceptances fraction "A^cor_i". 
 Pion ID efficiency: where the efficiency of pion ID in Pnn data "ε_π^data(π⁺νν)" can be described by: [studied by others, determined negligible with respect to MC approximation for precision of Pnn analysis]
 ε_π^data(π⁺νν) = ε_π^MC(π⁺νν)⋅^{ε_π^data(π⁺π⁰)}/_{ε_π^MC(π⁺π⁰)}
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+where "ε_π^MC(π⁺νν)" is the efficiency of pion ID in Pnn MC (which is used to calculate the Pnn acceptance), "ε_π^data(π⁺π⁰)" is the efficiency of pion ID in π⁺π⁰ data and "ε_π^MC(π⁺π⁰)" is the efficiency of pion ID in π⁺π⁰ MC. Therefore, the Acceptance of Pnn "A_π⁺νν" must be corrected to:
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+where "ε_π^MC(π⁺νν)" is the efficiency of pion ID in Pnn MC (which is used to calculate the Pnn acceptance), "ε_π^data(π⁺π⁰)" is the efficiency of pion ID in π⁺π⁰ data and "ε_π^MC(π⁺π⁰)" is the efficiency of pion ID in π⁺π⁰ MC. Therefore, the Acceptance of Pnn "A_π⁺νν" can be corrected to:
 A_π⁺νν⋅^{ε_π^data(π⁺π⁰)}/_{ε_π^MC(π⁺π⁰)}
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+ Matter interaction differences of muon and pion.
  Muon ID efficiency [should be done from the MC run]
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+ Matter interaction differences of muon and pion (assumed small).
  Muon ID efficiency (similarly to pion ID efficiency)
  Trigger efficiencies
  Anything we missed?
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+ Random veto: the additional loss of events due to both pileup and matter interactions affecting the multiplicity and photon rejection cuts, is not an issue for this normalisation as it cancels in the acceptance ratio (unlike π⁺π⁰ as it doesn't include these cuts)
 
Step 5: Calculate the single event sensitivity (SES) and compare it to the π⁺π⁰ normalisation. [done] 
 SES defined as the BR assuming a single event of signal with no background contributions
  The seqence of processes involved in NA62 Pnn (and similar) data analysis 

This section is written to later discus the efficiencies of the NA62 analysis and which efficiencies do not cancel between the Pnn channel and the muon normalisation.

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