Difference: ConnorsAnalysis-AnalysisTimeline (17 vs. 18)

Revision 182018-04-04 - ConnorGraham

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META TOPICPARENT	name="ConnorsAnalysis"

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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^total_i

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N_i = f_K ⋅ t ⋅ BR(K→i) ⋅ A^total_i

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...).

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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 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.

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BR(K⁺→π⁺νν) = BR(K⁺→μ⁺ν) ⋅ ^N_π⁺νν/_{D⋅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, D is the control trigger random downscaling factor (400), 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

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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

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This is simplified by introducing the calculated number of kaon decays from the normalisation sample information:

N_K = ^{N_μ⁺ν⋅D}/_{A_μ⁺ν⋅BR(K⁺→μ⁺ν)}

Then add the trigger efficiency correction and sum over the 4 pion momentum bins to give:

SES = ¹/_{N_K⋅∑_j[A_π⁺νν(p_j)⋅ε^trigger_π⁺νν(p_j)]}

Which differs from the π⁺π⁰ normalisation only in the lack of a random veto correction and the result was clearly consistent with the π⁺π⁰ SES to an estimated 10% muon sample error due to MC and within the fully calculated errors on the π⁺π⁰ sample

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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