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- Switch to event timeline
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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^{+}π^{0}) 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: | ||||||||

Changed: | ||||||||

< < | N_{i} = f_{K} ⋅ t ⋅ [BR(K→i)] ⋅ A_{i}_{} | |||||||

> > | N_{i} = f_{K} ⋅ t ⋅ [BR(K→i)] ⋅ A^{total}_{i} | |||||||

Changed: | ||||||||

< < | 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). | |||||||

> > | 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
where A
From here we define A | |||||||

From this we can construct an equation for: | ||||||||

Changed: | ||||||||

< < | BR(K^{+}→π^{+}νν) = BR(K^{+}→μ^{+}ν) ⋅ ^{Nπ+νν}/_{Nμ+ν} ⋅ ^{Aμ+ν}/_{Aπ+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. | |||||||

> > | BR(K^{+}→π^{+}νν) = BR(K^{+}→μ^{+}ν) ⋅ ^{Nπ+νν}/_{Nμ+ν} ⋅ ^{Aμ+ν}/_{Aπ+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
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Line: 49 to 57 | ||||||||

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
| ||||||||

Changed: | ||||||||

< < | 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]
| |||||||

> > | 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)⋅^{επdata(π+π0)}/_{επMC(π+π0)} | ||||||||

Changed: | ||||||||

< < | 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^{+}π^{0})" is the efficiency of pion ID in π^{+}π^{0} data and "ε_{π}^{MC}(π^{+}π^{0})" is the efficiency of pion ID in π^{+}π^{0} MC. Therefore, the Acceptance of Pnn "A_{π+νν}" must be corrected to: | |||||||

> > | 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^{+}π^{0})" is the efficiency of pion ID in π^{+}π^{0} data and "ε_{π}^{MC}(π^{+}π^{0})" is the efficiency of pion ID in π^{+}π^{0} MC. Therefore, the Acceptance of Pnn "A_{π+νν}" can be corrected to: | |||||||

A_{π+νν}⋅^{επdata(π+π0)}/_{επMC(π+π0)} | ||||||||

Changed: | ||||||||

< < | - Matter interaction differences of muon and pion.
- Muon ID efficiency [should be done from the MC run]
| |||||||

> > | - 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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Added: | ||||||||

> > | - 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
^{+}π^{0}as it doesn't include these cuts)
^{+}π^{0} normalisation. [done] - SES defined as the BR assuming a single event of signal with no background contributions
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## The seqence of processes involved in NA62 Pnn (and similar) data analysisThis 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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