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Interaction Length Interaction length • Made a 3D map for the interaction and radiation lengths over the full detector (ILD). – That is, calculated for each specific point in the detector volume the interaction and radiation length integrated from the IP to that point. The first vertical bin is not to be trusted; Mokka 'has no geometry' at exactly z=0. Solenoid Hcal Ecal TPC Vtx Yoke Ecal, Hcal Ecal, Hcal endcap barrels endcaps For some reason the radiation length increases slower for higher R at phi=0. This is the case for the full horizontal plane (not visible from only this picture) Solenoid Hcal Ecal TPC Vtx Yoke Ecal, Hcal Ecal, Hcal endcap barrels endcaps At the outside of the HCAL barrel At the outside of the Solenoid At the outside of the Yoke, i.e. the total detector For the interaction length map a uniform map is visible in the transverse plane. (Not to get messy with the Z=0 plane, I took a random Z=0.75m) Solenoid Hcal Ecal TPC Vtx For some reason the radiation length increases slower for higher R at phi=0. This is the case for the full horizontal plane (not visible from only this picture) - see next slide Solenoid Hcal Ecal TPC Vtx • On previous slide you could see a slower increase in radiation length at phi=0. • This is apparently only due to the HCAL: – Upper plot is at phi=43.2 – Lower plot is at phi=0 • • The increase (in absolute values) is the same for R = 0-2m, and also from ~3 up to 7.5m. • Only between R=2m and R=3m is the increase less at phi=0. This is the HCAL. – Have contacted Angela, she'll look into it. Muon ID algorithm Studied some more the hit distribution in the HCAL and YOKE for both muons and pions. • With the particle gun, broad energy range, full phi-range, eta~0.21 • To study the hit distributions, calculated the distance of each hit to the main axis of the PFO (axis defined by centre-of-gravity of the PFO cluster) – This results for each PFO (i.e. a reconstructed muon or pion) in three distributions: hitdistance in ECAL, HCAL and YOKE. – For each of these distributions calculate: • mean, rms, skewness and kurtosis Kurtosis • Kurtosis is a measure of the "peakedness" of a distribution. – Higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations. • Example of zero kurtosis: the normal distribution • Positive kurtosis: a distribution has a more acute peak around the mean and fatter tails. • Negative kurtosis: a lower, wider peak around the mean and thinner tails. CENTRAL MOMENTS: - The "zeroth" central moment μ0 is one. - The first central moment μ1 is zero. - The second central moment μ2 is the variance. - The third and fourth central moments are used the skewness and kurtosis. Skewness • skewness is a measure of the asymmetry of a distribution. (The skewness of a random variable X is the third standardized moment) – Qualitatively, a negative skew indicates that the tail on the left side of probability density function is longer than the right side and the bulk of the values (including the median) lie to the right of the mean. – A positive skew indicates that the tail on the right side is longer than the left side and the bulk of the values lie to the left of the mean. – A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not necessarily implying a symmetric distribution. Negative skewness Positive skewness RMS vs mean • In the HCAL it's easy For the muon system we used the 'new system', from Saveliev. – Very wide clusters, for both pions and muons. HCAL – skewness and kurtosis • Used TMVA to get a hit of the largest correlations between mean/rms/skewness/kurtosis – Mean & rms highly corr. – Skewness & kurtosis highly corr. • What is independent: – Mean vs kurtosis – RMS vs skewness • That is in the HCAL. In the yoke this is less the case. YOKE – skewness and kurtosis • Used TMVA to get a hit of the largest correlations between mean/rms/skewness/kurtosis – Mean & rms highly corr. – Skewness & kurtosis highly corr. • What is independent: – Mean vs kurtosis – RMS vs skewness • That is in the HCAL. In the YOKE this is less the case. Although we used a large range for the particle's energy, the dependence on E is low. – Only the HCAL observables are shown. First attempt for cut-based ID (non-cumulative) Muons Pions Total 2000 1000 True total E > 10 GeV 1982 968 Hcal hits mean < 75mm 1993 57 Hcal hits RMS < 20*skew 1883 2 E_yoke > 0.1 GeV 1961 161 E_hCal < 50 GeV & 1881 2 E_yoke >0.1 .
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