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Update on Photons. More on p 0 kinematic fit potential in hadronic events. Further H-matrix studies (with Eric Benavidez). Graham W. Wilson Univ. of Kansas. p 0 kinematic fit potential.
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Update on Photons • More on p0 kinematic fit potential in hadronic events. • Further H-matrix studies (with Eric Benavidez). Graham W. Wilson Univ. of Kansas
p0 kinematic fit potential • See Vancouver talk re intrinsic p0 energy resolution improvement given correct pairing of well measured photons. • Today, characterize better the multi-photon issues in Z → uu, dd, ss events. • Define prompt photons as originating within 10 cm of the origin (NB differs from standard ct < 10 cm definition)
Intrinsic prompt photon combinatorial background in mgg distribution assuming perfect resolution, and requiring Eg > 1 GeV. With decent resolution, the combinatorics are not so horrendous … Especially if one adopts a strategy of finding the most energetic and/or symmetric DK ones first. Next step: play with some algorithms
Conclusion on p0 kinematic fitting • Still very promising • Plan to work on developing algorithm for the photon-pairing problem • Non-prompt photons (K0S) are an important second order effect (certainly in s-sbar events !)
H-matrix Next 3 slides are from Snowmass 05 (As a reference for “standard usage”)
Standard Longitudinal HMatrix • Developed by Norman Graf. • Compare observed fractional energy deposition per layer with the average behavior of an ensemble of photons including correlations. • Current default implementation has a measurement vector with 31 variables: 30 fractional energies per layer and the logarithm of the energy. • Method: calculate, c2 = DT M-1 D where D is the difference vector, D = (xi – xave) (i=0, 30) and M is the covariance matrix of the 31 variables. • We were using FixedCone Clustering with q=60 mrad. • Used sidmay05 with low energy photons to avoid containment and issues regarding change in sampling (with 20+10 geometries).
Hmatrix Performance These photons used for evaluating the expected fractions and the covariance matrix, M. 5 GeV photons, 900, sidmay05 20 GeV neutrons, 900, sidmay05 Not perfectly distributed …………….. but a lot of discrimination
Hmatrix Performance 5 GeV photons, 900, sidmay05 20 GeV neutrons, 900, sidmay05 Eg. cut at p > 10-10 => eff (g) = 99.2%, eff (n) = 9.3% p > 10-5 => eff (g) = 98% , eff (n) = 4.6%
Perceived limitations of standard method • Chi-squared probability distribution is not flat. • Matrix variables mix energy fractions with cluster energy • Can cause technical difficulties • Implicitly uses the overall energy in the cuts • Gives some scope for a “one-size fits all” solution – but unlikely to be the best possible solution. • Matrix averages over the conversion layer • Number of actual layers with significant energy deposits can be << nmax (=> c2 not correctly normalized)
New Strategy • Use an H-matrix containing ONLY the cluster energy fractions per layer. • => cluster energy is something that can be used separately. • Use separate H-matrices depending on the layer with the first significant energy deposit. • Eg. for acme0605, we have H30, H29, H28, …. • This has the additional benefit that longitudinal changes in sampling fraction can be treated “seamlessly”. • => conversion point is something that can be added in afterwards as a further discriminant. • Disadvantage: need more MC statistics …
More details • Apply a cut of 50 keV per cell. (MIP gives 124 keV in 320 mm Si). • Use number of layers with non-zero number of cells in normalizing the c2 . • In order to avoid photon fragments, have required clusters to have ncells > 5 and raw cluster energy > 0.03 GeV (cf. mean of 0.08 GeV for 5 GeV photons) 5 GeV photon 90° acme0605
Cuts Require that the photon converts in the ECAL (r > 1260 mm) in the training samples (rejects conversions in the tracker) Interaction radius (mm)
5 GeV photons 90° acme0605 Resolution: (19.0 0.2%)/E
Probability Distributions Flatter, but still spike at zero.
Why is probability distribution not uniform ? (10 GeV photons, 90°, acme0605) layer0 layer 9 layer23 Response function is only Gaussian near shower max. Maybe a likelihood approach would have more potential ….
5 GeV Photon c2/dof = 37.1/23
Performance • Currently battling floating point errors associated with neutron clusters which are not at all photon-like.
10 GeV neutron c2/dof = 1562/25
10 GeV photons and 10 GeV neutrons Photon purity (assuming ng=nn) Photon efficiency I suspect this is worse than actual performance due to FP issues
Photon purity (assuming ng=nn) Photon efficiency
Conclusions on H-matrix • H-matrix work still a work in progress, but new approach looks to be promising. • Probably should include some simple preselection cuts which discard really un-photon like events from the background samples. • Suggestions on what to use as a performance metric appreciated. • Interested in looking into likelihood approach in the future.