An unbinned method to measure FBA of the B d K* + decay on LHCb
IC-22 Point Source Analysis with Unbinned Maximum Likelihood
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Transcript of IC-22 Point Source Analysis with Unbinned Maximum Likelihood
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IC-22 Point Source Analysis withUnbinned Maximum Likelihood
C. Finley, J. Dumm, T. Montaruli2008 May 2
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2008 Madison C. Finley 2
Overview
1. Basic Set of Cuts for point-source quality sample using Level 2 processing
• 14 days ( 12.6 days livetime) of Level 2 Filtered data (Sept. 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 29)
• 1000 files of Level 2, muon-filter Nugen E-1 (optimal for E-2 source sim.) Dataset 753
• 1000 files of Level 2, muon-filter Nugen E-2 (optimal for high statistics AtmNu) Dataset 768
2. First look at adding energy term to the likelihood in IC-22 (similar to method of J. Braun for AMANDA-II)
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2008 Madison C. Finley 3
Muon Filter + Pandel Zenith>90 Cut
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Paraboloid Sigma Cut
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Pandel Reduced Log Likelihood Cut
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Split Hit Series Cut: Pandel zen1>80 and zen2>80
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2008 Madison C. Finley 7
NDirC Cut
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2008 Madison C. Finley 8
Pandel SDir Cut
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Maximum Likelihood Analysis Part I: Point Spread Function
By now the maximum likelihood expression is familiar for point source searches:
where the source PDF is a Gaussian with width
given by the paraboloid sigma uncertainty estimate:
and the background PDF depends only on zenith angle:
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Sensitivity with Analysis-Level Cuts
E-2 average sensitivity 0 = 1.710-11 TeV-1 cm-2 s-1
Preliminary IC-22 Sensitivity for 250 d
( ~ 20 atmNu events per day )
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Sensitivity with Analysis-Level Cuts
E-2 average sensitivity 0 = 1.710-11 TeV-1 cm-2 s-1
IC-9 Sensitivity
IC22 Sensitivity
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Sensitivity with Analysis-Level Cuts
E-2
Sensitivity est. from Gent meeting, based on atmNu background simulation only
E-3
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Maximum Likelihood Analysis Part II: Energy
Now, want to add energy term to the Likelihood function, to weight higher energy events with greater significance:
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Maximum Likelihood Analysis Part II: Energy
Now, want to add energy term to the Likelihood function, to weight higher energy events with greater significance:
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Energy PDFs
Start with simplest energy estimator: NChan
P (Ei | =2)
P (Ei | =3)
Patm (Ei)
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Maximum Likelihood fit to nSrc and Gamma: Examples
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Examples: Simulated E-2 source at declination +30°
Left: 15 events injected (cross)
Right: 30 events injected (cross)
1-sigma and 2-sigma contours are shown for best fit to number of source events nSrc and spectral index gamma
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Maximum Likelihood fit to nSrc and Gamma: Examples
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Below: Simulated E-3 source at declination +30°
Left: 15 events injected; Right: 30 events injected
1-sigma and 2-sigma contours are shown for best fit to number of source events nSrc and spectral index gamma
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Effect of Energy Term on Discovery Potential
Simulated E-2 source at declination +30°:
5-sigma Discovery potential (Power 50%): without energy term in likelihood: 6.1 10-8 GeV-1 cm-2 s-1 (E/GeV)-2
(mean number of source events: 15) with energy term in likelihood: 4.2 10-8 GeV-1 cm-2 s-1 (E/GeV)-2
(mean number of source events: 10.5)
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Summary
Basic cuts on Level 2 parameters and basic maximum likelihood analysis
yield point source sensitivity ≈ 7x better from IC-9.
Many significant improvements coming soon:• Level 3 reconstructions• MPE reconstruction: better high energy efficiency, better angular resolution (see
talk by J. Dumm)• Time residuals of MPE should improve efficiency of NDirect cut
(or we may find an alternative cut for best high energy efficiency)
Adding energy term to likelihood: • Test with new energy estimators in level 3 (better than Nch estimate)• Reasonable to expect at least 30% improvement in discovery potential for hard
spectra.