Alternative Code to Calculate NMH Sensitivity J. Brunner 16/10/2015 1 Method to Determine NMH 2 Cos(zenith) : 40 bins from -1 to 0 E : 40 bin in log(E) from 2 to 100 GeV 1600 pairs of true values [E ,] (bin center) Oscillation probabilities from Globes Ingredients : Honda Flux Reference: Honda paper(2006) arxiv/astro- ph/ v3 Choices made: Frejus site no mountain Solar minimum azimuth averages 3 Honda Flux : Sanity check Low energy differences due to site & season 4 Honda Flux - Energy Flux * E 3 Raw Flux Averaged over zenith angle Flux steeply falling with energy e steeper than ; / almost identical 5 Honda Flux - Zenith Example plot for E=6 GeV Larger flux closer to horizon 6 Ingredients : Cross Sections From Genie, combination Oxygen, n, p Provided by Martijn 7 Detector Parameters Dependency on Zenith angle currently ignored 1-Dim parametrisation functions derived from input histograms Generally Gaussian smearing assumed 8 Angular Resolution 9 Gaussian smearing in cos(SpaceAngle) Width adjusted to approximately fit the shown distributions ( ~ m/E ) NC E replaced by E had (drawn according to B-y) Angular Resolution 10 Gaussian smearing in cos(SpaceAngle) Width adjusted to approximately fit the shown distributions ( ~ m/E ) NC E replaced by E had (drawn according to B-y) Angular Resolution 11 Gaussian smearing in cos(SpaceAngle) No artefacts close to pole in zenith angle True cos(zenith)True zenith Reco cos(zenith) Reco zenith 12 True cos(zenith) Xxxxx Parametrisation 7 GeV < E < 8 GeV Parametrisation 7 GeV < E < 8 GeV Full Simul/Reco Jannik 7 GeV < E < 8 GeV Full Simul/Reco Jannik 7 GeV < E < 8 GeV Comparison with full Simulation 13 Assume Gaussian smearing in E Two free parameter : mean value & width Fit for each bin in E Example : E reco distribution for E 10 GeV Energy Resolution ee Fit 9.57 2.55 GeV Fit 2.77 GeV 14 Gaussian smearing in E Showers width : 0.5 GeV + [x]*E Tracks : also quadratic term allowed NC E replaced by E had (drawn according to B-y) Energy Resolution 15 Gaussian smearing in E Showers width : 0.5 GeV + [x]*E Tracks : also quadratic term allowed NC E replaced by E had (drawn according to B-y) Energy Resolution 16 Gaussian smearing in E Showers width : 0.5 GeV + [x]*E Tracks : also quadratic term allowed NC E replaced by E had (drawn according to B-y) Energy Resolution 17 E reco shifted with respect to E Use quadratic template in log 10 (E ) Energy Shift 18 E reco shifted with respect to E Use quadratic template in log 10 (E ) Energy Shift Effective Mass Start from Martijns ICRC plot (before PID) Individual function for each channel Template : N*TanH((E-E0)/Sig) 19 Particle ID Results currently unstable Behaviour of muon channel incomprehensible Make educated guess template cascade : 1/E + E0 20 Particle ID Results currently unstable Behaviour of muon channel incomprehensible Make educated guess, template cascade : 1/E + E0 21 CC Method to Determine NMH 22 Start with 1600 pairs of [E ,] Apply Resolution matrices NE reco [i] = M E [i][j] NE true [j] N reco [i] = M [i][j][k] NE true [j][k] Apply Particle ID Below (IH-NH)/ NH for 1 year NH IH |m 2 31 | |m 2 31 | - 2m 2 21 |m 2 32 | |m 2 32 | Method to Determine NMH 23 Start with 1600 pairs of [E ,] Apply Resolution matrices NE reco [i] = M E [i][j] NE true [j] N reco [i] = M [i][j][k] NE true [j][k] Apply Particle ID Below (IH-NH)/ NH for 1 year NH IH |m 2 31 | |m 2 31 | - m 2 21 |m 2 32 | |m 2 32 | +m 2 21 Event Rate in ORCA CC 20,000 e CC 15,000 CC 2,300 NC 4,000 Events per year per GeV One example bin in cos (width 0.1 at ~45 0 ) Numbers for full angular range No Resolutions, no PID 24 NH IH |m 2 31 | |m 2 31 | - 2m 2 21 |m 2 32 | |m 2 32 | Event Rate in ORCA Events per year per GeV One example bin in cos (width 0.1 at ~45 0 ) Numbers for full angular range No Resolutions, no PID CC 20,000 e CC 15,000 CC 2,300 NC 4, NH IH |m 2 31 | |m 2 31 | - m 2 21 |m 2 32 | |m 2 32 | +m 2 21 Event Rate in ORCA CC 20,000 e CC 15,000 CC 2,300 NC 4,000 Events per year per GeV (Flux, CrossSection, M eff ) One example bin in cos (width 0.1 at ~45 0 ) Numbers for full angular range Resolutions added, no PID 26 Event Rate in ORCA Tracks 17,800 Cascades 24,000 Events per year per GeV (Flux, CrossSection, M eff ) One example bin in cos (width 0.1 at ~45 0 ) Numbers for full angular range Resolutions & PID added 27 Event Rate in ORCA Events per year per GeV (Flux, CrossSection, M eff ) One example bin in cos (width 0.1 at ~45 0 ) Linear scale & Zoom : CP phase : 0,90,180,270 28 Event Rate in ORCA Events per year per GeV (Flux, CrossSection, M eff ) One example bin in cos (width 0.1 at ~45 0 ) Linear scale & Zoom : CP phase : 0,90,180,270 29 NMH Sensitivity Calculation Calculate Event rates W for cascade/track[40,40] for true parameters (including hierarchy choice) Fit wrong hierarchy event rates all free parameters also fitted Minimizer : MIGRAD within Minuit2 from Root Significance from 2 = (NH-IH) 2 /NH No pseudo-experiments ( Asimov-Set ) Sanity check : Fitting true hierarchy yields 2 = 0 30 Fit Parameters Fixed oscillation parameters : 12, 13,m 21 Fitted oscillation parameters : 23,m 31, [ CP ] Fitted Nuisance parameter Individual normalisations for tracks, cascades, NC 6 parameters, no priors, i.e. no constraints Fit starting points at nominal values Convergence after ~200 calls (~10min) 31 Sensitivity to Neutrino Mass Hierarchy 32 True value for 23 varied, different CP conditions Dashed : CP = 0 not fitted Solid thin : CP = 0 fitted ; thick CP = 180 fitted Initial value for 23 : true value Sensitivity to Neutrino Mass Hierarchy 33 Introduce scan of starting values for 23 Look at fitted values for 23 NH true IH fitted : always second octant IH true NH fitted : always first octant Sensitivity to Neutrino Mass Hierarchy 34 Add nuisance parameters: spectral index, ratio / Small decrease of sensitivity Compatible with result from Martijn Sensitivity to Neutrino Mass Hierarchy 35 Add nuisance parameter: spectral index, ratio / Simplified resolution functions : identical for / Find systematic shift towards anti-neutrino 10-30% lower neutrino rate, 20-60% higher Antinu need prior here ?? Martijn : spread of 4% Inconsistent with above ? 36 Add nuisance parameter: spectral index, ratio / Channel dependent resolution function Ratio / much more stable need prior here ?? No !! Martijn : spread of 4% Consistent with above !! Sensitivity to Neutrino Mass Hierarchy 37 Add nuisance parameter: spectral index, ratio / Gaussian Prior with 10% width added Minor effect Dependency on CP and Plot presented at ICRC (Martijn) Tendency visible but scrambled due to limited statistics Dependency on CP and Same plot (for true NH) Symmetric pattern around CP = Highest sensitivity for CP = 0, and large 23 Dependency on CP and Same plot (for true IH) Symmetric pattern around CP = Highest sensitivity for CP = 0, and 23 close to 45 0 Sensitivity to Neutrino Mass Hierarchy 41 Crazy idea : fix 23 to 45 0 No ambiguity anymore, no measurement of 23 Works only well close to 45 42 Normalisations behave well without priors Jitter compatible with values from Martijn Martijn : 2.0% Martijn : 11.0% Nuisance Parameters Total NormNC Norm 43 Spectral Index & Track/Cascade ratio ok Jitter compatible with values from Martijn Martijn : 1.2% Spectral Index Track - Cascade Martijn : 0.5% Nuisance Parameters 44 M 2 very stable for IH CP always around even for true value 0 CP m 2 32 Oscillation Parameters 45 What happens if PID changes ? Reminder : Present values Effect of modified detector performance 46 Assume improvement of PID of muon-neutrinos at 10 GeV from 75% to 85% Below : Assumed performance and new results Moderate gain of 0.2 Effect of modified detector performance 47 What happens if energy resolution improves from ~20-25% to 10-15% ? (all channels) Reminder : Present values Effect of modified detector performance 48 What happens if energy resolution improves from ~20-25% to 10-15% ? (all channels) Below : Assumed performance and new results Average gain of 0.5 in 3 years Effect of modified detector performance Try ORCA Layout Optimization Effective mass (Mton) Median zenith res () Median Frac. E res Examples for cascades Resolutions stable M eff 5-10 GeV crucial 49 Preliminary results possible from this study Further Plans Put nuisance parameters on non-nominal values (e.g. norm = 1.2) Study more systematic effects Uncertainty in energy scale Uncertainty of resolution functions (!) Effect of Bjorken-Y 50 51 Flat PID track probability instead 1/E 80% for anti- 70% for Small effect on sensitivity Effect of modified detector performance