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 ν : 40 bin in log(E) from 2 to 100 GeV 1600 pairs of true values [E ν,θ] (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 ν e steeper than ν μ ; ν / ν 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 ν ) NC E ν 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 ν ) NC E ν 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 ν Two free parameter : mean value & width Fit for each bin in E ν Example : E reco distribution for E ν ≈ 10 GeV Energy Resolution νeνe νμνμ Fit 9.57 ± 2.55 GeV Fit ± 2.77 GeV

14 Gaussian smearing in E ν Showers width : 0.5 GeV + [x]*E ν Tracks : also quadratic term allowed NC E ν replaced by E had (drawn according to B-y) Energy Resolution

15 Gaussian smearing in E ν Showers width : 0.5 GeV + [x]*E ν Tracks : also quadratic term allowed NC E ν replaced by E had (drawn according to B-y) Energy Resolution

16 Gaussian smearing in E ν Showers width : 0.5 GeV + [x]*E ν Tracks : also quadratic term allowed NC E ν replaced by E had (drawn according to B-y) Energy Resolution

17 E reco shifted with respect to E ν Use quadratic template in log 10 (E ν ) Energy Shift

18 E reco shifted with respect to E ν Use quadratic template in log 10 (E ν ) Energy Shift

Effective Mass Start from Martijn’s 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 ν τ CC

Method to Determine NMH 22 Start with 1600 pairs of [E ν,θ] Apply Resolution matrices – NE reco [i] = Σ M E [i][j] NE true [j] – Nθ reco [i] = Σ M θ [i][j][k] NEθ true [j][k] Apply Particle ID Below (IH-NH)/√ NH for 1 year NH  IH |Δm 2 31 |  |Δm 2 31 | - 2Δm 2 21 |Δm 2 32 |  |Δm 2 32 |

Method to Determine NMH 23 Start with 1600 pairs of [E ν,θ] Apply Resolution matrices – NE reco [i] = Σ M E [i][j] NE true [j] – Nθ reco [i] = Σ M θ [i][j][k] NEθ true [j][k] Apply Particle ID Below (IH-NH)/√ NH for 1 year NH  IH |Δm 2 31 |  |Δm 2 31 | - Δm 2 21 |Δm 2 32 |  |Δm 2 32 | +Δm 2 21

Event Rate in ORCA ν μ CC 20,000 ν e CC 15,000 ν τ CC 2,300 NC 4,000 Events per year per GeV One example bin in cosθ (width 0.1 at ~45 0 ) Numbers for full angular range No Resolutions, no PID 24 NH  IH |Δm 2 31 |  |Δm 2 31 | - 2Δm 2 21 |Δm 2 32 |  |Δm 2 32 |

Event Rate in ORCA Events per year per GeV One example bin in cosθ (width 0.1 at ~45 0 ) Numbers for full angular range No Resolutions, no PID ν μ CC 20,000 ν e CC 15,000 ν τ CC 2,300 NC 4, NH  IH |Δm 2 31 |  |Δm 2 31 | - Δm 2 21 |Δm 2 32 |  |Δm 2 32 | +Δm 2 21

Event Rate in ORCA ν μ CC 20,000 ν e CC 15,000 ν τ CC 2,300 NC 4,000 Events per year per GeV (Flux, CrossSection, M eff ) One example bin in cosθ (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 cosθ (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 cosθ (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 cosθ (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 χ 2 = Σ (NH-IH) 2 /NH No pseudo-experiments (« Asimov-Set ») Sanity check : Fitting «true» hierarchy yields χ 2 = 0 30

Fit Parameters Fixed oscillation parameters : θ 12,θ 13,Δm 21 Fitted oscillation parameters : θ 23,Δm 31, [ δ 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 θ 23 varied, different δ CP conditions Dashed : δ CP = 0 not fitted Solid thin : δ CP = 0 fitted ; thick δ CP = 180 fitted Initial value for θ 23 : true value

Sensitivity to Neutrino Mass Hierarchy 33 Introduce scan of starting values for θ 23 Look at fitted values for θ 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 ν/ν Small decrease of sensitivity Compatible with result from Martijn

Sensitivity to Neutrino Mass Hierarchy 35 Add nuisance parameter: spectral index, ratio ν/ν Simplified resolution functions : identical for ν/ν 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 ν/ν Channel dependent resolution function Ratio ν/ν 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 ν/ν Gaussian Prior with 10% width added Minor effect

Dependency on δ CP and θ Plot presented at ICRC (Martijn) Tendency visible but scrambled due to limited statistics

Dependency on δ CP and θ Same plot (for true NH) Symmetric pattern around δ CP = Highest sensitivity for δ CP = 0, and large θ 23

Dependency on δ CP and θ Same plot (for true IH) Symmetric pattern around δ CP = Highest sensitivity for δ CP = 0, and θ 23 close to 45 0

Sensitivity to Neutrino Mass Hierarchy 41 Crazy idea : fix θ 23 to 45 0 No ambiguity anymore, no measurement of θ 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 ΔM 2 very stable for IH δ CP always around even for true value 0 δ CP Δm 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 0.2σ 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 0.5σ 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-ν μ 70% for ν μ Small effect on sensitivity Effect of modified detector performance