Statistical Approaches for IceCube, DeepCore, and PINGU Neutrino Oscillation Analyses Joshua Hignight for the IceCube-PINGU Collaboration September 21 st , 2016 September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 1 / 20
IceCube Without DeepCore: 78 strings, IceCube Lab IceTop 125 m string spacing, 81 Stations 50 m 324 optical sensors 17 m module vertical-spacing IceCube Array 86 strings including 8 DeepCore strings 5160 optical sensors Optimized for (very) High Energy neutrinos 1450 m DeepCore 8 strings-spacing optimized for lower energies 480 optical sensors Eiffel Tower 324 m 2450 m 2820 m Bedrock September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 2 / 20
Top view of the center of IceCube IceCube-DeepCore 100 Y (m) IceCube DeepCore 50 78 strings, 125 m string spacing 0 17 m modules vertical-spacing -50 8 strings, 40-75 m string -100 spacing -150 7 m modules vertical-spacing -100 -50 0 50 100 150 200 X (m) → Typical LE ν event → E ν µ = 12 GeV (w/ E µ = 8 GeV) September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 3 / 20
IceCube-DeepCore-PINGU 78 strings, 125 m string 100 spacing Y (m) IceCube Preliminary DeepCore 17 m modules vertical-spacing 50 PINGU 8 strings, 75 m string spacing 0 7 m modules vertical-spacing − 50 26 strings, 24 m string spacing − 100 1.5 m modules vertical-spacing − 150 − − 100 50 0 50 100 150 200 ◮ all optical modules in X (m) clearest ice September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 4 / 20
Atmospheric neutrinos ❅ 20 km ✲ ❘ ❅ ❄ ✯ ✟ ✟✟✟✟✟ ✕ ✁ ✻ ✄✄ ✗ ✒ � � ✁ � ✁ ✄ � ✁ ✄ � ✁ ✄ � 12760 km ✁ ✄ ✁ ✄ ✁ ✄ ✄ various baselines (L) available 2:1 ratio between ν µ : ν e similar rate of ν and ¯ ν ◮ however, x-sec for ¯ ν half of ν September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 5 / 20
Atmospheric neutrinos arXiv:1510.08127 20 km ❅ ✲ ❘ ❅ ❄ ✟ ✯ ✟✟✟✟✟ ✕ ✁ ✻ ✄✄ ✗ ✒ � � ✁ � ✁ ✄ � ✁ ✄ � ✁ ✄ � 12760 km ✁ ✄ ✁ ✄ ✁ ✄ ✄ various baselines (L) available ν energy over several orders of magnitude ⇒ wide range of L / E available for ν oscillation measurements September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 6 / 20
Atmospheric neutrino oscillations 1.0 ν ν ) : x ν x e ν ν 0.9 : → µ x ν ν : 0.8 τ µ x ν P( 0.7 ∆ 2 2 m = 7.59e-05 eV 21 ∆ 2 ± 2 0.6 m = 2.42e-03 eV 32 θ 0.5 2 sin (2 ) = 0.861 12 2 θ 0.4 sin (2 ) = 0.098 13 2 θ 0.3 sin ( ) = 0.490 23 δ ° 0.2 = 0 CP 0.1 NH IH 0.0 2 10 10 true E (GeV) ν Longest baseline (L=12760 km, cos θ z = − 1) has: ◮ First oscillation maxima at ∼ 25 GeV ◮ Matter effects below ∼ 12 GeV ◮ Potential for ν e appearance at 8 GeV September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 7 / 20
“Atmospheric mixing” parameters by IceCube IceCube: Phys.Rev. D 91, 072004 (2015); SK: AIP Conf. Proc. 1666, 100001 (2015) IceCube: fitting to data done in 2D space ( E , θ z ) ◮ χ 2 / ndf = 54 . 9 / 56 Contours obtained using Wilk’s theorem ◮ Calculate ∆ ln L = ln L − ln L bestfit for all points in 2D parameter space ◮ ∆ ln L calculated by maximizing L over nuisance parameters ◮ − 2 ∆ ln L is asymptotically a χ 2 distribution with 2 dof. Side plots: profile of ∆ ln L passing through best-fit September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 8 / 20
IceCube – towards future analysis PRD analysis focus in ν µ CC “clean” events ◮ Clear µ tracks ◮ Require several non-scattered γ ◮ Use only up-going events ⇒ very small atmospheric µ contamination ◮ Fits analytical formula for Cherenkov light front propagated to PMTs Currently working on new analysis based on new reconstruction: ◮ Planning to look at full-sky ⋆ More atmospheric µ contamination ⋆ But would give us better handle on flux systematics ◮ Use information from all hits in reconstruction ⋆ Reconstruction more sensitive to scattering ⋆ Unfortunately also more sensitive to noise ◮ Increased presence of ν e , ν τ and ν NC in sample ◮ And also increase significantly number of ν µ events at final level ⋆ significant improvement in final result expected September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 9 / 20
IceCube – new event reconstruction IceCube measures Cherenkov cones in “3D” PMTs embedded in the parameter space creates features in their vicinity Natural medium also has local variations Low number of hits → “bumpy” likelihood space Need to fit 8 parameters − 300 Log Likelihood Preliminary corresponding to ν µ DIS − 400 other dimensions interaction − 500 also “bumpy” − ◮ vertex (3), time, direction (2), 600 − 700 energies of µ and hadronic − 800 cascade − 900 Usual minimizers do not work well − − − − 500 400 300 200 ◮ currently using “MultiNest” Vertex Z (m) September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 10 / 20
The “event” likelihood space I 0 I 0 I 1 I 2 data Charge Charge Time Time expectation n i � � � � Q obs dt , Q exp dt ) L ( D | H ) = Poisson ( t ∈ I j t ∈ I j i ∈{ PMT } j = 0 Charge expectation ( Q exp ) distribution from spline tables ◮ Spline tables account for main local/global ice properties ◮ Derived from simulation Idea for the future: replace tables by simulated expectations ◮ For every L ( D | H ) calculation run simulation to estimate expectation ◮ Can account of more detailed/evolving ice models September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 11 / 20
The MultiNest algorithm See full description in paper by F. Feroz et al. [arXiv:0809.3437 and arXiv:1306.2144] MultiNest searches for maximum in multidimensional likelihood space ◮ Exploration of space via ellipsoidal nested sampling ⋆ New trials thrown in volume defined by ellipsoids obtained from distribution of previous trials → efficient sampling ⋆ New trials accepted/rejected depending on their LH ⋆ Posterior distributions provided could be used as error estimates ◮ Natively supports multi-modal distributions ⋆ In our case important to avoid local minima Common Points Peak 1 Peak 2 Likelihood Likelihood 5 5 4 4 3 3 L 2 2 1 1 0 -5 -5 5 0 -6 6 4 -4 -2.5 -2.5 2.5 -2 2 0 0 0 0 0 2 -2 x y 2.5 2.5 -2.5 x x y -4 4 6 -6 5 5 -5 (a) (b) Figure 6. Toy model 2: (a) two-dimensional plot of the likelihood function defined in Eqs. (32) and (33); (b) dots denoting the points with the lowest likelihood at successive iterations of the M ULTI N EST algorithm. Different colours denote points assigned to different isolated modes as the algorithm progresses. (Figure extracted from arXiv:0809.3437) September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 12 / 20 D ( Z ) ( Z ) ( Z ) ( Z 1 ) ( Z 2 ) 2 � 1 : 75 � 2 : 44 � 1 : 72 � 0 : 05 � 2 : 28 � 0 : 08 � 2 : 56 � 0 : 08 5 � 5 : 67 � 6 : 36 � 5 : 75 � 0 : 08 � 6 : 34 � 0 : 10 � 6 : 57 � 0 : 11 10 � 14 : 59 � 15 : 28 � 14 : 69 � 0 : 12 � 15 : 41 � 0 : 15 � 15 : 36 � 0 : 15 20 � 36 : 09 � 36 : 78 � 35 : 93 � 0 : 19 � 37 : 13 � 0 : 23 � 36 : 28 � 0 : 22 30 � 60 : 13 � 60 : 82 � 59 : 94 � 0 : 24 � 60 : 70 � 0 : 30 � 60 : 57 � 0 : 32 log ( Z ) D D N N lik e lik e 2 27 ; 658 15 : 98% 7 ; 370 70 : 77% 5 69 ; 094 9 : 57% 17 ; 967 51 : 02% 10 579 ; 208 1 : 82% 52 ; 901 34 : 28% 600 ; 000 20 43 ; 093 ; 230 0 : 05% 255 ; 092 15 : 49% 30 753 ; 789 8 : 39% D � = 0 k �
Measuring the ν Mass Ordering with atmospheric ν September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 13 / 20
Measuring the ν Mass Ordering with atmospheric ν ν ν NO True E, Zenith shown IO Different oscillation probabilities for ν and ν for NO and IO Measure combined ν + ν ◮ different cross-section ⇒ effect doesn’t vanish September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 14 / 20
Bin-by-bin significance of mass hierarchy signature Assuming no ν vs ν identification Tracks Cascades 30 30 0.20 Preliminary Preliminary 0.24 0.15 25 25 N NH N NH 0.16 0.10 Energy [GeV] Energy [GeV] 20 20 0.08 0.05 q q ( N IH − N NH ) / ( N IH − N NH ) / 0.00 0.00 15 15 0.05 0.08 10 10 0.10 0.16 0.15 5 5 0.24 0.20 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 cos( ϑ ) cos( ϑ ) Distinct hierarchy dependent signatures for tracks (mostly ν µ CC) and cascades (mostly ν e CC) ◮ Intensity is statistical significance of each bin with 1 year data ◮ Measurement is possible “statistically” by combining all bins – there is not one bin that would achieve that ◮ Particular expected “distortion pattern” helps mitigate impact of systematics September 21 st , 2016 Joshua Hignight PhyStat- ν Fermilab 2016 15 / 20
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