ν̅ oscillation analyses at T2K Raj Shah (STFC/Oxford) 19/07/16 1
Outline •Neutrino oscillations � •The T2K experiment � •Analysis strategy � •Results Raj Shah - STFC/Oxford Oscillation analysis @ T2K 2
Neutrino Mixing Atmospheric Reactor | LBL Solar θ 13 θ 23 ∆ m 2 12 ∆ m 2 δ CP 23 ∆ m 2 13 Raj Shah - STFC/Oxford Oscillation analysis @ T2K 3
CP Violation P ( ν µ → ν e ) − P ( ν ¯ e ) µ → ν ¯ = − 16 S 12 C 12 S 13 C 2 13 S 23 C 23 Sin ( δ ) Sin ( ∆ 12 ) Sin ( ∆ 23 ) Sin ( ∆ 13 ) ∆ ij = ∆ m ij L ∝ Sin ( ∆ 12 ) Sin ( ∆ 23 ) Sin ( ∆ 13 ) 4 E ∝ Sin ( θ 12 ) Sin ( θ 23 ) Sin ( θ 13 ) ∝ Sin ( δ CP ) P ( ν µ ! ν µ ) 6 = P (¯ ν µ ! ¯ ν µ ) CPT Violation!! Raj Shah - STFC/Oxford Oscillation analysis @ T2K 4
T2K Tokai to Kamioka μ -like e-like Raj Shah - STFC/Oxford Oscillation analysis @ T2K 5
Detectors + Beam Ingrid ND280 Raj Shah - STFC/Oxford Oscillation analysis @ T2K 6
Oscillation analysis Flux SK Efficiencies ND Constraint Cross section Oscillation Prob MC Prediction Data Oscillation fit Raj Shah - STFC/Oxford Oscillation analysis @ T2K 7
Oscillation analysis Flux SK Efficiencies ND Constraint Cross section Oscillation Prob MC Prediction Data Oscillation fit Good Fit! Raj Shah - STFC/Oxford Oscillation analysis @ T2K 8
Predicted spectra μ -like e-like ν � 7.00e20 POT ν̅� 7.41e20 POT Raj Shah - STFC/Oxford Oscillation analysis @ T2K 9
Joint analysis results ν : 7.00e20 POT ν ̅ : 7.41e20 POT Nuisance parameters marginalised Raj Shah - STFC/Oxford Oscillation analysis @ T2K 10
ν̅ e appearance μ -like e-like ν � 7.00e20 POT ν̅� 7.41e20 POT Raj Shah - STFC/Oxford Oscillation analysis @ T2K 11
ν̅ e appearance 7.41e20 POT Do ν̅ μ oscillate into ν̅ e ? Signal: ν ̅ μ ➡ ν ̅ e 2.786 Osc 𝝃 e Beam 𝝃 e NC Tot Background 0.71 1.04 1.47 3.22 Raj Shah - STFC/Oxford Oscillation analysis @ T2K 12
Frequentist analysis P Value: Probability to observe data as or more extreme than what was observed under the null hypothesis Null hypotheses No ν ̅ e appearance PMNS ν ̅ e appearance ( 𝛾 =0) ( 𝛾 =1) P osc ( ν ̅ μ ➡ ν ̅ e ) = 𝛾 · P osc (PMNS) P osc ( 𝝃 x ➡ 𝝃 y ) = P osc (PMNS) Statistic Δ 𝝍 2 = 𝝍 2 ( 𝛾 =0) - 𝝍 2 ( 𝛾 =1) Raj Shah - STFC/Oxford Oscillation analysis @ T2K 13
Results ) 2 χ -1.93 Data P-Value 0.07 ∆ ))/d( =1 0.099 β 0.06 2 χ =0 0.374 β ∆ 0.05 d(p( 0.04 0.03 0.02 0.01 0 5 0 5 10 15 20 − 2 2 2 = ( =0) - ( =1) ∆ χ χ β χ β Raj Shah - STFC/Oxford Oscillation analysis @ T2K 14
Bayesian results B 01 = Marginal Likelihood ratio P ( β = 0 | D ) P ( β = 1 | D ) = π ( β = 0) π ( β = 1) B 01 = π ( β = 0) π ( β = 1) e − 0 . 5 × ∆ χ 2 marg B 01 = 2.62 Weak preference for 𝛾 =0 Raj Shah - STFC/Oxford Oscillation analysis @ T2K 15
ν̅ μ Disappearance ν : 6.57e20 POT vs ν ̅ : 4.01e20 POT • Introduce new separate parameters sin 2 ( θ ̅ 23 ) and Δ m ̅ 232 for 𝝃 oscillations. • Fix all ν oscillation (background) PMNS parameters • Fit ν ̅ oscillation parameters and compare with ν fit. Raj Shah - STFC/Oxford Oscillation analysis @ T2K 16
Summary Joint Analysis � •Constraints on all ν oscillation parameters •Hint towards maximal CP violation � ν̅ e Appearance � •Preference for no ν̅ e appearance •10% p-value for PMNS appearance � ν̅ μ Disappearance � •Consistent constraints for ν and ν̅ oscillations Raj Shah - STFC/Oxford Oscillation analysis @ T2K 17
Back ups Raj Shah - STFC/Oxford Oscillation analysis @ T2K 18
Data vs Expectation 𝜉 𝜉̅ 1Rµ 1Re Raj Shah - STFC/Oxford Oscillation analysis @ T2K 19
ν̅ e Appearance Raj Shah - STFC/Oxford Oscillation analysis @ T2K 20
Null distribution #1 Prior knowledge : ν 1Re, ν 1R 𝜈 , ν̅ 1R 𝜈 � Method: � 1. Throw model parameters (osc and syst) based on priors 2. Generate all 4 predicted spectra (N exp ) 3. Compute likelihood ℒ ( ν 1R 𝜈 , ν 1Re, ν̅ 1R 𝜈 | data) � � � 4. Any toy dataset derived from N exp has a weight given by ℒ when filling the null hypothesis statistic distribution � Raj Shah - STFC/Oxford Oscillation analysis @ T2K 21
Null distribution #2 (1) Take N exp from method in previous slide � (2) Throw poisson from N exp ν̅ 1Re � (3) Calculate statistic Δ 𝜓 2 with ν̅ 1Re toy and ν 1Re, ν 1Rµ and ν̅ 1Rµ real data � (4) Fill distribution with null hypothesis statistic � (5) Repeat from (1) 10k times Raj Shah - STFC/Oxford Oscillation analysis @ T2K 22
Signal vs Background χ 2 ( β = 0) χ 2 ( β = 1) ∆ χ 2 # Obs # Exp ( β = 1) # Exp ( β = 0) 4 6.00 3.22 326.865 328.795 -1.930 Δ 𝜓 2 = 𝜓 2 ( β =0) - 𝜓 2 ( β =1) Raj Shah - STFC/Oxford Oscillation analysis @ T2K 23
Sensitivity vs datafit β = 1 β = 0 Asimov Data fit Raj Shah - STFC/Oxford Oscillation analysis @ T2K 24
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