oscillation analyses at T2K Raj Shah (STFC/Oxford) 19/07/16 1 - - PowerPoint PPT Presentation

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oscillation analyses at T2K Raj Shah (STFC/Oxford) 19/07/16 1 - - PowerPoint PPT Presentation

Sep 12, 2022 95 likes •353 views

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

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SLIDE 1

ν̅ oscillation analyses at T2K

Raj Shah (STFC/Oxford) 19/07/16

1

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Outline

  • Neutrino oscillations
  • The T2K experiment
  • Analysis strategy
  • Results
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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Neutrino Mixing

θ13 θ23

δCP

∆m2

12 ∆m2

23

∆m2

13

Solar Atmospheric Reactor | LBL

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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CP Violation

P(νµ → νe) − P(ν¯

µ → ν¯ e)

= −16S12C12S13C2

13S23C23Sin(δ)Sin(∆12)Sin(∆23)Sin(∆13)

∝ Sin(∆12)Sin(∆23)Sin(∆13) ∆ij = ∆mijL 4E ∝ Sin(θ12)Sin(θ23)Sin(θ13) ∝ Sin(δCP ) P(νµ ! νµ) 6= P(¯ νµ ! ¯ νµ) CPT Violation!!

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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T2K

Tokai to Kamioka

μ-like e-like

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Detectors + Beam

Ingrid ND280

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Oscillation analysis

Flux Cross section MC Prediction Oscillation fit ND Constraint SK Efficiencies Oscillation Prob Data

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SLIDE 8

Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Oscillation analysis

Flux Cross section MC Prediction Oscillation fit ND Constraint SK Efficiencies Oscillation Prob Data

Good Fit!

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Predicted spectra

μ-like e-like ν

7.00e20 POT

ν̅

7.41e20 POT

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Joint analysis results

ν: 7.00e20 POT ν ̅: 7.41e20 POT Nuisance parameters marginalised

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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ν̅e appearance

μ-like e-like ν

7.00e20 POT

ν̅

7.41e20 POT

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SLIDE 12

Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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ν̅e appearance

Do ν̅μ oscillate into ν̅e?

7.41e20 POT

Signal: ν ̅μ ➡ ν ̅e

2.786

1.04 1.47 0.71 3.22

Osc 𝝃e Beam 𝝃e NC Tot

Background

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Frequentist analysis

Null hypotheses

No ν ̅e appearance (𝛾=0) PMNS ν ̅e appearance (𝛾=1)

Posc(ν ̅μ ➡ ν ̅e) = 𝛾 · Posc(PMNS) Posc(𝝃x ➡ 𝝃y) = Posc(PMNS)

Statistic

Δ𝝍2 = 𝝍2(𝛾=0) - 𝝍2(𝛾=1)

P Value: Probability to observe data as or more extreme than what was observed under the null hypothesis

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Results

=1) β (

2

χ =0) - β (

2

χ =

2

χ ∆

5 − 5 10 15 20

)

2

χ ∆ ))/d(

2

χ ∆ d(p(

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Data P-Value =1 β 0.099 =0 β 0.374

  • 1.93
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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Bayesian results

P (β = 0|D) P (β = 1|D) = π(β = 0) π(β = 1)B01 = π(β = 0) π(β = 1)e−0.5×∆χ2

marg

B01 = 2.62 Weak preference for 𝛾=0

B01 = Marginal Likelihood ratio

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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ν̅μ Disappearance

  • Introduce new separate parameters sin2(θ

̅ 23) and Δm ̅ 232 for 𝝃 oscillations.

  • Fix all ν oscillation (background) PMNS parameters
  • Fit ν

̅ oscillation parameters and compare with ν fit.

ν: 6.57e20 POT vs ν ̅: 4.01e20 POT

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Summary

Joint Analysis

  • Constraints on all ν oscillation parameters
  • Hint towards maximal CP violation
  • ν̅e Appearance
  • Preference for no ν̅e appearance
  • 10% p-value for PMNS appearance
  • ν̅μ Disappearance
  • Consistent constraints for ν and ν̅ oscillations
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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Back ups

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Data vs Expectation

1Rµ 1Re 𝜉 𝜉̅

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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ν̅e Appearance

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Null distribution #1

Method:

  • 1. Throw model parameters (osc and syst) based on priors
  • 2. Generate all 4 predicted spectra (Nexp)
  • 3. Compute likelihood ℒ (ν 1R𝜈, ν 1Re, ν̅ 1R𝜈 | data)
  • 4. Any toy dataset derived from Nexp has a weight given by ℒ

when filling the null hypothesis statistic distribution

  • Prior knowledge: ν 1Re, ν 1R𝜈, ν̅ 1R𝜈
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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Null distribution #2

(1) Take Nexp from method in previous slide

  • (2) Throw poisson from Nexp ν̅ 1Re
  • (3) Calculate statistic Δ𝜓2 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
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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Signal vs Background

# Obs # Exp (β = 1) # Exp (β = 0) χ2(β = 0) χ2(β = 1) ∆χ2 4 6.00 3.22 326.865 328.795

  • 1.930

Δ𝜓2 = 𝜓2(β=0) - 𝜓2(β=1)

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Raj Shah - STFC/Oxford Oscillation analysis @ T2K

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Sensitivity vs datafit

β = 1 β = 0 Asimov Data fit