Matter E ff ect in Long Baseline Neutrino Oscillation Masafumi - PowerPoint PPT Presentation

Neutrino Frontier Workshop 2014 (Fuji Calm, 2014.12.21) Matter E ff ect in Long Baseline Neutrino Oscillation Masafumi Koike (Utsunomiya U.) working with Toshihiko Ota (Saitama U.) Masako Saito (Utsunomiya U.) Joe Sato (Saitama U.)

Introduction 1

Neutrino Mixings: Achievements From discovery to precision measurements PHYSICAL REVIEW D 89, 093018 (2014) Status of three-neutrino oscillation parameters, circa 2013 F. Capozzi, 1,2 G. L. Fogli, 1,2 E. Lisi, 2 A. Marrone, 1,2 D. Montanino, 3,4 and A. Palazzo 5 1 Dipartimento Interateneo di Fisica “ Michelangelo Merlin, ” Via Amendola 173, 70126 Bari, Italy Δ I-N ¼ Parameter Best fit 1 σ range 2 σ range δ m 2 = 10 − 5 eV 2 (NH or IH) 7.54 7.32 – 7.80 7.15 – 8.00 sin 2 θ 12 = 10 − 1 (NH or IH) 3.08 2.91 – 3.25 2.75 – 3.42 Δ m 2 = 10 − 3 eV 2 (NH) 2.43 2.37 – 2.49 2.30 – 2.55 Δ m 2 = 10 − 3 eV 2 (IH) 2.38 2.32 – 2.44 2.25 – 2.50 sin 2 θ 13 = 10 − 2 (NH) 2.34 2.15 – 2.54 1.95 – 2.74 sin 2 θ 13 = 10 − 2 (IH) 2.40 2.18 – 2.59 1.98 – 2.79 sin 2 θ 23 = 10 − 1 (NH) 4.37 4.14 – 4.70 3.93 – 5.52 sin 2 θ 23 = 10 − 1 (IH) 4.55 4.24 – 5.94 4.00 – 6.20 δ = π (NH) 1.39 1.12 – 1.77 0 . 00 − 0 . 16 ⊕ 0 . 86 − 2 . 00 δ = π (IH) 1.31 0.98 – 1.60 0 . 00 − 0 . 02 ⊕ 0 . 70 − 2 . 00

Neutrino Mixings: 
 Challenges δ m 231 ≷ 0 ? Mass Hierarchy Octant Degeneracy θ 23 ≷ π /4 ? Leptonic CP Violation sin δ CP = 0 ? Oscillation experiments with very long baseline (1000~10000 km) Exploiting the matter effect

Evaluating the Matter E ff ect K. Hagiwara, T. Kiwanami, N. Okamura, K.-i. Senda (2013) 50 20 (a1) OAB1.4( ν µ ) normal - Physics potential of neutrino oscillation experiment (b1) OAB1.4( ν µ ) normal BG+ ν µ →ν e - - BG+ ν µ →ν e - - - - ν e →ν e + ν e + ν - - 40 µ →ν e →ν with a far detector in Oki Island e ν e →ν e + ν µ →ν e + ν e →ν e - - - - e + ν ν µ →ν e →ν ν µ →ν e + ν e →ν e e - - ν e →ν ν e →ν e along the T2K baseline e 30 10 20 10 L = 693km 0 0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 E ν (GeV) E ν (GeV) 50 20 - (a2) OAB1.4( ν µ ) inverted (b2) OAB1.4( ν µ ) inverted BG+ ν µ →ν e - - BG+ ν µ →ν e - - - - - - 40 ν e →ν e + ν µ →ν e + ν e →ν e e + ν µ →ν e + ν e →ν e ν e →ν - - - - ν µ →ν e + ν e →ν ν µ →ν e + ν e →ν e e - - ν e →ν ν e →ν e e 30 10 20 10 0 0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 E ν (GeV) E ν (GeV) Event number/[2.5x10 21 POT] vs E ν /[GeV]

Earth Model 14 Preliminary Reference Earth Model 12 10 Density / [g/cm 3 ] outer core inner core 8 mantle crust 6 4 2 0 0 1000 2000 3000 4000 5000 6000 Length / [km]

Density Profile on a Baseline 12 10 8 3 ] Density / [g/cm L = 12,000 km 6 L = 7,500 km 4 2 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 Length / [km]

Matter Density Profile 12 12 Cosine 10 10 Crust & Mantle Crust & Mantle Density / [g/cm 3 ] Density / [g/cm 3 ] 8 8 Average Core 6 6 4 4 2 2 N = 0 N = 1 L = 12000km L = 12000km 0 0 0 0 2000 2000 4000 4000 6000 6000 8000 8000 10000 10000 12000 12000 Length / [km] Length / [km]

Constant vs. Earth Model L = 12000 km 2 V 5 e − 0 1 31 = 2 . 5 10 − 3 eV 2 9 7 . = 2 δ m 1 2 δ m 2 sin 2 2 θ 12 = 0 . 84 sin 2 2 θ 23 = 1 . 00 = 0 . 05 2 θ 3 2 1 sin δ = 0 . 00 sin ρ 0 = 7 . 58 g / cm 3 ρ 1 = − 2 . 16 g / cm 3

Matter Profile: Fourier Series 12 12 12 12 12 12 12 12 10 10 10 10 10 10 10 10 Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] Density / [g/cm 3 ] 8 8 8 8 8 8 8 8 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 N = 100 N = 10 N = 50 N = 5 N = 500 N = 3 N = 1 N = 0 L = 12000km L = 12000km L = 12000km L = 12000km L = 12000km L = 12000km L = 12000km L = 12000km 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2000 2000 2000 2000 2000 2000 2000 2000 4000 4000 4000 4000 4000 4000 4000 4000 6000 6000 6000 6000 6000 6000 6000 6000 8000 8000 8000 8000 8000 8000 8000 8000 10000 10000 10000 10000 10000 10000 10000 10000 12000 12000 12000 12000 12000 12000 12000 12000 Length / [km] Length / [km] Length / [km] Length / [km] Length / [km] Length / [km] Length / [km] Length / [km]

Formulation 2

Modeling Density Profiles Step function Akhmedov (1988), Krastev-Smirnov (1989), Krastev-Smirnov (1989), Liu-Smirnov (1998), Petcov (1998), Chizhov-Petcov (1998), ..., Akhmedov-Maltoni-Smirnov (2005), ... Fourier series Koike-Sato (1998), Ota-Sato (2003), Koike-Ota-Saito-Sato (2009)...

Two-Flavor Oscillation MK-Ota-Saito-Sato, PLB 675 , 69 (2009) Evolution equation of the two-flavor neutrino ⇤ δ m 2 � ⇥ � ⇥ � ⇥⌅ � ⇥ i d = 1 ν e ( x ) − cos 2 θ sin 2 θ a ( x ) 0 ν e ( x ) + ν µ ( x ) sin 2 θ cos 2 θ 0 0 ν µ ( x ) d x 2 E 2 Matter effect √ a ( x ) = 2 2 G F n e ( x ) E Second-order equation in dimensionless variables z �� ( ξ ) + 1 ⇥ 2 + ∆ 2 sin 2 2 θ + 2i ∆ � ⇤� ⌅ ∆ m ( ξ ) − ∆ cos 2 θ m ( ξ ) z ( ξ ) = 0 4 Dimensionless variables: ∆ ≡ δ m 2 L ∆ m ( ξ ) ≡ a ( ξ ) L ξ ≡ x 2 E L 2 E Matter effect Distance Reciprocal E ⇥ i � ξ � 2 = ⇤ � 2 � � � � � ν e ( ξ ) � z ( ξ ) z ( ξ ) = ν e ( ξ ) exp d s ∆ m ( s ) · · · 2 0 z (0) = 0 , z � (0) = − i ∆ Initial conditions , ν µ (0) = 1 2 sin 2 θ ν e (0) = 0

Constant-Density Matter Constant density: Δ m ( ξ ) ≡ Δ 0 = (const.) �� � z �� ( ξ ) + 1 � 2 + ∆ 2 sin 2 2 θ + 2i ∆ � ∆ m ( ξ ) − ∆ cos 2 θ m ( ξ ) z ( ξ ) = 0 4 � �� � (const.) ≡ ω 2 0 Prob( ν µ → ν e ) ∝ sin 2 ω 0 ξ ξ = 1 Dips at ω 0 = n π 3 2 1 1

Inhomogeneous Matter z �� ( ξ ) + 1 ⇥ 2 + ∆ 2 sin 2 2 θ + 2i ∆ � ⇤� ⌅ ∆ m ( ξ ) − ∆ cos 2 θ m ( ξ ) z ( ξ ) = 0 4 Fourier series of inhomogeneous matter ∞ ∞ ρ n cos 2 n π � � ρ ( x ) = ∆ m ( ξ ) = ∆ m n cos 2 n πξ L x , Mathieu Equation n =0 n =0 Presence of the n-th Fourier mode z �� ( t ) + ( ω 2 − 2 ε cos t ) z ( t ) = 0 ρ ( x ) = ρ 0 + ρ n cos 2 n π ∆ m ( ξ ) = ∆ m0 + ∆ m n cos 2 n πξ L x , ω 2 � ⇥ z �� ( ξ ) + 0 + α n cos 2 n πξ − i β n sin 2 n πξ + γ n cos 4 n πξ z ( ξ ) = 0 0 = 1 4( ∆ m0 − ∆ cos 2 θ ) 2 + 1 4 ∆ 2 sin 2 2 θ + 1 ω 2 8 ∆ 2 m n , α n = 1 γ n = 1 8 ∆ 2 β n = n π ∆ m n , 2( ∆ m0 − ∆ cos 2 θ ) ∆ m n , m n

Parametric Resonance • Periodic perturbation • Twice in a period • Grows amplitude of oscillation ω 0 • Matter effect as a bunch of periodic perturbations Pow! Pow! 2 ω 0 Ermilova et al. (1986), Akhmedov (1988), Krastev- Smirnov (1989), Liu-Smirnov (1998), Petcov (1998), Chizhov-Petcov (1998), ..., Akhmedov-Maltoni- Smirnov (2005), ...

Resonance Condition ω 2 � ⇥ z �� ( ξ ) + 0 + α n cos 2 n πξ − i β n sin 2 n πξ + γ n cos 4 n πξ z ( ξ ) = 0 n-th mode Matter Profile Parametric Resonance Mode 1 Condition Mode 1 1st dip n-th dip Mode 2 ω 0 = n π Mode 2 2nd dip δ m 2 L 1 E = E ( ± ) Mode 3 ≡ � n 2 m0 sin 2 2 θ 4 n 2 π 2 − ∆ 2 ∆ m0 cos2 θ ± Mode 3 3rd dip The values of other parameters used in this plot found in arXiv:0902.1597

E ff ect of the Mode 1 1st Dip ρ 1 = (0 → 5)g/cm 3

E ff ect of the Mode 2 2nd Dip ρ 2 = (0 → 5)g/cm 3

Matter-Profile E ff ects 3

Oscillogram: Full Profile 12 10 Density / [g/cm 3 ] 8 6 0.1 4 0.1 2 0.1 0.4 N = 0 L = 12000km 0.1 12500 0 0 2000 4000 6000 8000 10000 12000 0.4 Baseline Length / [km] Length / [km] 0.1 0 . 0.3 2 12000 0.3 0.1 0.4 0.1 0.1 0.1 0.3 0.3 11500 0.2 0.2 0.1 11000 Full (PREM) 0.1 0.1 0.2 0.4 0 . 3 10500 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Neutrino Energy / [GeV]

Fourier Coe ffi cients 8 –3 ] 0th (Average) 6 Coefficient / [g cm 4 2 2nd 0 3rd 1st -2 10500 11000 11500 12000 12500 Baseline Length / [km]

0.4 Full (PREM) 0.3 0.4 0.1 0.2 12500 0.2 Baseline Length / [km] 0.1 0.3 Oscillogram: First Few Modes 12000 0.3 0.1 0.3 11500 0.2 0.1 11000 0.1 0 0.1 . 1 0.2 0.1 0.4 0.3 10500 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0.4 0.4 0.3 0.3 Const. (0th) Up to 1st Neutrino Energy / [GeV] 0.3 0.1 0 0 0.3 . . 12500 12500 4 2 Baseline Length / [km] 0.2 0.3 0.2 0 . 4 0.1 0.1 0.1 0.2 0.1 12000 12000 0.1 0.3 0.3 11500 11500 0 . 2 0 . 1 0.1 11000 11000 0.1 0.1 0.2 0.4 0.3 0.1 0.2 0.4 0.3 10500 10500 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0.3 0.3 0.4 Up to 2nd Up to 3rd 0.3 0.3 0 0 0 0 0.4 . . . . 2 1 2 1 12500 12500 0.1 Baseline Length / [km] 0.2 0.4 12000 12000 0.1 0.1 3 0.1 0.3 . 0 0.3 0.3 11500 11500 0 . 0.2 2 0 0 . 1 . 1 0.2 11000 11000 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0 . 0.4 0.4 3 0.3 10500 10500 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 ν µ → ν e Neutrino Energy / [GeV] Neutrino Energy / [GeV]