CP violation in the neutrino sectorLecture 3: Matter effects in neutrino oscillations, extrinsic CP violation
Walter Winter
Nikhef, Amsterdam, 06.03.2014
Walter Winter | CPV Amsterdam | 06.02.2014 | Page 2
Contents (overall)
> Lecture 1:Introduction to neutrino physics, sources of CP violation
> Lecture 2:Neutrino oscillations in vacuum, measurement of dCP
> Lecture 3:Matter effects in neutrino oscillations: “extrinsic CP violation”
> Lecture 4:New sources of CP violation?
References:
> WW: “Lectures on neutrino phenomenology“, Nucl. Phys. Proc. Suppl. 203-204 (2010) 45-81
> Giunti, Kim: “Fundamentals of neutrino physics and astrophysics“, Oxford, 2007
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Contents (lecture 3)
>Matter effects in CP violation … and measurement of the mass hierarchy
> Extrinsic CP violation
>Neutrino oscillations in varying densities. Example: Sun
> Summary
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Matter effects in neutrino oscillations
… and measurement of the neutrino mass hierarchy
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Matter effect (MSW)
>Ordinary matter: electrons, but no m, t
>Coherent forward scattering in matter: Net effect on electron flavor
>Hamiltonian in matter (matrix form, flavor space):
Y: electron fraction ~ 0.5
(electrons per nucleon)
(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)
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Matter profile of the Earth … as seen by a neutrino
(PR
EM
: Prelim
inary R
eference E
arth M
odel)
Core
Innercore
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Parameter mapping … for two flavors, constant matter density
>Oscillation probabilities invacuum:matter:
For nm appearance, Dm312:
- r ~ 4.7 g/cm3 (Earth’s mantle): Eres ~ 6.4 GeV- r ~ 10.8 g/cm3 (Earth’s outer core): Eres ~ 2.8 GeV
Resonance energy (from ):
MH
(Wolfenstein, 1978; Mikheyev, Smirnov,
1985)
L=11810 km
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Application: Mass hierarchy measurement
>Matter resonance for
>Will be used in the future to determine the mass ordering:
8
8
NormalDm31
2 >0Inverted
Dm312 <0
Normal Inverted
Neutrinos Resonance Suppression
Antineutrinos Suppression Resonance
Neutrinos/Antineutrinos
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Mantle-core-mantle profile
> Probability for L=11810 km
(Parametric enhancement: Akhmedov, 1998; Akhmedov, Lipari, Smirnov, 1998; Petcov, 1998)
Core resonance
energy Mantleresonance
energy
Thresholdeffects
expected at:2 GeV 4-5 GeV
Naive L/E scalingdoes not apply!
Oscillation length ~mantle-core-mantle structure
Parametric enhancement.
!Best-fit values
from arXiv:1312.2878
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Emerging technologies: PINGU
> Fill in IceCube/DeepCore array with additional strings Lower threshold
Particle physics!?
> PINGU (“Precision IceCube Next Generation Upgrade“):
> 40 additional strings, 60 optical modules each
>Modest cost, US part ~ 55-80 M$, foreign ~ 25 M$ (including contingency)
>Completion 2019/2020?
> Similar idea in Mediterranean:ORCA (PINGU LOI, arXiv:1401.2046)
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Mass hierarchy measurement … PINGU, using atmospheric neutrinos
> 3s conceivable after three years of operation
>Complementary to beams+reactor
(WW, arXiv:1305.5539, PRD)
m tracks only
(PINGU LOI, arXiv:1401.2046)
3s after 3.5 yr
(WW
, arX
iv:1
305.
5539
, PR
D)
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Global context
> Bands: risk wrt q23 (PINGU, INO), dCP (NOvA, LBNE), energy resolution (JUNO)
> LBNE and sensitivity also scales with q23!
(version from PINGU LOI, arXiv:1401.2046, based on Blennow, Coloma, Huber, Schwetz, arXiv:1311.1822)
True NO
LBNE 10kt if q23 varied as well Fig. 9 in arXiv:1305.5539
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Extrinsic CP violation
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Extrinsic CP violation
>Matter effects violate CP and even CPT “extrinsically“
>Consequence: Obscure extraction of intrinsic CP violation
CPNeed an
anti-Earth
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Impact on CP violation measurement
>Matter effects mix up CP-conserving and CP-violating solutions
CP conservation
Matter effectsshift “pencils“ (regions for different hierarchies) away
q13
(from PRD 70, 033006)
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Effect on three flavor effects (repeat)
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004)
> Antineutrinos:
> Silver:
> Platinum, T-inv.: Ideal
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Matter effects in varying density profiles
Example: Sun
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Constant vs. varying matter density
> For constant matter density:
is the Hamiltonian in constant density is the mixing matrix described by
> For varying matter density: time-dep. Schrödinger equation (H explicitely time-dependent!)
Transition amplitudes; yx: mixture ym and yt
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Adiabatic limit
>Use transformation:
… and insert into time-dep. SE […]
> Adiabatic limit:
Matter density varies slowly enough such that differential equation system decouples!
Amplitudes of mass eigenstates in matter
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Propagation in the Sun
>Neutrino production as ne (fusion) at high ne
>Neutrino propagates as mass eigenstate in matter (DE decoupled); x: phase factor from propagation
> In the Sun: ne(r) ~ ne(0) exp(-r/r0) (r0 ~ Rsun/10); therefore density drops to zero!
>Detection as electron flavor:Disappearance
of solarneutrinos!
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Solar oscillations
> In practice: A >> 1 only for E >> 1 MeV
> For E << 1 MeV: vacuum oscillations
Borexino, PRL 108 (2012) 051302
Averaged vacuumoscillations:
Pee=1-0.5 sin22qAdiabatic
MSW limit:Pee=sin2 q ~ 0.3
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Summary
> Electron neutrinos interact with matter by coherent foward scattering
>Can be used to measure neutrino mass hierarchy
>However: can also obscure the extraction of “intrinsic CP violation“ (Earth matter violates CP and CPT explicitely)
>Matter effects in varying matter densities even more subtle; example: adiabatic flavor conversions in the Sun