cp violation in the neutrino sector

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 |

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


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


Matter effects in neutrino oscillations

… and measurement of the neutrino mass hierarchy


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)


Matter profile of the Earth … as seen by a neutrino

(PR

EM

: Prelim

inary R

eference E

arth M

odel)

Core

Innercore


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


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


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


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)


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)


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


Extrinsic CP violation


Extrinsic CP violation

>Matter effects violate CP and even CPT “extrinsically“

>Consequence: Obscure extraction of intrinsic CP violation

CPNeed an

anti-Earth


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)


Effect on three flavor effects (repeat)

(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004)

> Antineutrinos:

> Silver:

> Platinum, T-inv.: Ideal


Matter effects in varying density profiles

Example: Sun


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


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


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!


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


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

cp violation in the neutrino sector

Documents

matter effects

kmwalter winter cpv

matter profile

neutrino prem

neutrino sectorlecture

neutrino phenomenology

matter matrix form

extrinsic cp violationlecture