CP violation in the neutrino sector Lecture 3: Matter effects in neutrino oscillations, extrinsic CP violation Walter Winter Nikhef, Amsterdam,

Walter Winter | CPV Amsterdam | | Page 2 Contents (overall) > Lecture 1: Introduction to neutrino physics, sources of CP violation > Lecture 2: Neutrino oscillations in vacuum, measurement of  CP > 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 (2010) > Giunti, Kim: “ Fundamentals of neutrino physics and astrophysics “, Oxford, 2007

Walter Winter | CPV Amsterdam | | Page 3 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

Walter Winter | CPV Amsterdam | | Page 4 Matter effects in neutrino oscillations … and measurement of the neutrino mass hierarchy

Walter Winter | CPV Amsterdam | | Page 5 Matter effect (MSW) > Ordinary matter: electrons, but no ,  > 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)

Walter Winter | CPV Amsterdam | | Page 6 Matter profile of the Earth … as seen by a neutrino (PREM: Preliminary Reference Earth Model) Core Inner core

Walter Winter | CPV Amsterdam | | Page 7 Parameter mapping … for two flavors, constant matter density > Oscillation probabilities in vacuum: matter: For  appearance,  m 31 2 : -  ~ 4.7 g/cm 3 (Earth’s mantle): E res ~ 6.4 GeV -  ~ 10.8 g/cm 3 (Earth’s outer core): E res ~ 2.8 GeV Resonance energy (from ):  MH (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) L=11810 km

Walter Winter | CPV Amsterdam | | Page 8 Application: Mass hierarchy measurement > Matter resonance for > Will be used in the future to determine the mass ordering: 8 8 Normal  m 31 2 >0 Inverted  m 31 2 <0 NormalInverted NeutrinosResonanceSuppression AntineutrinosSuppressionResonance Neutrinos/Antineutrinos

Walter Winter | CPV Amsterdam | | Page 9 Mantle-core-mantle profile > Probability for L=11810 km (Parametric enhancement: Akhmedov, 1998; Akhmedov, Lipari, Smirnov, 1998; Petcov, 1998) Core resonance energy Mantle resonance energy Threshold effects expected at: 2 GeV 4-5 GeV Naive L/E scaling does not apply! Oscillation length ~ mantle-core-mantle structure Parametric enhancement. ! Best-fit values from arXiv:

Walter Winter | CPV Amsterdam | | Page 10 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 ~ M$, foreign ~ 25 M$ (including contingency) > Completion 2019/2020? > Similar idea in Mediterranean: ORCA (PINGU LOI, arXiv: )

Walter Winter | CPV Amsterdam | | Page 11 Mass hierarchy measurement … PINGU, using atmospheric neutrinos > 3  conceivable after three years of operation > Complementary to beams+reactor (WW, arXiv: , PRD)  tracks only (PINGU LOI, arXiv: )  after 3.5 yr (WW, arXiv: , PRD)

Walter Winter | CPV Amsterdam | | Page 12 Global context > Bands: risk wrt  23 (PINGU, INO),  CP (NOvA, LBNE), energy resolution (JUNO) > LBNE and sensitivity also scales with  23 ! (version from PINGU LOI, arXiv: , based on Blennow, Coloma, Huber, Schwetz, arXiv: ) True NO LBNE 10kt if  23 varied as well  Fig. 9 in arXiv:

Walter Winter | CPV Amsterdam | | Page 13 Extrinsic CP violation

Walter Winter | CPV Amsterdam | | Page 14 Extrinsic CP violation > Matter effects violate CP and even CPT “extrinsically“ > Consequence: Obscure extraction of intrinsic CP violation CP Need an anti-Earth

Walter Winter | CPV Amsterdam | | Page 15 Impact on CP violation measurement > Matter effects mix up CP-conserving and CP-violating solutions CP conservation Matter effects shift “pencils“ (regions for different hierarchies) away  13 (from PRD 70, )

Walter Winter | CPV Amsterdam | | Page 16 Effect on three flavor effects (repeat) (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004) > Antineutrinos: > Silver: > Platinum, T-inv.: Ideal

Walter Winter | CPV Amsterdam | | Page 17 Matter effects in varying density profiles Example: Sun

Walter Winter | CPV Amsterdam | | Page 18 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;  x : mixture   and  

Walter Winter | CPV Amsterdam | | Page 19 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

Walter Winter | CPV Amsterdam | | Page 20 Propagation in the Sun > Neutrino production as e (fusion) at high n e > Neutrino propagates as mass eigenstate in matter (DE decoupled);  : phase factor from propagation > In the Sun: n e (r) ~ n e (0) exp(-r/r 0 ) (r 0 ~ R sun /10); therefore density drops to zero! > Detection as electron flavor: Disappearance of solar neutrinos!

Walter Winter | CPV Amsterdam | | Page 21 Solar oscillations > In practice: A >> 1 only for E >> 1 MeV > For E << 1 MeV: vacuum oscillations Borexino, PRL 108 (2012) Averaged vacuum oscillations: P ee =1-0.5 sin 2 2  Adiabatic MSW limit: P ee =sin 2  ~ 0.3

Walter Winter | CPV Amsterdam | | Page 22 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