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CP violation in the neutrino sector. Lecture 3: Matter effects in neutrino oscillations, extrinsic CP violation. Walter Winter Nikhef, Amsterdam, 06.03.2014. Contents (overall). Lecture 1: Introduction to neutrino physics, sources of CP violation

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## CP violation in the neutrino sector

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**CP violation in the neutrino sector**Lecture 3: Matter effects in neutrino oscillations, extrinsic CP violation Walter Winter Nikhef, Amsterdam, 06.03.2014**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): (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) Y: electron fraction ~ 0.5 (electrons per nucleon)**Matter profile of the Earth … as seen by a neutrino**Core (PREM: Preliminary Reference Earth Model) Innercore**Parameter mapping … for two flavors, constant matter**density • Oscillation probabilities invacuum:matter: (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) L=11810 km 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 MH Resonance energy (from ):**Application: Mass hierarchy measurement**Neutrinos/Antineutrinos • Matter resonance for • Will be used in the future to determine the mass ordering: 8 8 NormalDm312 >0 InvertedDm312 <0**Mantle-core-mantle profile**(Parametric enhancement: Akhmedov, 1998; Akhmedov, Lipari, Smirnov, 1998; Petcov, 1998) • Probability for L=11810 km Best-fit valuesfrom arXiv:1312.2878 ! Oscillation length ~mantle-core-mantle structureParametric enhancement. Core resonanceenergy Mantleresonanceenergy Naive L/E scalingdoes not apply! Thresholdeffects expected at: 2 GeV 4-5 GeV**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 (WW, arXiv:1305.5539, PRD) • 3s conceivable after three years of operation • Complementary to beams+reactor 3s after 3.5 yr m tracks only (PINGU LOI, arXiv:1401.2046) (WW, arXiv:1305.5539, PRD)**Global context**LBNE 10kt if q23 varied as well Fig. 9 inarXiv:1305.5539 • Bands: risk wrt q23 (PINGU, INO), dCP (NOvA, LBNE), energy resolution (JUNO) • LBNE and sensitivity also scales with q23! True NO (version from PINGU LOI, arXiv:1401.2046,based on Blennow, Coloma, Huber, Schwetz, arXiv:1311.1822)**Extrinsic CP violation**• Matter effects violate CP and even CPT “extrinsically“ • Consequence: Obscure extraction of intrinsic CP violation Need ananti-Earth CP**Impact on CP violation measurement**Matter effectsshift “pencils“ (regions for different hierarchies) away • Matter effects mix up CP-conserving and CP-violating solutions CP conservation q13 (from PRD 70, 033006)**Effect on three flavor effects (repeat)**Antineutrinos: Silver: Platinum, T-inv.: Ideal (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004)**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**Amplitudes of mass eigenstates in matter • Use transformation: … and insert into time-dep. SE […] • Adiabatic limit: • Matter density varies slowly enough such that differential equation system decouples!**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 Averaged vacuumoscillations:Pee=1-0.5 sin22q AdiabaticMSW limit:Pee=sin2q ~ 0.3 Borexino, PRL 108 (2012) 051302**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

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