Neutrino Oscillations And Sterile Neutrinos Keshava Prasad Gubbi University of Bonn s6nagubb@uni-bonn.de May 27, 2016 Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 1 / 26
Overview 1 Neutrinos - A Brief Introduction Pauli s Letter Standard Model Of Particle Physics 2 Neutrino Oscillations Standard Neutrino Oscillation Formula Two Flavor Oscillations Anomalies Observed so far And Hints for New Physics? 3 Sterile Neutrinos-A Brief Introduction What is Sterile about Sterile Neutrinos? Theoretical Motivations-BSM Physics Range of Right Handed Neutrino Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 2 / 26
Pauli s Letter Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 3 / 26
Standard Model Of Particle Physics Image Source: www.wikipedia.org Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 4 / 26
Main Take Away - 1.Neutrinos are assumed to be Massless in Standard Model 2.Experiments Results confirm NEUTRINOS are MASSIVE. For more details-refer to Fernando s Talk. 3.Leads to Flavor Oscillations among Neutrinos. Image Source: T2K experiment j-parc.jp Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 5 / 26
Neutrino Oscillation Probability Assumption:(ν) s in Oscillation Experiment are considered Ultra-Relativistic Leptonic Charged-Current(CC) Lagrangian: L (CC) I,L = g 2 2 (j ρ W,L W ρ + j ρ W,L W ρ ) (1) where in the Leptonic Charged-Current: (for both Dirac and Majorana Neutrinos) j ρ W,L = 2 ν αl γ ρ l αl = 2 Uαk ν αlγ ρ l αl (2) α=e,µ,τ α=e,µ,τ The Fourier expansion of field operator ν K : d 3 p ν kl (x) = (2π) 3 [a ν (h) 2E k (p)u (h) ν k L (p)e ip.x + b ν (h) k (p)v (h) h=±1 k ν k L (p)eip.x ] (3) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 6 / 26
A Neutrino Flavor state (ν α ) with Flavors α = e, µ, τ is created in a charged-current(cc) weak interaction, is described by a Flavor state ν α = k U αk ν k (α = e, µ, τ) (4) U is a Unitary matrix. For simplicity, consider finite normalization volume V with Orthonormal massive neutrino states and flavor states are also Orthonormal ν k ν j = δ kj (5) ν α ν β = δ αβ (6) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 7 / 26
The massive Neutrino states (ν K ) are Eigenstates of Hamiltonian: H ν k = E k ν k (7) With Energy Eigenvalues E k = p 2 + m 2 k (8) The Schrodinger Equation implies: i d dt ν k(t) = H ν k (t) (9) Massive Neutrinos Evolve in time as Plane Waves ν k (t) = e iekt ν k (t) (10) Therefore, the Time evolution of a Neutrino with Flavor state ν α (t) = k U αk e ie kt ν k (t) (11) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 8 / 26
For time t=0, ν α (t = 0) = ν α (12) Using the Unitarity relation, U U = 1 α U αk U αj = δ jk (13) Massive States in terms of Flavor states: ν k = α U αk ν α (14) Putting it all together: ν α (t) = β=e,µ,τ( k U αk e ie kt U βk ) ν β (15) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 9 / 26
The amplitude of transition, as a function of time is A να ν β (t) = k U αk U βkexp( ie k t) (16) The Transition Probability is given by, P να ν β = A 2 ν α ν β = k,j U αk U βku αj U βj exp( i(e k E j )t) (17) For Ultra-relativistic Neutrinos, approximate as: E k E + m2 k 2E ; (18) E k E j m2 kj 2E The squared Mass difference is given by: m kj 2 = m k 2 m j 2 (19) (20) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 10 / 26
Transition Probability is approximated by: P να ν β (t) = k,j U αk U βku αk U βk exp( i m2 kj t 2E ) (21) Ultra-relativistic neutrinos propagate almost at speed of light, hence can approximate t=l, to obtain P να ν β (L, E) = kj U αk U βku αk U βk exp( i m2 kj L 2E ) (22) Phase of Neutrino Oscillation Φ kj = m2 kj L 2E (23) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 11 / 26
Two Neutrino Mixing Approximation: Consider only two of the Three Massive Neutrinos. Advantages: 1 Simpler; Fewer Parameters 2 Certain experiments - NOT sensitive to three Neutrino Mixing; Data can be analyzed via an Effective Model with three Neutrino Mixing The flavor Neutrinos ν α and ν β = Linear Superposition of massive neutrinos ν 1 and ν 2 weighted by elements of mixing matrix ( ) cosθ sinθ U = sinθ cosθ where θ is the Mixing angle. The only squared mass difference is (24) m 2 m 2 21 m 2 2 m 2 1 (25) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 12 / 26
Assume ν 1 to be lighter m 2 Positive Hence, Probability of transition Or Equivalently, P να ν β (L, E) = 1 2 sin2 2θ[1 cos( m2 L 2E )] (26) For α = β, the Survival Probability, P να ν β (L, E) = sin 2 2θsin 2 ( m2 L 4E ) (27) P να ν α (L, E) = 1 P να ν β (L, E) = 1 sin 2 2θsin 2 ( m2 L 4E ) (28) wherein the Oscillation Length L is L osc = 4πE m 2 (29) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 13 / 26
For Reactor Oscillation experiments [E 1Mev] and Accelerator Oscillation experiments [E 1Gev], convenient to write P να νβ (L, E) = sin 2 2θsin 2 (1.27 m2 [ev 2 ]L[m] ) E[MeV ] (30) and the Oscillation length as Results So far: L osc = 2.47 E[MeV ] m 2 [ev 2 [m] (31) ] Atmospheric neutrinos suggest m 2 3 10 3 ev 2 Solar neutrino observations, together with results from the KamLAND reactor neutrino experiment m 2 5 10 5 ev 2 Easily accomodated in extensions of SM by giving masses to at least two of the neutrinos Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 14 / 26
Anomalies in Neutrino Physics LSND Experiment And Later MiniBoone 1 L=30m, L E 1m/MeV ; seeking evidence of Oscillations 2 Observation:ν µ ν e events Observed; Excess of ν e for ν µ ν e modes(at 3.3 σ); m 2 nearly 1Kev 3 MiniBooNE saw NO excesses in ν µ ν e Low energy LSND region Refutes simple 2-neutrino oscillation interpretation of the LSND results! 4 ν µ ν e modes observed. Is 3 Neutrino picture Complete? 5 Possible Explanation: Involvement of 1 or more Sterile Neutrinos; ν µ ν e goes through ν µ ν s ν e 6 Sterile state separated by active states by a mass scale in the range of 0.6 ev 2 m 2 LSND 2 ev 2 Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 15 / 26
Gallium Anomaly 1 GALLEX And SAGE Collaborations-Gallium target radio-chemical experiments 2 objective to study solar neutrinos;observed Flux to expected flux ratio: 0.86 ± 0.06 3 Possible Explanation: Some Neutrinos vanish into sterile ones. Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 16 / 26
Reactor Anomaly 1 Detectors placed near Nuclear power stations to measure ν e 2 Detected flux less than anticipated by about 1 sigma! 3 SBL Reactor neutrino expts: Observed to expected rate= 0.943 ± 0.023 2.5 sigma discrepancy 4 Possible explanation: Are ν e Sterile Neutrino? 5 More Clarity possible in NUCIFER experiment. Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 17 / 26
What is Sterile About Sterile Neutrino? 1 Singlet under all SM Gauge Interactions;does NOT have electric charge, weak hypercharge,weak isospin,color charge 2 Interacts only with Gravity Sterile! 3 Usually refers to Right handed Neutrinos Image Source: www.symmetrymagazine.org Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 18 / 26
Theoretical Motivations-The Missing Piece? Matter fermions with spin 1/2 Weyl Spinors that transforms under irreducible representations of Poincare Group G SM = SU(3) C SU(2) L U(1) Y One generation or family of quarks and leptons: [Q= I L + Y 2 ] q L = (u L,d L ) (3,2 )(1/3),l L = (ν L, e L ) (1,2 )(-1), d R (3, 1)(-2/3),u R (3, 1)(4/3) e R (1, 1)(-2) ν R Missing Piece! Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 19 / 26
Spoils the Quark-Lepton Symmetry Aesthetically Imperfect! But, Aesthetics Do Matter! Add ν R to SM: Introduce n RH fermions ν R,i to SM; couples to LH fermions via Yukawa Interactions L = L SM + iν R / ν R l L F νr Φ νr F l L Φ 1 2 (νc R M Mν R + ν R M M νc R ) i: Flavor index, F:Yukawa couplings Matrix, M M : Majorana Mass term for ν R, ν c R = C.ν R T where C=iγ 0 γ 2 in the Weyl representation (32) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 20 / 26
At E M W, approximate Φ by vev=174gev. Hence, L = L SM + iν R,I / ν R,I (m D ) αi ν L,α ν R,I (m D ) αi ν R,I ν L,α 1 2 [(M M) IJ ν c R,I ν R,J + (M M ) IJ ν R,I ν c R,J ] (33) where Dirac mass matrix m D =F.v at T< T EW Yukawa Interaction ONLY generates m D Only way ν R Interacts with SM is via their mixing with ν L due to m D Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 21 / 26
SM + GR-Still Incomplete! 1 Flavour violation in neutrinos 2 Cosmological origin of the baryonic matter in universe 3 Composition and origin of the observed dark matter 4 Overall geometry of the universe (isotropy, homogeneity and spatial flatness) Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 22 / 26
Range Of Right Handed Neutrino Masses Scale of M M provides various scenarios: M M 10 9 GeV: For F 1, ν R with mass as per GUT models, reproduces Neutrino oscillations Generates the observed baryon density in the universe (Problem II) in CP-violating decays of ν R s M M TeV: Favorable Mass range as it s accessible by high energy experiments of today Problem 2 Can be explained via Leptogenesis from ν R CP-violating oscillations Problem 1 explained via seesaw mechanism Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 23 / 26
M M GeV: Problems(1)-(3) can be described by L alone;no other physics between the electroweak and Planck scales required M M KeV:RH neutrinos with KeV masses promising DM candidates M M ev: Provides explanation Neutrino Anomalies M M =0: Most Interesting Case! With n=3 ν R s, leptonic And quark sector similar without strong interactions neutrinos are Dirac particles Neutrino mass generation via Higgs mechanism Tiny Neutrino masses attributed to very tiny Yukawa couplings. No known principle that forbids M M for the gauge singlet fields ν R Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 24 / 26
References MARCO DREWES (2013) International Journal of Modern Physics EInt. J. Mod. Phys. E, 22, 1330019 Fumihiko Suekane Lecture Notes in Physics Volume 898 Neutrino Oscillations: A Practical Guide to Basics and Applications Raymond R Volkas (2001) ArXiv:hep-ph/0111326v1 Introduction to Sterile Neutrinos Carlo Giunti and Chung W Kim (2007) Fundamentals of Neutrino Physics And Astrophysics Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 25 / 26
Thank You for your Attention! Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 26 / 26