Keshava Prasad Gubbi - uni-bonn.de...Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile...

Neutrino Oscillations And Sterile Neutrinos

Keshava Prasad Gubbi

University of Bonn

[email protected]

May 27, 2016

Keshava Prasad Gubbi (Uni Bonn) Neutrino Oscillations,Sterile Neutrinos May 27, 2016 1 / 26

Overview

1 Neutrinos - A Brief IntroductionPauli’s LetterStandard Model Of Particle Physics

2 Neutrino OscillationsStandard Neutrino Oscillation FormulaTwo Flavor OscillationsAnomalies Observed so far And Hints for New Physics?

3 Sterile Neutrinos-A Brief IntroductionWhat is Sterile about Sterile Neutrinos?Theoretical Motivations-BSM PhysicsRange of Right Handed Neutrino


Pauli’s Letter


Standard Model Of Particle Physics

Image Source: www.wikipedia.org


Main Take Away -1.Neutrinos are assumed to be Massless in Standard Model2.Experiments Results confirm NEUTRINOS are MASSIVE. For moredetails-Refer to Fernando’s Talk.3.Leads to Flavor Oscillations among Neutrinos.

Image Source: T2K experiment j-parc.jp


Neutrino Oscillation Probability

Assumption:(ν)’s in Oscillation Experiment are consideredUltra-RelativisticLeptonic Charged-Current(CC) Lagrangian:

L(CC)I ,L = − g

2√

2(jρW ,LWρ + jρ†W ,LW

†ρ ) (1)

where in the Leptonic Charged-Current: (for both Dirac and MajoranaNeutrinos)

jρW ,L = 2∑

α=e,µ,τ

ναLγρlαL = 2

∑α=e,µ,τ

∑k

U∗αkναLγρlαL (2)

The Fourier expansion of field operator νK :

νkL(x) =

∫d3p

(2π)32E

∑h=±1

[a(h)†νk(p)u

(h)νkL

(p)e−ip.x + b(h)νk(p)v

(h)νkL

(p)e ip.x ]

(3)


A Neutrino Flavor state (να) with Flavors α = e, µ, τ is created in acharged-current(CC) weak interaction, is described by a Flavor state

|να〉 =∑k

U∗αk |νk〉 (α = e, µ, τ) (4)

U is a Unitary matrix. For simplicity, consider finite normalization volumeV with Orthonormal massive neutrino states

〈νk |νj〉 = δkj (5)

and flavor states are also Orthonormal

〈να|νβ〉 = δαβ (6)


The amplitude of transition, as a function of time is

Aνα→νβ (t) =∑k

U∗αkUβkexp(−iEkt) (16)

The Transition Probability is given by,

Pνα→νβ = A2να→νβ =

∑k,j

U∗αkUβkUαjU∗βjexp(−i(Ek − Ej)t) (17)

For Ultra-relativistic Neutrinos, approximate as:

Ek ≈ E +m2

k

2E; (18)

Ek − Ej ≈∆m2

kj

2E(19)

The squared Mass difference is given by:

∆mkj2 = mk

2 −mj2 (20)


Transition Probability is approximated by:

Pνα→νβ (t) =∑k,j

U∗αkUβkUαkU∗βkexp(−i

∆m2kj t

2E) (21)

Ultra-relativistic neutrinos propagate almost at speed of light, hence canapproximate t=L, to obtain

Pνα→νβ (L,E ) =∑kj

U∗αkUβkUαkU∗βkexp(−i

∆m2kjL

2E) (22)

Phase of Neutrino Oscillation

Φkj = −∆m2

kjL

2E(23)


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; Datacan be analyzed via an Effective Model with three Neutrino Mixing

The flavor Neutrinos να and νβ = Linear Superposition of massiveneutrinos ν1 and ν2 weighted by elements of mixing matrix

U =

(cosθ sinθ−sinθ cosθ

)(24)

where θ is the Mixing angle.The only squared mass difference is

∆m2 ≡ ∆m221 ≡ m2

2 −m21 (25)


Assume ν1 to be lighter ⇒ ∆m2 PositiveHence, Probability of transition

Pνα→νβ (L,E ) =1

2sin22θ[1− cos(

∆m2L

2E)] (26)

Or Equivalently,

Pνα→νβ (L,E ) = sin22θsin2(∆m2L

4E) (27)

For α = β, the Survival Probability,

Pνα→να(L,E ) = 1− Pνα→νβ (L,E ) = 1− sin22θsin2(∆m2L

4E) (28)

wherein the Oscillation Length L is

Losc =4πE

∆m2(29)


For Reactor Oscillation experiments [E ≈ 1Mev ] and AcceleratorOscillation experiments [E ≈ 1Gev ], convenient to write

Pνα→νβ (L,E ) = sin22θsin2(1.27∆m2[eV 2]L[m]

E [MeV ])

(30)

and the Oscillation length as

Losc = 2.47E [MeV ]

∆m2[eV 2][m] (31)

Results So far:

Atmospheric neutrinos suggest ∆m2 ∼ 3 × 10−3 eV 2

Solar neutrino observations, together with results from the KamLANDreactor neutrino experiment ∆m2 ∼ 5 × 10−5 eV 2

⇒ Easily accomodated in extensions of SM by giving masses to at leasttwo of the neutrinos


Anomalies in Neutrino Physics

LSND Experiment And Later MiniBoone

1 L=30m, LE ∼ 1m/MeV ; seeking evidence of Oscillations

2 Observation:νµ → νe events Observed; Excess of νe for νµ → νemodes(at 3.3 σ); ∆m2 nearly 1Kev

3 MiniBooNE saw NO excesses in νµ → νe Low energy LSND region ⇒Refutes simple 2-neutrino oscillation interpretation of the LSNDresults!

4 νµ → νe modes observed. ⇒ Is 3 Neutrino picture Complete?

5 Possible Explanation: Involvement of 1 or more Sterile Neutrinos;νµ → νe goes through νµ → νs → νe

6 Sterile state separated by active states by a mass scale in the range of0.6 eV 2 ≤ ∆m2

LSND ≤ 2 eV 2


Gallium Anomaly

1 GALLEX And SAGE Collaborations-Gallium target radio-chemicalexperiments

2 objective to study solar neutrinos;Observed Flux to expected fluxratio: 0.86 ± 0.06

3 Possible Explanation: Some Neutrinos vanish into sterile ones.


Reactor Anomaly

1 Detectors placed near Nuclear power stations to measure νe2 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 νe → Sterile Neutrino?

5 More Clarity possible in NUCIFER experiment.


What is ”Sterile” About Sterile Neutrino?

1 Singlet under all SM Gauge Interactions;does NOT have electriccharge, weak hypercharge,weak isospin,color charge

2 Interacts only with Gravity ⇒ Sterile!3 Usually refers to Right handed Neutrinos

Image Source: www.symmetrymagazine.org


Theoretical Motivations-The Missing Piece?

Matter ⇒ fermions with spin 1/2 ⇒Weyl Spinors that transforms under irreducible representations of PoincareGroupGSM= SU(3)C ⊗ SU(2)L ⊗ U(1)YOne generation or family of quarks and leptons: [Q= IL + Y

2 ]qL= (uL,dL) ∼ (3,2 )(1/3),lL= (νL, eL) ∼ (1,2 )(-1),dR ∼ (3, 1)(-2/3),uR ∼ (3, 1)(4/3)eR ∼ (1, 1)(-2)νR → Missing Piece!


Spoils the Quark-Lepton Symmetry ⇒ Aesthetically Imperfect!But, Aesthetics Do Matter!Add νR to SM: Introduce ’n’ RH fermions νR,i to SM; couples to LHfermions via Yukawa Interactions

L = LSM + iνR /∂νR − lLFνR Φ̃− νRF †lLΦ̃† − 1

2(νcRMMνR + νRM

†Mν

cR)

(32)

i: Flavor index ,F:Yukawa couplings Matrix,MM : Majorana Mass term for νR ,νcR= C.νR

T where C=iγ0γ2 in the Weyl representation


At E ≪ MW , approximate Φ by vev=174GeV. Hence,

L = LSM + iνR,I /∂νR,I − (mD)αIνL,ανR,I − (mD)∗αIνR,IνL,α

−1

2[(MM)IJν

cR,IνR,J + (MM)∗IJνR,Iν

cR,J ]

(33)

where Dirac mass matrix mD=F.v

at T< TEW Yukawa Interaction ONLY generates mD

⇒ Only way νR Interacts with SM is via their mixing with νL due tomD


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 spatialflatness)


Range Of Right Handed Neutrino Masses

Scale of MM provides various scenarios:

MM ≥ 109GeV:

For F ∼ 1, νR with mass as per GUT models, reproduces NeutrinooscillationsGenerates the observed baryon density in the universe (Problem II) inCP-violating decays of νR ’s

MM ∼ TeV: Favorable Mass range as it’s accessible by high energyexperiments of today

Problem 2 Can be explained via Leptogenesis from νR CP-violatingoscillationsProblem 1 explained via seesaw mechanism


MM ∼ GeV:

Problems(1)-(3) can be described by L alone;No other physics betweenthe electroweak and Planck scales required

MM ∼ KeV:RH neutrinos with KeV masses → promising DMcandidates

MM ∼ eV: Provides explanation Neutrino Anomalies

MM=0: Most Interesting Case!

With n=3 νR ’s, leptonic And quark sector similar without stronginteractions ⇒ neutrinos are Dirac particlesNeutrino mass generation via Higgs mechanismTiny Neutrino masses attributed to very tiny Yukawa couplings.No known principle that forbids MM for the gauge singlet fields νR


References

MARCO DREWES (2013)International Journal of Modern Physics EInt. J. Mod. Phys. E, 22,1330019

Fumihiko SuekaneLecture Notes in Physics Volume 898 Neutrino Oscillations: APractical 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


Thank You for your Attention!


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