CP violation in the neutrino sector

CP violation in the neutrino sectorLecture 1: Introduction to neutrino physics

Walter Winter

Nikhef, Amsterdam, 06.03.2014

lepton

Walter Winter | CPV Amsterdam | 05.02.2014 | Page 2

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 1)

> Introduction to neutrinos

>Neutrinos and CP violation … some theory

>Constraining neutrino mass

> Summary


What are neutrinos?

>Ordinary matter consists of protons, neutrons, and electrons

> But that‘s not all. There are many other particles …

For instance, for each of the above, there are about1.000.000.000 (1 billion) neutrinos in the universe= almost massless particles without electric charge

e-

e-


Where do the neutrinos come from?

Natural sources

Man-madesources

10-4 10-3 104103 105 106 107 1010109 1011108 1012

keV MeV GeV TeV

E [eV]

Electron mass Proton mass LHC c.o.m. energy


How many neutrinos are there?

> So, why don‘t we care?

>Neutrinos interact extremely weakly

>Neutrinos escape even from very dense environments (e.g. Sun‘s interior, nuclear reactor, …)

About 100.000.000.000.000 per second (100 trillions)

n


Who “invented“ the neutrino?

> From energy and momentum conservation, we have for the decay into N particles:

N=2: have particular, discrete energies

N>2: have continuous spectra Wolfgang Pauli

n


How to observe the neutrino?

>Extremely difficult to catchthe neutrinos

>Thus: Build huge detectors(O(1000 t)), often deepunder ground (background reduction!)

(SNO)

Flux: extremely large

Cross section:extremely small

Observation time:1-10 years

Detector mass:matches the product


The mystery of the missing neutrinos

>Raymond Davis Jr. (Nobel Prize 2002) found fewer solar neutrinos than predicted by theory (John Bahcall)

>Do the neutrinos disappear?Or was the theory wrong?Discrepany over 30 years (1960s to 90s)

pp-fusion chain Neutrino spectra


Neutrinos from the atmosphere

> The rate of neutrinos should be the same from below and above

> But: About 50% missing from below

>Neutrino change their flavor on the path from production to detection: Neutrino oscillations

>Neutrinos are massive!

(Super-Kamiokande: “Evidence for oscillations of atmospheric neutrinos”, 1998)


Neutrinos and CP violation … some theory


What is CP violation?

>C stands for “Charge conjugation“

> P stands for “Parity“

> “CP“ corresponds to particle – anti-particle interchange

>Do particles and anti-particles behave the same?

>Why is “C“ (charge conjugation) not sufficient?

> Peculiarity of the Standard Model: couplings to left-handed particles and right-handed anti-particles (V-A interactions)

>Need to flip parity as well to go from left-handed particle to right-handed anti-particle


Why would one care about CP violation?

> Baryogenesis = dynamical mechanism to create the matter-anti-matter asymmetry in the early universe from a symmetric state

> Three necessary conditions (Sakharov conditions):

1) B violation (need to violate baryon number)Need to create net baryon number

2) Out of equilibrium processesOtherwise any created asymmetry will be washed out again

3) CP violationParticles and anti-particles need to “behave“ differently Critical: the Standard Model does not have enough CP violation for that!Requires physics beyond the Standard Model (BSM)

> There are many theories for baryogensis, e.g. electroweak baryogenesis, thermal leptogenesis, GUT baryogenesis etc

> Addendum to 1): Can be also L violation, which is translated into a violation of baryon number by sphaleron processes before the electroweak phase transition


Related question: Why is the neutrino mass so small?

>Why are the neutrinos morethan 250.000 times lighter than the electron?

Cannot be described in simple extensions of the Standard Model

> Seesaw mechanism: Neutrino mass suppressed by heavy partner, which only exists in the early universe (GUT seesaw)?

Decay of (thermally produced) MR origin of matter-antimatter-asymmetry?Thermal leptogenesis

CP violation? Test in neutrino oscillations!

Requires Majorana nature of neutrino!Test in neutrinoless double beta decay (0nbb)

Other SM particles

Heavy partner


> Example: Type I seesaw (heavy SM singlets Nc)

Charged leptonmass terms

Eff. neutrinomass terms

Block-diag.

CC

Flavor model(depends on UV completion)

Sectorial origin ofCP violation?

Observable CP violation(completely model-indep.)

Could also be type-II, III seesaw,

radiative generation of neutrino mass, etc.

Depending on model, actual masses and mixings derived in non-trivial way!

Where does the CP violation come from?


Three flavors: Mixings

>Use same parameterization as for CKM matrix

Pontecorvo-Maki-Nakagawa-Sakata matrix

>Neutrinos Anti-neutrinos: U U* (neutrino oscillations)

> If neutrinos are their own anti-particles (Majorana neutrinos): U U diag(1,eia,eib) - do enter 0nbb, but not neutrino oscillations

( ) ( ) ( )= xx

(sij = sin qij cij = cos qij)

Potential CP violation ~ q13


> Two independent mass squared splittings, typically (solar) (atmospheric)

Will be relevant for neutrino oscillations!

> The third is given by

> The (atmospheric) mass ordering (hierarchy) is unknown (normal or inverted)

> The absolute neutrino massscale is unknown (< eV)

Three active flavors: Masses

8

8

Normal Inverted


The flavor problem

Masses?

Mixings?

Degenerate neutrinos: m1 ~ m2 ~ m3

Hierarchical neutrinos: m1 << m2 << m3

(hep-ph/0111263)

How can one describe the differences amongthe generations and species?

Where does the CPV come from?

~


The tri-bimaximal mixing (TBM) “prejudice“

> Tri-bimaximal mixings probably most discussed approach for neutrinos (Ul often diagonal, )

>Can be obtained in flavor symmetry models (e.g., A4, S4)

>Consequence: no CPV since q13=0 Obviously not! (next lecture)

>Ways out for large q13?


Impact of large q13 on theory of flavor?

Structure:A4, S4, TBM, …

Anarchy:Random draw?

q13 ?very small very large

Different flavor symmetry?

TBM Corrections?CL sector?

RGR running?

Some structure + randomness:

Froggatt-Nielsen?

vs.

Quark-leptoncomplementarity:

q13 ~ qC?

e.g. q12 = 35 + q13 cosd (Antusch, King, Masina, …)


Anarchy?

> Idea: perhaps the mixing parameters are a “random draw“?

>Challenge: define measure which is independent of how random numbers generated

>Result: large q13 “natural“, no magic needed

>Consequence: CP violation from a random draw of phases?

(Hall, Murayama, Weiner, 2000; de Gouvea, Murayama, 2003, 2012)


What is the origin of the CP violation, then, after all?

> Fundamental parameters in Yukawas/couplings, i.e., interactions with the Higgs field? Example:

> Are these mass matrices fundamental parameters?

> Possible additions modifications aim to describe the masses and mixings, such as in this model, from more “fundamental“ models

>Origin of CPV?

Through spontaneous symmetry breaking (e.g. flavon models)?

“Geometric“, such as by Clebsch-Gordan coefficients of a group?

Coincidence/random choice?


Constraining neutrino mass


Tritium end point experiments

>Direct test of neutrino mass by decay kinematics

>Current bound: 1/250.000 x me (2 eV) TINY!

> Future experiment: KATRIN (Karlsruhe Tritium Neutrino Experiment) 1/2.500.000 x me (0.2 eV)

~8800 km


n

n

> Two times simple beta decay:

>Neutrinoless double beta decay:

0nbb: Is the neutrino its own anti-particle?

p

e-

W-

p

n

e-

W-

p

e-

W-

2 x n2 x e

0 x n2 x e

n

p

e-

W-

=


Mixing matrix for Majorana neutrinos

> Additional phases in mixing matrix without effect in neutrino oscillations

>Cannot be rotated away by re-definition of lepton fields if neutrinos are their own anti-particles

>Relevant vor neutrinoless double beta decay

> Potential additional source of CP violation

> These CP phases are potentially connected with the CP violation in the early universe


0nbb phenomenology

>Rate ~ |mee|2 x |nucl. matrix element|

(Lindner, Merle, Rodejohann, 2005)

Majorana phases


>Normal ordering: Lightest mass is m1

> Inverted ordering: Lightest mass is m3

0nbb phenomenology (2)

Potentially small parameters: cancellation possible

Always largest term, no

cancellationsBands:

Impact ofphases/current

knowledge

Lightest mass m1 or m3

(Lindner, Merle, Rodejohann, 2005)

Very difficultto access

(~ s132)


Measurement of Majorana phase a?

>Measurement of a difficult because of nuclear matrix element uncertainty

>Come potential to exclude some values by combination of data

(if external measurement of absolute mass scale)

a/(2p)

Minakata, Nunokawa, Quiroga, arXiv:1402.6014


Cosmological tests of neutrino mass

> Example:Relativistic neutrinos damp the formation of structure

> Essentially sensitive to sum of neutrino masses

> Information from different cosmological datasets used in literature

> Limit ~ eV

(S. Hannestad)


Summary

>CP violation is required to describe the matter-anti-matter asymmetry of the universe (baryogenesis)

> A new source of CP violation beyond the Standard Model is needed

>Massive neutrinos are a scientific fact from neutrino oscillations. Thus, neutrino masses need to be added to the Standard Model

> This requires new fields and implies that there are potentially new sources of CP violation

> Thermal leptogenesis with heavy Majorana neutrinos is a straightforward extension of the Standard Model, which describes

Massive neutrinos

Smallness of neutrino mass

Baryogenesis through leptogenesis

> This is often believed to be the simplest possible extension of the Standard Model to solve these problems

> Experimental evidence (indirect): 0nbb, CPV in neutrino oscillations

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CP violation in the neutrino sector

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