Leptogenesis and Neutrino Physics

2011.4.7연세대학교강신규 (서울과학기술대 )

Outline• Introduction - baryogenesis• Baryogenesis in some models• Leptogenesis• Informations on neutrino masses from leptogene-

sis• Neutrinoless double beta decay• Connection between leptogenesis and neutrino-

less double beta decay• Summary

Inflation explains r=rcr

Big-bang explains ne=np, n4He/np=0.125, nD/np=1.5x10-5, nn/ng=3/22 , etc.

We do not understand nB/ng

Introduction

Measuring nB/ng = 6 · 10−10

- Tnow ~ 3K directly tells ng~ T3now ~ 400/cm3.

- nB ~ 1/m3 follows from(1) Anisotropies in the cosmic microwave background: nB/ng = (6.3±0.3)x10−10.

(2) Big Bang Nucleosynthesis: the D abundancy implies nB/ng = (6.1±0.5)x10−10. arisen from many g push in the direction reactions like p n D g(1) and (2) are indirect but different: their agreement makes the result trustable.

nB/ng = 6 · 10−10 is a strange number, because means that when the universe cooled below T ~ mp , we sur-vived to nucleon/antinucleon annihilations as

Nucleons and anti-nucleons got together…

10,000,000,001 nucleons

10,000,000,000 anti-nucleons

They have all annihilated away except for the tiny

difference.

1 nucleon

That created tiny excess of matter in the present universe (unnatural !!!)

nB/ng = 6 · 10−10

Can a asymmetry can be generated dynamically from nothing?

Yes, if 3 Sakharov conditions are satisfied

• Necessary requirements for baryogenesis:– Baryon number violation : – C & CP violation : – Non-equilibrium

X q

l

Xq

l

0, BB nn

BB nn /

Out-of-Equilibrium Decay

Out-of Equilibrium obtained due to expansion of the Universe as a background for heavy decaying parti-cles.

XXX M

Condition for out-of-equilibrium decay

XMTX H |

Boltzmann Equation

If interactions becomes too slow to catch up with expand-ing Universe, NX start to become overabundant.

We must consider inverse decays, scatterings and annihi-lations

)()1)(1(-

)()1)(1( 3,,

mljXWffff

jXmlWffffHndt

dn

mljX

mljjXmlX

X

RHS NX variation due to all elementary processes for X

Epd

f ji

2)(21g processes, thefor squared amplitude:W

fermions : (-) bosons : )( j,..i, species of densities space phase:3

3

..,

Abundance as a function of temperature

Coupled Equations for nX and nB-L

)(13 ,AsDeqX

XX

X

nn

Hndtdn

g

BVLVeqL

LBDeq

X

XLB

LB

nn

nnHn

dtdn

,13 gg

CP asymmetry washout at T<M

In the SM not all of the dynamics is described by pertur-bative effects; There are non-perturbative interactions that violate B+L.

Sphaleron

Non-perturbative finite temperature interactions, involv-ing all left chiral fermions (due to chiral nature of weak interactions)

Above EW-scale sphaleron processes (violating B+L) are in equilibrium and conserve B-L. GeV 10~ 12

SphEW TTT

Below EW-scale Higgs vev suppresses sphaleron rates constrains models of EW Baryogenesis.

45~ TWsph

• Sakharov’s conditions– B violation EW anomaly (S-

phaleron)– CP violation KM phase– Non-equilibrium 1st order phase trans.Standard Model may satisfy all 3 condi-

tions!

Electroweak Baryogenesis (Kuzmin, Rubakov, Shaposh-nikov)

• Two big problems in the Standard Model– 1st order phase transition requires mH <

60GeV– CP violation too small because

J det[Yu†Yu, Yd

†Yd] ~ 10–20 << 10–10

Baryogenesis in the standard model

Original GUT Baryogenesis• GUT necessarily breaks B. (there exist several B violating interac-

tions)

• A GUT-scale particle X decays out-of-equilibrium with direct CP violation

• But keeps B–L0 “anomaly washout”• Monopole problem• Alternative scenarios required (B-L vio-

lation)

)()( qXqX

Leptogenesis : role of neutrinos in baryogenesis

Seesaw MechanismPrerequisite for Leptogenesis

• Why is neutrino mass so small?• Need right-handed neutrinos to generate tiny

neutrino mass, but nR SM neutral

To obtain m3~(Dm2atm)1/2, mD~mt , M3~1015GeV

(GUT!)

..0

)(21 cc

Mmm

LR

L

D

DRLmass

nn

nn

2

DmM M

• Majorana neutrinos: violate lepton number (B-L violation)

Basic Leptogenesis Mechanism Fukugita and Yanagida ’86

Based on standard out-of-equilibrium decay of a heavy particle:

1. CP violating decay of a heavy particle through an L-vio-lating interaction can produce a lepton asymmetry.

2. This lepton asymmetry is transformed into a baryon asymmetry through sphaleron interactions :

RN H

L

RN H

L

(SM)

CP Asymmetry CP violation through phases in neutrino sector.

CP asymmetry produced through interference of tree and one-loop contribution of decay rate.

) (if *11

*1

*1

**11 1111

hhLHLNhLHNhLHNhHLNhL RRRR

2*23,21

*1

*1

223,2

*111 ||)(||)( hAhhHLNhAhhLHN

(N1 ni H) (N1 n i H)(N1 ni H) (N1 n i H)

~ 18

Im(h13h13h33* h33

* )h13

2M1M3

Lepton number asymmetry

Decay rate : 11181 MhhD

snn

RR NNL

abundance at eq.

- : CP asymmetry determined by the particle physics model that

produces couplings and masses for NR- efficiency : incorporates washout effects by L-violating in-

teractions after the RH neutrinos decay.

Baryon asymmetry determined by 4 parameters

CP asymmetry 1 Mass of decaying neutrino M1 Effective light neutrino mass (coupling strength of N1)

Light neutrino masses 1

211

1

)(~M

vhhm

222321 nnn mmmm

)( 212 mML D

efficiency as function of 1~m

Maximal efficiency :

Some constraints from Leptogenesis

(i) Very hierarchical Assuming 13,2 / MM

► When vertex diagram becomes dominant (Davidson &

Ibarra) 11

11*

21

)(])Im[(

163

hh

hmhv

M v

(1) Heavy neutrino mass depends on the NR mass hierarchy

► for hierarchical mn, 2

3 atmmm Dn GeV 102 91 M

)(163)(

163||

13

13

2

21

21

nnnn

mm

mvMmm

vM atm

D

► implying that N1 cannot be too light & mn not be too heavy

(ii) hierarchical M2,3~10-100M1

CMM

mmm

vM atm

23,2

21

2

21

)(163||

13

D

nn

small

can be large

For example) arecompatible with successful leptogenesis with specialYukawa matrix

GeV 10~ eV, 5.0~ 613

Mmn

(iii) Quasi-degenerate case M1~M2

21

22

21

1~NNiMM

Huge resonance peak if )( ~iN21 iMMM

No more mn constraints on leptogenesis No more lower limit on heavy Majorana

mass TeV scale leptogenesis possible Resonant leptogenesis

(2) Light neutrino masses

washout no 11 HN

increaseswashout increases ifwashout eV10 if

eV10

1

111

3

3n

nn

mmm

HN

mn constraints on the size of

Refinement by Buchmuller et al. for constraint on ε

Considering the efficiency which depends on 1

211

1

)(~M

vhhm

Thermal leptogenesis fails if ns are too heavy and degen-erate due to:

1

13

13

132/ small 2

22

nnn

nnnn mm

mmmm

mm atmD

),,~( 211

max

mMmfnnB

g

the domain shirnks to zero yields upper limits on mi

n 3at eV 15.0m

No dependence on intialabundance of N1 for

GeV 10

eV 10~13

1

31

M

m

Since , leptogenesis window for neutrino mass

compatible with neutrino oscillation

11~

nmm

eV 15.0 eV 101

3 nm

Can we prove it experimentally?

• Unfortunately, no: it is difficult to reconstruct rel-evant CP-violating phases from neutrino data

• But: we will probably believe it if– 0nbb and/or LNV processes found– CP violation found in neutrino oscillation– EW baryogenesis ruled out

CP Violation

• Possible only if:– Dm12

2, s12 large enough (LMA)– q13 large enough

• Can we see CP violation?

KamLAND Reactor Exp. ? ?

It may need better parameter determination using solar pp neutrinos

D

D

D

LE

mLE

mLE

m

cscscsPP ee

4sin

4sin

4sinsin

16)()(

223

213

212

2323213131212

nnnn

Neutrinoless double beta decay and

Leptogenesis

• With the discovery that neutrinos are not mass-less, there is intense interest in neutrinoless dou-ble-beta decay (0nbb measurements.

• 0nbb decay probes fundamental questions : Lepton number violation : leptogenesis might be

the explanantion for the observed matter-antimatter asymmetry. Neutrino properties : the practical technique to determine if neutrinos are their own anti-particle : Majorana particles.

If 0nbb decay ob-served :

• Violates lepton number :

• Neutrino is a Majorana particle.

• Provides a promising lab. method for determining the absolute neutrino mass scale that is complementary to other measurement techniques

• Measurements in a series of different isotopes poten-tially can reveal the underlying interaction processes.

2DL

• Establishing that neutrinos are Majorana particles would be as important as the discovery of neutrino oscillations

Neutrinoless double beta decay

Lepton number violation

Baryon asymmetry Leptogenesis due to violation of B-L number

• The half-life time, , of the 0nbb decay can be factorized as :

2/10nT

2200

012/10 ||||),(][

nnn

n mMZEGT

),( 00 ZEG n

3121 233

222

211

n

ie

iee eUmeUmUmm

n0M: phase space factor

: Nuclear matrix element

:depends on neutrino mass hierarchy

Best present bound :

eV 50.035.0 nm

eeSeGe 7676 Heidel-Moscow

Ge76 Half-life ysT 252/1 102.1

Consistent with cosmological bound

eV 0.2 imn

Neutrino mass spectrum

If neutrinos are Majorana particles

• Neutrino oscillations : - not sensitive to the nature of neutrinos - provide information on , but not on the absolute values of neutrino masses.

222kjjk mmm D

Neutrino mass scale and its property can be probedby 0nbb

3121 233

222

211

n

ie

iee eUmeUmUmm

Prediction of depends on neutrino mass hierarchy

nm

4 3eefew 10 m 6 10 (eV)

ee0.01 m 0.05(eV)

321 mmm

)(23

2223

2 2131||sin)||1( n q DD i

eatmsolesolee eUmUmmm

213 ~ mmm

)||1( 2cos)||1( 21

221

2eatmeesoleatm UmmUm DD q

soleatm Umm

q n

2sin1

)||1(1

2sin 222

12

221312

D

• Normal hierarchy:

• Inverted hierarchy

Quasi-degenerate

ee0.05 m 0.35

321 mmm

]sincos)sin[(cos 312113

213

222 nn qqqq ii

solsolee eemmm

• Estimate by using the best fit values of parameters in-cluding uncertainties in Majorana phases

( Hirsch et al. , hep-ph/0609146 )

For inverted hierarchy, a lower limit on <mn> obtained

8 meV

In principle, a measurement of |<m>| com-bined with a measurement of m1(mass scale)

(in tritium beta-decay exp. and/or cosmology)would allow to establish if CP is violated.

To constrain the CPV phases,once the neutrino mass spectrum is known

• Due to the experimental errors on the parameters and nuclear matrix elements uncertainties, deter-mining that CP is violated in the lepton sector due to Majorana CPV phases is challenging.

• Given the predicted values of , it might be possible only for IH or QD sepctra. In these two cases, the CPV region is inversely proportional to

• Establishing CPV due to Majorana CP phases re-quires

nm

solq2cos

nm

solq2cos

jjYY 2

11 )Im( nn1

Small experimental errors on and neu-trino masses

Small values of depends on the CPV phases :

Connection between low energy CPV and leptogenesis

• High energy parameters Low energy parame-ters

• 9 parameters are lost, of which 3 phases.

• In a model-independent way there is no direct connection between the low-energy phases and the ones entering leptogenesis.

6 9 :0 3:

nYM R

3 3 :0 3:

Umv

Using the biunitary parameterization,

depends only on the mixing in RH sector.

mn depends on all the parameters in Yn .

If there is CPV in VR, we can expect to have CPV in mn .

In models with a reduced number of model parame-ters,

it is possible to link directly the Dirac and Majorana phases to the leptogenesis one.

Additional information can be obtained in LFV charged lepton decays which depend on VL.

RL yVVY n

1

• In minimal seesaw with two heavy Majorana neutrinos

(Glashow, Frampton, Yanagida,02)

mD contains 3 phases

1 ( ) ( 1 3; )2

1,2 cLi Dij Rj Rj j RjL m N N M jN in

4 ( , ) ( ) ( ) J P P b b n n n n

21 12 11Im[( ) ] /( ) D D D Dm m m m

Existence of a correlationbetween

1J &

(Endo,Kaneko,SK,Morozumi,Tanimoto) (2002)

In Type II seesaw model :

D MMforYY

mYYv

MR

fgIILLgfR

1

1 )(

])()()Im[(83

11

1*

1*

2n

nn

Type II Seesaw (for MR1 << MR2, MR3 , MD S.F.King 04

Bound on lepton asymmetry

for neutrino mass scale

For successful thermal leptogenesis : MR1 for neutrino mass scale

Bound on type II MR 1 lower than Type I bound

max1

(in sharp contrast to type I)

Summary• Although current precision observation on baryon

asymmetry in the universe, we do not know how it can be dynamically generated.

• Leptogenesis is a plausible mechanism for baryo-genesis.

• Since neutrinos play an important role in leptogen-esis,

we can obtain some informations on neutrino masses

requiring for successful leptogenesis• Neutrinoless double beta decay can probe neutrino

property and mass hiererchy and CP violation, which are

closed related with leptogenesis.

Constraints on leptogenesis

Type I Seesaw (for MR1 << MR2, MR3) (S. Davidson et al. 02)

Bound on lepton asymmetry

for neutrino mass scale

For successful thermal leptogenesis : MR1 for neutrino mass scale

Lower bound on MR1 :

max1

GeV 1091RM