Lepton number violation in cosmology and particle physics

　　　　　　　　　　　　　　 M. Yoshimura

• Introduction: Symmetry and its breakdown・　 Sources of B 　 non-conservation : electroweak 　 at

high T• Leptogenesis: 　　 L-nonconservation in universe 　 　　　　　　　・　 Thermal L-genesis and general remarks・ 　 Possible nightmare : 　 gravitino overproduction・ Ways out・　 L-number violation in terrestrial laboratories• Conclusion

Symmetry principle and its breakdown

• Symmetry organizes indivisual events and leads to conservation law

• 2 important discoveries of last century 1. Local gauge symmetry Associated with force (interaction)　 2. Spontaneous breaking of symmetry Symmetric dynamical law and breaking in

realized states

Well known example

• Electric charge conservation:

1st case of gauge symmetry and led to successful QED

• Standard theory of particle physics:

unified weak and electromagnetic forces, and explained difference of force ranges

How about baryon and lepton numbers ?

・ My personal prejudice: Breakdown of empirical conservation laws not protected by the gauge principle, such as the lepton number, the baryon number, the flavor changing process, CP violation are all expected. Question is only the rate.

• We might already have many hints on these!

Recent developments in particle physics

SUSY coupling unification

,2

Neutrino mass via seesaw

new p

q l

hysicsMm

m

12

25(10

10 )

100new physics

GeG

eVV

VM e

152 hints towards unification @ 10 GeV

Neutrino physics

• Neutrino oscillation

Evidence of

neutrino mass!

Cosmic rays

Cosmic rays

Neutrinos

Neutrinos

Upward Downward

WMAP 　 results

Precise measurement of baryon abundance and bound on neutrino mass

1010)3.01.6( n

nB

m < 0.23eV

Mystery of our existence Why are we here ?

• Despite that the law of microphysics is almost matter-antimatter symmetric, and

• Despite that in the early universe antimatter production is energetically possible and equilibrium has been established by the laws of gravity and thermodynamics

Generation of B-asymmetry

after annihila before annihilation tion

1Bn OB

Bn

B

B

• Key quantity

10imply 1 excess of B out of 10 pairs

10Observation 10Bn On

Is imbalance for matter is a hint on some symmetry breakdown ?

How to produce the asymmetry ：　

3 conditions

B CP out of equilibrium

Necessary ingredients

　　　　　　　　　　　　

in the early universe

without suppression of inverse

Need of

process

arrow of ti

,

B = B

me

B 0

Delicacy of CP ：　 Quantum interferenceBaryon excess from a pair of particle and

antiparticle process, e.g.

22 *

*1

*1 1 2 2 1 1 2

2*

1

2

2I Im(m( ) )4

g f g f g f g f

g g f f

*

1 2Im( ) 0g g *

1 2Im( ) 0f f

XX

CP violationRescattering phase

Interference computed by Landau-Cutkovsky rule

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　＝　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

q

Sources of B nonconservation

• GUT

• Electroweak at high T

• SUSY （ Affleck-Dine mechanism)

• Black hole evaporation

Electroweak damping

137eElectroweak baryon noncnoservation suppressed at T=0 by

enhanced at finite T by barrier crossing

Can destroy preexisting B and L while keeping B-L

Gauge and Higgs

Mechanism due to level crossing of fermions caused by nontrivial gauge and higgs configuration of sphaleron and alike

Electroweak baryon nonconservation

Baryogenesis in standard model• unsuppressed at finite T

• KM phase• Out of equilibrium: 1st order phase transition via bubble

formation

B

CP

/spM Te

4[1] Wo T ][@ TeVOMT sp

Difficulties of EW B-genesis

• No strong 1st order phase transition due to experimental Higgs lower mass bound: >115GeV

Theory requires a large radiative correction to the Higgs potential, to obtain more than quartic terms

• Magnitude too small due to KM phase alone

21 25[10 10 ]Bn on

Electroweak redistribution of B and L

12200 10GeV T GeV

8 4 28

22 13 79g H

g H

n na

n n

For standard model of 3 generations

Ｄａｍｐｉｎｇ　ｅｆｆｅｃｔｉｖｅ　＠　

B-L conserved and never washed out.

e.g. Luty

( ),B a B L

L genesis and B conversion

• L-genesis of amount first and electroweak conversion into B, via

For standard model of 3 generations

28

79B L

Interesting in view of possible connection to observed neutrino masses

L

Likely mechanism of small neutrino mass generation

• Seesaw mechanism Heavy Majorana type of masses of neutrino partner , independent of

standard theory of particle physics, generates a tiny left-handed neutrino masses and mixing a la

• Necessarily violates lepton number conservation • Agent of L-asymmetry generation provided by righthanded partner

,2

Neutrino mass via seesaw

new p

q l

hysicsMm

m

RN

Thermal L genesis Fukugita-Yanagida

• Minimal extention of standard model with seesaw

Right-handed Majorana decay

†111

1 †211

Im( *)3

16 ( )D D

D D

m m mM

v m m

CP asymmetry with neutrino mass matrix 1 TD Dm m M m

For 3 R-Majoranas

= CP phase

HllHNR ,

][2

1

v

mMO

321 MMM

Great impacts on neutrino masses and thermal history of universe

• Connection to neutrino masses

heaviest neutrino (WMAP 0.23eV)

lightest R-neutrino

• Reheat temperature

3

81

0.13

5 10

m eV

M GeV

1RHT M

1 1, ,M

With hierarchy of masses, dependence on 3 parameters Giudice et al

1

211)(

M

vhhm

Prejudices for simplification

• Completely general analysis meaningless due to many (18) parameters of 　　　　　　　 matrices

• Constraints: known quantities

• Some sort of hierarchy

hierarchy for Dirac masses• Symmetry GUT or flavor symmetry for Dirac term Effective parameters 　 not directly observable

, Nm M

2 223 12 23 12, , , , Bnm m

s

1 1, ,M

321321321 ,, MMMMMMMMM

321321321 ,, mmmmmmmmm

m

Gravitino problem: a possible nightmare both for GUT B- and L-genesis

• Superpartner of graviton

mass

lifetime

• Usual estimate of gravitino abundance and constraint from nucleosynthesis, including hadronic decay

3/ 2 [ ]m O TeV3

5 1 33/ 2 3/ 22[ ] [(10 sec) ( ) ]

pl

m mO O

TeVm

Possible to produce 　　　　　 　　？

GeVT

m

TO

s

n

RH

pl

RH

86

22/3

1010

]10[

RN

Ways out

• EW baryogenesis

• Affleck-Dine mechanisim

• Gauge mediation

• LSP = gravitino

• Preheating

SuperWIMP scenarioFeng, Su, Takayama

hep-ph/0404198 0404231• LSP = gravitino NLSP = stau• Lifetime of stau =

stau -> gravitino + tau

possibility of making a reservoir of stau @LHC

sec1010 84

A possible resolution, using preheating after inflation

• Important new element for particle production and B- and L-genesis after inflation

Non-perturbative effect of parametric resonance, leading to

Complicated high energy phase of reheating, i.e. preheating 、

　 including dilution of gravitino abundance　 and generation of proper amount of B-asymmetry

Theory of particle production with chaotic potential

• Inflaton field oscillation given by

(spatially homogeneous, periodic)

Interaction by

Producing a pair of particles

For each momentum mode of massive particle

0( ) cos( )t mt

2

.

0

...

223 ( co ))s 0(k k k

ak m g m t

a 2

02

k gh

m

0

2

g

m

Problem of parametric resonance

for large amplitude oscillation

How to swing ： Need to vary center of your body periodically

Non-perturbative effect of parametric resonance, producing large mass particles

・ n-th band contribution like

• Large mass production possible if 　 with large n

• Perturbative Born decay; from E-conservation

n

2 2

m nm m

2

mm

New features : preheating

Initially highly non-thermal

Possibility of producing GUT scale and R-Majorana particles

Estimate based on a single reheat temperature doubtful

Violent process of particle production

after O 10 oscillations

Preheating stage and gravitino abundance

• e.g. B-generation during preheating and

gravitino abundance lowed by perturbative estimate is possible

Lepton number violation in laboratories

• Work with Lim and Takasugi For details: talk by Lim @WG4

• Systematically studied processes given by

• Still most promising is neutrinoless double beta・　　 But neutrinoless double beta can vanish, despite all positive results

of disapperance and appearance neutrino oscillation experiments

• High intensity beam and high density target is indispensable to determine complex

• Muon capture realizes both, but BR very small

qqqqllE

mGO F ][

2

2

kkk UmUm 222 EmGF

Towards verification of (Majorana) CP violation

• 7 experiments needed, 4 more besides neutrino oscillation• Both disappearance and appearance of

• Lepton number violating processes like

• A long way and many more works for important physics

eee ,,,

nnppeppeenn ,,,

Summary

• (B-L) genesis is a great hint on physics beyond the standard model, linking the micro and the macro worlds

• L-genesis interesting due to its possible connection to the neutrino sector and lepton flavor violation

• Watch out gravitino overproduction

• Test of L-nonconservation with CP violation in laboratories is not easy, needs fresh ideas

Model of inflation: Chaotic inflation

• Damped inflaton oscillation wth its mass

and initial dimensionless amplitude

1310m O GeV 2

0plm

Om

Theory of reheating

• Old view

Coherent inflaton oscillation = aggregate of 0-momentum particles

Independent particle decay

Instantaneous thermalization due to fast interaction

leading to reheat temperature

with Born decay rate

4RHT

RH plT m

Integration, with back-reaction and Einstein equation