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
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Lepton number violation in cosmology and particle physics M. Yoshimura Introduction: Symmetry and its breakdown ・ Sources of B non-conservation : electroweak.
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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