leptogenesis and neutrino physics
DESCRIPTION
Leptogenesis and Neutrino Physics. 2011.4.7 연세대학교 강신규 ( 서울과학기술대 ). Outline. Introduction - baryogenesis Baryogenesis in some models Leptogenesis Informations on neutrino masses from leptogenesis Neutrinoless double beta decay - PowerPoint PPT PresentationTRANSCRIPT
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