Leptogenesis and neutrino physics
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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

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Leptogenesis and neutrino physics

Leptogenesis and Neutrino Physics






  • Introduction

    - baryogenesis

  • Baryogenesis in some models

  • Leptogenesis

  • Informations on neutrino masses from leptogenesis

  • Neutrinoless double beta decay

  • Connection between leptogenesis and neutrinoless double beta decay

  • Summary

Leptogenesis and neutrino physics


  • 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

Leptogenesis and neutrino physics

  • Measuring nB/ng= 6 · 10−10

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

  • - nB ~ 1/m3 follows from

  • 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.

Leptogenesis and neutrino physics

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

10,000,000,001 nucleons

10,000,000,000 anti-nucleons

Nucleons and anti-nucleons got together…

Leptogenesis and neutrino physics

  • 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

Leptogenesis and neutrino physics

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

Leptogenesis and neutrino physics

Out-of-Equilibrium Decay

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

Condition for out-of-equilibrium decay

Leptogenesis and neutrino physics

Boltzmann Equation

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

We must consider inverse decays, scatterings and annihilations

RHS  NXvariation due to all elementary processes for X

Leptogenesis and neutrino physics

Abundance as a function of temperature

Leptogenesis and neutrino physics

Coupled Equations for nX and nB-L

CP asymmetry

washout at T<M

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

Leptogenesis and neutrino physics


Non-perturbative finite temperature interactions, involving 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.

Below EW-scale Higgs vev suppresses sphaleron rates

 constrains models of EW Baryogenesis.

Leptogenesis and neutrino physics

  • Baryogenesis in the standard model

  • Sakharov’s conditions

    • B violation EW anomaly (Sphaleron)

    • CP violationKM phase

    • Non-equilibrium1st order phase trans.

    • Standard Model may satisfy all 3 conditions!

  • Electroweak Baryogenesis(Kuzmin, Rubakov, Shaposhnikov)

  • 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

Leptogenesis and neutrino physics

  • Original GUT Baryogenesis

  • GUT necessarily breaks B.

  • (there exist several B violating interactions)

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

  • But keeps B–L0  “anomaly washout”

  • Monopole problem

  • Alternative scenarios required (B-L violation)

Leptogenesis and neutrino physics


role of neutrinos in baryogenesis

Leptogenesis and neutrino physics

Seesaw MechanismPrerequisite for Leptogenesis

  • Why is neutrino mass so small?

  • Need right-handed neutrinos to generate tiny neutrino mass, but nR SM neutral

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

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


Leptogenesis and neutrino physics


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-violating interaction can produce a lepton asymmetry.

  • 2. This lepton asymmetry is transformed into a

  • baryon asymmetry through sphaleroninteractions :

Leptogenesis and neutrino physics

CP Asymmetry

  • CP violation through phases in neutrino sector.

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

Leptogenesis and neutrino physics

abundance at eq.

  • Decay rate :

  • Lepton number asymmetry

  • e : CP asymmetry determined by the particle physics model that

  • produces couplings and masses for NR

  • k (efficiency) : incorporates washout effects by L-violating interactions

  • after the RH neutrinos decay.

Leptogenesis and neutrino physics

Baryon asymmetry determined by 4 parameters

  • CP asymmetry e1

  • Mass of decaying neutrino M1

  • Effective light neutrino mass (coupling strength of N1)

  • Light neutrino masses

Leptogenesis and neutrino physics

k(efficiency) as function of

Leptogenesis and neutrino physics

Maximalefficiency :

Leptogenesis and neutrino physics

Some constraints from Leptogenesis

(1) Heavy neutrino mass

 depends on the NR mass hierarchy

(i) Very hierarchical


  • When vertex diagram becomes dominant

  • (Davidson & Ibarra)

Leptogenesis and neutrino physics

  • implying that N1 cannot be too light & mnnot be too heavy

  • for hierarchical mn,

Leptogenesis and neutrino physics

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


can be large

For example) are

compatible with successful leptogenesis with special

Yukawa matrix

Leptogenesis and neutrino physics

(iii) Quasi-degenerate case M1~M2

Huge resonance peak if

  • No more mn constraints on leptogenesis

  • No more lower limit on heavy Majorana mass

  •  TeV scale leptogenesis possible

  •  Resonant leptogenesis

Leptogenesis and neutrino physics

(2) Light neutrino masses

  • mnconstraints on the size of e

Leptogenesis and neutrino physics

  • Refinement by Buchmuller et al. for constraint on ε

Considering the efficiency k which depends on

Leptogenesis and neutrino physics

Thermal leptogenesis fails if ns are too heavy and degenerate due to:

the domain shirnks to zero


upper limits on mi

Leptogenesis and neutrino physics

Nodependence on intial

abundance of N1 for

Leptogenesis and neutrino physics

Since , leptogenesis window for neutrino mass

compatible with neutrino oscillation

Can we prove it experimentally

Can we prove it experimentally?

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

  • But: we will probably believe it if

    • 0nbband/or LNV processesfound

    • CP violation found in neutrino oscillation

    • EW baryogenesis ruled out

Cp violation

CP Violation

  • Possible only if:

    • Dm122, s12 large enough (LMA)

    • q13 large enough

  • Can we see CP violation?


 Reactor Exp. ?

 ?

It may need better parameter determination using solar pp neutrinos

Leptogenesis and neutrino physics

Neutrinoless double beta decay



Leptogenesis and neutrino physics

  • With the discovery that neutrinos are not massless, there is intense interest in neutrinoless double-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 0 nbb decay observed

If 0nbb decay observed :

  • 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 potentially can reveal the underlying interaction processes.

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

Neutrinoless double beta decay

Neutrinoless double beta decay

Lepton number violation

Baryon asymmetry  Leptogenesis due to

violation of B-L number

Leptogenesis and neutrino physics

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

: phase space factor

: Nuclear matrix element

:depends on neutrino mass hierarchy

Best present bound

Best present bound :



Consistent with cosmological bound

Leptogenesis and neutrino physics

Neutrino mass spectrum

Leptogenesis and neutrino physics

  • 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.

Leptogenesis and neutrino physics

  • Neutrino mass scale and its property can be probed

  • by 0nbb

  • Prediction of depends on neutrino mass hierarchy

Leptogenesis and neutrino physics

  • Normal hierarchy:

  • Inverted hierarchy

Leptogenesis and neutrino physics


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

Leptogenesis and neutrino physics

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

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

8 meV

Leptogenesis and neutrino physics

  • In principle, a measurement of |<m>| combined 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

Leptogenesis and neutrino physics

  • Due to the experimental errors on the parameters and nuclear matrix elements uncertainties, determining 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 requires

  • Small experimental errors on and neutrino masses

  • Small values of

  • depends on the CPV phases :

Connection between low energy cpv and leptogenesis

Connection between low energy CPV and leptogenesis

  • High energy parameters Low energy parameters

  • 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.

Leptogenesis and neutrino physics

  • Using the biunitary parameterization,

  • depends only on the mixing in RH sector.

  • mndepends on all the parameters in Yn .

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

  • In models witha reduced number of model parameters,

  • 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.

Leptogenesis and neutrino physics

Existence of a correlation


  • In minimal seesaw with two heavy Majorana neutrinos

  • (Glashow, Frampton, Yanagida,02)

  •  mDcontains 3 phases



Leptogenesis and neutrino physics

In Type II seesaw model :

Leptogenesis and neutrino physics

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

Bound on lepton asymmetry

for neutrino mass scale

(in sharp contrast to type I)

For successful thermal leptogenesis :

MR1for neutrino mass scale

Bound on type II MR 1lower than Type I bound



  • 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 baryogenesis.

  • Since neutrinos play an important role in leptogenesis,

    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.

Leptogenesis and neutrino physics

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 :

MR1for neutrino mass scale

Lower bound on MR1 :

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