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

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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


  • 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

  • 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.

  • 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…

  • 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

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

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

Abundance as a function of temperature

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.


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.

  • 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

  • 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)


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

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

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



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 :

CP Asymmetry

  • CP violation through phases in neutrino sector.

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

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.

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

k(efficiency) as function of

Maximalefficiency :

Some constraints from Leptogenesis

(1) Heavy neutrino mass

 depends on the NR mass hierarchy

(i) Very hierarchical


  • When vertex diagram becomes dominant

  • (Davidson & Ibarra)

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

  • for hierarchical mn,

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


can be large

For example) are

compatible with successful leptogenesis with special

Yukawa matrix

(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

(2) Light neutrino masses

  • mnconstraints on the size of e

  • Refinement by Buchmuller et al. for constraint on ε

Considering the efficiency k which depends on

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

the domain shirnks to zero


upper limits on mi

Nodependence on intial

abundance of N1 for

Since , leptogenesis window for neutrino mass

compatible with neutrino oscillation

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

  • 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

Neutrinoless double beta decay



  • 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 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

Lepton number violation

Baryon asymmetry  Leptogenesis due to

violation of B-L number

  • 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 :



Consistent with cosmological bound

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.

  • Neutrino mass scale and its property can be probed

  • by 0nbb

  • Prediction of depends on neutrino mass hierarchy

  • Normal hierarchy:

  • Inverted hierarchy


  • Estimate by using the best fit values of parameters including 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>| 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

  • 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

  • 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.

  • 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.

Existence of a correlation


  • In minimal seesaw with two heavy Majorana neutrinos

  • (Glashow, Frampton, Yanagida,02)

  •  mDcontains 3 phases



In Type II seesaw model :

  • 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.

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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