Cosmological matter-antimatter asymmetry

&possible CP violation in neutrino

oscillations

Zhi-zhong Xing (IHEP)

International UHE Tau Neutrino Workshop

23 – 26 April 2006, IHEP, Beijing

2

Outline

MotivationMotivation

RGE Telescope

RGE Telescope minimal

Seesaw Model

minimal

Seesaw Model

Motivation Motivation

4

New Physics

• Dark matter• Dark energy• Cosmic inflation• Solar neutrino oscillations• Atmospheric neutrino oscillations• Cosmological matter-antimatter

asymmetry

3-year WMAP Observations

astro-ph/0603449astro-ph/0603450astro-ph/0603451astro-ph/0603452

5

前苏联氢弹之父

Cosmological matter-antimatter asymmetry

(observational evidence)

Atmospheric and solar neutrino oscillations

(experimental evidence)

Connection

??Dark energy

Dark matter

Big BangInflation

Can 1 Stone Kill 3 Birds?

6

Yes, if SM + Right-handed neutrinos N

• -masses: Yukawa interactions

• Small -masses: Seesaw mechanism

• Flavor mixing: MNS matrix (3 CPV phases)

• Macro-CPV: Out-of-equilibrium N-decays

• B-violation: L-violation (sphaleron process)

• Baryogenesis: Leptogenesis mechanism

Yes or No

Question: Are the CP-violating phases at low- and high-energy scales correlated?

Quantum correction

10 GeV14 M3

M2M1

Leptogenesis

10 GeV 2

m 3m 2m 1

-oscillations ()_0 decay

Seesaw

RGE TelescopeRGE Telescope

The New Physics Scale

The Electroweak Scale

RGEs = Cable Car

If you feel sick in the cable car from the top down to the bottom, you have got significant radiative corrections.

An easy way to imagine radiative corrections

Radiative Corrections

Quark mixing (CKM):

θ12 ～ 13° → θ23 ～ 2° → θ13 ～ 0.2° → δ ～ 65°

Lepton mixing (MNS):

θ23 ～ 45° → θ12 ～ 33° → θ13 <10° → δ/ρ/σ

Flavor Mixing and CP Violation

RGEs of Neutrino Masses

Below the seesaw scale (MSSM)

After SSB at the electroweak scale

One-loop renormalization group equation of (with diagonal):

Of 3 angles, is most sensitive to RGE effects

RGEs of Mixing Angles

The RGE evolution of the Dirac phase depends on and :

If and were vanishing, the leading terms would vanish;The radiative generation of is possible. (Luo, Mei, Xing 05).

RGEs of CP-violating Phases (I)

The RGE evolution of Majorana phases and depends on :

RGEs of CP-violating Phases (II)

Numerical Examples (1-I)

We concentrate on the case that 3 neutrino masses are nearly degenerate and . (Luo, Mei, Xing 2005)

Seesaw scale Electroweak scale

Numerical Examples (1-II)

SSEW EWEW SS SS

Numerical Examples (2)

Neutrinoless double-beta decay:

Allowed!

EW SS

Numerical Examples (3)

Simultaneous generation of appreciable

and from , no problem;

and from , no problem.

But and from , suppressed

SSEW

Three CP-violating phases are entangled with one another in the one-loop RGE evolution.

The Dirac phase can be radiatively generated from one or two Majorana phases; even is achievable. The radiative generation of either Majorana phase or is okay, but difficult to simultaneously generate both of them.

The parameters of Majorana neutrinos run faster than those of Dirac neutrino in most cases (Xing, Zhang 06)

Helpful for model building, to establish a kind of connection between the phenomena of CP violation at high and low scales.

RGE Running of CPV Phases

But a specific relation between leptogenesis and CP violation in neutrino oscillations is strongly model-dependent.

minimal

Seesaw Model

minimal

Seesaw Model

The Minimal Seesaw Model

The minimal seesaw model (MSM):2 Right-handed neutrinos added to MSSM

2

1R N

Nv

Seesaw relation

• Principle of minimal particle content

• SU(2)U(1) gauge symmetry preserved

• Lepton number violating

MR integrated out, leading to a dimension-5 operator with an effective coupling matrix:

An incomplete list of recent works on the MSM and leptogenesis• Frampton, Glashow, Yanagida hep-ph/0208157 (PLB)

• Endoh et al hep-ph/0209020 (PRL)

• Raidal, Strumia hep-ph/0210021 (PLB)

• Raby hep-ph/0302027 (PLB)

• Dutta, Mohapatra hep-ph/0305059 (PRD)

• Barger, Dicus, He, Li hep-ph/0310278 (PLB)

• Guo, Xing hep-ph/0310326 (PLB)

• Ibarra, Ross hep-ph/0312138 (PLB)

• Mei, Xing hep-ph/0312167 (PRD)

• Turzynski hep-ph/0401219 (PLB)

• Chang, Kang, Siyeon hep-ph/0404187 (PLB)

Leptogenesis in the MSM

CPV phase entanglement

Radiative corrections

There is a massless neutrino eigenstate!

is of rank 2, hence Det()=0 holds, or

0321 mmm

• Normal -mass hierarchy:

01 m eV104.8 32sun2

mm

eV102.5 22sun

2atm3

mmm

• Inverted -mass hierarchy::

03 m eV101.5 22atm2

mm

eV100.5 22sun

2atm1

mmm

Smirnov Plot

Neutrino Masses in the MSM

Some comments on the features of MSM:

• The seesaw models with a single right-handed neutrino ruled out (if of rank 1, 2 massless -eigenstates, no CP violation). • The 2N-seesaw models may serve as an approximation of the 3N-seesaw models with N3 decoupled in the limit of M3 » M1,2 .• The texture of is essentially stable against RGE effects from M1 to MZ . So is Det()=0 or m1 =0 or m3 =0.

Some Comments

One-loop RGE:

Det() keeps vanishing at MZ

Results (Mei, Xing 04):

6 parameters of Y at MZ

RGE-running Functions

The seesaw mechanism itself is not quantitatively predictive, unless a specific lepton flavor structure is assumed.

A combination of the seesaw mechanism and a certain flavor symmetry or a few texture zeros, whose empirical role is to reduce the number of free parameters, is therefore needed.

FGY Ansatz in the MSM

Flavor structure: texture zeros?

012 caFrampton-Glashow-Yanagida ansatz (02)

A typical example:

01 m

0)( 13 M

16.03

2 m

m

CP-violating Phases

It turns out that two CP-violating phases are calculable! (Guo, Xing 04)

Due to m1=0, the phase can be rotated away.

08.007.0~sin 13 %1~CPJ

eV10~ 3ee

m

atlow

scale

Pattern Condition

2121 // MMiaa

012 ba 021 baor

or 012 ca 021 ca

2121 // MMibb

2121 // MMicc

012 cb or 021 cb

01 m 03 m

One-zero textures selected by data (Xing 04):

Leptogenesis at the seesaw scale (Fukugita, Yanagida 86)

Lepton-number-violating and CP-violating decays: )MSSM(c2Hh

Leptogenesis in the MSM

Interference leads to CPV 2,1

If the interactions of N1 are in thermal equilibrium when N2 decays, can be erased before N1 decays. Then only , produced by the out-of-equilibrium decay of N1 , can survive.

21 MM

2

1

Quantities at M1 are expressed by those at MZ .

Leptogenesis in the MSM

If the RGE effect were neglected, one would obtain:

Independent of M2 !(Guo, Xing 04)

In both cases, is directly related to . will vanish if vanishes, or vice versa.

Then the RGE-corrected result is (Mei, Xing 04)

I/1̂1

Direct link between high and low scale CP-violating phenomena!

Cosmological baryon asymmetry:

Lepton number asymmetry from :If the effective neutrino mass parameter lies in the range ,then dilution factor d will approximately read as follows:

eV10~eV10 31

2 m

*1LLL //)( gdsnnY

)MSSM(75.228* g

1

22

111/sin)(~ MYYm

Leptogenesis in the MSM

1

~m

The above lepton number asymmetry is eventually converted into a net baryon number asymmetry via the non-perturbative sphaleron process (Kuzmin, Rubakov, Shaposhnikov 85):

LBBB 35.0/)( YsnnY

1

Numerical Illustration

03 m01 m

GeV(SM)120H m)MSSM(50tan

YB YB

θ13 (MZ) θ13 (MZ)

Some comments:

• M1 must be heavy enough ( ). And a conflict between achieving the successful thermal leptogenesis and avoiding the over-production of gravitinos ( ) exists in MSSM.

GeV1010

GeV1081 M

• Distinguishing between the SM and MSSM results needs other experimental information (for example, those MSSM-motivated LFV processes etc.) e

• Distinguishing between and is possible at low energy scales, as they belong separately to normal and inverted neutrino mass hierarchies.

01 m 03 m

Leptogenesis in the MSM

Concluding remark: Leptonic CP violation to be observed might be one of the key reasons for the observed matter-antimatter asymmetry of our universe—fundamentally important

34

LB

something occurred over there

one billion years ago

today

so

we

are

here

35

Thank You