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 Motivatio n RGE Telescope minimal Seesaw Model minimal Seesaw Model

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/ astro-ph/ astro-ph/ astro-ph/

5 前苏联氢弹之父 Cosmological matter-antimatter asymmetry (observational evidence) Atmospheric and solar neutrino oscillations (experimental evidence) Connectio n? Dark energy Dark matter Big Bang Inflation 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 GeV 14 M 3 M 2 M 1 Leptogenesis 10 GeV 2 m 3 m 2 m 1 -oscillations (  ) _0 decay Seesaw

RGE 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): θ 12 ～ 13° → θ 23 ～ 2° → θ 13 ～ 0.2° → δ ～ 65° Lepton mixing (MNS): θ 23 ～ 45° → θ 12 ～ 33° → θ 13 <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 scaleElectroweak scale

Numerical Examples (1-II)

Numerical Examples (2) Neutrinoless double-beta decay: Allowed!

Numerical Examples (3) Simultaneous generation of appreciable and from, no problem; and from, no problem. But and from, suppressed

 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 Seesaw relation Principle of minimal particle content SU(2)  U(1) gauge symmetry preserved Lepton number violating M R 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/ (PLB) Endoh et al hep-ph/ (PRL) Raidal, Strumia hep-ph/ (PLB) Raby hep-ph/ (PLB) Dutta, Mohapatra hep-ph/ (PRD) Barger, Dicus, He, Li hep-ph/ (PLB) Guo, Xing hep-ph/ (PLB) Ibarra, Ross hep-ph/ (PLB) Mei, Xing hep-ph/ (PRD) Turzynski hep-ph/ (PLB) Chang, Kang, Siyeon hep-ph/ (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 Normal -mass hierarchy: Inverted -mass hierarchy: : 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 N 3 decoupled in the limit of M 3 » M 1,2. The texture of  is essentially stable against RGE effects from M 1 to M Z. So is Det(  )=0 or m 1 =0 or m 3 =0. Some Comments One-loop RGE:

Det(  ) keeps vanishing at M Z Results (Mei, Xing 04): 6 parameters of Y at M Z 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? Frampton-Glashow-Yanagida ansatz ( 02 ) A typical example:

CP-violating Phases It turns out that two CP-violating phases are calculable! (Guo, Xing 04) Due to m 1 =0, the phase  can be rotated away. at low scale

Pattern Condition or  One-zero textures selected by data (Xing 04):     

Leptogenesis at the seesaw scale (Fukugita, Yanagida 86) Lepton-number-violating and CP-violating decays: Leptogenesis in the MSM Interference leads to CPV If the interactions of N 1 are in thermal equilibrium when N 2 decays, can be erased before N 1 decays. Then only, produced by the out-of- equilibrium decay of N 1, can survive.

Quantities at M 1 are expressed by those at M Z. Leptogenesis in the MSM If the RGE effect were neglected, one would obtain: Independent of M 2 ! (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) 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: Leptogenesis in the MSM The above lepton number asymmetry is eventually converted into a net baryon number asymmetry via the non-perturbative sphaleron process (Kuzmin, Rubakov, Shaposhnikov 85):

Numerical Illustration YBYB YBYB θ 13 ( M Z )

Some comments: M 1 must be heavy enough ( ). And a conflict between achieving the successful thermal leptogenesis and avoiding the over-production of gravitinos ( ) exists in MSSM. Distinguishing between the SM and MSSM results needs other experimental information (for example, those MSSM-motivated LFV processes etc.) Distinguishing between and is possible at low energy scales, as they belong separately to normal and inverted neutrino mass hierarchies. 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 LBLB something occurred over there one billion years ago today so we are here

35 Thank You