Neutrino mixing angle θ 13 In a SUSY SO(10) GUT
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Transcript of Neutrino mixing angle θ 13 In a SUSY SO(10) GUT
Neutrino mixing angle θ13
In a SUSY SO(10) GUT
Xiangdong Ji Peking University
University of Maryland
Outline
1. Neutrino (lepton) mixing2. Why SUSY SO(10)? 3. A new SUSY SO(10) model4. Looking ahead
X. Ji, Y. Li, R. Mohapatra, Phys. Lett. B633, 755 (2006) hep-ph/0510353
Neutrino (lepton) mixing
Neutrinos, like quarks, have both masses and weak charges (flavor), and the mass eigenstates are not the same as the flavor eigenstates. One can write the neutrino of a definite flavor as
Where U is the neutrino (or lepton) mixing matrix.
Three flavors
From the standard model, we know there are at least 3 neutrino flavor (e,μ,τ), therefore, there are at least three mass eigenstates.
In the minimal case, we have 3-mixing angle (θ12 θ23 θ13) and 1(Dirac)+2(Majorana) CP-violating phases
PNMS matrix
U Ue1 Ue2 Ue3
U1 U2 U 3
U1 U 2 U 3
1 0 0
0 cos23 sin23
0 sin23 cos23
cos13 0 e iCP sin13
0 1 0
e iCP sin13 0 cos13
cos12 sin12 0
sin12 cos12 0
0 0 1
1 0 0
0 e i / 2 0
0 0 e i / 2i
What do we know?
From past experiments, we know θ12 & θ23 quite well Solar-ν mixing angle θ12
Super-K, SNO, KamLand
sin2 θ12 = 0.30 ±0.07
Atmosphetic-ν mixing angle θ23
Super-K, K2K,
sin2 θ23 = 0.52 ±0.20
There is an upper bound on θ13
sin2 θ23 < 0.054 or sin2 2θ23 < 0.1 from Chooz exp.
Solar mixing angle
Current limit on θ13
Chooz
Why do we care about precision on θ13
Three important questions in neutrino physics What is the neutrino mass hierarchy? Are neutrinos Dirac or Majorana particles? What is the CP violation in lepton sector?
CP violation Important for understanding baryon genesis in the
universe One of the major goals for neutrino superbeam
expts. Is related to the size of θ13 (Jarlskog invariant)
Upcoming experiments
Reactor neutrinos Double Chooz, <0.03 approved Daya Bay <0.01? US-China collaboration? Braidwood <0.01 $100M
Neutrino superbeams Much more expensives
hundreds of Million $
nuclear reactor
detector 1
detector 2
Distance (km)
PeePe e
Theories on neutrino mixing angles
Top-down approach
Assume a fundamental theory which accommodates the neutrino mixing and derive the mixing parameters from the constraints of the model.
Bottom-up approach
From experimental data, look for symmetry patterns and derive neutrino texture.
Why a GUT theory?
Unifies the quarks and leptons, and treat the neutrinos in the same way as for the other elementary particles.
A SO(10) GUT naturally contains a GUT scale mass for right-handed neutrinos and allows the sea-saw mechanism
Which explains why neutrino mass is so much smaller than other fermions!
2~ /D Rm m m
SUSY SO(10) GUT
There are two popular ways to break SUSY SO(10) to SU(5) to SM Low-dimensional Higgs 16, 16-bar, 45, 10
16s (break B-L symmetry) can be easily obtained from string theory
High-dimensional Higgs 126, 126-bar, 120, 10
does not break R-parity (Z2), hence allows SUSY dark matter candidates.
R = (-1)3(B-L)+2S
What can SUSY SO(10) GUTs achieve?
SUSY GUT Stabilize weak scale & dark matter Coupling constant unification Delay proton decay
Mass pattern for quarks and leptons Flavor mixing & CP violation Neutrino masses and mixing Mixing θ13
126H large θ13 sin2 2θ13 ~ 0.16 (Mohapatra etal)
16H small θ13 sin2 2θ13 < 0.01 (Albright, Barr)
Albright-Barr Model
Fermions in 16-spinor rep. 16 = 3 (up) + 3 (up-bar) + 3 (down) + 3 (down-bar) +
1 (e) + 1 (e-bar) + 1(nu-L) + 1(nu-R)
Assume 3-generations 16i (i=1,2,3) Mass term
For example, eta contribute the mass to the first family, up quark, down quark, electrons and electron neutrino
1 1 2 3
1 2 ' 1 3 ' 2 3 '
16 16 10 16 16 10 45
16 16 16 16 '16 16 16 16 16 16 16 16H H H
H H H H H H
L
Mass matrices
Dirac masses
Majorana Masses Lopsidedness
Diagonalization
An arbitrary complex matrix can be diagonalized by two unitary matrices
MD = L (m1, m2 m3)R+
Majorana neutrino mass matrix is complex and symmetric, and can be diagonalized by a unitary matrix
MM = U (m1, m2 m3)U*
CKM & lepton mixing
The quark-mixing CKM matrix is almost diagonal
The lepton mixing matrix (large mixing)
† CKM U DV L L
† PMNS LV L L
Large solar mixing angle
It can either be generated from lepton or neutrino or a combination of both. From lepton matrix,
Babu and Barr, PLB525, 289 (2002)
again very small sin2 2θ13 < 0.01
If it is generated from neutrino mass matrix, it can come from either Dirac or Majorana mass or a mixture of both. In the Albright-Barr model, the large solar mixing
comes from the Majorana mass.Fine tuning….
Lopsided mass matrix
Generate the large atmospheric mixing angle from lepton mass matrix.
Georgi-Jarlskog relation
Why
A model (Ji,Li,Mohapatra)
Assume the large solar mixing is generated from the neutrino Dirac mass and the Majorana mass term is simple
The above mass terms can be generated from 16, 16-bar & 45
What can the model predict ?
In the non-neutrino sector, there are 10 parameters, which can be determined by 3 up-type, and 3-lepton masses, and 4 CKM parameters. 3 down quark masses come out as predictions
In the neutrino sector, we use solar mixing angle and mass ratios as input Prediction: right-handed neutrino spectrum Atmospheric mixing and θ13
Predictions
Looking ahead
Leptogenesis Baryon number asymmetry cannot be generated
at just the EW scale (CP violation too small) CP-violating decay of heavy majorana neutrino
generates net lepton number L. The lepton number can be converted into B-
number through sphaleron effects (B-L conserved.)
Does model generates enough lepton number asymmetry?
Looking ahead
Proton Decay Is the proton decay too fast?
Dimension-5 operator from the exchange of
charged Higgsino.