Neutrino mixing angle θ13
In a SUSY SO(10) GUT
University of Maryland
1. Neutrino (lepton) mixing
2. Why SUSY SO(10)?
3. A new SUSY SO(10) model
4. 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.
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
e1 U e 2 U e 3
U 1 U 2 U 3
1 U 2 U 3
1 0 0 cos13 0 ei CP sin 13 cos12 sin 12 0 1 0 0
0 sin 23 0 1 0 sin 12 cos12 0 0 e i / 2 0
0 cos 23 e sin 13 0 cos13 0
0 1 0 0 e i / 2i
What do we know?
From past experiments, we know θ12 & θ23
Solar-ν mixing angle θ12
Super-K, SNO, KamLand
sin2 θ12 = 0.30 ±0.07
Atmosphetic-ν mixing angle θ23
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
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?
Important for understanding baryon genesis in the
One of the major goals for neutrino superbeam
Is related to the size of θ13 (Jarlskog invariant)
Double Chooz, <0.03 approved
Daya Bay <0.01? US-China collaboration?
Braidwood <0.01 $100M
Much more expensives Distance (km)
hundreds of Million $
Theories on neutrino mixing angles
Assume a fundamental theory which
accommodates the neutrino mixing and
derive the mixing parameters from the
constraints of the model.
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
A SO(10) GUT naturally contains a GUT
scale mass for right-handed neutrinos and
allows the sea-saw mechanism
m ~ mD 2 / m R
Which explains why neutrino mass is so
much smaller than other fermions!
SUSY SO(10) GUT
There are two popular ways to break SUSY
SO(10) to SU(5) to SM
16, 16-bar, 45, 10
16s (break B-L symmetry) can be easily obtained
from string theory
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?
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
126H large θ13 sin2 2θ13 ~ 0.16 (Mohapatra etal)
16H small θ13 sin2 2θ13 < 0.01 (Albright, Barr)
Fermions in 16-spinor rep.
16 = 3 (up) + 3 (up-bar) + 3 (down) + 3 (down-bar) +
1 (e) + 1 (e-bar) + 1(nu-L)
Assume 3-generations 16i (i=1,2,3)
L 16 116110H 16216310H 45H
16116216H16H ' '16116316H16H ' 16216 H16316 H '
For example, eta contribute the mass to the first family, up
quark, down quark, electrons and electron neutrino
Majorana Masses Lopsidedness
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
VCKM L†U LD
The lepton mixing matrix (large mixing)
VPMNS L† 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.
Lopsided mass matrix
Generate the large atmospheric mixing angle
from lepton mass matrix.
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
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
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
Does model generates enough lepton number
Is the proton decay too fast?
Dimension-5 operator from the exchange of