Zhizhong Xing IHEP, Beijing

1
Unitarity of Lepton Sector

• Zhi-zhong Xing (IHEP, Beijing)

0) Lessons from Quarks 1) Is the MNS Matrix
Unitary or Nearly Unitary? 2) Unitarity Triangles
in Vacuum and in Matter 3) A Sterile Neutrino and
Unitarity Quadrangles 4) Concluding Remarks
ISS of a future Neutrino Factory and Superbeam
Facility, KEK, 23 25, 2006
2
Lessons from Quarks
Lesson 1
CKM quark mixing
?12 ? ?23 ? ?13 ? d ?
new physics ? 13 2 0.2 65
unitarity ?
Exp. steps
MNS lepton mixing
Exp. steps ?23 ? ?12 ? ?13 ? d/?/s
new physics ? 45
33 lt10 ? ? ? unitarity ?
In the era of precision measurements, the test of
unitarity is a big deal.
3
Lessons from Quarks
Lesson 2
How to test unitarity of the CKM matrix?

• Test the normalization conditions
• Test the orthogonality conditions
• Examine the new physics scenario

Blucher et al, hep-ph/0512039
Similar strategies in the leptonic sector.
(Precision Neutrino Experiments).
4
Is the MNS Matrix Unitary?
In the SM, unitarity is the only constraint
imposed on the CKM matrix.
But the origin of neutrino masses must be beyond
the SM. In this case, whether the MNS matrix is
unitary or not relies on the model or theory.
The MNS matrix is NOT exactly unitary in the
seesaw mechanism!
Small particle content SU(2)_L ? U(1)_Y
Lepton number violating
Z.Z. Xing S. Zhou, hep-ph/0512290
5
Is the MNS Matrix Unitary?
A preliminary upper bound on the elements of R
is at the 0.1 level, given by precise
electroweak data E. Nardi et al., PLB344, 225
(1995)
Z.Z. Xing S. Zhou, hep-ph/0512290
The seesaw relation and the unitarity of V (or U)
The accuracy is much better than imagined!!
Conclusion V is almost unitary in all realistic
seesaw models.
6
Unitarity Triangles
H. Fritzsch Z.Z. Xing, hep-ph/9912358, Prog.
Part. Nucl. Phys. 45 (2000) 1
7
Unitarity Triangles
Typical Example
Another interesting triangle J. Sato, Nucl.
Instrum. Meth. A 472 (2000) 434 Y. Farzan,
A.Yu. Smirnov, Phys. Rev. D 65 (2002) 113001.
8
Matter Effects
Effective Hamiltonians for neutrino propagations
in vacuum matter
Constant earth profile ----a very good
approximation for most of the long baseline
neutrino experiments proposed at present.
9
Matter Effects
3 linear equations for 3 parameters
1
Z.Z. Xing H. Zhang, Phys. Lett. B 618, 131
(2005)
2
3
10
Moduli CP Violation
11
Modified Unitarity Triangles
Sides of 3 triangles in matter
12
Shape Evolution
Long-baseline
Is CP violation establishable via a triangles
three sides of comparable magnitudes ?
H. Zhang Z.Z. Xing, Eur. Phys. J. C 41, 143
(2005)
Neutrinos
13
Shape Evolution
Long-baseline
Is CP violation establishable via a triangles
three sides of comparable magnitudes ?
H. Zhang Z.Z. Xing, Eur. Phys. J. C 41, 143
(2005)
Antineutrinos
14
Shape Evolution
Long-baseline
Is CP violation establishable via a triangles
three sides of comparable magnitudes ?
H. Zhang Z.Z. Xing, Eur. Phys. J. C 41, 143
(2005)
Neutrinos
15
Shape Evolution
Long-baseline
Is CP violation establishable via a triangles
three sides of comparable magnitudes ?
H. Zhang Z.Z. Xing, Eur. Phys. J. C 41, 143
(2005)
Antineutrinos
16
A Sterile Neutrino
A generic SU(2)_L ? U(1)_Y model of electroweak
interactions with 3 charged leptons, 3 active
neutrinos and 1 sterile neutrino. LSND ???
The lepton flavor mixing matrix appearing in the
charged-current weak interactions is a 3 4
matrix. The 3 3 MNS matrix as a sub-matrix is
not unitary. see, e.g., W.L. Guo Z.Z. Xing,
Phys. Rev. D 65, 073020 (2002)
34 lepton flavor mixing matrix
33 M N S
A parametrization of the 4 4 unitary matrix
needs 6 mixing angles 6 CP-violating phases
the number of parameters is now doubled. The
unitarity violation of the 3 3 MNS matrix would
point to new physics.
17
Unitarity Quadrangles
The unitarity of the 4 4 matrix yields 12
unitarity quadrangles. Each quadrangle has 3
distinct topologies in the complex plane. Totally
36 !
W.L. Guo Z.Z. Xing, Phys. Rev. D 66, 097302
(2002)
18
Concluding Remarks
? Testing the unitarity of lepton flavor mixing
is an important task in the era of precision
measurements. A way to explore new physics.
? In realistic seesaw models, the 3 3 MNS
matrix is almost unitary.
? First of all, it is desirable to measure the
smallest mixing angle , so as to check the
normalization condition in the first row of V_MNS.
?13
? Unitarity is so powerful that it can lead to
many self-consistent and testable results in
vacuum and matter. Many jobs to do in a
?-factory.
? The existence of sterile neutrinos would
violate the unitarity of the 3 3 MNS matrix (at
a detectable level?) LSND vs
MiniBOONE
? Explicit strategies to do numerical tests need
to be considered,
Thanks a lot (??) !