Quark-Lepton Complementarityin light of recent T2K & MINOS experi-
ments
November 18, 2011 Yonsei University
Sin Kyu Kang (서울과학기술대학교 )
Outline• Introduction - current status of neutrino mixing angles• Parameterizations of neutrino mixing matrix• Quark mixing angles and Quark-Lepton
Complementarity (QLC)• QLC parameterizations and Triminimal
parametrization• Predictions of physical observables• Summary
Purposes of this work • To investigate whether neutrino mixing matrix
based on Quark-Lepton Complementarity (QLC) reflecting GUT relations or quark-lepton symmetry is consistent with current neutrino data or not.
• To investigate how we can achieve large values of mixing angle q13 so as to accommodate recent T2K or MINOS experimental results.
• To point out that nonzero values of q13 can be re-lated to the deviation of q12 from maximal mixing or tri-bimaximal mixing
Neutrino Mixing Matrixe
Le
L
L
Atmo-spheric angle
Reactor angle and Dirac CP phase
Solar angle Majorana phases
Standard Model states
Neutrino mass states
3
2
1
321
321
321
UUUUUUUUU eeee
1000000
10000
0010
0
00
0012
1
1212
1212
1313
1313
2323
2323
i
i
i
i
ee
cssc
ces
esc
csscU
CP
CP
Neutrino mixing anlges before T2K( Schwetz, Tortola, Valle, New J.Phys.13:063004,2011. )
)(2 10.2 , 51.439.9 , 4.369.31
75.5 , 6.45 , 9.33
132312
132312
qqq
qqq
Neutrino data for neutrino mixing angles is consistent with “Tri-bimaximal mixing” pattern at 2σ
21
31
61
21
31
61
03
16
2
U
0 , 45 , 3.35 132312 qqq
3
13
13
12 e
2
12
13
It can be derived from some discrete symmet-ries such as A4, S4 etc.
Recent T2K experimentThe results show
(CPC) eV 102.4|m|
0.12sinfor
C.L. 90%at )34.0(28.02sin)04.0(03.0
23-223
232
132
q
q
For non-maximal 23 mix-ing
132
232
132 2cossin22sin qqq
More data needed to firmly establish νe appearance and to better deter-mine θ13
155 13 q
Recent MINOS experiment( 1.7 excess of e events )
0.6 , 100 1313 bestqq 5.8 , 130 1313 bestqq
Although TB mixing can be achieved by imposing some flavor symmetries, the current neutrino data indicates that TB is a good zeroth order approxima-tion to reality and there may be deviations from TB in general. To accommodate deviations from TB, neutrino mixing angles can be parameterized (S.F.King 2008)
2sin , )1(
21sin , )1(
31sin 132312
ras qqq
The global fit of the neutrino mixing angles can be translated into the 3σ
0.14 a 0.18- , 0.03 s 0.10- , 31.00 r
Alternatively, triminimal parametrization has been proposed
)()()(
300121-012
611-0110002
31sin),,,(
4
212113132323
11221132323
RURURU
U
RURUTMin
(Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100 ,2008 )
The neutrino mixing observables up to 2nd order in
ie eU
133
323222
2121212
sin 21sin ,
31
322
31sin
ij
Quark Mixing Angles
Current data for quark mixing angles0.9739 0.9751 0.221 0.227 0.0029 0.00450.221 0.227 0.9730 0.9744 0.039 0.044
0.0048 0.014 0.037 0.043 0.9990 0.9992
The standard parameterization of VCKM
quark-s and -d of Rotation
rphasefacto plusquark-b and -d of Rotationquark-b and -s of Rotation
10000
0010
0
00
001
1212
1212
1313
1313
2323
2323, cssc
ces
esc
csscV
i
i
SCKM
SCKMV ,
Wolfenstein Parameterization of quark mixing matrix
0.82,A
2 3
2 2
3 2
11 ( )2
112
(1 ) 1
A i
V A
A i A
0.2243 0.0016, 0.20, 0.33.
L. Wolfenstein, Phys. Rev. Lett. 51 (1983)
Quark Lepton ComplimentarityLepton mix-ings
Quark mix-ings
Present experimental data allows for relations like:
Raidal (2004) Smirnov, Minakata (2004)
'Quark-Lepton Complementarity‘
45
45
2323
12
q
C
QLC is well in consistent with the current data within 2σ
QLC may serve as a clue to quark-lepton symmetry or unification. So, QLC motivates measurements of neutrino mixing angles to at least the accuracy of the meas-ured quark mixing angles. In the light of QLC, neutrino mixing matrix can be composed of CKM mixing matrix and maximal mixing matrix. Three possible combinations of maximal mixing and CKM as parametrization of neutrino mixing matrix (Cheung, Kang, Kim, Lee (2005), Datta, Everett, Ramond (2005) )
)4()4( )3(
)4()4( )2(
)4()4( )1(
1223
1223
1223
RUR
URR
RRU
CKM
CKM
CKM
Among three possible combinations, 4)4( 1223max RRVVVU CKMbiCKMPMNS
2 ,
4 ,
24 132 qqq Aatmsol
Mixing angles in powers of λ
9 , 43 , 36 1323 qqq sol
consistent with the current experimental data.
Among three possible combinations, 4 )4(23 RVRU CKMPMNS
313
2 ,4
,4
qqq AAatmsol
Mixing angles in powers of λ
5.0 , 43 , 33 1323 qqq sol
consistent with the current experimental data, but disfavored by T2K measurement of q13
Among three possible combinations, CKMPMNS VRRU 4)4( 1223
213
2 ,4
,24
qqq AAatmsol
Mixing angles in powers of λ
2 , 43 , 36 1323 qqq sol
consistent with the current experimental data , but disfavored by only T2K measurement of q13 at 90%CL.
The flavor mixings stem from the mismatch be-tween the LH rotations of the up-type and down-type quarks, and the charged leptons and neutri-nos.
In general, the quark Yukawa matrices
DdiagDDD
UdiagUUU
VYUY
VYUY
DUCKM UUV
For charged lepton sector : LdiagLLL VYUY
How to derive those parameterizations
For neutrino sector : Introducing one RH singlet neutrino per family which leads to the seesaw mechanism
Rewriting neutrino mass,
MLPMNS VUUU 0
In SO(10), TDLU YYYY ,
Taking symmetric YD , MCKMPMNS VVU
UDL UUVU 0* ,
Taking )4(23 RUV DTD MCKMPMNS VVRU )4(23
Taking maxbiD
TD VUV CKMPMNS VRRU /4)()4( 1223
Realistic neutrino mixing matrix,
4)4()( 1223 RRVUPMNS
We need to modify
5.3 , 43 , 41 1323 qqq sol
Then, neutrino mixing angles becomes
From the empirical relation, m
mmmV e
S
dUS 3
)(12
213331
~ 2
2
VVCKM
In GUT framework,
At low energies, the Yukawa operators of the SM (MSSM) are generated from integrating out heavy fields X which lead to GUT relations be-tween q and l
In SU(5) GUT,
4)4()( 1223 RRVUPMNS
6 , 43 , 39 1323 qqq sol
Then, neutrino mixing angles becomes
232 ,
4 ,
232
4 132 qqq atmsol
In Pati-Salam GUT (Antusch & Sinrath (2009) ),
2 ,
4 ,
24 2
113
2
2
1
cc
cc
atmsolqqq
it is possible to have 6 , 2/9 21 cc
8 , 43 , 36 1323 qqq sol
What if replacing R12(/4) with tri-bimaximal type ?
))3/1((sin)4( 11223
RRUCKM
))3/1((sin)4/( 11212
RR
QLC parameterizations become
For realistic GUT relation, we replace UCKM U()
23 ,
4 ,
36 132max qqqq
atmbitri
solsol
It is possible to obtain rather large q13 while keeping small deviation of q12
Lepton Flavor Violation in the SUSY caused by the misalignment of lepton and slepton mass matrices
RG inducesX
ijl MM
YYAmmij
log))(3(81 2
020
2~
)4()()4( 232
23 RUYURYY CKM
DCKM
]1,,[ 48 DiagyY tD Taking
1::)(:)(:)( 66 BReBReBR
(cf)
1::)(:)(:)()4()4(
1::)(:)(:)()4()4(44
1223
481223
BReBReBRURR
BReBReBRRRU
CKM
CKM
4)4( 1223 RRVU CKMPMNS
Predictions for Physical Observables Neutrino mixing probabilities for phased averaged propa-gation(Δm2L/4E >>1) iiii UUUUP
|||| 22
AAS 22
(Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100 ,2008 )
Using the previous formulae, we obtain
, )1(21
83 ,)
211(
41
, 21
83 ,)
211(
41
, )1(21
83 ,2
21
22
22
22
APAP
PAP
APP
e
e
ee
Using the best fit values for the parameters
, 421.0 ,401.0
, 380.0 ,178.0
, 220.0 ,602.0
PP
PP
PP
e
e
ee
The phase-averaged mixing matrix modi-fies the flavor composition of the neutrino fluxes.
iU
The most common source for atmospheric and astrophysical neutrinos is thought to be pion production and decay. The pion decay chain generates an initial neutrino flux with a flavor composition given approximately for the neutrino fluxes :
(P. Lipari, M. Lusignoli, and D. Meloni (2007))
0:2:1:: 000 e
At the Earth :
1:1 : 1.2
)5.01(:)5.01(:)41(:: 222
AAAe
Matching with triminimal parametrization
6/)12(6/)12(s 1sin
sin
)1(sin
22
2
12
23232
31313
ccs
cscs
A
iAee ii
31sin),,,()4(
4 )4(1
1212132323
1223
RUR
RVRU CKMPMNS
In the light of recent data from T2K,
Final Remark
)4()4( 1223 RRUCKM
more favorable because it predicts
2sin 13
q
Summary• We have discussed that neutrino mixing matrix based on
Quark-Lepton Complementarity (QLC) reflecting GUT rela-tions or quark-lepton symmetry is consistent with global fit to current neutrino data at 2 but some of QLC param-eterizations disfavored by T2K
• We have shown how we can achieve large values of mix-ing angle q13 so as to accommodate recent T2K or MINOS experimental results.
• We have observed that QLC based on GUT relations lead to the relation between nonzero values of q13 and the de-viation of q12 from maximal mixing or tri-bimaximal mixing