what if is very small ? c.s. lam, mcgill/ubc/triumf hep-ph/0104116 [plb 507(2001)214] hep-ph/0503159...
TRANSCRIPT
What if is very small ?What if is very small ?
C.S. Lam, McGill/UBC/TRIUMFC.S. Lam, McGill/UBC/TRIUMF
Hep-ph/0104116 [PLB 507(2001)214]
hep-ph/0503159 [PRD 71(2005)093001]
hep-ph/0508008
13
IntroductionIntroduction
• Standard Model works extremely well, but…Standard Model works extremely well, but…
1.1. it assumes neutrinos to be massless it assumes neutrinos to be massless (X)(X)
2.2. it can accommodate but not explain it can accommodate but not explain fermion massesfermion masses
3.3. it does not answer Rabi’s old questionit does not answer Rabi’s old question
• An elucidation of these questions may point An elucidation of these questions may point us a way to how the SM should be extendedus a way to how the SM should be extended
• Horizontal symmetryHorizontal symmetry
• Neutrino acts weird, maybe it is Neutrino acts weird, maybe it is trying to tell us something …….trying to tell us something …….
I come into this business with a certain skepticism regarding standard ideologies, and
have a penchant to looking for something really different. This is based on the notion that neutrinos are behaving very differently
from the quarks and charged leptons in two respects: very large mixings, and relatively small
mass splittings. (J.D. Bjorken)
Neutrinos masses and mixingsNeutrinos masses and mixings12
23
13
13
2
0.3
quark
2 2 2 22 1
2 2 2 23 2
| | | | (9 )
| | | | (52 )atm
m m m meV
m m m meV
3| |m
2| |m
1| |m 3| |m
2| |m
1| |m
12 32
23
13
45
12
atm
reac
2.2em eV
12
13
Neutrino masses are tiny, mixings are very unlike quarks
Is it trying to tell us something special about neutrinos?
59
77K
3
1| | 0.47 ( )iim eV astro
0.12( )im leptogenesis
e
neutrinos
1 2 3
u
c
t
quarks
s bd
Neutrinos have masses, and they Neutrinos have masses, and they mixmix
2 2 2 22 1
2 2 2 23 2
| | | | (9 )
| | | | (52 )atm
m m m meV
m m m meV
3| |m
2| |m
1| |m 3| |m
2| |m
1| |m
0
12 32
13 12reac 13 0reac
2.2em eV
12
13
21252( ) 1 0.84sin ( / 2)eem meV
77K
3
1| | 0.47 ( )iim eV astro
0.12( )im leptogenesis
23 45atm 23 45atm
Horizontal symmetry
Left-Handed 2-3 SymmetryLeft-Handed 2-3 SymmetryT
L R L LdL M M
021
21
2
1
c
U s c
s
s
c
12 12sin , coss c
T dM U M U
1
2
3
d
m
M m
m
22
11
12 23
12 2
12 1
22
2
3
T dM U M U
2 211 1 2
12 2 1
2 222 1 2 3
2 223 1 2 3
/ 2
1( )
21
( )2
c m s m
cs m m
s m c m m
s m c m m
TP M P
1 0 0
0 0 1
0 1 0
P
23 1345 , 0 TM P M P
2-3 symmetry
TL LL M TT
L LP M P
L LP L L
2-3 symmetry for left-handed neutrinos
3| |m
2| |m
1| |m 3| |m
2| |m
1| |m
neutrino masses tiny: seesaw mechanism
Seesaw MechanismSeesaw Mechanism
det( ) 0DM
3 0m
TL LL M
TL R RD R RM M
seesaw
1TD R DM M M M
L LP L L
TD DM P M
row
det( ) 0M
3| |m
2| |m
1| |m
0
Double Protection withDouble Protection withRight-Handed 2-3 SymmetryRight-Handed 2-3 Symmetry
TL LL M
TL R RD R RM M
seesaw
1TD R DM M M M
L LP L L
R RP L L
suggests
TR R
TD D D
M P M P
M P M M P
L R
1TD R DM M M M
TD D DM P M M P L R
det( ) 0DM
det( ) 0M
3 0m
3| |m
2| |m
1| |m
0
row column
even when one of the two symmetries is broken
SummarySummary
23 1345 , 0
2-3 symmetry for left-handed
neutrinosWith seesaw mechanism
Double protection from right-handed 2-3 symmetry
3| |m
2| |m
1| |m
0
Other Work on 2-3 SymmetryOther Work on 2-3 Symmetry
• Mohapatra, Nasri, Yu: hep-ph/0410369, 0502026, Mohapatra, Nasri, Yu: hep-ph/0410369, 0502026, 05050210505021
• Grimus, Lavoura, et al: hep-ph/0305046, Grimus, Lavoura, et al: hep-ph/0305046, 0310050, 0405261, 0407112, 0408123, 05041530310050, 0405261, 0407112, 0408123, 0504153
• Koide et al: hep-ph/0209333, 0303256;Koide et al: hep-ph/0209333, 0303256;Matsuda and Nishiura: hep-ph/0506192Matsuda and Nishiura: hep-ph/0506192
• Datta, O’Donnell: hep-ph/0508314Datta, O’Donnell: hep-ph/0508314
END