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