Upload
hop-moss
View
39
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Models of Neutrino Mass. Introduction (neutrino masses,mixings) Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices) Natural hierarchy (sequential right-handed neutrino dominance) Relation between neutrino factory CP violation and leptogenesis? - PowerPoint PPT Presentation
Citation preview
04/19/23 Steve King, Coseners House 1
Models of Neutrino Mass
•Introduction (neutrino masses,mixings)
•Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices)
•Natural hierarchy (sequential right-handed neutrino dominance)
•Relation between neutrino factory CP violation and leptogenesis?
•SUSY and lepton flavour violation: see-saw vs. SUGRA
•GUTs and Family Symmetry
04/19/23 Steve King, Coseners House 2
Possible three neutrino mass patterns with LMA and .
21m
22m
23m
23m
22m21m
232m
232m
221m
221m
“Normal” “Inverted”
232 0m 2
32 0m
2(0.00 )eV 2(0.10 )eV 2(0.20 )eV
2 232| | (0.05 )m eV 2 2
21 (0.008 )m eV
2(0.23 )eV 2(0.00 )eV
04/19/23 Steve King, Coseners House 3
126
4 23
2. 0 13
Large Mixing Angles
1
23 13 12 2
3
e
R R R
atmospheric
solar LMA MSW
CHOOZ
04/19/23 Steve King, Coseners House 4
The Neutrino Mixing Matrix U
†0 0
0 0
0 0
L R
eE EE
LR
m
V m V m
m
†L LEU V V
23 13 12 12U R U R P
23 23 23
23 23
1 0 0
0
0
R c s
s c
13 13
13
13 13
0
0 1 0
0
i
i
c s e
U
s e c
12 12
12 12 12
0
0
0 0 1
c s
R s c
Parametrising
Constructing
Majorana matrix
3
2
1
00
00
00
m
m
m
VmVT
LLLL
1
212
0 0
0 0
0 0 1
i
i
e
P e
04/19/23 Steve King, Coseners House 5
In the Standard Model neutrinos are massless, and a neutrino and anti-neutrino are distinguished by a (total)
conserved lepton number L.
cLLLLm
Origin of neutrino mass
Majorana mass
Dirac mass LR L Rm
Majorana or Dirac?
(conserves L)
CP conjugate of left-handed
neutrino
Right-handed neutrinos
cRR R RM
from Yukawa couplings
(violates L)
04/19/23 Steve King, Coseners House 6
See-saw mechanism
1 TLL LR RR LRm m M m
cLL L Lm
0 cLRc L
L R TLR RR R
m
m M
Diracmatrix
Heavy Majorana matrix
Light Majorana matrix
Diagonalise
04/19/23 Steve King, Coseners House 7
0 0
0 1 12
0 1 1
0HILL
mm
( )
1 1
1 0 02
1 0 0
0IH ALL
mm
Inverted hierarchy
Type A (zero in 11)
( )
0 0
0 1 2 1 2
0 1 2 1 2
1IH BLLm m
Degenerate Pseudo-Dirac
Type B (non-zero 11)
( 2)
0 0
0 0 1
0 1 0
1DEG BLLm m
( 1)
0 0
0 1 0
0 0 1
1DEG BLLm m
( )
1 1
2 21 1 1
2 221 1 1
2 22
0
DEG ALLm m
Large neutrinoless double beta decay (Petcov,…)
Hierarchy
Leading order consistent with LMA MSW Barbieri,Hall,Smith,Strumia,Weiner;Altarelli,Feruglio;…
Natural cases: SFK hep-ph/0204360
2 2 21 2 3m m m
2 2 21 2 3m m m
2 2 21 2 3m m m
LLm
04/19/23 Steve King, Coseners House 8
Natural Neutrino Hierarchy?
Natural eigenvalues are why ?
Technically need a small 23 sub-determinant:
222 23
23 33
detm m
mm m
2 3m m
But why should the sub-determinant be small ?
How can we get this from the see-saw mechanism?
0 0
0 1 12
0 1 1
0HILL
mm
2 22 3m m 2 2
2 3m m
04/19/23 Steve King, Coseners House 9
0 0
0 0
0 0RR
Y
X
M X
LR
a a d
m b b
c c
e
f
2 2 2
21
2 2
2
2
2
.
. .
TLL LR RR LR
a a d a b ab d a c ac d
X X X X X X
b b b c bcm m M m
X X X X
e f
Y Y Y
e ef
Y Y
c
X
fc
YX
If one right-handed neutrino of mass Y dominates then sub-determinant is naturally small: single right-handed
neutrino dominance (SFK PLB 98, NPB 99)
See-saw with diagonal heavy Majorana matrix
0 0
0 0
0 0RRM X
X
Y
'LR
d a a
m b b
c c
e
f
Columns can be re-ordered without loss of generality
2 2 | | | |,
, , , , ,
|
, ,
| ,| | ,| | xy x y
X Xx y a b c x
e f e
y cY
a
f
b
Sequential dominance (SFK NPB2000)
04/19/23 Steve King, Coseners House 10
| || | || e fd
Analytic estimates for neutrino masses and mixing angles (valid for sequential dominance)
SFK hep-ph/0204360
2 2 | | | |,
, , , , ,
|
, ,
| ,| | ,| | xy x y
X Xx y a b c x
e f e
y cY
a
f
b
23t|
an|
| |
e
f
1223 23
| |tan
| | cos( ) | | cos( )b c
a
c b s c
2
3
2| | | |m
e f
Y
1 2 3m m m
Sequential dominance
2
2 212
| |am
Xs
1 ( )x y
m OX
* *( )
13 3/ 22 2
| | ( )
| | | |a ei a e b f c Y
ee f X
23 23| | sin( ) | | sin( )b cc b s c
b b a c c a e f
* *arg( )e a e b f c
(set d=0 below)
Phases fixed by real 12 angle condition
and is fixed by the real 13 angle condition
where
Mass hierarchy and large
mixing angles naturally!
04/19/23 Steve King, Coseners House 11
0 0
0 0
0 0RR
Y
X
M X
0 0 0
0 0
0
1
10LR
a a d
Y b b
fc c
e
Light or Heavy Sequential Dominance?
0 0
0 0
0 0RRM X
X
Y
0 0 0
0 0 0
' 0 0 1LR
d a a
Y b b
c
e
f c
Light Sequential Dominance (LSD)
Heavy Sequential Dominance (HSD)
Y X X
X X Y
“Lop-sided” (large 23 element)
“Quark-like” (no large off-diagonal
entries)Note that X’ is irrelevent for neutrino masses, mixings (and leptogenesis-see later), and the model reduces to an effective 2 right-handed neutrino
model SFK 2000; Frampton,Glashow,Yanagida 2002; Raidal,Strumia 2002.
04/19/23 Steve King, Coseners House 12
•Right-handed neutrinos are produced in early universe and decay out of equilibrium giving net lepton number L
•CP violation from complex Yukawa couplings
•L is processed into B via B-L conserving sphalerons
Fukugita,Yanagida; Buchmuller,Plumacher; Di Bari, Davidson…
10 *110 /B
baryonsY d g
photons
Leptogenesis
† 21 12
1 †2 11
Im{[( ) ] }3
8 ( )LR LR
LR LR
M Y Y
M Y Y
1 1
11 1
( ) ( )
( ) ( )R j U R j U
R j U R j U
L H L H
L H L H
1R 1R†
jLjL
UHUH
UH
iL
2R
2R1R
Relation between CP violation at a neutrino factory and in leptogenesis? SFK
hep-ph/0211228
0 0
0 0
0 0RRM X
X
Y
0
1LR e
f
a a
Y b b
c
Heavy RH neutrino of mass X’ is irrelevant for both leptogenesis and neutrino masses, mixings
† 212Im{[( ) ] } sin 2B LR LR COSMOY Y Y * *arg( )COSMO e b f c
23 2 23 3
23 2 23 3
| | sin | | sintan( )
| | cos | | cosCOSMO
b s c c
b s c c
23 2 23 3
23 2 23 3
| | sin | | sintan( )
| | cos | | cosCOSMO
b c c s
b c c s
2 3,b e c f Neutrino factory phase and leptogenesis phase are linked in terms of two invariant see-saw
phasesRemarkably the leptogenesis phase is equal to
the phase which enters neutrinoless double beta decay !
0| | | |COSMO
Assume 11 texture zero (see
later)
12' 10X X GY eV LSD
Di Bari,Buchmuller,Plumacher
In HSD (Hirsch,SFK) and gravitino bound may be respected (but no leptogenesis-MNS link since X’ couplings are relevant for
leptogenesis but not neutrino masses, mixings)
9' 10X X GeY V
04/19/23 Steve King, Coseners House 14
SUSY and Lepton Flavour Violation
If SUSY is present then neutrino masses inevitably lead to lepton flavour violation due to radiatively generated off-diagonal slepton
masses
Borzumati, Masiero; Hisano, Moroi, Tobe, Yamaguchi; SFK, Oliveira; Casas, Ibarra; Lavignac, Masina, Savoy;Blazek,SFK
0 0 0
0
1
0 1
0 0
HSD/lopsided will lead to large due to
large 23 Yukawa.Blazek, SFK
32 ln ln lnGUT GUT GUTM M MC b c bc ef
X X Y
32
32 2 2
32 22( ) ( , , ) | | tan
LF
BR f M m mG
32
2 22( ) 0 0
322
(3 )
8LLA
L
m Am C
LR e
a a d
Y b b
c c f
0 0
0 0
0 0RR
Y
X
M X
( )BR
2 2 2 2†0 0
2
0
(3 )
16LR
L LLR LR
Y
dm dm m AY Y
dt dt
04/19/23 Steve King, Coseners House 16
3 14
0 0 0
0 0 3.10
0 0 1
RRM GeV
212
222
232
1
1
0
LR t
a
Y a h
a
Lepton Flavour Violation in Constrained Minimal Supersymmetric Standard Model
6
3 14
0 0
0 0 3.10
0 0 1
RRM GeV
212
3
3
222
232
0
1
LR t
a
Y a h
a221232
0.15m
m
Blazek,SFK hep-ph/0211368
Large 23 element (lop-sided)
HSD parametrisation with dominant heaviest RH neutrino in
33 position
LSD parametrisation with dominant lightest RH neutrino in
11 position
04/19/23 Steve King, Coseners House 17
Blazek,SFK hep-ph/0211368
tan 50
13 angle depends on a ratio of
Yukawa couplings
32
22
a
a
HSD
04/19/23 Steve King, Coseners House 18
HSD predictions for
constrained MSSM
32
22
tan 50,
1.
a
ra
61.1 10 (90% . .)C L 111.2 10 (90% . .)C L
Blazek,SFK hep-ph/0211368
04/19/23 Steve King, Coseners House 19
LSD predictions for constrained
MSSM
32
22
tan 50,
1.
a
ra 61.1 10 (90% . .)C L 111.2 10 (90% . .)C L
Blazek,SFK hep-ph/0211368
04/19/23 Steve King, Coseners House 20
Supergravity LFV can mimic see-saw LFV
Iain Peddie, SFK (preliminary)
04/19/23 Steve King, Coseners House 21
t
b
cs
ud
e
The goal is to describe the quark and lepton mass hierarchies
Charge +2/3 quarks
Charge –1/3 quarks
Charged leptons
A neutrino hierarchy
GGUTGFamily
1
2
3
310
1
110210
110
110
2101210
310410
1210
1110
04/19/23 Steve King, Coseners House 22
GUTs
E 6
(5) (1)SU U (3) (3) (3)C L RSU SU SU
(4) (2) (2)PS L RSU SU SU
(3) (2) (2) (1)C L R B LSU SU SU U
(3) (2) (1)C L YSU SU U
(5)SU
(10)SO
04/19/23 Steve King, Coseners House 23
Family Symmetry
U(1)
SU(2)
SU(3)
SO(3)
S(3)Nothing
Democracy, Fritzsch,…Hierarchy
Froggatt,Nielsen,Ross…
1 1 1
1 1 1
1 1 1
demm
0 0 0
0 0 0
0 0 1
hierm
(3) (3)L RO O
(3) (3)L RS S
Harrison, Scott
04/19/23 Steve King, Coseners House 24
G.Ross, SFK
G.Ross, Velasco-Sevilla
3 3
3 2 22 23 3
3 223
0
1
uY
6
23
6
3 0 0
0 0
0 0 1RRM M
• Allows a universal form for mass matrices
• Example of Light Sequential Dominance (LSD)
• Texture zero in 11 position leptogenesis-neutrino factory link
Leads to approximately symmetric mass matrices
(3) (10)SU SO
3 3
3 2 2
3 2
0
1
dY
3 3
3 2 2
3 2
0
3 3
3 1
eY
3 3
3 2 2
3 2
0
1
Y
0.05, 0.15
Flavour Unification
04/19/23 Steve King, Coseners House 25
Conclusion• Small neutrino masses can be elegantly explained by see-saw
mechanism• Sequential dominance then provides a natural explanation of a
neutrino mass hierarchy and large mixing angles• The dominant right-handed neutrino may be either the heaviest (HSD)
or the lightest one (LSD)• LSD with 11 zero links leptogenesis phase and the CP phase which is
measurable at a neutrino factory, but is inconsistent with SUSY models• HSD has no such link, but may be consistent with SUSY models• SUSY leads to lepton flavour violating processes, which can
discriminate HSD from LSD• SUGRA LFV can mimic see-saw LFV• GUTs and family symmetry can solve flavour problem G.Ross talk