[PDF] - T exture mo dels, neutrino observ ables and Leptogenesis PDF Document

SLIDE 1 T exture mo dels, neutrino

bserv

ables and Leptogenesis Martin Hirsch Univ ersit y

f

Southampton 1. Neutrino

scillation

data and neutrino masses 2. T exture mo dels, U (1) family symmetries and O (1) co ecien ts 3. Neutrino

bserv

ables and Leptogenesis 4. Summary

M.

Hirsc h and S.F. King, in preparation

SLIDE 2 Neutrino masses: Exp erimen tal facts A) Limits (PDG2000): m

e
3

eV m

190

k eV m

18:2

MeV hm

i
(0:2
0:6)

eV B) \Hin ts"

n

non-zero neutrino masses: ) A tmospheric neutrinos: Ratio

f
e

=

ev

en ts disagrees with exp ectation, Sup erKamiok ande conrms earlier exp erimen ts with high statistics ) Solar neutrinos 5 exp erimen ts (using 3 exp erimen tal tec hniques)

bserv

e less neutrinos than exp ected ) neutrinos as hot dark matter (HDM) Small (O [eV ]) neutrino mass migh t help structure formation ) LSND exp erimen t

SLIDE 3 Neutrino masses and the seesa w mec hanism ) In the SM neutrinos are massless, b ecause N

R

do es not exist ) Supp

se

N exists, add the follo wing mass terms: L = m D

L

N + M M N N ) Giv es the follo wing mass matrix (one generation notation): M

N

= B @ m D m D M M 1 C A : ) Assuming m D

M

M ,

ne

arriv es at the famous seesa w form ula: m

'

m 2 D M M ) Smallness

f
bserv

ed neutrino masses explained b y large mass scale M M ) Ho w ev er, seesa w mec hanism alone do es not x relativ e size

f

dieren t en tries in the mass matrix

SLIDE 4 F rogatt-Nielson mec hanism Assume some hea vy singlet

exists.

Additional exotic v ector matter with mass M V allo ws an expansion parameter

to

b e generated b y a F roggatt-Nielsen mec hanism, <

>

M V = <

>

M V =

0:22

Assign U (1) c harges to L i , N Ri , etc: L 3 (l 3 ) N 3 (n 3 ) h i (1) H' (l 3 + n 3 ) (M) H (0) (+ insertions) The ab

v

e diagram generates mass term: m L 3 ;N 3

jl

3 +n 3 j hH i Ev en if coupling at v ertex is

f

O (1), strong suppression can b e generated!

SLIDE 5 U (1) F amily Symmetry and T extures Using basic idea

f

F rogatt-Nielsen mec hanism, assign a v

ur

c harges (F C) to all elds, leading to mass matrices

f

the form: Y

B

B B B B @ a 11

jl

1 +n 1 j a 12

jl

1 +n 2 j a 13

jl

1 +n 3 j a 21

jl

2 +n 1 j a 22

jl

2 +n 2 j a 23

jl

2 +n 3 j a 31

jl

3 +n 1 j a 32

jl

3 +n 2 j a 33

jl

3 +n 3 j 1 C C C C C A M RR

B

B B B B @ A 11

j2n

1 + j A 12

jn

1 +n 2 + j A 13

jn

1 +n 3 + j A 12

jn

1 +n 2 + j A 22

j2n

2 + j A 23

jn

2 +n 3 + j A 13

jn

1 +n 3

j

A 23

jn

2 +n 3 + j A 33

j2n

3 + j 1 C C C C C A ) Since

is
1,

a high p

w

er in the exp

nen

t leads to v ery small en tries in the mass matrices, so-called texture zeros Example (F C1): l 1 = 2, l 2 = 0, l 3 = 0, n 1 = 2, n 2 = 1, n 3 = and

=

0, leads to (after the seesa w): m F C 1 LL

B

B B B B @

4
2
2
2

1 1

2

1 1 1 C C C C C A + O B B B B B @

4
2
2
2
2
2
2
2
2

1 C C C C C A : ) Adv an tage: Smallness

f

mass and relativ e size

f

en tries can b e easily xed ) Disdv an tage: Co ecien ts a ij and A ij (assumed to b e O (1) couplings) not predicted

SLIDE 6 O (1) co ecien ts Basic idea: ) Since O (1) co ecien ts not predicted, assume them to b e a random n um b ers ) Cho

se

in terv al for co ecien ts suc h that texture structure

f

mass matrix is not destro y ed ) Run a h uge sample

f

mo dels in a computer program ) Plot the lo garithmic al ly binne d distributions with cor- rect relativ e normalisation for eac h mo del ) A mo del is then considered to b e a \go

d"

mo del, if the p eaks

f

the distributions coincide with (or are close to) the preferred exp erimen tal v alue

SLIDE 7 The atmospheric angle Figure: The atmospheric angle for 5 dieren t mo dels (10 8 random sets p er mo del): a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y (No structure in neutrino mass matrix).

0.15 0.2 0.3 0.5 0.7 1

arbitrary units s atm It is easy to generate large atmospheric angle!

SLIDE 8 The solar angle Figure: The solar angle for 5 dieren t mo dels: a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y.

0.001 0.01 0.1 1

arbitrary units s

Anarc

h y prefers large solar angle Fla v

ur

mo dels can b e constructed for either, large (F C1, F C3 and F C4)

r

small (F C2) solar angle

SLIDE 9 The \Cho

z

angle" Figure: s C = 4jU e3 j 2 (1

jU

e3 j 2 ) for 5 dieren t mo dels: a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y.

0.001 0.01 0.1 1

arbitrary units s C Exp erimen tally: s C

(0:1
0:3)

in SK region Anarc h y prefers large s C , p eaks at s C = 1! Cho

z

angle imp

rtan

t discriminator!

SLIDE 10 Ratio

f

m 2 's Figure: R

jm

2 12 j=jm 2 23 j for 5 dieren t mo dels: a) red: F C1, b) F C2 (dot-dashes), c) F C3 (thic k dots), d) F C4 (thin dots), e) blue: neutrino mass anarc h y.

10-5 10-4 10-3 10-2 10-1 100

arbitrary units R Spread in R h uge! Co ecien ts a ij and A ij can not b e neglected! Small v alues

f

R disfa v

ur

neutrino mass anarc h y

SLIDE 11 V ariation in range

f

co ecien ts Figure: Solar angle for 3 dieren t ranges

f

co ecien ts for the mo del F C2: a) red: [ p 2; 1= p 2], b) magen ta: [0:82; 1:18], c) blue [0:95; 1:05].

0.001 0.01 0.1 1

arbitrary units s

Choice
f

co ecien ts v ery imp

rtan

t! ) Theoretical w

rk

in texture mo dels should concen trate

n

calculation

f

co ecien ts!

SLIDE 12 Leptogenesis ) CP violation in deca y

f

ligh test N R comes from in terference b et w een tree-lev el and

ne-lo
p

amplitude:

=

(N R1 ! L j + H 2 )

(N

y R1 ! L j y + H y 2 ) (N R1 ! L j + H 2 ) + (N y R1 ! L j y + H y 2 ) = 1 8 (Y y

Y
)

11 X i6=1 I m

(Y

y

Y
)

1i

2

! B @ f ( M 2 1 M 2 i ) + g ( M 2 1 M 2 i ) 1 C A where f (x) = p x 2 4 1

(1

+ x) ln @ 1 + x x 1 A 3 5 ; g (x) = p x 1

x

: ) T exture mo dels x

rder
f

magnitude

f

Y

)

T aking in to accoun t O (1) co ecien ts

can

b e calculated lik e an y lo w-energy

bserv

able ) Con v ersion

$

Y B dep ends

n

assumed thermal history

f

the univ erse

SLIDE 13

and

Y B for F C1-F C4

10-6 10-5 10-4 10-3 10-2 10-1 100

10-9 10-8 10-7 10-6 10-5 10-4

Y B

SLIDE 14 Neutrino

bserv

ables for v arian ts

f

F C3

0.02 0.05 0.1 0.2 0.5 1 0.15 0.2 0.3 0.5 0.7 1

s atm s

0.001

0.01 0.1 1

10-5 10-4 10-3 10-2 10-1

s C R ) V arian ts dier

nly

in l i , while k eeping n i and

constan

t ) Keeps lo w-energy

bserv

ables unc hanged, re-scales Y uk a w a matrix Mo dels l 1 l 2 l 3 n 1 n 2 n 3

Colour:

F actor: F C3

1

1 1 1=2

1=2
1

red 1 F C3a

2

2 2 1=2

1=2
1

blue 1:05 F C3b

3

3 3 1=2

1=2
1

magen ta 1:1 F C3c

4

4 4 1=2

1=2
1

green 1:15

SLIDE 15 Leptogenesis and LA-MSW solution: V arian ts

f

F C3

10-7 10-6 10-5 10-4 10-3 10-2

10-12

10-10 10-8 10-6

Y B ) without sp ecic assumptions ab

ut

Y uk a w a matrix, Leptogenesis indep enden t from lo w energy

bserv

ables!

SLIDE 16 Leptogenesis and SA-MSW solution: V arian ts

f

F C2

10-4 10-3 10-2 10-1 100 10-5 10-4 10-3 10-2 10-1 100

s

s

C

10-7 10-6 10-5 10-4 10-3 10-13 10-11 10-9 10-7

Y

B Mo dels l 1 l 2 l 3 n 1 n 2 n 3

Colour:

F actor: F C2

3
1
1
3
1

3 red 1 F C2a

4
2
2
3
1

3 blue 1:1 F C2b

4
1
1
3
1

3 magen ta 1 F C2c

5
2
2
3
1

3 green 1:1

SLIDE 17 Leptogenesis and LO W-MSW solution:

10-5 10-4 10-3 10-2 10-1

R

10-7 10-6 10-5 10-4 10-3 10-2

a)

blue: F C5, dened as (l 1 ; l 2 ; l 3 ; n 1 ; n 2 ; n 3 ;

)

= (3; 3; 3; 0; 1=2; 1; 1) b) for comparison red: F C2b

SLIDE 18 Summary ) O (1) co ecien ts in texture mo dels are v ery imp

rtan

t: F uture progress in texture mo dels will b e p

ssible
nly

if these co ecien ts can b e calculated sucien tly accurate ) Without sp ecic assumptions

n

Y uk a w a matrix, Leptogenesis completely indep enden t from lo w-energy

bserv-

ables ) Leptogenesis can pro vide information

n

mo dels

therwise

unaccesible