Neutrinos and the Universe

1
The Flavour Problem and Family Symmetry

• Flavour problem
• Family symmetry
• 1.
• 2.

2
The Flavour Problem

• Understanding the origin of Yukawa couplings (and
  heavy Majorana masses in the see-saw mechanism)
  which lead to low energy quark and lepton masses
  and mixing angles (including neutrino masses and
  mixing angles)
• In low energy SUSY also need to understand why
  flavour changing (and/or CP violating) processes
  induced by SUSY loops are so small
• A theory of flavour must address both problems
  simultaneously

3
Example of a SUSY loop .

Off-diagonal slepton mass
4
Sources of off-diagonal slepton masses

• Primordial
• the slepton masses are off-diagonal in the SCKM
  basis at the high energy scale generated by the
  SUSY breaking mechanism
• RGE generated
• from running the GUT theory from the Planck mass
  to the GUT scale (if Higgs triplet couplings are
  present)
• from running the MSSM with right-handed neutrinos
  from the Planck scale to the lightest
  right-handed neutrino mass scale

In general both sources will be present.
Theories of flavour are concerned with
suppressing the primordial off-diagonal soft SUSY
masses.
5
Family Symmetry
We discuss two examples in this talk 1.
U(1) family symmetry theory, which controls quark
and lepton masses. The
primordial SUSY soft masses are controlled by
embedding the model in a type I string framework
?SO(10)xU(1)
model 2. SU(3) family symmetry, which controls
the quark and lepton masses.
The primordial soft SUSY masses are
controlled by the SU(3) symmetry itself
?SO(10)xSU(3) model
6
Allanach,SFK, Oliveira, Leontaris,Lola
Family symmetry
N.B. no Higgs triplets
breaks
breaks
7
Froggatt-Nielsen Operators
Yukawa
Majorana
Majorana Matrix
Third right-handed neutrino dominates
8
Blazek,SFK,Parry hep ph/0303192
Yukawa matrices
9
This model is consistent with all laboratory data

• Global analysis assumes universal gaugino masses
  and universal sfermion masses, but allows
  non-universal Higgs mass.
• Laboratory data included
• sparticle and higgs mass limits
• fermion masses and mixing angles including LMA
  MSW
• muon g-2 signal
• b ?sgamma
• LFV
• Blazek,SFK,Parry hep ph/0303192

contours
10
predictions
Blazek,SFK,Parry (to appear)
Watch this space!
11
Primordial soft SUSY masses controlled by
type I string embedding
Everett, Kane, SFK, Rigolin, Wang (see also
SFK,Rayner Shiu,Tye)

• Higgs states are present which can lead to such
  breaking.
• U(1)s broken by GS mechanism, but one U(1)
  remains.
• Hard to decouple exotics due to U(1)s.
• R_2ltltR_1 single brane limit, have approximate
  gauge unification
• Sum rule
  .

3rd Family
1st,2nd Families
12
SUSY breaking and soft mass predictions
(in theory basis, not SCKM basis)
13
In addition Froggatt-Nielsen fields can develop
F-term vevs and contribute to SUSY breaking
A-terms leading to a new source of flavour
violation
Abel,Servant Abel, Khalil,Lebedev Ross,Vives Pe
ddie,SFK.
14
What is the relative importance of the different
sources of flavour violation? Consider four
SUGRA points
SUGRA A minimum flavour violation
SUGRA B SUGRA flavour violation
SUGRA C FN flavour violation
SUGRA D Higgs flavour violation
15
Peddie, SFK
Experimental limit
Experimental limit
B SUGRA with see-saw
A MFV with see-saw
B SUGRA without see-saw
Experimental limit
Experimental limit
D Higgs without see-saw)
C FNwith see-saw
D Higgs with see-saw
C FN without see-saw
16
Peddie, SFK
Experimental limit
Experimental limit
B SUGRA with see-saw
A MFV with see-saw
B SUGRA without see-saw
Experimental limit
Experimental limit
C FN with see-saw
D Higgs with see-saw
C FN without see-saw
D Higgs without see-saw
17
SFK, Ross hep-ph/0307190
Wilson line
Wilson line,
Yukawa operators restricted by discrete symmetry
18
SFK, Ross hep-ph/0307190
Yukawa matrices
First right-handed neutrino dominates
LMA MSW
19
SUSY Soft Masses
Most general soft SUSY Lagrangian allowed by the
symmetry of the model
Ramage, Ross Ross,Velasco-Sevilla,Vives SFK,Pedd
ie
? Characteristic pattern of SUSY masses, with
suppressed FCNCs
20
Conclusions

• U(1) family symmetry allows an understanding of
  quark and lepton masses and mixings, but does not
  address problem of SUSY flavour changing without
  additional theoretical input.
• Such models are motivated by string theories
  where U(1)s are abundant, and SUSY flavour
  changing may be controlled by the high energy
  string theory.
• We considered a type I string embedding, but even
  if the theory controls sparticle masses,
  dangerous new sources of flavour changing masses
  in general arise from Yukawa operators which lead
  to large off-diagonal soft trilinears.
• SU(3) family symmetry allows (anti)symmetric
  Yukawa matrices, with SUSY flavour changing
  controlled by the family symmetries.
• SU(3) from string theory?