1. The Flavour Problem and Family Symmetry1. 2.
23/11/2018
Steve King, SP03,Durham

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
23/11/2018
Steve King, SP03,Durham

3. Off-diagonal slepton mass
Example of a SUSY loop:
Off-diagonal slepton mass
23/11/2018
Steve King, SP03,Durham

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.
23/11/2018
Steve King, SP03,Durham

5. We discuss two examples in this talk:
Family Symmetry
We discuss two examples in this talk:
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
23/11/2018
Steve King, SP03,Durham

6. Allanach,SFK, Oliveira, Leontaris,Lola
Family symmetry
N.B. no Higgs triplets
breaks
breaks
23/11/2018
Steve King, SP03,Durham

7. Froggatt-Nielsen Operators
Yukawa
Majorana
Majorana Matrix
Third right-handed neutrino dominates
23/11/2018
Steve King, SP03,Durham

8. Blazek,SFK,Parry hep ph/0303192
Yukawa matrices
23/11/2018
Steve King, SP03,Durham

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 s+gamma
LFV
Blazek,SFK,Parry hep ph/
contours
23/11/2018
Steve King, SP03,Durham

10. Blazek,SFK,Parry (to appear)
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_2<<R_1 “single brane limit”, have approximate gauge unification
Sum rule
3rd Family
1st,2nd Families
23/11/2018
Steve King, SP03,Durham

12. SUSY breaking and soft mass predictions (in theory basis, not SCKM basis)
23/11/2018
Steve King, SP03,Durham

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;
Peddie,SFK.
23/11/2018
Steve King, SP03,Durham

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”
23/11/2018
Steve King, SP03,Durham

15. B “SUGRA” without see-saw
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 “FN”with see-saw
D “Higgs” with see-saw
C “FN” without see-saw

16. B “SUGRA ” without see-saw
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. Yukawa operators restricted by discrete symmetry
SFK, Ross hep-ph/
Wilson line
Wilson line,
Yukawa operators restricted by discrete symmetry
23/11/2018
Steve King, SP03,Durham

18. First right-handed neutrino dominates
Yukawa matrices
SFK, Ross hep-ph/
First right-handed neutrino dominates
LMA MSW
23/11/2018
Steve King, SP03,Durham

19. SUSY Soft Masses
Most general soft SUSY Lagrangian allowed by the symmetry of the model
Ramage, Ross;
Ross,Velasco-Sevilla,Vives;
SFK,Peddie
 Characteristic pattern of SUSY masses, with suppressed FCNCs
23/11/2018
Steve King, SP03,Durham

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?
23/11/2018
Steve King, SP03,Durham