The Flavour Problem and Family Symmetry Flavour problem
The Flavour Problem and Family Symmetry • Flavour problem • Family symmetry 1. 2. 9/15/2020 Steve King, SP 03, Durham 1
The Flavour Problem 1. 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) 2. In low energy SUSY also need to understand why flavour changing (and/or CP violating) processes induced by SUSY loops are so small • 9/15/2020 A theory of flavour must address both problems simultaneously Steve King, SP 03, Durham 2
Example of a SUSY loop: . Off-diagonal slepton mass 9/15/2020 Steve King, SP 03, Durham 3
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. 9/15/2020 Steve King, SP 03, Durham 4
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)x. U(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)x. SU(3) model 9/15/2020 Steve King, SP 03, Durham 5
Allanach, SFK, Oliveira, Leontaris, Lola Family symmetry N. B. no Higgs triplets breaks 9/15/2020 Steve King, SP 03, Durham 6
Froggatt-Nielsen Operators Yukawa Majorana Matrix Third right-handed neutrino dominates 9/15/2020 Steve King, SP 03, Durham 7
Yukawa matrices 9/15/2020 Steve King, SP 03, Durham Blazek, SFK, Parry hep ph/0303192 8
This model is consistent with all laboratory data Global analysis assumes universal gaugino masses and universal sfermion masses, but allows non-universal Higgs mass. contours 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 ph/0303192 9/15/2020 Steve King, SP 03, Durham hep 9
predictions Blazek, SFK, Parry (to appear) Watch this space!
Primordial soft SUSY masses controlled by type I string embedding Everett, Kane, SFK, Rigolin, Wang (see also SFK, Rayner; Shiu, Tye) v Higgs states are present 3 rd Family 1 st, 2 nd Families which can lead to such breaking. v. U(1)’s broken by GS mechanism, but one U(1) remains. v. Hard to decouple exotics due to U(1)’s. v. R_2<<R_1 “single brane limit”, have approximate gauge unification v. Sum rule. 9/15/2020 Steve King, SP 03, Durham 11
SUSY breaking and soft mass predictions (in theory basis, not SCKM basis) 9/15/2020 Steve King, SP 03, Durham 12
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. 9/15/2020 Steve King, SP 03, Durham 13
What is the relative importance of the different sources of flavour violation? Consider four SUGRA points 9/15/2020 SUGRA A SUGRA B “minimum flavour violation” “SUGRA flavour violation” SUGRA C “FN flavour violation” SUGRA D “Higgs flavour violation” Steve King, SP 03, Durham 14
Peddie, SFK Experimental limit B “SUGRA” with see-saw A “MFV” with see-saw B “SUGRA” without see-saw Experimental limit D “Higgs” without see -saw) C “FN”with see-saw C “FN” without see-saw D “Higgs” with see-saw
Peddie, SFK Experimental limit A “MFV” with see-saw Experimental limit B “SUGRA ” with see-saw B “SUGRA ” without see-saw Experimental limit C “FN” with see-saw C “FN” without see-saw Experimental limit D “Higgs” with see-saw D “Higgs” without see-saw
SFK, Ross hep-ph/0307190 Wilson line, Yukawa operators restricted by discrete symmetry 9/15/2020 Steve King, SP 03, Durham 17
SFK, Ross hep-ph/0307190 Yukawa matrices First right-handed neutrino dominates LMA MSW 9/15/2020 Steve King, SP 03, Durham 18
SUSY Soft Masses Most general soft SUSY Lagrangian allowed by the symmetry of the model Characteristic pattern of SUSY masses, with suppressed FCNCs Ramage, Ross; Ross, Velasco. Sevilla, Vives; SFK, Peddie 9/15/2020 Steve King, SP 03, Durham 19
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 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? 9/15/2020 Steve King, SP 03, Durham 20
- Slides: 20