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The Flavour Problem and Family Symmetry

This talk discusses the flavour problem and family symmetry in physics, focusing on understanding the origin and control of Yukawa couplings, low energy particle masses and mixing angles, and the role of supersymmetry in flavour-changing processes. Examples of family symmetry theories are presented, along with predictions and implications for laboratory data.

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The Flavour Problem and Family Symmetry

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  1. The Flavour Problem and Family Symmetry • Flavour problem • Family symmetry • 1. • 2. 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 Steve King, SP03,Durham

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

  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 Steve King, SP03,Durham

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

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

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

  10. predictions Blazek,SFK,Parry (to appear) Watch this space!

  11. Primordial soft SUSY masses controlled by type I string embeddingEverett, 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 Steve King, SP03,Durham

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

  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 “FN”with 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 Steve King, SP03,Durham

  18. SFK, Ross hep-ph/0307190 Yukawa matrices First right-handed neutrino dominates LMA MSW 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 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? Steve King, SP03,Durham

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