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Fermion Masses and Unification

Fermion Masses and Unification. Lecture I Fermion Masses and Mixings Lecture II Unification Lecture III Family Symmetry and Unification Lecture IV SU(3), GUTs and SUSY Flavour Steve King University of Southampton. Lecture I Fermion Masses and Mixings. The Flavour Problem and See-Saw

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Fermion Masses and Unification

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  1. Fermion Masses and Unification Lecture I Fermion Masses and Mixings Lecture II Unification Lecture III Family Symmetry and Unification Lecture IV SU(3), GUTs and SUSY Flavour Steve King University of Southampton

  2. Lecture IFermion Masses and Mixings The Flavour Problem and See-Saw From low energy data to high energy data Textures in a basis Appendix 1 References Appendix 2 Basis Changing

  3. 1.The Flavour Problem and See-Saw

  4. Horizontal u c t Quarks up charm top s d b down bottom strange n ne n Vertical t m Leptons m-neutrino t-neutrino e-neutrino e t m muon tau electron Generations of matter I II III The Flavour Problem1. Why are there three families of quarks and leptons?

  5. The Flavour Problem2. Why are quark and charged lepton masses so peculiar? t u d c e s b Family symmetry e.g. SU(3) GUT symmetry e.g. SO(10)

  6. The Flavour Problem3. Why is lepton mixing so large? e.g.Tri-bimaximal Harrison, Perkins, Scott c.f. small quark mixing

  7. Lepton CP Violation? The Flavour Problem4. What is the origin of CP violation? a g b

  8. Normal Inverted The Flavour Problem5. Why are neutrino masses so small? See-saw mechanism is most elegant solution

  9. The See-Saw Mechanism Light neutrinos Heavy particles

  10. Heavy triplet The see-saw mechanism Type II see-saw mechanism (SUSY) Type I see-saw mechanism Lazarides, Magg, Mohapatra, Senjanovic, Shafi, Wetterich (1981) P. Minkowski (1977), Gell-Mann, Glashow,Mohapatra, Ramond, Senjanovic, Slanski, Yanagida (1979/1980) Type I Type II

  11. See-Saw Standard Model (type I) Yukawa couplings to 2 Higgs doublets (or one with ) Insert the vevs Rewrite in terms of L and R chiral fields, in matrix notation

  12. The See-Saw Matrix Dirac matrix Type II contribution (ignored here) Heavy Majorana matrix Diagonalise to give effective mass Light Majorana matrix

  13. Lepton mixing matrix VMNS Neutrino mass matrix (Majorana) Defined as Can be parametrised as Solar Reactor Atmospheric Oscillation phase

  14. Quark mixing matrix VCKM Defined as Can be parametrised as Phase convention independent

  15. From low energy data to high energy data

  16. (From Particle Data Book)

  17. Quark data (low energy) Ross and Serna

  18. Inverted Normal Andre de Gouvea Neutrino Masses and Mixings c.f. quark mixing angles

  19. RGEs for gauge couplings (to one loop accuracy) RG running Parameter at MU Parameter at MEW MSUSY MEW MU M1 M2 M3 [GeV] 1016 102 RH neutrino masses Renormalisation Group running SM beta functions MSSM beta functions

  20. SM couplings at low energy Latest coupling constant measurements at energy scale:

  21. Evolution of SM couplings Two-loop RGEs for the SM: . . . .

  22. MSSM Two-loop RGEs for the MSSM with 1 TeV effective SUSY threshold: . . . .

  23. MSSM Two-loop RGEs for the MSSM with 1 TeV effective SUSY threshold:

  24. MSSM Two-loop RGEs for the MSSM with 250 GeV effective SUSY threshold:

  25. RGEs for t,b, in the MSSM

  26. RGEs for Yukawa matrices in MSSM RGEs (one-loop accuracy) Wavefunction anomalous dimensions

  27. SUSY thresholds Charged fermion data (high energy) Ross and Serna

  28. 3. Textures in a basis

  29. Hierarchical Symmetric Textures Symmetric hierarchical matrices with 11 texture zero motivated by Gatto et al This motivates the symmetric down texture at GUT scale of form ¼ 0.2 is the Wolfenstein Parameter

  30. Up quarks are more hierarchical than down quarks This suggests different expansion parameters for up and down Detailed fits require numerical (order unity) coefficients

  31. Ross and Serna Detailed fits at the GUT Scale No SUSY thresholds

  32. Ross and Serna With SUSY thresholds Georgi-Jarlskog

  33. Final remarks on choice of basis We have considered a particular choice of quark texture in a particular basis But it is shown in the Appendix that all choices of quark mass matrices that lead to the same quark masses and mixing angles may be related to each other under a change of basis. For example all quark mass matrices are equivalent to the choice However this is only true in the Standard Model, and a given high energy theory of flavour will select a particular preferred basis. Also in the see-saw mechanism all choices of see-saw matrices are NOT equivalent.

  34. Appendix 1 References W. De Boer hep-ph/9402266 S.Raby ICTP Lectures 1994 G.G.Ross ICTP Lectures 2001 J.C. Pati ICTP Lectures 2001 S. Barr ICTP Lectures 2003 S. Raby hep-ph/0401115 S.Raby PDB 2006 A. Ceccucci et al PDB 2006 G. Ross and M. Serna 0704.1248 D. Chung et al hep-ph/0312378 S.F. King hep-ph/0310204

  35. S.F. King hep-ph/0610239 Appendix 2 Basis Changing 2.1 Quark sector 2.2 Effective Majorana sector 2.3 See-saw sector

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