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Javier Ferrandis IFIC Barcelona, January 12th 2005

Supersymmetry breaking as the origin of flavor (from empirical formulas for the fermion spectra to radiative fermion mass generation). J.F ph/0406004 PRD70 J.F. ph/0404068 PRD70 J.F & N. Haba ph/0404077 EPJC. Javier Ferrandis IFIC Barcelona, January 12th 2005.

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Javier Ferrandis IFIC Barcelona, January 12th 2005

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  1. Supersymmetry breaking as the origin of flavor (from empirical formulas for the fermion spectra to radiative fermion mass generation) J.F ph/0406004 PRD70 J.F. ph/0404068 PRD70 J.F & N. Haba ph/0404077 EPJC Javier Ferrandis IFIC Barcelona, January 12th 2005

  2. I will argue that there is evidence for low energy empirical formulas that connect six dimensionless fermion mass ratios and the CKM elements There is a plausible reconstruction of the underlying SM Yukawa matrices that accounts for these empirical formulas I will present an effective SUSY GUT flavor model for the radiative generation of 1st and 2nd generation of fermion masses and mixing angles that can explain some of the features of the reconstructed Yukawa matrices Outline

  3. 3

  4. Some precision analysis of SUSY GUT models asymmetric 12 input parameters CP-phases symmetric 10 input parameters CP-phases Texture analysis Roberts-Romanino-Ross-Velasco hep-ph/0104088 -> H.D.Kim-Raby-Schradin ph/0401169 Ross-Velasco hep-ph/0208208 SO(10)/SU(3) Ross-Velasco-Vives hep-ph/0401064 SO(10)/SU(2)xSU(2)xSU(4) Babu-Pati-Rastogi ph/0410200

  5. A simple and predictive set of Yukawa matrices 6 parameters

  6. Precision predictions(using quark data)

  7. running fermion masses n is the number of light quarks O.V. Tarasov, A.A.Vladimirov, A.Y.Zharkov PLB93(1980) R.Tarrach NPB183 (1981) N.Gray, D.J.Broadhurst, W.Grafe, K.Schilcher Z.Phy s C48 (1990) J.Fleischer, F.Jegerlehner, O.V.Tarasov, O.L.Veretin NPB539 (1999) K.G.Chetyrkin, M.Steinhauser NPB573 (2000) K. Melnikov, T.V.Ritbergen PLB482 (2000) self-energy correction

  8. Fermion masses and CKM elements GeV GeV GeV MeV MeV MeV MeV MeV MeV PDG 2003 off year partial update A.H.Hoang PRD61(2000), K.Melnikov & A.Yelkhovsky PRD59(99) M.Eidemuller PRD67(2003), J.H.Kuhn & M.Steinhauser NPB619(2001) D.Beciveric, V.Lubicz & G.Martinelli. , PLB524 (2002) E.Gamiz, M.Jamin, A.Pich, J.Prades, F.Schwab. , JHEP0301 (2003) M.Jamin,J.A.Oller, A.Pich , EJPC24 (2002) PDG 2003 off year partial update 2002 CERN Workshop CKM Fitter

  9. 3

  10. Why should we expect correlations between dimensionless ratios of fermion masses ? • Third generation is much heavier than 1st and 2nd generations • We expect the theory of flavor to provide a perturbative calculation of the fermion mass ratios and mixing angles • are perturbative flavor breaking parameters, <0.22 • The same parameters describe the Yukawa matrices in the three sectors

  11. Correlations between mass ratios Charged leptons Down-type quarks Up-type quarks

  12. First empirical formula the exact relation is compatible with measurements

  13. Scale evolution of fermion mass ratios PRD47 Babu-Shafi ph/9210251 The second empirical relation gets spoiled when extrapolated at very high energy scales

  14. Second empirical formula the exact relation is compatible with measurements 9 and 10 give the better fit

  15. Fermion mass ratios and CKM elements requiring unitarity

  16. Reconstructed Yukawa matrices without CP-violation 5 parameters

  17. Introducing CP-violation requiring hermiticity

  18. Characteristics of the reconstructed SM Yukawa matrices • They work at low or intermediate energy scales • All the entries execpt (33) in the normalized Yukawa matrices are proportional to a factor • The factor 3 between down-type quark and the charged lepton Yukawa matrices 6 parameters

  19. Radiative Yukawas in the MSSM † † † † W.Buchmuller & D.Wyler, PLB121 (Oct 82) A.Lahanas & D.Wyler, PLB122 (Nov 82) L.Hall & Kostelecky & Raby NPB267 (Oct 85) T.Banks, NPB303 (Sep 87) E.Ma PRD39 (Jul 88) E.Ma & D.Ng PRD65 (May 90) E.Ma & McIlhany MPLA6 (Dec 90)

  20. Radiative mass matrix generation • There is FV only in the (LR), i.e. trilinear, soft mass matrices • There is no FV in the (LL) and (RR) soft mass matrices • I will assume a particular one parameter soft trilinear texture tree level

  21. Radiative down-type quark mass matrix † Non degenerate down squarks

  22. Flavor breaking F-terms No flavor violation at tree level in the Yukawa couplings

  23. U(2)+ SUSY breaking flavor model flavor singlets R.Barbieri, G. Dvali & L.J. Hall PLB377 (96) flavor vectors Borzumati et al.,(May 98) flavor breaking fields (F-terms) J.F & N.Haba ph/0404077

  24. U(2)+ SUSY breaking flavor model Superpotential (only third generation) Soft trilinears J is a second flavor singlet G is a flavor singlet Soft masses

  25. Boundary conditions for soft parameters Tree level Yukawa matrices

  26. SU(5), lepton and up-type quark Yukawas does not mix with up-type sector (discrete symmetry) charm quark mass too light up quarm massless

  27. FCNCs suppression by radiative alignement(degenerate squarks) † superKM basis † diagonal gaugino vertex non diagonal gaugino vertex †

  28. Constraints from FCNCs(degenerate squarks) average squark mass Gabbiani et al., NPB477 (96) Berolini et al. PLB192, 437 (87)

  29. Constraints from FCNCs on soft mass matrices (degenerate squarks) average squark mass Gabbiani et al., NPB477 (96) LL contribution to suppressed compared with the LR contribution

  30. Lepton flavor violation If sleptons are non degenerate non-holomorphic soft trilinear Borzumati et al.,(May 98) W.Buchmuller & D.Wyler, PLB121 (Oct 82) E.Ma PRD39 (Jul 88)

  31. Proton decay suppresion SU(5) superpotential dimension 5 operators n-loop generated, n>1 u t Tree level cancellation of dimension five operators b d s

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