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A viable RS Model for Quarks and Leptons with T´ Flavor Symmetry

Explore the application of the RS1 model with bulk fermions to explain fermion mass hierarchy and FCNC suppression. Discuss the T´ group and its representations for leptons and quarks, leading to a framework for realistic fermion masses and mixings.

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A viable RS Model for Quarks and Leptons with T´ Flavor Symmetry

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  1. A viable RS Model for Quarks and Leptons with T´ Flavor Symmetry Felix Yu University of California, Irvine Pheno 2010 M-C. Chen, K. T. Mahanthappa, FY – Phys. Rev. D 81, 036004 (2010) [arXiv: 0907.3963 [hep-ph]]

  2. Motivation • Fermion mass hierarchy unexplained • Gauge hierarchy problem motivates new physics at about TeV • Randall-Sundrum (RS1) model with bulk fermions provides a good framework • Can get fermion mass hierarchy with O(1) coefficients • Need to suppress FCNCs

  3. Randall-Sundrum • RS1 Model – warped geometry • 5th dimension compactified via S1/2 • Higgs field confined to TeV brane (y = R), other fields propagate in bulk • From compactification and boundary conditions, can find Fourier modes for bulk fields • SM masses and mixings arise from zero modes • Integrate out y to find overlap between SM fields and Higgs Randall, Sundrum (1999) Gherghetta, Pomarol (2000), Huber, Shafi (2000), Grossman, Neubert (1999)

  4. † Flavor Changing Neutral Currents in RS • Change from gauge interaction basis to mass basis • Generically get FCNCs if bulk masses are not equal • Solutions: (1) alignment, (2) degeneracy

  5. The Finite Group T´ • Double covering of A4 • A4 is the discrete invariant rotations of a tetrahedron • Has two generators: S=(1234) (4321), T=(1234) (2314) • S2=R, T3=1, (ST)3=1, R2=1 • R=1: 1, 1´, 1´´, 3 (vector) [use for leptons] • R=-1: 2, 2´, 2´´ (spinorial) [use for quarks] Frampton, Kephart (1995)

  6. Assignment of T´ Representations • Motivated by neutrino mixing data: assign L ~ 3 (LH lepton doublets), N ~ 3 (RH neutrinos) under T to obtain the tri-bimaximal mixing pattern • Introduce e ~ 1,  ~ 1,  ~ 1 for charged lepton masses • Tree-level lepton FCNCs are eliminated via degeneracy (left-handed lepton doublets share a common bulk mass term) and alignment (right-handed lepton singlets can freely rotate) • Motivated by quark masses, use 2  1 assignment • Tree-level quark FCNCs involving first and second generations are eliminated via degeneracy (up- and down-type first two generations share a common bulk mass term) • Require additional flavon fields to break T symmetry on the IR brane

  7. Leptons in T´ Purely Dirac neutrino masses Seesaw type 1 neutrino masses

  8. Quarks in T´:2 1 Framework Down-type Yukawa Lagrangian is exactly analogous

  9. Parameter Counting • Input parameters (Naïve counting) • Charged lepton: 8 (= 4 bulk + 3 Yukawa + 1 flavon) • Neutrino: [seesaw] 6 [7] (= 2 bulk + 2 [3] Yukawa + 2 flavon) • Quark: 24 = (6 bulk + 8 Yukawa + 10 flavon) • Actual number of independent input combinations • 16 = Lepton matrix (3) + Neutrino matrix (2) + Quark matrices (6 + 5) • Contrast with anarchic case • 36 [30] for leptons, 36 for quarks • Fit parameters • Lepton and quark masses (3 + 6 = 9) • CKM matrix (+ CP violating phase) (3 + 1 = 4) • Neutrino mixing angles (3) 16 Inputs, 16 Outputs

  10. Results –Leptons Set all leptonic Yukawas to 1. Renormalization effects negligible. Gives me=511 keV, m=105.7 MeV, m=1.777 GeV For normal hierarchy Normal, Dc: msol2 = 7.6370  10-5 eV2, matm2 = 2.4031  10-3 eV2 For normal hierarchy Normal, SS: msol2 = 7.6520  10-5 eV2, matm2 = 2.4001  10-3 eV2 For inverted hierarchy Inverted, SS: msol2 = 7.6560  10-5 eV2, matm2 = –2.4009  10-3 eV2 Experimental: msol2 = 7.65  10-5 eV2, matm2 = 2.40  10-3 eV2 Fusaoka, Koide (1998), Schwetz, Tortola, Valle (2008)

  11. Bulk mass parameters Results – Quarks Flavons and Yukawas Other Yukawas set to 1 Csaki, Falkowski, Weiler (2008)

  12. Results – CKM and Jarlskog Corrections to quark mixings from running are small. Perform fit at mZ Fusaoka, Koide (1998), Charles, et al. (CKMfitter Group) (2009)

  13. Leading FCNC Estimate • Leading contribution is from dim-6 operators arising from fermion zero-modes mixing with KK modes • Scaled to Z-coupling, leading contribution is • Using MKK ~ 3 TeV, kR ~ 11, v = 246 GeV: • coefficient is 2.96510-6 for u-c transition • coefficient is 4.15610-6 for d-s transition

  14. Conclusions • RS1 + T´ provides a framework for realistic fermion masses and mixings • Motivated by neutrino mixings and quark masses, we choose T´ representations • This choice eliminates tree-level lepton FCNCs and first-second generation quark FCNCs • Can fit for all SM fermion masses, CKM matrix, and Jarlskog invariant with 16 input parameter combinations • Allows a low first KK mass scale, testable at colliders

  15. Group Algebra of T´ 2 S=A1, T=A2, 2´ S=A1, T=2A2, 2´´ S=A1, T=A2 1 S=1, T=1, 1´ S=1, T=, 1´´ S=1, T=2 3 Feruglio, Hagedorn, Lin, Merlo (2007)

  16. Neutrino Constraints • Neutrino measurements (at 2) • (at 1) • Well-fit by Tri-Bimaximal Mixing (TBM) Schwetz, Tortola, Valle (2008) Harrison, Perkins, Scott (1999) TBM can be easily obtained from A4 or T´ group symmetries Ma, Rajasekeran (2001)

  17. Leptons in T´ T´ contraction: Diagonal charged lepton mass matrix because of T´ assignments and flavon VEVs

  18. 2  1 Quarks in T´: The2 1 Framework

  19. 2  1 Quarks in T´: The2 1 Framework

  20. Citations C. Amsler et al. (Particle Data Group), Phys. Lett. B667, 1 (2008) S. Bar-Shalom and A. Rajaraman, Phys. Rev. D 77, 095011 (2008). arXiv:0711.3193 [hep-ph] S. Bar-Shalom, A. Rajaraman, D. Whiteson, FY, Phys. Rev. D 78, 033003 (2008). arXiv:0803.3795 [hep-ph] CKMfitter Group (J. Charles et al.), Eur. Phys. J. C41, 1-131 (2005). arXiv:hep-ph/0406184 M.C. Chen and S.F. King, arXiv:0903.0125 [hep-ph] M.C. Chen and K.T. Mahanthappa, arXiv:0904.1721 [hep-ph] V. Cirigliano, B. Grinstein, G. Isidori and M. B. Wise, Nucl. Phys. B 728, 121 (2005). arXiv:hep-ph/0507001 G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B 645, 155 (2002). arXiv:hep-ph/0207036 G. Engelhard, J.L. Feng, I. Galon, D. Sanford and FY, arXiv:0904.1415 [hep-ph] J.L. Feng, C.G. Lester, Y. Nir and Y. Shadmi, Phys. Rev. D 77, 076002 (2008) arXiv:0712.0674 [hep-ph]. F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Nucl. Phys. B 775, 120 (2007) arXiv:hep-ph/0702194 P.H. Frampton and T.W. Kephart, Int. J. Mod. Phys. A 10, 4689 (1995). arXiv:hep-ph/9409330 T. Gherghetta and A. Pomarol, Nucl. Phys. B 586, 141 (2000). arXiv:hep-ph/0003129 Y. Grossman and M. Neubert, Phys. Lett. B 474, 361 (2000). arXiv:hep-ph/9912408 P.F. Harrison, D.H. Perkins and W.G. Scott, Phys. Lett. B 458, 79 (1999). arXiv:hep-ph/9904297 S.J. Huber and Q. Shafi, Phys. Lett. B 544, 295 (2002). arXiv:hep-ph/0205327 C.I. Low and R.R. Volkas, Phys. Rev. D 68, 033007 (2003). arXiv:hep-ph/0305243 E. Ma and G. Rajarasekaran, Phys. Rev. D 64, 113012 (2001). arXiv:hep-ph/0106291 L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). arXiv:hep-th/9906064 L. Randall and R. Sundrum, Phys. Rev. Lett 83, 3370 (1999). arXiv:hep-ph/9905221 L. Randall and R. Sundrum, Nucl. Phys. B 557, 79 (1999). arXiv:hep-th/9810155 T. Schwetz, M. Tortola and J.W.F. Valle, New J. Phys. 10, 113011 (2008). arXiv:0808.2016 [hep-ph]

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