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Quark Mass Matrix from Dimensional Deconstruction

Quark Mass Matrix from Dimensional Deconstruction. Andrea Soddu. National Taiwan University. Academia Sinica. P.Q Hung, A.S., N.-K. Tran. hep-ph/0410179. Taipei November 17, 2004. OUTLOOK. What if the world is not four dimensional ?.

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Quark Mass Matrix from Dimensional Deconstruction

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  1. Quark Mass Matrix from Dimensional Deconstruction Andrea Soddu National Taiwan University Academia Sinica P.Q Hung, A.S., N.-K. Tran hep-ph/0410179 Taipei November 17, 2004

  2. OUTLOOK What if the world is not four dimensional ? Dimensional Deconstruction Deconstructing 5D QED Deconstructing 5D SU(2)xU(1) Fermion zero modes and Quark Mass Matrices Numerical results Possible projects Conclusions

  3. World is apparently four dimensional The Universe may be better described by a theory with more than the conventional one time and three space coordinates at energies not yet probed Simple scenario: theory of fields living in a space-time with four extended dimensions, plus one or more additional compact dimensions At distances large compared to the size of compact dimensions, the world appears four dimensional: gauge forces fall off like the square of the distance At energies corresponding to the inverse compactification size, Kaluza-Klein excitations appear with a spectrum depending on the detailed nature of the compact space At energies much higher than the compactification scale the extra dimensions become manifest. Physics is insensitive to the compactification and the theory appears higher dimensional

  4. Higher-dimensional field theories have dimensionful couplings and therefore require a cutoff As energy approaches the cutoff physics becomes strongly coupled and this makes difficult to address what happens at energies above the cutoff Dimensional (De)Construction provides a possible scenario for UV completing higher-dimensional field theories N. Arkani-Hamed, A.G. Cohen, and H. Georgi Dimensional Deconstruction provides a manifestly gauge invariant description of n KK modes for an SU(m) gauge theory in the bulk C. T. Hill, S. Pokorski, and J. Wang Dimensional Deconstruction provides at low energy a theory with a similar spectrum of particles as higher dimensional theories A natural light axion can be obtained as a WLPNGB C. T. Hill, and K. Leibovich

  5. 1=N+1 2 n n+1 N-1 N … … U(1) gauge theory in 1+4 dim.’s periodically compactified to 1+3 dim.’s Latticization of a U(1) gauge theory with periodic 5th dim. gives a theory in 1+3 dim.s for N copies of the U(1) gauge group invariant under has replaced translational invariance Good approximation in the large N case for quantities that are insensitive to short distance (UV) structure of the theory B.C.

  6. causes each to develop a common VEV compactification scale From the point of view of 1+3 dim.’s each is effectively a non linear model field

  7. gauge transformation

  8. ( SM photon ) is the zero mode of tower of doubled KK modes ( massive photons ) N-1 are eaten to become longitudinal modes is a massless scalar field (WLPNGB) At low energy the deconstructed model has the same spectrum as an higher dimensional model

  9. The master gauge group U(1)N is broken to the diagonal subgroup U(1) by the N-1 of the link fields are eaten, giving N-1 massive vector fields (KK modes) One massless vector field and one massless scalar field are left When fermions are introduced becomes massive The mass of the field is obtained by expanding about the minimum of its Coleman-Weinberg potential Similar result is obtained in a non-Abelian gauge theory has been proposed as a candidate for an axion

  10. Moose Diagram Moose not for “chocolate moose” Moose is a large deer, “ELK”

  11. Deconstructing SU(2)xU(1) 2x2 matrix

  12. Because of the potential develop a VEV [SU(2)xU(1)]N is broken down to the diagonal group SU(2)xU(1) Four zero modes are left

  13. We are interested in the SM Chiral Fermions Impose Chiral Boundary Conditions on Fermions One more LH d.o.f over RH for Q field One more RH d.o.f over LH for U and D fields

  14. all couplings remain real is complex

  15. for for Zero Mode Zero Eigenvalue for for Zero Mode Zero Eigenvalue for for Zero Mode Zero Eigenvalue

  16. has the same eigenvalues as except the zero eigenvalue unitary (not just orthogonal)

  17. Zero Mode localized at n = 1 C.B.C. N.C. Zero Mode localized at n = N N.C. C.B.C.

  18. localized in n=1 localized in n=1 localized in n=N theory space bigger is a more localized is the zero mode w. f.

  19. The diagonal group SU(2)xU(1) is broken down to U(1)Q by SSB Fermion zero modes obtain mass through Yukawa interaction with a Higgs field as in the SM SU(2)xU(1) is equally broken at each site n Comment: in Higgless theories [SU(2)xU(1)]N is broken completely through the deconstruction process. The SM massive gauge bosons correspond to the lightest KK modes. R.S. Chivukula, M. Kurachi, and M. Tanabashi

  20. zero modes are the SM particles

  21. assign The system always takes a downhill step transition no transition The system sometimes takes an uphill step Simulated Annealing Method When a liquid is cooled down sufficiently slowly, the atoms are often able to line themselves up and form a pure crystal, state of minimum energy to the change Assign a probability from a configuration with energy to one with energy The temperature T is reduced with a given schedule

  22. Q, U and D localized at n=1

  23. Q, U and D localized at n=1

  24. Q and U localized at n=1 D localized at n=N

  25. Q and U localized at n=1 D localized at n=N

  26. is localized at lives in the bulk is delocalized

  27. new source of CP violation mediated by KK gluons One can have CP violation with only two families A. Delgado, A. Pomarol, and M. Quiros KK gluons mediate FCNC at tree level In a split fermion scenario from deconstructed models one can have a new source of CP violation as well One can constrain from FCNC

  28. Conclusions The world could have more than four dimensions Deconstructed theories have the same low energy behavior as higher dimensional theories but gauge invariance is preserved (De)constructed theories can offer a UV completion of higher dimensional theories Zero mode fermions can be localized in the theory space Realistic quark mass matrices can be constructed starting from universal Yukawa coupling Future projects Study of split fermion scenarios from deconstruction and FCNC Generation of small Dirac neutrino masses without See-Saw

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