Journal of High Energy Physics

, 2011:112 | Cite as

Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs

  • Pablo G. Cámara
  • Emilian Dudas
  • Eran Palti
Open Access


We study the coupling of MSSM fields to heavy modes through cubic superpotential interactions in F-theory SU(5) GUTs. The couplings are calculated by integrating the overlap of two massless and one massive wavefunctions. The overlap integral receives contributions from only a small patch around a point of symmetry enhancement thereby allowing the wavefunctions to be determined locally on flat space, drastically simplifying the calculation. The cubic coupling between two MSSM fields and one of the massive coloured Higgs triplets present in SU(5) GUTs is calculated using a local eight-dimensional SO(12) gauge theory. We find that for the most natural regions of local parameter space the coupling to the triplet is comparable to or stronger than in minimal four-dimensional GUTs thereby, for those regions, reaffirming or strengthening constraints from dimension-five proton decay. We also identify possible regions in local parameter space where the couplings to the lightest generations are substantially suppressed compared to minimal four-dimensional GUTs. We further apply our results and techniques to study other phenomenologically important operators arising from coupling to heavy modes. In particular we calculate within a toy model flavour non-universal soft masses induced by integrating out heavy modes which lead to FCNCs.


F-Theory Intersecting branes models 


  1. [1]
    G. Aldazabal, S. Franco, L.E. Ibáñez, R. Rabadán and A. Uranga, Intersecting brane worlds, JHEP 02 (2001) 047 [hep-ph/0011132] [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  5. [5]
    M. Bershadsky, K.A. Intriligator, S. Kachru, D.R. Morrison, V. Sadov, et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [INSPIRE].
  8. [8]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theoryI, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theoryII: experimental predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  10. [10]
    R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, arXiv:0808.2223 [INSPIRE].
  11. [11]
    F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
  12. [12]
    J.J. Heckman, Particle physics implications of F-theory, Ann. Rev. Nucl. Part. Sci. (2010) [arXiv:1001.0577] [INSPIRE].
  13. [13]
    T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    D. Cremades, L. Ibáñez and F. Marchesano, Computing Yukawa couplings from magnetized extra dimensions, JHEP 05 (2004) 079 [hep-th/0404229] [INSPIRE].CrossRefADSGoogle Scholar
  15. [15]
    J.J. Heckman and C. Vafa, Flavor hierarchy from F-theory, Nucl. Phys. B 837 (2010) 137 [arXiv:0811.2417] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    H. Hayashi, T. Kawano, R. Tatar and T. Watari, Codimension-3 singularities and Yukawa couplings in F-theory, Nucl. Phys. B 823 (2009) 47 [arXiv:0901.4941] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    A. Font and L. Ibáñez, Matter wave functions and Yukawa couplings in F-theory grand unification, JHEP 09 (2009) 036 [arXiv:0907.4895] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    S. Cecotti, M.C. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [INSPIRE].
  19. [19]
    J.P. Conlon and E. Palti, Aspects of flavour and supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor structure in F-theory compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  21. [21]
    L. Aparicio, A. Font, L.E. Ibáñez and F. Marchesano, Flux and instanton effects in local F-theory models and hierarchical fermion masses, JHEP 08 (2011) 152 [arXiv:1104.2609] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    H. Abe, T. Kobayashi and H. Ohki, Magnetized orbifold models, JHEP 09 (2008) 043 [arXiv:0806.4748] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    J.P. Conlon, A. Maharana and F. Quevedo, Wave functions and Yukawa couplings in local string compactifications, JHEP 09 (2008) 104 [arXiv:0807.0789] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  24. [24]
    P. Di Vecchia, A. Liccardo, R. Marotta and F. Pezzella, Kähler metrics and Yukawa couplings in magnetized brane models, JHEP 03 (2009) 029 [arXiv:0810.5509] [INSPIRE].CrossRefGoogle Scholar
  25. [25]
    I. Antoniadis, A. Kumar and B. Panda, Fermion wavefunctions in magnetized branes: theta identities and Yukawa couplings, Nucl. Phys. B 823 (2009) 116 [arXiv:0904.0910] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  26. [26]
    P.G. Cámara and F. Marchesano, Open string wavefunctions in flux compactifications, JHEP 10 (2009) 017 [arXiv:0906.3033] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    F. Marchesano, P. McGuirk and G. Shiu, Chiral matter wavefunctions in warped compactifications, JHEP 05 (2011) 090 [arXiv:1012.2759] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  28. [28]
    H. Georgi and C. Jarlskog, A new lepton-quark mass relation in a unified theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].ADSGoogle Scholar
  29. [29]
    S. Weinberg, Supersymmetry at ordinary energies. 1. Masses and conservation laws, Phys. Rev. D 26 (1982) 287 [INSPIRE].ADSGoogle Scholar
  30. [30]
    S. Dimopoulos, S. Raby and F. Wilczek, Proton decay in supersymmetric models, Phys. Lett. B 112 (1982) 133 [INSPIRE].ADSGoogle Scholar
  31. [31]
    N. Sakai and T. Yanagida, Proton decay in a class of supersymmetric grand unified models, Nucl. Phys. B 197 (1982) 533 [INSPIRE].CrossRefADSGoogle Scholar
  32. [32]
    J.R. Ellis, D.V. Nanopoulos and S. Rudaz, GUTs 3: SUSY GUTs 2, Nucl. Phys. B 202 (1982) 43 [INSPIRE].CrossRefADSGoogle Scholar
  33. [33]
    J.R. Ellis, J. Hagelin, D.V. Nanopoulos and K. Tamvakis, Observable gravitationally induced baryon decay, Phys. Lett. B 124 (1983) 484 [INSPIRE].ADSGoogle Scholar
  34. [34]
    L.E. Ibáñez and G.G. Ross, Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model, Nucl. Phys. B 368 (1992) 3 [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    J. Hisano, H. Murayama and T. Yanagida, Nucleon decay in the minimal supersymmetric SU(5) grand unification, Nucl. Phys. B 402 (1993) 46 [hep-ph/9207279] [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    T. Goto and T. Nihei, Effect of RRRR dimension five operator on the proton decay in the minimal SU(5) SUGRA GUT model, Phys. Rev. D 59 (1999) 115009 [hep-ph/9808255] [INSPIRE].ADSGoogle Scholar
  37. [37]
    H. Murayama and A. Pierce, Not even decoupling can save minimal supersymmetric SU(5), Phys. Rev. D 65 (2002) 055009 [hep-ph/0108104] [INSPIRE].ADSGoogle Scholar
  38. [38]
    B. Bajc, P. Fileviez Perez and G. Senjanović, Proton decay in minimal supersymmetric SU(5), Phys. Rev. D 66 (2002) 075005 [hep-ph/0204311] [INSPIRE].ADSGoogle Scholar
  39. [39]
    B. Bajc, P. Fileviez Perez and G. Senjanović, Minimal supersymmetric SU(5) theory and proton decay: where do we stand?, hep-ph/0210374 [INSPIRE].
  40. [40]
    S. Raby, Proton decay, hep-ph/0211024 [INSPIRE].
  41. [41]
    D. Emmanuel-Costa and S. Wiesenfeldt, Proton decay in a consistent supersymmetric SU(5) GUT model, Nucl. Phys. B 661 (2003) 62 [hep-ph/0302272] [INSPIRE].ADSGoogle Scholar
  42. [42]
    J.P. Conlon and D. Cremades, The neutrino suppression scale from large volumes, Phys. Rev. Lett. 99 (2007) 041803 [hep-ph/0611144] [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    J.P. Conlon, Gauge threshold corrections for local string models, JHEP 04 (2009) 059 [arXiv:0901.4350] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  44. [44]
    J.P. Conlon and E. Palti, Gauge threshold corrections for local orientifolds, JHEP 09 (2009) 019 [arXiv:0906.1920] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  45. [45]
    J.P. Conlon and E. Palti, On gauge threshold corrections for local IIB/F-theory GUTs, Phys. Rev. D 80 (2009) 106004 [arXiv:0907.1362] [INSPIRE].ADSGoogle Scholar
  46. [46]
    A. Font and L. Ibáñez, Yukawa structure from U(1) fluxes in F-theory grand unification, JHEP 02 (2009) 016 [arXiv:0811.2157] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, Phys. Rev. Lett. 104 (2010) 231601 [arXiv:0910.5496] [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    E. Dudas and E. Palti, Froggatt-Nielsen models from E 8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  49. [49]
    S. King, G. Leontaris and G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  50. [50]
    E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  51. [51]
    G. Leontaris and G. Ross, Yukawa couplings and fermion mass structure in F-theory GUTs, JHEP 02 (2011) 108 [arXiv:1009.6000] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  52. [52]
    C. Lüdeling, H.P. Nilles and C.C. Stephan, The potential fate of local model building, Phys. Rev. D 83 (2011) 086008 [arXiv:1101.3346] [INSPIRE].ADSGoogle Scholar
  53. [53]
    J.C. Callaghan, S.F. King, G.K. Leontaris and G.G. Ross, Towards a realistic F-theory GUT, arXiv:1109.1399 [INSPIRE].
  54. [54]
    J.J. Heckman and C. Vafa, F-theory, GUTs and the weak scale, JHEP 09 (2009) 079 [arXiv:0809.1098] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  55. [55]
    V. Bouchard, J.J. Heckman, J. Seo and C. Vafa, F-theory and neutrinos: Kaluza-Klein dilution of flavor hierarchy, JHEP 01 (2010) 061 [arXiv:0904.1419] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  56. [56]
    R. Donagi and M. Wijnholt, Higgs bundles and UV completion in F-theory, arXiv:0904.1218 [INSPIRE].
  57. [57]
    J.J. Heckman, A. Tavanfar and C. Vafa, The point of E 8 in F-theory GUTs, JHEP 08 (2010) 040 [arXiv:0906.0581] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  58. [58]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, fluxes and compact three-generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [INSPIRE].CrossRefADSGoogle Scholar
  59. [59]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1)PQ, JHEP 04 (2010) 095 [arXiv:0912.0272] [INSPIRE].CrossRefADSGoogle Scholar
  60. [60]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, More on dimension-4 proton decay problem in F-theorySpectral surface, discriminant locus and monodromy, Nucl. Phys. B 840 (2010) 304 [arXiv:1004.3870] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  61. [61]
    T.W. Grimm and T. Weigand, On abelian gauge symmetries and proton decay in global F-theory GUTs, Phys. Rev. D 82 (2010) 086009 [arXiv:1006.0226] [INSPIRE].ADSGoogle Scholar
  62. [62]
    J. Pawelczyk, F-theory inspired GUTs with extra charged matter, Phys. Lett. B 697 (2011) 75 [arXiv:1008.2254] [INSPIRE].ADSMathSciNetGoogle Scholar
  63. [63]
    J. Marsano, Hypercharge flux, exotics and anomaly cancellation in F-theory GUTs, Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [INSPIRE].CrossRefADSGoogle Scholar
  64. [64]
    M.J. Dolan, J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory GUTs with U(1) symmetries: generalities and survey, Phys. Rev. D 84 (2011) 066008 [arXiv:1102.0290] [INSPIRE].ADSGoogle Scholar
  65. [65]
    M.J. Dolan, J. Marsano and S. Schäfer-Nameki, Unification and phenomenology of F-theory GUTs with U(1)PQ, arXiv:1109.4958 [INSPIRE].
  66. [66]
    T.W. Grimm, M. Kerstan, E. Palti and T. Weigand, Massive abelian gauge symmetries and fluxes in F-theory, arXiv:1107.3842 [INSPIRE].
  67. [67]
    L.B. Anderson, J. Gray, A. Lukas and E. Palti, Two hundred heterotic standard models on smooth Calabi-Yau threefolds, arXiv:1106.4804 [INSPIRE].
  68. [68]
    M. Buican, D. Malyshev, D.R. Morrison, H. Verlinde and M. Wijnholt, D-branes at singularities, compactification and hypercharge, JHEP 01 (2007) 107 [hep-th/0610007] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  69. [69]
    D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, Compactification effects in D-brane inflation, Phys. Rev. Lett. 104 (2010) 251602 [arXiv:0912.4268] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  70. [70]
    F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model, Nucl. Phys. B 477 (1996) 321 [hep-ph/9604387] [INSPIRE].CrossRefADSGoogle Scholar
  71. [71]
    D. Choudhury, F. Eberlein, A. Konig, J. Louis and S. Pokorski, Constraints on nonuniversal soft terms from flavor changing neutral currents, Phys. Lett. B 342 (1995) 180 [hep-ph/9408275] [INSPIRE].ADSGoogle Scholar
  72. [72]
    R. Blumenhagen, A. Deser and D. Lüst, FCNC processes from D-brane instantons, JHEP 02 (2011) 079 [arXiv:1007.4770] [INSPIRE].CrossRefADSGoogle Scholar
  73. [73]
    V. Oikonomou, F-theory Yukawa couplings and supersymmetric quantum mechanics, Nucl. Phys. B 856 (2012) 1 [arXiv:1107.0497] [INSPIRE].CrossRefADSGoogle Scholar
  74. [74]
    V. Oikonomou, F-theory and the Witten index, Nucl. Phys. B 850 (2011) 273 [arXiv:1103.1289] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar

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Authors and Affiliations

  • Pablo G. Cámara
    • 1
    • 2
  • Emilian Dudas
    • 3
    • 4
  • Eran Palti
    • 3
  1. 1.CERN, PH-TH DivisionGeneve 23Switzerland
  2. 2.Departament de Física Fonamental and Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  3. 3.Centre de Physique Théorique, Ecole Polytechnique, CNRSPalaiseauFrance
  4. 4.LPT, UMR du CNRS 8627, Bat 210, Université de Paris-SudOrsay CedexFrance

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