Abstract
In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified [1]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.
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C. Lawrie, S. Schäfer-Nameki and J.-M. Wong, F-theory and all things rational: surveying U(1) symmetries with rational sections, JHEP 09 (2015) 144 [arXiv:1504.05593] [INSPIRE].
H. Hayashi, C. Lawrie, D.R. Morrison and S. Schäfer-Nameki, Box graphs and singular fibers, JHEP 05 (2014) 048 [arXiv:1402.2653] [INSPIRE].
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].
A.P. Braun, A. Collinucci and R. Valandro, G-flux in F-theory and algebraic cycles, Nucl. Phys. B 856 (2012) 129 [arXiv:1107.5337] [INSPIRE].
C. Mayrhofer, E. Palti and T. Weigand, U(1) symmetries in F-theory GUTs with multiple sections, JHEP 03 (2013) 098 [arXiv:1211.6742] [INSPIRE].
D.R. Morrison and D.S. Park, F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds, JHEP 10 (2012) 128 [arXiv:1208.2695] [INSPIRE].
J. Borchmann, C. Mayrhofer, E. Palti and T. Weigand, Elliptic fibrations for SU(5) × U(1) × U(1) F-theory vacua, Phys. Rev. D 88 (2013) 046005 [arXiv:1303.5054] [INSPIRE].
M. Cvetič, D. Klevers and H. Piragua, F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections, JHEP 06 (2013) 067 [arXiv:1303.6970] [INSPIRE].
J. Borchmann, C. Mayrhofer, E. Palti and T. Weigand, SU(5) tops with multiple U(1)s in F-theory, Nucl. Phys. B 882 (2014) 1 [arXiv:1307.2902] [INSPIRE].
M. Cvetič, D. Klevers and H. Piragua, F-theory compactifications with multiple U(1)-factors: addendum, JHEP 12 (2013) 056 [arXiv:1307.6425] [INSPIRE].
M. Cvetič, D. Klevers, H. Piragua and P. Song, Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1) × U(1) × U(1) gauge symmetry, JHEP 03 (2014) 021 [arXiv:1310.0463] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, New global F-theory GUTs with U(1) symmetries, JHEP 09 (2013) 154 [arXiv:1302.1854] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Geometric engineering in toric F-theory and GUTs with U(1) gauge factors, JHEP 12 (2013) 069 [arXiv:1306.0577] [INSPIRE].
M. Kuntzler and S. Schäfer-Nameki, Tate trees for elliptic fibrations with rank one Mordell-Weil group, arXiv:1406.5174 [INSPIRE].
C. Lawrie and D. Sacco, Tate’s algorithm for F-theory GUTs with two U(1)s, JHEP 03 (2015) 055 [arXiv:1412.4125] [INSPIRE].
V. Braun, T.W. Grimm and J. Keitel, Complete intersection fibers in F-theory, JHEP 03 (2015) 125 [arXiv:1411.2615] [INSPIRE].
D. Klevers, D.K. Mayorga Peña, P.-K. Oehlmann, H. Piragua and J. Reuter, F-theory on all toric hypersurface fibrations and its Higgs branches, JHEP 01 (2015) 142 [arXiv:1408.4808] [INSPIRE].
D.R. Morrison and W. Taylor, Sections, multisections and U(1) fields in F-theory, arXiv:1404.1527 [INSPIRE].
F. Baume, E. Palti and S. Schwieger, On E 8 and F-theory GUTs, JHEP 06 (2015) 039 [arXiv:1502.03878] [INSPIRE].
M. Cvetič, D. Klevers, H. Piragua and W. Taylor, General U(1) × U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure, arXiv:1507.05954 [INSPIRE].
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].
R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — II: experimental predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
J. Marsano, H. Clemens, T. Pantev, S. Raby and H.-H. Tseng, A global SU(5) F-theory model with Wilson line breaking, JHEP 01 (2013) 150 [arXiv:1206.6132] [INSPIRE].
E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [INSPIRE].
J. Marsano, Hypercharge flux, exotics and anomaly cancellation in F-theory GUTs, Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [INSPIRE].
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].
E. Palti, A note on hypercharge flux, anomalies and U(1)s in F-theory GUTs, Phys. Rev. D 87 (2013) 085036 [arXiv:1209.4421] [INSPIRE].
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].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1) PQ , JHEP 04 (2010) 095 [arXiv:0912.0272] [INSPIRE].
H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, More on dimension-4 proton decay problem in F-theory — spectral surface, discriminant locus and monodromy, Nucl. Phys. B 840 (2010) 304 [arXiv:1004.3870] [INSPIRE].
M.J. Dolan, J. Marsano and S. Schäfer-Nameki, Unification and phenomenology of F-theory GUTs with U(1) PQ , JHEP 12 (2011) 032 [arXiv:1109.4958] [INSPIRE].
R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
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].
J.J. Heckman and C. Vafa, Flavor hierarchy from F-theory, Nucl. Phys. B 837 (2010) 137 [arXiv:0811.2417] [INSPIRE].
A. Font and L.E. Ibáñez, Yukawa structure from U(1) fluxes in F-theory grand unification, JHEP 02 (2009) 016 [arXiv:0811.2157] [INSPIRE].
R. Tatar, Y. Tsuchiya and T. Watari, Right-handed neutrinos in F-theory compactifications, Nucl. Phys. B 823 (2009) 1 [arXiv:0905.2289] [INSPIRE].
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].
F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, Phys. Rev. Lett. 104 (2010) 231601 [arXiv:0910.5496] [INSPIRE].
H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor structure in F-theory compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [INSPIRE].
J.P. Conlon and E. Palti, Aspects of flavour and supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [INSPIRE].
S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [INSPIRE].
S.F. King, G.K. Leontaris and G.G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [INSPIRE].
G.K. Leontaris and G.G. Ross, Yukawa couplings and fermion mass structure in F-theory GUTs, JHEP 02 (2011) 108 [arXiv:1009.6000] [INSPIRE].
P.G. Camara, E. Dudas and E. Palti, Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs, JHEP 12 (2011) 112 [arXiv:1110.2206] [INSPIRE].
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].
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].
A. Font, L.E. Ibáñez, F. Marchesano and D. Regalado, Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) unification, JHEP 03 (2013) 140 [Erratum ibid. 07 (2013) 036] [arXiv:1211.6529] [INSPIRE].
A. Font, F. Marchesano, D. Regalado and G. Zoccarato, Up-type quark masses in SU(5) F-theory models, JHEP 11 (2013) 125 [arXiv:1307.8089] [INSPIRE].
F. Marchesano, D. Regalado and G. Zoccarato, Yukawa hierarchies at the point of E 8 in F-theory, JHEP 04 (2015) 179 [arXiv:1503.02683] [INSPIRE].
J.J. Heckman, Particle physics implications of F-theory, Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [INSPIRE].
A. Maharana and E. Palti, Models of particle physics from type IIB string theory and F-theory: a review, Int. J. Mod. Phys. A 28 (2013) 1330005 [arXiv:1212.0555] [INSPIRE].
E. Dudas and E. Palti, Froggatt-Nielsen models from E 8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [INSPIRE].
S. Krippendorf, D.K. Mayorga Peña, P.-K. Oehlmann and F. Ruehle, Rational F-theory GUTs without exotics, JHEP 07 (2014) 013 [arXiv:1401.5084] [INSPIRE].
L. Lin and T. Weigand, Towards the Standard Model in F-theory, Fortsch. Phys. 63 (2015) 55 [arXiv:1406.6071] [INSPIRE].
A. Grassi, J. Halverson, J. Shaneson and W. Taylor, Non-Higgsable QCD and the Standard Model spectrum in F-theory, JHEP 01 (2015) 086 [arXiv:1409.8295] [INSPIRE].
M. Cvetič, D. Klevers, D.K. Mayorga Peña, P.-K. Oehlmann and J. Reuter, Three-family particle physics models from global F-theory compactifications, JHEP 08 (2015) 087 [arXiv:1503.02068] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory compactifications for supersymmetric GUTs, JHEP 08 (2009) 030 [arXiv:0904.3932] [INSPIRE].
R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys. B 829 (2010) 325 [arXiv:0908.1784] [INSPIRE].
A.P. Braun, A. Collinucci and R. Valandro, Hypercharge flux in F-theory and the stable Sen limit, JHEP 07 (2014) 121 [arXiv:1402.4096] [INSPIRE].
G.F. Giudice and A. Masiero, A natural solution to the μ problem in supergravity theories, Phys. Lett. B 206 (1988) 480 [INSPIRE].
J.E. Kim and H.P. Nilles, The μ problem and the strong CP problem, Phys. Lett. B 138 (1984) 150 [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Gauge mediation in F-theory GUT models, Phys. Rev. D 80 (2009) 046006 [arXiv:0808.1571] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
H. Baer and X. Tata, Weak scale supersymmetry, Cambridge University Press, Cambridge U.K. (1996).
I. Hinchliffe and T. Kaeding, B+L violating couplings in the minimal supersymmetric Standard Model, Phys. Rev. D 47 (1993) 279 [INSPIRE].
A. Yu. Smirnov and F. Vissani, Large R-parity violating couplings and grand unification, Nucl. Phys. B 460 (1996) 37 [hep-ph/9506416] [INSPIRE].
R. Barbier et al., R-parity violating supersymmetry, Phys. Rept. 420 (2005) 1 [hep-ph/0406039] [INSPIRE].
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].
C.D. Froggatt and H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
S. Weinberg, Electromagnetic and weak masses, Phys. Rev. Lett. 29 (1972) 388 [INSPIRE].
A.B. Lahanas and D. Wyler, Radiative fermion masses and supersymmetry, Phys. Lett. B 122 (1983) 258 [INSPIRE].
G. Ross and M. Serna, Unification and fermion mass structure, Phys. Lett. B 664 (2008) 97 [arXiv:0704.1248] [INSPIRE].
P. Ramond, R.G. Roberts and G.G. Ross, Stitching the Yukawa quilt, Nucl. Phys. B 406 (1993) 19 [hep-ph/9303320] [INSPIRE].
Y. Nir, Gauge unification, Yukawa hierarchy and the μ problem, Phys. Lett. B 354 (1995) 107 [hep-ph/9504312] [INSPIRE].
L. Wolfenstein, Parametrization of the Kobayashi-Maskawa matrix, Phys. Rev. Lett. 51 (1983) 1945 [INSPIRE].
L.E. Ibáñez and G.G. Ross, Fermion masses and mixing angles from gauge symmetries, Phys. Lett. B 332 (1994) 100 [hep-ph/9403338] [INSPIRE].
H.K. Dreiner and M. Thormeier, Supersymmetric Froggatt-Nielsen models with baryon and lepton number violation, Phys. Rev. D 69 (2004) 053002 [hep-ph/0305270] [INSPIRE].
N. Haba, Composite model with neutrino large mixing, Phys. Rev. D 59 (1999) 035011 [hep-ph/9807552] [INSPIRE].
K.S. Babu, T. Enkhbat and I. Gogoladze, Anomalous U(1) symmetry and lepton flavor violation, Nucl. Phys. B 678 (2004) 233 [hep-ph/0308093] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. II, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
C. Lawrie, S. Schäfer-Nameki and J.-M. Wong, Singular sections and U(1) charges in F-theory, to appear.
L.J. Hall and A. Rasin, On the generality of certain predictions for quark mixing, Phys. Lett. B 315 (1993) 164 [hep-ph/9303303] [INSPIRE].
E. Dudas, S. Pokorski and C.A. Savoy, Yukawa matrices from a spontaneously broken Abelian symmetry, Phys. Lett. B 356 (1995) 45 [hep-ph/9504292] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
N. Haba and H. Murayama, Anarchy and hierarchy, Phys. Rev. D 63 (2001) 053010 [hep-ph/0009174] [INSPIRE].
M. Kuntzler and C. Lawrie, Smooth: a Mathematica package for studying resolutions of singular fibrations, version 0.4.
S. Katz, D.R. Morrison, S. Schäfer-Nameki and J. Sully, Tate’s algorithm and F-theory, JHEP 08 (2011) 094 [arXiv:1106.3854] [INSPIRE].
D.R. Morrison and W. Taylor, Non-Higgsable clusters for 4D F-theory models, JHEP 05 (2015) 080 [arXiv:1412.6112] [INSPIRE].
J. Halverson and W. Taylor, \( {\mathrm{\mathbb{P}}}^1 \) -bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models, JHEP 09 (2015) 086 [arXiv:1506.03204] [INSPIRE].
L.J. Mordell, Diophantine equations, Pure Appl. Math. 30, Academic Press, London U.K. and New York U.S.A. (1969).
H.K. Dreiner, C. Luhn and M. Thormeier, What is the discrete gauge symmetry of the MSSM?, Phys. Rev. D 73 (2006) 075007 [hep-ph/0512163] [INSPIRE].
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Krippendorf, S., Schäfer-Nameki, S. & Wong, JM. Froggatt-Nielsen meets Mordell-Weil: a phenomenological survey of global F-theory GUTs with U(1)s. J. High Energ. Phys. 2015, 8 (2015). https://doi.org/10.1007/JHEP11(2015)008
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DOI: https://doi.org/10.1007/JHEP11(2015)008