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Effects of localized \(\mu\)-terms at the fixed points in magnetized orbifold models. (English) Zbl 1435.81253
Summary: We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called \(\mu\)-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the \(\mu\)-term matrix in the 4D effective theory generated by the localized sources on \(T^2 / Z_2\) orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical \(\mu\)-terms for the multiple Higgs fields. The lightest ones can be exponentially suppressed due to the localized wavefunctions of zero-modes determined by the fluxes, while the others are of the order of the compactification scale, which can provide a dynamical origin of the electroweak scale as well as a simultaneous decoupling of extra Higgs fields. We also show that a certain linear combination of the lightest Higgs fields could generate the observed mass ratios of down-type quarks through their Yukawa couplings determined by the wavefunctions.
MSC:
81V22 Unified quantum theories
81T60 Supersymmetric field theories in quantum mechanics
57R18 Topology and geometry of orbifolds
81T12 Effective quantum field theories
81V10 Electromagnetic interaction; quantum electrodynamics
81T33 Dimensional compactification in quantum field theory
81V05 Strong interaction, including quantum chromodynamics
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[1] Bachas, C., A way to break supersymmetry
[2] Cremades, D.; Ibanez, L. E.; Marchesano, F., Computing Yukawa couplings from magnetized extra dimensions, J. High Energy Phys., 05, Article 079 pp. (2004)
[3] Ibanez, L. E.; Uranga, A. M., String Theory and Particle Physics: An Introduction to String Phenomenology (2012), Cambridge University Press · Zbl 1260.81001
[4] Braun, A. P.; Hebecker, A.; Trapletti, M., Flux stabilization in 6 dimensions: D-terms and loop corrections, J. High Energy Phys., 02, Article 015 pp. (2007)
[5] Abe, H.; Kobayashi, T.; Ohki, H., Magnetized orbifold models, J. High Energy Phys., 09, Article 043 pp. (2008) · Zbl 1245.81254
[6] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Three generation magnetized orbifold models, Nucl. Phys. B, 814, 265-292 (2009) · Zbl 1194.81248
[7] Abe, H.; Choi, K.-S.; Kobayashi, T.; Ohki, H., Magnetic flux, Wilson line and orbifold, Phys. Rev. D, 80, Article 126006 pp. (2009)
[8] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K., Superfield description of 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B, 863, 1-18 (2012) · Zbl 1246.81347
[9] Abe, H.; Kobayashi, T.; Ohki, H.; Oikawa, A.; Sumita, K., Phenomenological aspects of 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B, 870, 30-54 (2013) · Zbl 1262.81250
[10] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K.; Tatsuta, Y., Flavor landscape of 10D SYM theory with magnetized extra dimensions, J. High Energy Phys., 04, Article 007 pp. (2014)
[11] Abe, H.; Kobayashi, T.; Ohki, H.; Sumita, K.; Tatsuta, Y., Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions, J. High Energy Phys., 06, Article 017 pp. (2014)
[12] Abe, H.; Kawamura, J.; Sumita, K., The Higgs boson mass and SUSY spectra in 10D SYM theory with magnetized extra dimensions, Nucl. Phys. B, 888, 194-213 (2014) · Zbl 1326.81254
[13] Abe, H.; Kobayashi, T.; Sumita, K.; Tatsuta, Y., Gaussian Froggatt-Nielsen mechanism on magnetized orbifolds, Phys. Rev. D, 90, 10, Article 105006 pp. (2014)
[14] Buchmuller, W.; Dierigl, M.; Ruehle, F.; Schweizer, J., Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux, Phys. Rev. D, 92, 10, Article 105031 pp. (2015)
[15] Buchmuller, W.; Dierigl, M.; Ruehle, F.; Schweizer, J., Split symmetries, Phys. Lett. B, 750, 615-619 (2015) · Zbl 1364.83058
[16] Abe, H.; Kobayashi, T.; Sumita, K.; Tatsuta, Y., Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms, Phys. Rev. D, 95, 1, Article 015005 pp. (2017)
[17] Kobayashi, T.; Nishiwaki, K.; Tatsuta, Y., CP-violating phase on magnetized toroidal orbifolds, J. High Energy Phys., 04, Article 080 pp. (2017)
[18] Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K.; Sakamoto, M., Shifted orbifold models with magnetic flux, Phys. Rev. D, 87, 8, Article 086001 pp. (2013)
[19] Abe, T.-H.; Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K.; Sakamoto, M., \(Z_N\) twisted orbifold models with magnetic flux, J. High Energy Phys., 01, Article 065 pp. (2014)
[20] Abe, T.-h.; Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K.; Sakamoto, M., Operator analysis of physical states on magnetized \(T^2 / Z_N\) orbifolds, Nucl. Phys. B, 890, 442-480 (2014) · Zbl 1326.81255
[21] Abe, T.-h.; Fujimoto, Y.; Kobayashi, T.; Miura, T.; Nishiwaki, K.; Sakamoto, M.; Tatsuta, Y., Classification of three-generation models on magnetized orbifolds, Nucl. Phys. B, 894, 374-406 (2015) · Zbl 1328.81219
[22] Fujimoto, Y.; Kobayashi, T.; Nishiwaki, K.; Sakamoto, M.; Tatsuta, Y., Comprehensive analysis of Yukawa hierarchies on \(T^2 / Z_N\) with magnetic fluxes, Phys. Rev. D, 94, 3, Article 035031 pp. (2016)
[23] Buchmuller, W.; Dierigl, M.; Dudas, E.; Schweizer, J., Effective field theory for magnetic compactifications, J. High Energy Phys., 04, Article 052 pp. (2017)
[26] Martin, S. P., A supersymmetry primer, Adv. Ser. Dir. High Energy Phys., 18, 1 (1998) · Zbl 1106.81320
[27] Ishida, M.; Nishiwaki, K.; Tatsuta, Y., Brane-localized masses in magnetic compactifications, Phys. Rev. D, 95, 9, Article 095036 pp. (2017)
[28] Ishida, M.; Nishiwaki, K.; Tatsuta, Y., Seesaw mechanism in magnetic compactifications, J. High Energy Phys., 07, Article 125 pp. (2018)
[29] Hamada, Y.; Kobayashi, T., Massive modes in magnetized brane models, Prog. Theor. Phys., 128, 903-923 (2012)
[30] Conlon, J. P.; Maharana, A.; Quevedo, F., Wave functions and Yukawa couplings in local string compactifications, J. High Energy Phys., 09, Article 104 pp. (2008) · Zbl 1245.83057
[31] Abe, H.; Horie, T.; Sumita, K., Superfield description of (4+2n)-dimensional SYM theories and their mixtures on magnetized tori, Nucl. Phys. B, 900, 331-365 (2015) · Zbl 1331.81184
[32] Arkani-Hamed, N.; Gregoire, T.; Wacker, J. G., Higher dimensional supersymmetry in 4-D superspace, J. High Energy Phys., 03, Article 055 pp. (2002)
[33] Green, M. B.; Schwarz, J. H., Anomaly cancellation in supersymmetric D=10 Gauge theory and superstring theory, Phys. Lett. B, 149, 117-122 (1984)
[34] Sakamura, Y., Spectrum in the presence of brane-localized mass on torus extra dimensions, J. High Energy Phys., 10, Article 083 pp. (2016)
[35] Ibanez, L. E.; Uranga, A. M., Neutrino Majorana masses from string theory instanton effects, J. High Energy Phys., 03, Article 052 pp. (2007)
[36] Blumenhagen, R.; Cvetic, M.; Weigand, T., Spacetime instanton corrections in 4D string vacua: the seesaw mechanism for D-brane models, Nucl. Phys. B, 771, 113-142 (2007) · Zbl 1117.81112
[37] Abe, H.; Kobayashi, T.; Tatsuta, Y.; Uemura, S., D-brane instanton induced \(μ\) terms and their hierarchical structure, Phys. Rev. D, 92, 2, Article 026001 pp. (2015)
[38] Kobayashi, T.; Tatsuta, Y.; Uemura, S., Majorana neutrino mass structure induced by rigid instantons on toroidal orbifold, Phys. Rev. D, 93, 6, Article 065029 pp. (2016)
[39] Lust, D.; Reffert, S.; Scheidegger, E.; Stieberger, S., Resolved toroidal orbifolds and their orientifolds, Adv. Theor. Math. Phys., 12, 1, 67-183 (2008) · Zbl 1152.81883
[40] Groot Nibbelink, S.; Trapletti, M.; Walter, M., Resolutions of C**n/Z(n) orbifolds, their U(1) bundles, and applications to string model building, J. High Energy Phys., 03, Article 035 pp. (2007)
[41] Groot Nibbelink, S.; Held, J.; Ruehle, F.; Trapletti, M.; Vaudrevange, P. K.S., Heterotic Z(6-II) MSSM orbifolds in blowup, J. High Energy Phys., 03, Article 005 pp. (2009)
[42] Blaszczyk, M.; Groot Nibbelink, S.; Ruehle, F.; Trapletti, M.; Vaudrevange, P. K.S., Heterotic MSSM on a resolved orbifold, J. High Energy Phys., 09, Article 065 pp. (2010) · Zbl 1291.81296
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