Abstract
We discuss non-Abelian discrete R symmetries which might have some conceivable relevance for model building. The focus is on settings with \( \mathcal{N}=1 \) supersymmetry, where the superspace coordinate transforms in a one-dimensional representation of the non-Abelian discrete symmetry group. We derive anomaly constraints for such symmetries and find that novel patterns of Green-Schwarz anomaly cancellation emerge. In addition we show that perfect groups, also in the non-R case, are always anomaly-free. An important property of models with non-Abelian discrete R symmetries is that superpartners come in different representations of the group. We present an example model, based on a \( {{\mathbb{Z}}_3}\rtimes \mathbb{Z}_8^R \) symmetry, to discuss generic features of models which unify discrete R symmetries, entailing solutions to the μ and proton decay problems of the MSSM, with non-Abelian discrete flavor symmetries.
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References
L.M. Krauss and F. Wilczek, Discrete gauge symmetry in continuum theories, Phys. Rev. Lett. 62 (1989) 1221 [INSPIRE].
L.E. Ibáñez and G.G. Ross, Discrete gauge symmetry anomalies, Phys. Lett. B 260 (1991) 291 [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].
T. Banks and M. Dine, Note on discrete gauge anomalies, Phys. Rev. D 45 (1992) 1424 [hep-th/9109045] [INSPIRE].
K. Fujikawa, Path integral measure for gauge invariant fermion theories, Phys. Rev. Lett. 42 (1979) 1195 [INSPIRE].
K. Fujikawa, Path integral for gauge theories with fermions, Phys. Rev. D 21 (1980) 2848 [Erratum ibid. D 22 (1980) 1499] [INSPIRE].
T. Araki, Anomaly of discrete symmetries and gauge coupling unification, Prog. Theor. Phys. 117 (2007) 1119 [hep-ph/0612306] [INSPIRE].
T. Araki et al., (Non-)abelian discrete anomalies, Nucl. Phys. B 805 (2008) 124 [arXiv:0805.0207] [INSPIRE].
M.-C. Chen, M. Ratz, C. Staudt and P.K. Vaudrevange, The μ term and neutrino masses, Nucl. Phys. B 866 (2013) 157 [arXiv:1206.5375] [INSPIRE].
H.M. Lee et al., Discrete R symmetries for the MSSM and its singlet extensions, Nucl. Phys. B 850 (2011) 1 [arXiv:1102.3595] [INSPIRE].
C. Lüdeling, F. Ruehle and C. Wieck, Non-universal anomalies in heterotic string constructions, Phys. Rev. D 85 (2012) 106010 [arXiv:1203.5789] [INSPIRE].
M.-C. Chen, M. Fallbacher and M. Ratz, Supersymmetric unification and R symmetries, Mod. Phys. Lett. A 27 (2012) 1230044 [arXiv:1211.6247] [INSPIRE].
H.M. Lee et al., A unique \( Z_4^R \) symmetry for the MSSM, Phys. Lett. B 694 (2011) 491 [arXiv:1009.0905] [INSPIRE].
P. Ramond, Group theory: a physicist’s survey, Cambridge University Press, Cambridge U.K. (2010).
K. Babu, I. Gogoladze and K. Wang, Natural R parity, μ term and fermion mass hierarchy from discrete gauge symmetries, Nucl. Phys. B 660 (2003) 322 [hep-ph/0212245] [INSPIRE].
GAP Group, GAP — Groups, Algorithms, and Programming, version 4.5.5 (2012).
S.-L. Chen, M. Frigerio and E. Ma, Large neutrino mixing and normal mass hierarchy: a discrete understanding, Phys. Rev. D 70 (2004) 073008 [Erratum ibid. D 70 (2004) 079905] [hep-ph/0404084] [INSPIRE].
S. Morisi and M. Picariello, The flavor physics in unified gauge theory from an S 3 × P discrete symmetry, Int. J. Theor. Phys. 45 (2006) 1267 [hep-ph/0505113] [INSPIRE].
R. Dermisek and S. Raby, Bi-large neutrino mixing and CP-violation in an SO(10) SUSY GUT for fermion masses, Phys. Lett. B 622 (2005) 327 [hep-ph/0507045] [INSPIRE].
F. Caravaglios and S. Morisi, Fermion masses in E 6 grand unification with family permutation symmetries, hep-ph/0510321 [INSPIRE].
T. Teshima, Flavor mass and mixing and S 3 symmetry: An S 3 invariant model reasonable to all, Phys. Rev. D 73 (2006) 045019 [hep-ph/0509094] [INSPIRE].
N. Haba and K. Yoshioka, Discrete flavor symmetry, dynamical mass textures and grand unification, Nucl. Phys. B 739 (2006) 254 [hep-ph/0511108] [INSPIRE].
M. Picariello, Neutrino CP-violating parameters from nontrivial quark-lepton correlation: a S 3 × GUT model, Int. J. Mod. Phys. A 23 (2008) 4435 [hep-ph/0611189] [INSPIRE].
R. Mohapatra, S. Nasri and H.-B. Yu, Grand unification of μ-τ symmetry, Phys. Lett. B 636 (2006) 114 [hep-ph/0603020] [INSPIRE].
R. Mohapatra, S. Nasri and H.-B. Yu, S 3 symmetry and tri-bimaximal mixing, Phys. Lett. B 639 (2006) 318 [hep-ph/0605020] [INSPIRE].
F. Feruglio and Y. Lin, Fermion mass hierarchies and flavour mixing from a minimal discrete symmetry, Nucl. Phys. B 800 (2008) 77 [arXiv:0712.1528] [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].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
H. Ishimori et al., Non-abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
R. Kappl et al., String-derived MSSM vacua with residual R symmetries, Nucl. Phys. B 847 (2011) 325 [arXiv:1012.4574] [INSPIRE].
N.G. Cabo Bizet et al., R-charge conservation and more in factorizable and non-factorizable orbifolds, JHEP 05 (2013) 076 [arXiv:1301.2322] [INSPIRE].
T. Kobayashi, H.P. Nilles, F. Plöger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020] [INSPIRE].
S.J. Konopka, Non Abelian orbifold compactifications of the heterotic string, JHEP 07 (2013) 023 [arXiv:1210.5040] [INSPIRE].
M. Fischer, S. Ramos-Sanchez and P.K.S. Vaudrevange, Heterotic non-Abelian orbifolds, arXiv:1304.7742 [INSPIRE].
S.P. Martin, A supersymmetry primer, hep-ph/9709356 [INSPIRE].
R.S. Chivukula and H. Georgi, Composite technicolor standard model, Phys. Lett. B 188 (1987) 99 [INSPIRE].
A. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Universal unitarity triangle and physics beyond the standard model, Phys. Lett. B 500 (2001) 161 [hep-ph/0007085] [INSPIRE].
K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
O. Lebedev, H.P. Nilles and M. Ratz, De Sitter vacua from matter superpotentials, Phys. Lett. B 636 (2006) 126 [hep-th/0603047] [INSPIRE].
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ArXiv ePrint: 1306.5112
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Chen, MC., Ratz, M. & Trautner, A. Non-Abelian discrete R symmetries. J. High Energ. Phys. 2013, 96 (2013). https://doi.org/10.1007/JHEP09(2013)096
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DOI: https://doi.org/10.1007/JHEP09(2013)096