[en] We present in this paper the SOSpin library, which calculates an analytic decomposition of the Yukawa interactions invariant under SO(2N) in terms of an SU(N) basis. We make use of the oscillator expansion formalism, where the SO(2N) spinor representations are expressed in terms of creation and annihilation operators of a Grassmann algebra acting on a vacuum state. These noncommutative operators and their products are simulated in SOSpin through the implementation of doubly-linked-list data structures. These data structures were determinant to achieve a higher performance in the simplification of large products of creation and annihilation operators. We illustrate the use of our library with complete examples of how to decompose Yukawa terms invariant under SO(2N) in terms of SU(N) degrees of freedom for N=2 and 5. We further demonstrate, with an example for SO(4), that higher dimensional field-operator terms can also be processed with our library. Finally, we describe the functions available in SOSpin that are made to simplify the writing of spinors and their interactions specifically for SO(10) models.
Disciplines :
Physics
Author, co-author :
Da Silva Simoes, Catarina ; Université de Liège > Département d'astrophys., géophysique et océanographie (AGO) > Inter. fondamentales en physique et astrophysique (IFPA)
Cardoso, Nuno; Instituto Superior Técnico > Departamento de Física > CFTP
Emmanuel-Costa, David; Instituto Superior Técnico, Universidade de Lisboa > Departamento de Física > CFTP
Gonçalves, Nuno; University of Coimbra > Department of Electrical and Computer Engineering > Institute of Systems and Robotics
Language :
English
Title :
SOSpin, a C++ library for Yukawa decomposition in SO(2N) models
Baez, J.C., Huerta, J., The algebra of grand unified theories (2010) Bull. Am. Math. Soc., 47, p. 483. , arxiv:0904.1556 [hep-th]
Georgi, H., Glashow, S.L., Unity of all elementary particle forces (1974) Phys. Rev. Lett., 32, p. 438
Georgi, H., The state of the art - Gauge theories (1975) AIP Conf. Proc., 23, p. 575
Georgi, H., Unified gauge theories, in:∗Coral Gables 1975 (1975) Proceedings, Theories and Experiments in High Energy Physics∗, pp. 329-339. , New York
Fritzsch, H., Minkowski, P., Unified interactions of leptons and hadrons (1975) Ann. Physics, 93, p. 193
Minkowski, P., μ→Eγ at a rate of one out of 109 muon decays? (1977) Phys. Lett. B, 67, p. 421
Yanagida, T., Horizontal symmetry and masses of neutrinos (1979) Conf. Proc. C, p. 95. , 7902131 Conf. Proc. C 7902131 1979 95
Mohapatra, R.N., Senjanovic, G., Neutrino mass and spontaneous parity violation (1980) Phys. Rev. Lett., 44, p. 912
Schechter, J., Valle, J.W.F., Neutrino masses in SU(2)×U(1) theories (1980) Phys. Rev. D, 22, p. 2227
Gell-Mann, M., Ramond, P., Slansky, R., Complex spinors and unified theories (1979) Conf. Proc. C, p. 315. , 790927 arxiv:1306.4669 [hep-th]
Georgi, H., Glashow, S.L., Gauge theories without anomalies (1972) Phys. Rev. D, 6, p. 429
Harvey, J.A., Ramond, P., Reiss, D.B., CP violation and mass relations in SO(10) (1980) Phys. Lett. B, 92, p. 309
Rajpoot, S., Symmetry breaking and intermediate mass scales in the SO(10) grand unified theory (1980) Phys. Rev. D, 22, p. 2244
Harvey, J.A., Reiss, D.B., Ramond, P., Mass relations and neutrino oscillations in an SO(10) model (1982) Nuclear Phys. B, 199, p. 223
Wilczek, F., Zee, A., Families from spinors (1982) Phys. Rev. D, 25, p. 553
Barr, S.M., A new symmetry breaking pattern for SO(10) and proton decay (1982) Phys. Lett. B, 112, p. 219
Babu, K.S., Pati, J.C., Wilczek, F., Fermion masses, neutrino oscillations, and proton decay in the light of Super-Kamiokande (2000) Nuclear Phys. B, 566, p. 33. , arxiv:hep-ph/9812538
Bertolini, S., Di Luzio, L., Malinsky, M., Intermediate mass scales in the non-supersymmetric SO(10) grand unification: A Reappraisal (2009) Phys. Rev. D, 80. , arxiv:0903.4049 [hep-ph]
Drees, M., Kim, J.M., Neutralino dark matter in an SO(10) model with two-step intermediate scale symmetry breaking (2008) J. High Energy Phys., 812, p. 095. , arxiv:0810.1875 [hep-ph]
Fong, C.S., Meloni, D., Meroni, A., Nardi, E., Leptogenesis in SO(10) (2015) J. High Energy Phys., 1501, p. 111. , arxiv:1412.4776 [hep-ph]
Fonseca, R.M., On the chirality of the SM and the fermion content of GUTs (2015) Nuclear Phys. B, 897, p. 757. , arxiv:1504.03695 [hep-ph]
Babu, K.S., Khan, S., A Minimal Non-Supersymmetric SO(10) Model: Gauge Coupling Unification, Proton Decay and Fermion Masses, , arxiv:1507.06712 [hep-ph]
Rajpoot, S., Sithikong, P., Implications of the SO(12) gauge symmetry for grand unification (1981) Phys. Rev. D, 23, p. 1649
Ida, M., Kayama, Y., Kitazoe, T., Inclusion of generations in SO(14) (1980) Progr. Theoret. Phys., 64, p. 1745
Chang, D., Mohapatra, R.N., SO(18) unification of fermion generations (1985) Phys. Lett. B, 158, p. 323
Hubsch, T., Pal, P.B., Economical unification of three families in SO(18) (1986) Phys. Rev. D, 34, p. 1606
Kim, H.D., Raby, S., Unification in 5-D SO(10) (2003) J. High Energy Phys., 301, p. 056. , arxiv:hep-ph/0212348
Feruglio, F., Patel, K.M., Vicino, D., Order and Anarchy hand in hand in 5D SO(10) (2014) J. High Energy Phys., 1409, p. 095. , arxiv:1407.2913 [hep-ph]
Hebecker, A., March-Russell, J., The structure of GUT breaking by orbifolding (2002) Nuclear Phys. B, 625, p. 128. , arxiv:hep-ph/0107039
Asaka, T., Buchmuller, W., Covi, L., False vacuum decay after inflation (2001) Phys. Lett. B, 510, p. 271. , arxiv:hep-ph/0104037
Asaka, T., Buchmuller, W., Covi, L., Gauge unification in six-dimensions (2001) Phys. Lett. B, 523, p. 199. , arxiv:hep-ph/0108021
Asaka, T., Buchmuller, W., Covi, L., Exceptional coset spaces and unification in six-dimensions (2002) Phys. Lett. B, 540, p. 295. , arxiv:hep-ph/0204358
Asaka, T., Buchmuller, W., Covi, L., Quarks and leptons between branes and bulk (2003) Phys. Lett. B, 563, p. 209. , arxiv:hep-ph/0304142
Buchmuller, W., Covi, L., Emmanuel-Costa, D., Wiesenfeldt, S., Flavour structure and proton decay in 6D orbifold GUTs (2004) J. High Energy Phys., 409, p. 004. , arxiv:hep-ph/0407070
Buchmuller, W., Covi, L., Emmanuel-Costa, D., Wiesenfeldt, S., CP violation and neutrino masses and mixings from quark mass hierarchies (2007) J. High Energy Phys., 712, p. 030. , arxiv:0709.4650 [hep-ph]
Cosme, N., Frere, J.M., CP violation in weak interactions from orbifold reduction: Possible unification structures (2004) Phys. Rev. D, 69. , arxiv:hep-ph/0303037
Hosotani, Y., Yamatsu, N., Gauge-Higgs Grand Unification, , arxiv:1504.03817 [hep-ph]
Slansky, R., Group theory for unified model building (1981) Phys. Rep., 79, p. 1
Mohapatra, R.N., Sakita, B., SO(2n) grand unification in an SU(N) basis (1980) Phys. Rev. D, 21, p. 1062
Nandi, S., Stern, A., Sudarshan, E.C.G., Structure of proton decay in SO(n) family unification (1982) Phys. Rev. D, 26, p. 1653
Nath, P., Syed, R.M., Analysis of couplings with large tensor representations in SO(2N) and proton decay (2001) Phys. Lett. B, 506, p. 68. , arxiv:hep-ph/0103165 Phys. Lett. B 508 2001 216
Nath, P., Syed, R.M., Complete cubic and quartic couplings of 16 and bar-16 in SO(10) unification (2001) Nuclear Phys. B, 618, p. 138. , arxiv:hep-th/0109116
Nath, P., Syed, R.M., Couplings of vector-spinor representation for SO(10) model building (2006) J. High Energy Phys., 602, p. 022. , arxiv:hep-ph/0511172
Anderson, G.W., Blazek, T., E(6) Unification Model Building. 3. Clebsch-Gordan Coefficients in E(6) Tensor Products of the 27 with Higher Dimensional Representations, , arxiv:hep-ph/0101349
He, X.G., Meljanac, S., Symmetry breaking and mass spectra in supersymmetric SO(10) models (1990) Phys. Rev. D, 41, p. 1620
Fukuyama, T., Ilakovac, A., Kikuchi, T., Meljanac, S., Okada, N., SO(10) group theory for the unified model building (2005) J. Math. Phys., 46. , arxiv:hep-ph/0405300
Aulakh, C.S., Girdhar, A., SO(10) a la Pati-Salam (2005) Internat. J. Modern Phys. A, 20, p. 865. , arxiv:hep-ph/0204097
Aulakh, C.S., On the consistency of MSGUT spectra (2005) Phys. Rev. D, 72. , arxiv:hep-ph/0501025
Kuipers, J., Ueda, T., Vermaseren, J.A.M., Vollinga, J., FORM version 4.0 (2013) Comput. Phys. Comm., 184, p. 1453. , arxiv:1203.6543 [cs.SC]
Horst, C., Reuter, J., CleGo: A package for automated computation of Clebsch-Gordan coefficients in tensor product representations for Lie Algebras A - G (2011) Comput. Phys. Comm., 182, p. 1543. , arxiv:1011.4008 [math-ph]
Fonseca, R.M., Calculating the renormalisation group equations of a SUSY model with Susyno (2012) Comput. Phys. Comm., 183, p. 2298. , arxiv:1106.5016 [hep-ph]
Staub, F., SARAH 4: A tool for (not only SUSY) model builders (2014) Comput. Phys. Comm., 185, p. 1773. , arxiv:1309.7223 [hep-ph]
West, P.C., Supergravity, brane dynamics and string duality, in:∗Cambridge (1997) Duality and Supersymmetric Theories∗, pp. 147-266. , arxiv:hep-th/9811101
