Abstract
We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. In both cases we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Moreover, we predict the masses of the other Higgses too, as well as the supersymmetric spectrum, the latter being in very confortable agreement with the LHC bounds on supersymmetric particles.
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J. C. Pati and A. Salam, “Is baryon number conserved?,” Phys. Rev. Lett. 31, 661–664 (1973); H. Georgi and S. L. Glashow, “Unity of all elementary particle forces,” Phys. Rev. Lett. 32, 438–441 (1974); H. Georgi, H. R. Quinn, and S. Weinberg, “Hierarchy of interactions in unified Gauge theories,” Phys. Rev. Lett. 33, 451–454 (1974); H. Fritzsch and P. Minkowski, “Unified interactions of leptons and hadrons,” Ann. Phys. 93, 193–266 (1975); H. Georgi, “Particles and Fields: Williamsburg 1974,” in AIP Conference Proceedings, No. 23, Ed. by C. E. Carlson (American Institute of Physics, New York DOI, 1974); S. Dimopoulos and H. Georgi, “Softly Broken supersymmetry and SU(5),” Nucl. Phys., Ser. B 193, 150 (1981); N. Sakai, “Naturalness in supersymmetric GUTs,” Zeit. Phys., Ser. C 11, 153 (1981).
D. Kapetanakis, M. Mondragon, and G. Zoupanos, “Finite unified models,” Z. Phys., Ser. C 60, 181–186 (1993), hep-ph/9210218; J. Kubo, M. Mondragon, and G. Zoupanos, “Reduction of couplings and heavy top quark in the minimal SUSY GUT,” Nucl. Phys., Ser. B 424, 291–307 (1994); J. Kubo, M. Mondragon, N. D. Tracas, and G. Zoupanos, “Gauge-Yukawa unification in asymptotically nonfree theories,” Phys. Lett., Ser. B 342, 155–162 (1995), hep-th/9409003; J. Kubo, M. Mondragon, M. Olechowski, and G. Zoupanos, “Gauge-Yukawa unification and the top-bottom hierarchy” (1995), hep-ph/9510279; M. Mondragon and G. Zoupanos, “Finite unified theories and the top quark mass,” Nucl. Phys. Proc. Suppl., Ser. C 37, 98–105 (1995).
J. Kubo, M. Mondragon, M. Olechowski, and G. Zoupanos, “Testing Gauge-Yukawa-unified models by M t,” Nucl. Phys., Ser. B 479, 25–45 (1996), hepph/9512435; J. Kubo, M. Mondragon, and G. Zoupanos, “Unification beyond GUTs: Gauge-Yukawa unification,” Acta Phys. Polon., Ser. B 27, 3911–3944 (1997), hep-ph/9703289; T. Kobayashi, J. Kubo, M. Mondragon, and G. Zoupanos, “Exact finite and Gauge-Yukawa unified theories and their predictions,” Acta Phys. Polon., Ser. B 30, 2013–2027 (1999).
J. Kubo, M. Mondragon, and G. Zoupanos, “Perturbative unification of soft supersymmetry-breaking terms,” Phys. Lett., Ser. B 389, 523–532 (1996), hepph/9609218.
W. Zimmermann, “Reduction in the number of coupling parameters,” Commun. Math. Phys. 97, 211 (1985); R. Oehme and W. Zimmermann, “Relation between effective couplings for asymptotically free models,” Commun. Math. Phys. 97, 569 (1985); R. Oehme, “Reduction and reparametrization of quantum field theories,” Prog. Theor. Phys. Suppl. 86, 215 (1986).
C. Lucchesi, O. Piguet, and K. Sibold, “Vanishing beta functions in N = 1 supersymmetric gauge theories,” Helv. Phys. Acta 61, 321 (1988); O. Piguet and K. Sibold, “Nonrenormalization theorems of chiral anomalies and finiteness in supersymmetric Yang-Mills theories,” Int. J. Mod. Phys., Ser. A 1, 913 (1986); C. Lucchesi and G. Zoupanos, “All-order finiteness in N = 1 SYM theories: criteria and applications,” Fortschr. Phys. 45, 129–143 (1997), hep-ph/9604216.
I. Jack and D. R. T. Jones, “Renormalization group invariance and universal soft supersymmetry breaking,” Phys. Lett., Ser. B 349, 294–299 (1995), hepph/9501395.
Y. Kawamura, T. Kobayashi, and J. Kubo, “Soft scalar-mass sum rule in Gauge-Yukawa unified models and its superstring interpretation,” Phys. Lett., Ser. B 405, 64–70 (1997), hep-ph/9703320.
T. Kobayashi, J. Kubo, M. Mondragon, and G. Zoupanos, “Constraints on finite soft supersymmetry-breaking terms,” Nucl. Phys., Ser. B 511, 45–68 (1998), hep-ph/9707425.
A. Parkes and P. C. West, “Finiteness in rigid supersym-metric theories,” Phys. Lett., Ser. B 138, 99 (1984); P. C. West, “The Yukawa beta function in N = 1 rigid supersymmetric theories,” Phys. Lett., Ser. B 137, 371 (1984); D. R. T. Jones and A. J. Parkes, “Search for a three loop finite chiral theory,” Phys. Lett., Ser. B 160, 267 (1985); D. R. T. Jones and L. Mezincescu, “The chiral anomaly and a class of two loop finite supersymmetric Gauge theories,” Phys. Lett., Ser. B 138, 293 (1984); A. J. Parkes, “Three loop finiteness conditions in N = 1 Superyang-Mills,” Phys. Lett., Ser. B 156, 73 (1985).
J. Wess and B. Zumino, “A Lagrangian model invariant under supergauge transformations,” Phys. Lett., Ser. B 49, 52 (1974); J. Iliopoulos and B. Zumino, “Broken supergauge symmetry and renormalization,” Nucl. Phys., Ser. B 76, 310 (1974).
K. Fujikawa and W. Lang, “Perturbation calculations for the scalar multiplet in a superfield formulation,” Nucl. Phys., Ser. B 88, 61 (1975).
R. Delbourgo, “Superfield perturbation theory and renormalization,” Nuovo Cim., Ser. A 25, 646 (1975); A. Salam and J. A. Strathdee, “Feynman rules for superfields,” Nucl. Phys., Ser. B 86, 142–152 (1975); M. T. Grisaru, W. Siegel, and M. Rocek, “Improved methods for supergraphs,” Nucl. Phys., Ser. B 159, 429 (1979).
L. Girardello and M. T. Grisaru, “Soft breaking of supersymmetry,” Nucl. Phys., Ser. B 194, 65 (1982).
J. Hisano and M. A. Shifman, “Exact results for soft supersymmetry breaking parameters in supersymmetric gauge theories,” Phys. Rev., Ser. D 56, 5475–5482 (1997), hep-ph/9705417; L. V. Avdeev, D. I. Kazakov, and I. N. Kondrashuk, “Renormalizations in softly broken SUSY Gauge theories,” Nucl. Phys., Ser. B 510, 289–312 (1998), hep-ph/9709397; D. I. Kazakov, “Exploring softly broken SUSY theories via grassmannian Taylor expansion,” Phys. Lett., Ser. B 449, 201–206 (1999), hep-ph/9812513.
I. Jack and D. R. T. Jones, “The gaugino beta-function,” Phys. Lett., Ser. B 415, 383–389 (1997), hepph/9709364.
D. I. Kazakov, “Finiteness of soft terms in finite N = 1 SUSY Gauge theories,” Phys. Lett., Ser. B 421, 211–216 (1998), hep-ph/9709465; I. Jack, D. R. T. Jones, and A. Pickering, “Renormalisation invariance and the soft beta functions,” Phys. Lett., Ser. B 426, 73–77 (1998), hep-ph/9712542.
V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Instanton effects in supersymmetric theories,” Nucl. Phys., Ser. B 229, 407 (1983); V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Beta function in supersymmetric Gauge theories: instantons versus traditional approach,” Phys. Lett., Ser. B 166, 329–333 (1986).
T. Kobayashi, J. Kubo, and G. Zoupanos, “Further all-loop results in softly-broken super-symmetric Gauge theories,” Phys. Lett., Ser. B 427, 291–299 (1998), hep-ph/9802267.
M. Mondragón, N. Tracas, and G. Zoupanos, “Reduction of couplings in the MSSM,” Phys. Lett., Ser. B 728, 51–57 (2014), 1309.0996.
I. Jack and D. Jones, “RG invariant solutions for the soft supersymmetry breaking parameters,” Phys. Lett., Ser. B 465, 148–154 (1999), hep-ph/9907255.
T. Kobayashi, J. Kubo, M. Mondragon, and G. Zoupanos, “Finite and Gauge-Yukawa unified theories: theory and predictions,” AIP Conf. Proc. 490, 279–309 (1999).
L. Randall and R. Sundrum, “Out of this world super-symmetry breaking,” Nucl. Phys., Ser. B 557, 79–118 (1999), hep-th/9810155.
R. Hodgson, I. Jack, D. Jones, and G. Ross, “Anomaly mediation, Fayet-Iliopoulos D-terms and precision sparticle spectra,” Nucl. Phys., Ser. B 728, 192–206 (2005), hep-ph/0507193.
M. S. Carena, M. Olechowski, S. Pokorski, and C. Wagner, “Electroweak symmetry breaking and bottom-top Yukawa unification,” Nucl. Phys., Ser. B 426, 269–300 (1994), hep-ph/9402253; J. Guasch, W. Hollik, and S. Penaranda, “Distinguishing Higgs models in H→b anti-b/H→tau+ tau−,” Phys. Lett., Ser. B 515, 367–374 (2001), hep-ph/0106027.
K. Nakamura et al., “Review of particle physics,” J. Phys., Ser. G 37, 075021 (2010).
M. S. Carena, H. Haber, S. Heinemeyer, et al., “Reconciling the two loop diagrammatic and effective field theory computations of the mass of the lightest CP—even Higgs boson in the MSSM,” Nucl. Phys. J., Ser. B 580, 29–57 (2000), hep-ph/0001002; S. Heinemeyer, “MSSM Higgs physics at higher orders,” Int. J. Mod. Phys., Ser. A 21, 2659–2772 (2006), hep-ph/0407244.
S. Heinemeyer, M. Mondragon, and G. Zoupanos, “Finite unified theories and the Higgs boson,” 1201.5171 (2012).
S. Chatrchyan et al., “Search for neutral Higgs bosons decaying to tau pairs in pp collisions at sqrt(s) = 7 TeV,” Phys. Lett., Ser. B 713, 68–90 (2012), 1202.4083; P. Pravalorio, “SUSY searches at ATLAS,” in SUSY2012 (2012); C. Campagnari, “SUSY searches at CMS,” in SUSY2012 (2012).
G. Degrassi, S. Heinemeyer, W. Hollik, et al., “Towards high-precision predictions for the MSSM Higgs sector,” Eur. Phys. J., Ser. C 28, 133–143 (2003), hep-ph/0212020.
G. Aad et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett., Ser. B 716, 1–29 (2012), 1207.7214; “Combined measurements of the mass and signal strength of the Higgs-like boson with the ATLAS detector using up to 25 fb-1 of proton-proton collision data,” in ATLAS-CONF-2013-014, ATLAS-COM-CONF-2013-025 (2013); S. Chatrchyan et al., “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Phys. Lett., Ser. B 716, 30–61 (2012), 1207.7235; S. Chatrchyan et al., “Observation of a new boson with mass near 125 GeV in pp collisions at sqrt(s) = 7 and 8 TeV,” 2013, 1303.4571.
D. R. T. Jones, L. Mezincescu, and Y. P. Yao, “Soft breaking of two loop finite N = 1 supersymmetric Gauge theories,” Phys. Lett., Ser. B 148, 317–322 (1984).
S. Heinemeyer, M. Mondragon, and G. Zoupanos, “Finite unification: theory, models and predictions,” 1101.2476 (2011).
A. V. Ermushev, D. I. Kazakov, and O. V. Tarasov, “Finite N = 1 Supersymmetric Grand Unified Theories,” Nucl. Phys., Ser. B 281, 72–84 (1987); D. I. Kazakov, “Finite N = 1 SUSY gauge field theories,” Mod. Phys. Lett., Ser. A 2, 663–674 (1987); R. G. Leigh and M. J. Strassler, “Exactly marginal operators and duality in four-dimensional N = 1 super-symmetric gauge theory,” Nucl. Phys., Ser. B 447, 95–136 (1995), hep-th/9503121.
M. A. Shifman, “Little miracles of supersymmetric evolution of gauge couplings,” Int. J. Mod. Phys., Ser. A 11, 5761–5784 (1996), hep-ph/9606281.
C. Lucchesi, O. Piguet, and K. Sibold, “Necessary and sufficient conditions for all order vanishing beta functions in supersymmetric Yang-Mills theories,” Phys. Lett., Ser. B 201, 241 (1988).
I. Jack and D. R. T. Jones, “Soft supersymmetry breaking and finiteness,” Phys. Lett., Ser. B 333, 372–379 (1994), hep-ph/9405233.
M. Mondragon and G. Zoupanos, “Finite unified theories,” J. Phys. Conf. Ser. 171, 012095 (2009).
J. Leon, J. Perez-Mercader, M. Quiros, and J. Ramirez-Mittelbrunn, “A sensible finite SU(5) susy GUT?,” Phys. Lett., Ser. B 156, 66 (1985); S. Hamidi and J. H. Schwarz, “A realistic Finite Unified Theory?,” Phys. Lett., Ser. B 147, 301 (1984); D. R. T. Jones and S. Raby, “A two loop finite supersymmetric SU(5) theory: towards a theory of fermion masses,” Phys. Lett., Ser. B 143, 137 (1984).
Heavy Flavour Averaging Group, www.slac.stanford.edu/xorg/hfag/.
R. Aaij et al., “Strong constraints on the rare decays B s → μ+μ− and B 0 → μ+μ−,” Phys. Rev. Lett. 108, 231801 (2012), 1203.4493.
CMS and LHCb Collab., http://cdsweb.cern.ch/record/1374913/files/BPH-11-019-pas.pdf.
S. Heinemeyer, W. Hollik, and G. Weiglein, “Feyn-Higgs: a program for the calculation of the masses of the neutral CP-even Higgs bosons in the MSSM,” Comput. Phys. Commun. 124, 76–89 (2000), hepph/9812320; S. Heinemeyer, W. Hollik, and G. Weiglein, “The masses of the neutral CP-even Higgs bosons in the MSSM: accurate analysis at the two-loop level,” Eur. Phys. J., Ser. C 9, 343–366 (1999), hep-ph/9812472; M. Frank et al., “The Higgs boson masses and mixings of the complex MSSM in the Feynman-diagrammatic approach,” JHEP 02, 047 (2007), hep-ph/0611326.
T. Hahn, S. Heinemeyer, W. Hollik, et al., “High-precision predictions for the light CP-even Higgs boson mass of the MSSM,” 1312.4937 (2013).
S. Heinemeyer, M. Mondragon, and G. Zoupanos, “Confronting finite unified theories with low-energy phenomenology,” JHEP 07, 135 (2008), 0712.3630; S. Heinemeyer, M. Mondragon, and G. Zoupanos, “Finiteness and the Higgs mass prediction,” 0810.0727 (2008); S. Heinemeyer, M. Mondragon, and G. Zoupanos, “Phenomenology of SU(5) finite unified theories,” J. Phys. Conf. Ser. 171, 012096 (2009).
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Heinemeyer, S., Mondragón, M., Tracas, N. et al. Reduction of couplings in a finite GUT and the MSSM. Phys. Part. Nuclei Lett. 11, 910–919 (2014). https://doi.org/10.1134/S1547477114070231
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DOI: https://doi.org/10.1134/S1547477114070231