Exact SU(5) Yukawa matrix unification in the general flavour violating MSSM

Open Access
Regular Article - Theoretical Physics


We investigate the possibility of satisfying the SU(5) boundary condition Y d = Y eT at the GUT scale within the renormalizable R-parity conserving Minimal Supersymmetric Standard Model (MSSM). Working in the super-CKM basis, we consider non-zero flavour off-diagonal entries in the soft SUSY-breaking mass matrices and the A-terms. At the same time, the diagonal A-terms are assumed to be suppressed by the respective Yukawa couplings. We show that a non-trivial flavour structure of the soft SUSY-breaking sector can contribute to achieving precise Yukawa coupling unification for all three families, and that the relevant flavour-violating parameters are \( \left({m}_{\tilde{d}}^2\right)23 \), \( \left({m}_{\tilde{d}}^2\right)12 \), \( \left({m}_{\tilde{d}}^2\right)13 \) and A 12/21 d . We indicate the parameter space regions where the Yukawa unification condition can be satisfied, and we demonstrate that it is consistent with a wide set of experimental constraints, including flavour and electroweak observables, Higgs physics and the LHC bounds. However, as a consequence of the down-electron Yukawa unification requirement, the MSSM vacuum in our scenario is metastable, though long-lived. We also point out that the lightest neutralino needs to be almost purely bino-like and relatively light, with the mass in the ballpark of 250 GeV. Since the proper value of the dark matter relic density is in this case obtained through co-annihilation with a sneutrino, at least one generation of sleptons must be light. Such a clear experimental prediction makes the flavour-violating SU(5) Yukawa unification scenario fully testable at the LHC \( \sqrt{s}=14 \) TeV with the 3-lepton searches for electroweakino production.


Supersymmetry Phenomenology 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    S. Dimopoulos and H. Georgi, Softly broken supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    H. Georgi and C. Jarlskog, A new leptonQuark mass relation in a unified theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D. Emmanuel-Costa and S. Wiesenfeldt, Proton decay in a consistent supersymmetric SU(5) GUT model, Nucl. Phys. B 661 (2003) 62 [hep-ph/0302272] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    S. Antusch and M. Spinrath, New GUT predictions for quark and lepton mass ratios confronted with phenomenology, Phys. Rev. D 79 (2009) 095004 [arXiv:0902.4644] [INSPIRE].ADSGoogle Scholar
  5. [5]
    S. Antusch, S.F. King and M. Spinrath, GUT predictions for quark-lepton Yukawa coupling ratios with messenger masses from non-singlets, Phys. Rev. D 89 (2014) 055027 [arXiv:1311.0877] [INSPIRE].ADSGoogle Scholar
  6. [6]
    W. Buchmüller and D. Wyler, CP violation and R invariance in supersymmetric models of strong and electroweak interactions, Phys. Lett. B 121 (1983) 321 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    L.J. Hall, V.A. Kostelecky and S. Raby, New flavor violations in supergravity models, Nucl. Phys. B 267 (1986) 415 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.L. Diaz-Cruz, H. Murayama and A. Pierce, Can supersymmetric loops correct the fermion mass relations in SU(5)?, Phys. Rev. D 65 (2002) 075011 [hep-ph/0012275] [INSPIRE].ADSGoogle Scholar
  9. [9]
    T. Enkhbat, SU(5) unification for Yukawas through SUSY threshold effects, arXiv:0909.5597 [INSPIRE].
  10. [10]
    M. Iskrzynski, Effects of supersymmetric threshold corrections on the Yukawa matrix unification, Eur. Phys. J. C 75 (2015) 51 [arXiv:1408.2165] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Crivellin, L. Hofer and J. Rosiek, Complete resummation of chirally-enhanced loop-effects in the MSSM with non-minimal sources of flavor-violation, JHEP 07 (2011) 017 [arXiv:1103.4272] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    A. Crivellin and U. Nierste, Supersymmetric renormalisation of the CKM matrix and new constraints on the squark mass matrices, Phys. Rev. D 79 (2009) 035018 [arXiv:0810.1613] [INSPIRE].ADSGoogle Scholar
  13. [13]
    A. Crivellin, Effective Higgs vertices in the generic MSSM, Phys. Rev. D 83 (2011) 056001 [arXiv:1012.4840] [INSPIRE].ADSGoogle Scholar
  14. [14]
    A. Crivellin and J. Girrbach, Constraining the MSSM sfermion mass matrices with light fermion masses, Phys. Rev. D 81 (2010) 076001 [arXiv:1002.0227] [INSPIRE].ADSGoogle Scholar
  15. [15]
    J. Guasch and J. Solà, FCNC top quark decays: a door to SUSY physics in high luminosity colliders?, Nucl. Phys. B 562 (1999) 3 [hep-ph/9906268] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    J.J. Cao et al., SUSY-induced FCNC top-quark processes at the large hadron collider, Phys. Rev. D 75 (2007) 075021 [hep-ph/0702264] [INSPIRE].ADSGoogle Scholar
  17. [17]
    S. Fichet, B. Herrmann and Y. Stoll, A new flavour imprint of SU(5)-like grand unification and its LHC signatures, Phys. Lett. B 742 (2015) 69 [arXiv:1403.3397] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  18. [18]
    B. Herrmann, M. Klasen and Q. Le Boulc’h, Impact of squark flavour violation on neutralino dark matter, Phys. Rev. D 84 (2011) 095007 [arXiv:1106.6229] [INSPIRE].ADSGoogle Scholar
  19. [19]
    S. Heinemeyer, W. Hollik, F. Merz and S. Penaranda, Electroweak precision observables in the MSSM with nonminimal flavor violation, Eur. Phys. J. C 37 (2004) 481 [hep-ph/0403228] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J. Cao, G. Eilam, K.-i. Hikasa and J.M. Yang, Experimental constraints on stop-scharm flavor mixing and implications in top-quark FCNC processes, Phys. Rev. D 74 (2006) 031701 [hep-ph/0604163] [INSPIRE].
  21. [21]
    M. Arana-Catania, S. Heinemeyer, M.J. Herrero and S. Penaranda, Higgs boson masses and B-physics constraints in non-minimal flavor violating SUSY scenarios, JHEP 05 (2012) 015 [arXiv:1109.6232] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Arana-Catania, S. Heinemeyer and M.J. Herrero, Updated constraints on general squark flavor mixing, Phys. Rev. D 90 (2014) 075003 [arXiv:1405.6960] [INSPIRE].ADSGoogle Scholar
  23. [23]
    K. Kowalska, Phenomenology of SUSY with general flavour violation, JHEP 09 (2014) 139 [arXiv:1406.0710] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A. Fowlie et al., The CMSSM favoring new territories: the impact of new LHC limits and a 125 GeV Higgs, Phys. Rev. D 86 (2012) 075010 [arXiv:1206.0264] [INSPIRE].ADSGoogle Scholar
  25. [25]
    F. Feroz, M.P. Hobson and M. Bridges, MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics, Mon. Not. Roy. Astron. Soc. 398 (2009) 1601 [arXiv:0809.3437] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    W. Porod and F. Staub, SPheno 3.1: extensions including flavour, CP-phases and models beyond the MSSM, Comput. Phys. Commun. 183 (2012) 2458 [arXiv:1104.1573] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].Google Scholar
  28. [28]
  29. [29]
    A. Crivellin et al., SUSY FLAVOR v2: a computational tool for FCNC and CP-violating processes in the MSSM, Comput. Phys. Commun. 184 (2013) 1004 [arXiv:1203.5023] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2014, arXiv:1412.7515 [INSPIRE].
  32. [32]
    M. Misiak et al., Estimate of \( B\left(\overline{B}\to {X}_s\gamma \right) \) at O(α s2), Phys. Rev. Lett. 98 (2007) 022002 [hep-ph/0609232] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    C. Bobeth et al., B s,d + in the standard model with reduced theoretical uncertainty, Phys. Rev. Lett. 112 (2014) 101801 [arXiv:1311.0903] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    J. Brod and M. Gorbahn, Next-to-next-to-leading-order charm-quark contribution to the cp-violation parameter ϵ K and ΔM K, Phys. Rev. Lett. 108 (2012) 121801 [arXiv:1108.2036] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    P. Gondolo et al., DarkSUSY: computing supersymmetric dark matter properties numerically, JCAP 07 (2004) 008 [astro-ph/0406204] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak and G. Weiglein, High-precision predictions for the light CP-even Higgs boson mass of the minimal supersymmetric standard model, Phys. Rev. Lett. 112 (2014) 141801 [arXiv:1312.4937] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    M. Frank et al., The Higgs boson masses and mixings of the complex MSSM in the Feynman-diagrammatic approach, JHEP 02 (2007) 047 [hep-ph/0611326] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein, Towards high precision predictions for the MSSM Higgs sector, Eur. Phys. J. C 28 (2003) 133 [hep-ph/0212020] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S. Heinemeyer, W. Hollik and G. Weiglein, FeynHiggs: a program for the calculation of the masses of the neutral CP even Higgs bosons in the MSSM, Comput. Phys. Commun. 124 (2000) 76 [hep-ph/9812320] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  40. [40]
    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds: confronting arbitrary Higgs sectors with exclusion bounds from LEP and the Tevatron, Comput. Phys. Commun. 181 (2010) 138 [arXiv:0811.4169] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  41. [41]
    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds 2.0.0: confronting neutral and charged Higgs sector predictions with exclusion bounds from LEP and the Tevatron, Comput. Phys. Commun. 182 (2011) 2605 [arXiv:1102.1898] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  42. [42]
    P. Bechtle et al., HiggsBounds-4: improved tests of extended Higgs sectors against exclusion bounds from LEP, the Tevatron and the LHC, Eur. Phys. J. C 74 (2014) 2693 [arXiv:1311.0055] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    P. Bechtle et al., HiggsSignals: confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC, Eur. Phys. J. C 74 (2014) 2711 [arXiv:1305.1933] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    LUX collaboration, D.S. Akerib et al., First results from the LUX dark matter experiment at the Sanford Underground Research Facility, Phys. Rev. Lett. 112 (2014) 091303 [arXiv:1310.8214] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    K. Cheung et al., Global study of the simplest scalar phantom dark matter model, JCAP 10 (2012) 042 [arXiv:1207.4930] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    K. Kowalska, L. Roszkowski, E.M. Sessolo and S. Trojanowski, Low fine tuning in the MSSM with higgsino dark matter and unification constraints, JHEP 04 (2014) 166 [arXiv:1402.1328] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].CrossRefGoogle Scholar
  48. [48]
    CMS collaboration, Combination of standard model Higgs boson searches and measurements of the properties of the new boson with a mass near 125 GeV, CMS-PAS-HIG-13-005 (2013).
  49. [49]
    CMS, LHCb collaboration, V. Khachatryan et al., Observation of the rare B s0 → μ + μ decay from the combined analysis of CMS and LHCb data, arXiv:1411.4413 [INSPIRE].
  50. [50]
    C.A. Baker et al., An improved experimental limit on the electric dipole moment of the neutron, Phys. Rev. Lett. 97 (2006) 131801 [hep-ex/0602020] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    CMS Collaboration, Search for direct production of bottom squark pairs, CMS-PAS-SUS-13-018 (2013).
  52. [52]
    ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using \( \sqrt{s}=8 \) TeV proton-proton collision data, JHEP 09 (2014) 176 [arXiv:1405.7875] [INSPIRE].ADSGoogle Scholar
  53. [53]
    ATLAS collaboration, Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, JHEP 05 (2014) 071 [arXiv:1403.5294] [INSPIRE].ADSGoogle Scholar
  54. [54]
    XENON1T collaboration, E. Aprile, The XENON1T dark matter search experiment, Springer Proc. Phys. C12-02-22 (2013) 93 [arXiv:1206.6288] [INSPIRE].
  55. [55]
    K. Kowalska and E.M. Sessolo, Natural MSSM after the LHC 8 TeV run, Phys. Rev. D 88 (2013) 075001 [arXiv:1307.5790] [INSPIRE].ADSGoogle Scholar
  56. [56]
    CMS collaboration, Search for direct EWK production of SUSY particles in multilepton modes with 8TeV data, CMS-PAS-SUS-12-022 (2012).
  57. [57]
    J.M. Frere, D.R.T. Jones and S. Raby, Fermion masses and induction of the weak scale by supergravity, Nucl. Phys. B 222 (1983) 11 [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    L. Álvarez-Gaumé, J. Polchinski and M.B. Wise, Minimal low-energy supergravity, Nucl. Phys. B 221 (1983) 495 [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    J.P. Derendinger and C.A. Savoy, Quantum effects and SU(2) × U(1) breaking in supergravity gauge theories, Nucl. Phys. B 237 (1984) 307 [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    C. Kounnas, A.B. Lahanas, D.V. Nanopoulos and M. Quirós, Low-energy behavior of realistic locally supersymmetric grand unified theories, Nucl. Phys. B 236 (1984) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    J.A. Casas, A. Lleyda and C. Muñoz, Strong constraints on the parameter space of the MSSM from charge and color breaking minima, Nucl. Phys. B 471 (1996) 3 [hep-ph/9507294] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    J.A. Casas and S. Dimopoulos, Stability bounds on flavor violating trilinear soft terms in the MSSM, Phys. Lett. B 387 (1996) 107 [hep-ph/9606237] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    J.-H. Park, Metastability bounds on flavour-violating trilinear soft terms in the MSSM, Phys. Rev. D 83 (2011) 055015 [arXiv:1011.4939] [INSPIRE].ADSGoogle Scholar
  64. [64]
    MEG collaboration, J. Adam et al., New constraint on the existence of the μ +e + γ decay, Phys. Rev. Lett. 110 (2013) 201801 [arXiv:1303.0754] [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsUniversity of WarsawWarsawPoland
  2. 2.National Centre for Nuclear ResearchWarsawPoland

Personalised recommendations