Advertisement

Theory and phenomenology of μ in M theory

  • Bobby Samir Acharya
  • Gordon Kane
  • Eric Kuflik
  • Ran Lu
Article

Abstract

We consider a solution to the μ-problem within M theory on a G 2-manifold. Our study is based upon the discrete symmetry proposed by Witten that forbids the μ-term and solves the doublet-triplet splitting problem. We point out that the symmetry must be broken by moduli stabilization, describing in detail how this can occur. The μ-term is generated via Kahler interactions after strong dynamics in the hidden sector generate a potential which stabilizes all moduli and breaks supersymmetry with m 3/2 ∼ 20–30 TeV. We show that μ is suppressed relative to the gravitino mass, by higher dimensional operators, μ ∼ 0.1m 3/2 ∼ 2–3 TeV. This necessarily gives a Higgsino component to the (mostly Wino) LSP, and a small but non-negligible LSP-nucleon scattering cross-section. The maximum spin-independent cross-sections are not within reach of the current XENON100 experiment, but are within reach of upcoming runs and upgrades.

Keywords

Strings and branes phenomenology 

References

  1. [1]
    S.P. Martin, A supersymmetry primer, hep-ph/9709356 [SPIRES].
  2. [2]
    J.E. Kim and H.P. Nilles, The μ problem and the strong CP problem, Phys. Lett. B 138 (1984) 150 [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Effective μ term in superstring theory, Nucl. Phys. B 432 (1994) 187 [hep-th/9405024] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    P. Nath and T.R. Taylor, Modular invariance, soft breaking, μ and tan β in superstring models, Phys. Lett. B 548 (2002) 77 [hep-ph/0209282] [SPIRES].ADSGoogle Scholar
  5. [5]
    D. Suematsu and Y. Yamagishi, Radiative symmetry breaking in a supersymmetric model with an extra U(1), Int. J. Mod. Phys. A 10 (1995) 4521 [hep-ph/9411239] [SPIRES].ADSGoogle Scholar
  6. [6]
    M. Cvetič and P. Langacker, Implications of abelian extended gauge structures from string models, Phys. Rev. D 54 (1996) 3570 [hep-ph/9511378] [SPIRES].ADSGoogle Scholar
  7. [7]
    M. Cvetič, D.A. Demir, J.R. Espinosa, L.L. Everett and P. Langacker, Electroweak breaking and the μ problem in supergravity models with an additional U(1), Phys. Rev. D 56 (1997) 2861 [hep-ph/9703317] [SPIRES].ADSGoogle Scholar
  8. [8]
    O. Lebedev and S. Ramos-Sanchez, The NMSSM and string theory, Phys. Lett. B 684 (2010) 48 [arXiv:0912.0477] [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    S. Ramos-Sanchez, The μ-problem, the NMSSM and string theory, Fortsch. Phys. 58 (2010) 748 [arXiv:1003.1307] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    M. Ratz, Stringy surprises, Prog. Theor. Phys. Suppl. 180 (2010) 96 [arXiv:1003.0549] [SPIRES].ADSCrossRefGoogle Scholar
  11. [11]
    J.A. Casas and C. Muñoz, A natural solution to the μ problem, Phys. Lett. B 306 (1993) 288 [hep-ph/9302227] [SPIRES].ADSGoogle Scholar
  12. [12]
    R. Kappl et al., Large hierarchies from approximate R symmetries, Phys. Rev. Lett. 102 (2009) 121602 [arXiv:0812.2120] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    L.E. Ibáñez and A.M. Uranga, Instanton induced open string superpotentials and branes at singularities, JHEP 02 (2008) 103 [arXiv:0711.1316] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    L.E. Ibáñez and R. Richter, Stringy instantons and Yukawa couplings in MSSM-like orientifold models, JHEP 03 (2009) 090 [arXiv:0811.1583] [SPIRES].ADSCrossRefGoogle Scholar
  15. [15]
    D. Green and T. Weigand, Retrofitting and the μ problem, arXiv:0906.0595 [SPIRES].
  16. [16]
    M. Cvetič, J. Halverson and R. Richter, 2, Realistic Yukawa structures from orientifold compactifications, JHEP 12 (2009) 063 [arXiv:0905.3379] [SPIRES].ADSCrossRefGoogle Scholar
  17. [17]
    P. Langacker and M.-X. Luo, Implications of precision electroweak experiments for M t , ρ 0 , sin2 ΘW and grand unification, Phys. Rev. D 44 (1991) 817 [SPIRES].ADSGoogle Scholar
  18. [18]
    H. Murayama and A. Pierce, Not even decoupling can save minimal supersymmetric SU(5), Phys. Rev. D 65 (2002) 055009 [hep-ph/0108104] [SPIRES].ADSGoogle Scholar
  19. [19]
    E. Witten, Deconstruction, G 2 holonomy and doublet-triplet splitting, hep-ph/0201018 [SPIRES].
  20. [20]
    B.S. Acharya, K. Bobkov, G. Kane, P. Kumar and D. Vaman, An M-theory solution to the hierarchy problem, Phys. Rev. Lett. 97 (2006) 191601 [hep-th/0606262] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    B.S. Acharya, On realising N =1 super Yang-Mills in M-theory, hep-th/0011089 [SPIRES].
  22. [22]
    B.S. Acharya, M theory, Joyce orbifolds and super Yang-Mills, Adv. Theor. Math. Phys. 3 (1999) 227 [hep-th/9812205] [SPIRES].MathSciNetMATHGoogle Scholar
  23. [23]
    E. Witten, Anomaly cancellation on G 2 manifolds, hep-th/0108165 [SPIRES].
  24. [24]
    B.S. Acharya and E. Witten, Chiral fermions from manifolds of G 2 holonomy, hep-th/0109152 [SPIRES].
  25. [25]
    B.S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds, Phys. Rept. 392 (2004) 121 [hep-th/0409191] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    T. Pantev and M. Wijnholt, Hitchin’s equations and M-theory phenomenology, J. Geom. Phys. 61 (2011) 1223 [arXiv:0905.1968] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  27. [27]
    M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [SPIRES].MathSciNetADSGoogle Scholar
  28. [28]
    S.M. Barr, A new symmetry breaking pattern for SO(10) and proton decay, Phys. Lett. B 112 (1982) 219 [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    J.P. Derendinger, J.E. Kim and D.V. Nanopoulos, Anti-SU(5), Phys. Lett. B 139 (1984) 170 [SPIRES].ADSGoogle Scholar
  30. [30]
    I. Antoniadis, J.R. Ellis, J.S. Hagelin and D.V. Nanopoulos, Supersymmetric flipped SU(5) revitalized, Phys. Lett. B 194 (1987) 231 [SPIRES].ADSGoogle Scholar
  31. [31]
    E. Kuflik and J. Marsano, Comments on flipped SU(5) (and F-theory), JHEP 03 (2011) 020 [arXiv:1009.2510] [SPIRES].ADSCrossRefMathSciNetGoogle Scholar
  32. [32]
    B.S. Acharya, K. Bobkov, G.L. Kane, P. Kumar and J . Shao, Explaining the electroweak scale and stabilizing moduli in M-theory, Phys. Rev. D 76 (2007) 126010 [hep-th/0701034] [SPIRES].MathSciNetADSGoogle Scholar
  33. [33]
    B.S. Acharya, G. Kane and E. Kuflik, String theories with moduli stabilization imply non-thermal cosmological history and particular dark matter, arXiv:1006.3272 [SPIRES].
  34. [34]
    D.D. Joyce, Compact manifolds with special holonomy, Oxford University Press, Oxford U.K. (2000).MATHGoogle Scholar
  35. [35]
    B.S. Acharya, K. Bobkov, G.L. Kane, J. Shao and P. Kumar, The G 2 -MSSM — An M theory motivated model of particle physics, Phys. Rev. D 78 (2008) 065038 [arXiv:0801.0478] [SPIRES].ADSGoogle Scholar
  36. [36]
    Y. Hosotani, Dynamical gauge symmetry breaking as the Casimir effect, Phys. Lett. B 129 (1983) 193 [SPIRES].ADSGoogle Scholar
  37. [37]
    E. Witten, Symmetry breaking patterns in superstring models, Nucl. Phys. B 258 (1985) 75 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    H.M. Lee et al., A unique Z 4 R symmetry for the MSSM, Phys. Lett. B 694 (2011) 491 [arXiv:1009.0905] [SPIRES].ADSGoogle Scholar
  39. [39]
    G.F. Giudice and A. Masiero, A natural solution to the μ problem in supergravity theories, Phys. Lett. B 206 (1988) 480 [SPIRES].ADSGoogle Scholar
  40. [40]
    J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).Google Scholar
  41. [41]
    A. Brignole, L.E. Ibáñez and C. Muñoz, Soft supersymmetry-breaking terms from supergravity and superstring models, hep-ph/9707209 [SPIRES].
  42. [42]
    B.S. Acharya and M. Torabian, Supersymmetry breaking, moduli stabilization and hidden U(1) breaking in M-theory, arXiv:1101.0108 [SPIRES].
  43. [43]
    Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].ADSGoogle Scholar
  44. [44]
    M. Ambroso and B.A. Ovrut, The mass spectra, hierarchy and cosmology of B-L MSSM heterotic compactifications, arXiv:1005.5392 [SPIRES].
  45. [45]
    H.K. Dreiner, An introduction to explicit R -parity violation, hep-ph/9707435 [SPIRES].
  46. [46]
    M.H. Reno and D. Seckel, Primordial nucleosynthesis: the effects of injecting hadrons, Phys. Rev. D 37 (1988) 3441 [SPIRES].ADSGoogle Scholar
  47. [47]
    J.R. Ellis, G.B. Gelmini, J.L. Lopez, D.V. Nanopoulos and S. Sarkar, A strophysical constraints on massive unstable neutral relic particles, Nucl. Phys. B 373 (1992) 399 [SPIRES].ADSCrossRefGoogle Scholar
  48. [48]
    V. Berezinsky, A. Masiero and J.W.F. Valle, Cosmological signatures of supersymmetry with spontaneously broken R -parity, Phys. Lett. B 266 (1991) 382 [SPIRES].ADSGoogle Scholar
  49. [49]
    E.A. Baltz and P. Gondolo, Limits on R -parity violation from cosmic ray antiprotons, Phys. Rev. D 57 (1998) 7601 [hep-ph/9704411] [SPIRES].ADSGoogle Scholar
  50. [50]
    A. Arvanitaki et al., Decaying dark matter as a probe of unification and TeV spectroscopy, Phys. Rev. D 80 (2009) 055011 [arXiv:0904.2789] [SPIRES].ADSGoogle Scholar
  51. [51]
    S. Shirai, F. Takahashi and T.T. Yanagida, R-violating decay of Wino dark matter and electron/positron excesses in the PAMELA/Fermi experiments, Phys. Lett. B 680 (2009) 485 [arXiv:0905.0388] [SPIRES].ADSGoogle Scholar
  52. [52]
    S.F. King, G.K. Leontaris and G.G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    B.C. Allanach, SOFTSUSY:aprogram forcalculatingsupersymmetricspectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [SPIRES].ADSMATHCrossRefGoogle Scholar
  54. [54]
    D. Feldman, G. Kane, R. Lu and B.D. Nelson, Dark matter as a guide toward a light gluino at the LHC, Phys. Lett. B 687 (2010) 363 [arXiv:1002.2430] [SPIRES].ADSGoogle Scholar
  55. [55]
    J.L. Feng, K.T. Matchev and T. Moroi, Focus points and naturalness in supersymmetry, Phys. Rev. D 61 (2000) 075005 [hep-ph/9909334] [SPIRES].ADSGoogle Scholar
  56. [56]
    K.L. Chan, U. Chattopadhyay and P. Nath, Naturalness, weak scale supersymmetry and the prospect for the observation of supersymmetry at the Tevatron and at the LHC, Phys. Rev. D 58 (1998) 096004 [hep-ph/9710473] [SPIRES].ADSGoogle Scholar
  57. [57]
    D.M. Pierce, J.A. Bagger, K.T. Matchev and R.-j. Zhang, Precision corrections in the minimal supersymmetric standard model, Nucl. Phys. B 491 (1997) 3 [hep-ph/9606211] [SPIRES].ADSCrossRefGoogle Scholar
  58. [58]
    B.S. Acharya et al., Non-thermal dark matter and the moduli problem in string frameworks, JHEP 06 (2008) 064 [arXiv:0804.0863] [SPIRES].ADSCrossRefGoogle Scholar
  59. [59]
    B.S. Acharya, G. Kane, S. Watson and P. Kumar, A non-thermal WIMP miracle, Phys. Rev. D 80 (2009) 083529 [arXiv:0908.2430] [SPIRES].ADSGoogle Scholar
  60. [60]
    P. Grajek, G. Kane, D.J. Phalen, A. Pierce and S. Watson, Neutralino dark matter from indirect detection revisited, arXiv:0807.1508 [SPIRES].
  61. [61]
    J. Hisano, M. Kawasaki, K. Kohri and K. Nakayama, Positron/gamma-ray signatures of dark matter annihilation and Big-Bang nucleosynthesis, Phys. Rev. D 79 (2009) 063514 [arXiv:0810.1892] [SPIRES].ADSGoogle Scholar
  62. [62]
    G. Kane, R. Lu and S. Watson, PAMELA satellite data as a signal of non-thermal Wino LSP dark matter, Phys. Lett. B 681 (2009) 151 [arXiv:0906.4765] [SPIRES].ADSGoogle Scholar
  63. [63]
    D. Feldman, Z. Liu, P. Nath and B.D. Nelson, Explaining PAMELA and WMAP data through coannihilations in extended SUGRA with collider implications, Phys. Rev. D 80 (2009) 075001 [arXiv:0907.5392] [SPIRES].ADSGoogle Scholar
  64. [64]
    N. Chen, D. Feldman, Z. Liu, P. Nath and G. Peim, Higgsino dark matter model consistent with galactic cosmic ray data and possibility of discovery at LHC-7, Phys. Rev. D 83 (2011) 023506 [arXiv:1010.0939] [SPIRES].ADSGoogle Scholar
  65. [65]
    N. Chen, D. Feldman, Z. Liu, P. Nath and G. Peim, Low mass gluino within the sparticle landscape, implications for dark matter and early discovery prospects at LHC-7, Phys. Rev. D 83 (2011) 035005 [arXiv:1011.1246] [SPIRES].ADSGoogle Scholar
  66. [66]
    The CDMS-II collaboration, Z. Ahmed et al., Dark matter search results from the CDMS II experiment, Science 327 (2010) 1619 [arXiv:0912.3592] [SPIRES].ADSCrossRefGoogle Scholar
  67. [67]
    XENON100 collaboration, E. Aprile et al., Firstdarkmatterresultsfrom the XENON 100 experiment, Phys. Rev. Lett. 105 (2010) 131302 [arXiv:1005.0380] [SPIRES].ADSCrossRefGoogle Scholar
  68. [68]
    LEP Working Group for Higgs boson searches collaboration, R. Barate et al., Search for the standard model Higgs boson at LEP, Phys. Lett. B 565 (2003) 61 [hep-ex/0306033] [SPIRES].ADSGoogle Scholar
  69. [69]
    T. Cohen, D.J. Phalen and A. Pierce, On the correlation between the spin-independent and spin-dependent direct detection of dark matter, Phys. Rev. D 81 (2010) 116001 [arXiv:1001.3408] [SPIRES].ADSGoogle Scholar
  70. [70]
    M.M. El Kheishen, A.A. Aboshousha and A.A. Shafik, Analytic formulas for the neutralino masses and the neutralino mixing matrix, Phys. Rev. D 45 (1992) 4345 [SPIRES].ADSGoogle Scholar
  71. [71]
    V.D. Barger, M.S. Berger and P. Ohmann, The supersymmetric particle spectrum, Phys. Rev. D 49 (1994) 4908 [hep-ph/9311269] [SPIRES].ADSGoogle Scholar
  72. [72]
    G. Bertone, D. Hooper and J. Silk, Particle dark matter: evidence, candidates and constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175] [SPIRES].ADSCrossRefGoogle Scholar
  73. [73]
    P. Gondolo et al., DarkSUSY: computing supersymmetric dark matter properties numerically, JCAP 07 (2004) 008 [astro-ph/0406204] [SPIRES].ADSGoogle Scholar
  74. [74]
    PAMELA collaboration, O. Adriani et al., An anomalous positron abundance in cosmic rays with energies 1.5-100 GeV, Nature 458 (2009) 607 [arXiv:0810.4995] [SPIRES].ADSCrossRefGoogle Scholar
  75. [75]
    J.M. Frere and G.L. Kane, On the possibility of finding light uncolored supersymmetric partners at present and future machines, Nucl. Phys. B 223 (1983) 331 [SPIRES].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Bobby Samir Acharya
    • 1
    • 2
  • Gordon Kane
    • 1
  • Eric Kuflik
    • 1
  • Ran Lu
    • 1
  1. 1.Michigan Center for Theoretical PhysicsUniversity of MichiganAnn ArborU.S.A.
  2. 2.Abdus Salam International Centre for Theoretical PhysicsTriesteItaly

Personalised recommendations