The photino sector and a confining potential in a supersymmetric Lorentz-symmetry-violating model

  • H. Belich
  • L. D. Bernald
  • Patricio Gaete
  • J. A. Helayël-Neto
Regular Article - Theoretical Physics

Abstract

We study the spectrum of the minimal supersymmetric extension of the Carroll–Field–Jackiw model for Electrodynamics with a topological Chern–Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the gauge-invariant but path-dependent variables formalism which are alternative to the Wilson loop approach. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges.

Keywords

Dispersion Relation SUSY Breaking Lorentz Symmetry Majorana Fermion Standard Model Extension 

Notes

Acknowledgements

The authors (HB, LDB and JAH-N) express their gratitude to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq-Brazil) for the financial support. P.G. was partially supported by Fondecyt (Chile) grant 1130426.

References

  1. 1.
    D. Colladay, V.A. Kostelecký, Phys. Rev. D 55, 6760 (1997) ADSGoogle Scholar
  2. 2.
    D. Colladay, V.A. Kostelecký, Phys. Rev. D 58, 116002 (1998) ADSGoogle Scholar
  3. 3.
    V.A. Kostelecky, S. Samuel, Phys. Rev. Lett. 63, 224 (1989) ADSGoogle Scholar
  4. 4.
    V.A. Kostelecky, S. Samuel, Phys. Rev. Lett. 66, 1811 (1991) ADSGoogle Scholar
  5. 5.
    V.A. Kostelecky, S. Samuel, Phys. Rev. D 39, 683 (1989) ADSGoogle Scholar
  6. 6.
    V.A. Kostelecky, S. Samuel, Phys. Rev. D 40, 1886 (1989) ADSGoogle Scholar
  7. 7.
    V.A. Kostelecky, R. Potting, Nucl. Phys. B 359, 545 (1991) MathSciNetADSGoogle Scholar
  8. 8.
    V.A. Kostelecky, R. Potting, Phys. Lett. B 381, 89 (1996) ADSGoogle Scholar
  9. 9.
    V.A. Kostelecky, R. Potting, Phys. Rev. D 51, 3923 (1995) ADSGoogle Scholar
  10. 10.
    C. Adam, F.R. Klinkhamer, Nucl. Phys. B 607, 247 (2001) ADSMATHGoogle Scholar
  11. 11.
    C. Adam, F.R. Klinkhamer, Nucl. Phys. B 657, 214 (2003) ADSGoogle Scholar
  12. 12.
    C. Adam, F.R. Klinkhamer, Phys. Lett. B 513, 245 (2001) ADSMATHGoogle Scholar
  13. 13.
    C. Kaufhold, F.R. Klinkhamer, Nucl. Phys. B 734, 1 (2006) ADSMATHGoogle Scholar
  14. 14.
    R. Montemayor, L.F. Urrutia, Phys. Rev. D 72, 045018 (2005) ADSGoogle Scholar
  15. 15.
    X. Xue, J. Wu, Eur. Phys. J. C 48, 257 (2006) ADSGoogle Scholar
  16. 16.
    A.A. Andrianov, R. Soldati, Phys. Rev. D 51, 5961 (1995) ADSGoogle Scholar
  17. 17.
    A.A. Andrianov, R. Soldati, Phys. Lett. B 435, 449 (1998) ADSGoogle Scholar
  18. 18.
    A.A. Andrianov, R. Soldati, L. Sorbo, Phys. Rev. D 59, 025002 (1999) MathSciNetADSGoogle Scholar
  19. 19.
    Q.G. Bailey, V.A. Kostelecky, Phys. Rev. D 70, 076006 (2004) ADSGoogle Scholar
  20. 20.
    M. Frank, I. Turan, Phys. Rev. D 74, 033016 (2006) ADSGoogle Scholar
  21. 21.
    B. Altschul, Phys. Rev. D 72, 085003 (2005) ADSGoogle Scholar
  22. 22.
    R. Lehnert, R. Potting, Phys. Rev. Lett. 93, 110402 (2004) ADSGoogle Scholar
  23. 23.
    R. Lehnert, R. Potting, Phys. Rev. D 70, 125010 (2004) ADSGoogle Scholar
  24. 24.
    B. Altschul, Phys. Rev. Lett. 98, 041603 (2007) ADSGoogle Scholar
  25. 25.
    B. Altschul, Phys. Rev. D 72, 085003 (2005) ADSGoogle Scholar
  26. 26.
    B. Altschul, Phys. Rev. D 73, 036005 (2006) MathSciNetADSGoogle Scholar
  27. 27.
    B. Altschul, Phys. Rev. D 73, 045004 (2006) MathSciNetADSGoogle Scholar
  28. 28.
    M.B. Cantcheff, Eur. Phys. J. C 46, 247–254 (2006) ADSGoogle Scholar
  29. 29.
    H. Belich et al., Rev. Bras. Ensino Fis. 29, 57 (2007) Google Scholar
  30. 30.
    R. Jackiw, V.A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999) ADSGoogle Scholar
  31. 31.
    J.M. Chung, B.K. Chung, Phys. Rev. D 63, 105015 (2001) ADSGoogle Scholar
  32. 32.
    J.M. Chung, Phys. Rev. D 60, 127901 (1999) ADSGoogle Scholar
  33. 33.
    G. Bonneau, Nucl. Phys. B 593, 398 (2001) MathSciNetADSMATHGoogle Scholar
  34. 34.
    M. Perez-Victoria, Phys. Rev. Lett. 83, 2518 (1999) ADSGoogle Scholar
  35. 35.
    M. Perez-Victoria, J. High Energy Phys. 0104, 032 (2001) MathSciNetADSGoogle Scholar
  36. 36.
    O.A. Battistel, G. Dallabona, Nucl. Phys. B 610, 316 (2001) ADSMATHGoogle Scholar
  37. 37.
    O.A. Battistel, G. Dallabona, J. Phys. G 28, L23 (2002) ADSGoogle Scholar
  38. 38.
    O.A. Battistel, G. Dallabona, J. Phys. G 27, L53 (2002) Google Scholar
  39. 39.
    A.P. Baêta Scarpelli, M. Sampaio, M.C. Nemes, B. Hiller, Phys. Rev. D 64, 046013 (2001) ADSGoogle Scholar
  40. 40.
    F.A. Brito, T. Mariz, J.R. Nascimento, E. Passos, R.F. Ribeiro, J. High Energy Phys. 0510, 019 (2005) MathSciNetGoogle Scholar
  41. 41.
    B. Altschul, Phys. Rev. D 70, 056005 (2004) ADSGoogle Scholar
  42. 42.
    G.M. Shore, Nucl. Phys. B 717, 86 (2005) ADSGoogle Scholar
  43. 43.
    D. Colladay, V.A. Kostelecky, Phys. Lett. B 511, 209 (2001) ADSGoogle Scholar
  44. 44.
    M.M. Ferreira Jr., Phys. Rev. D 70, 045013 (2004) ADSGoogle Scholar
  45. 45.
    M.M. Ferreira Jr., Phys. Rev. D 71, 045003 (2005) MathSciNetADSGoogle Scholar
  46. 46.
    M.M. Ferreira Jr., M.S. Tavares, Int. J. Mod. Phys. A 22, 1685 (2007) ADSMATHGoogle Scholar
  47. 47.
    J. Alfaro, A.A. Andrianov, M. Cambiaso, P. Giacconi, R. Soldati, Phys. Lett. B 639, 586–590 (2006) ADSGoogle Scholar
  48. 48.
    V. Barger, S. Pakvasa, T.J. Weiler, K. Whisnant, Phys. Rev. Lett. 85, 5055 (2000) ADSGoogle Scholar
  49. 49.
    V.A. Kostelecky, M. Mewes, Phys. Rev. D 69, 016005 (2004) ADSGoogle Scholar
  50. 50.
    V.A. Kostelecky, M. Mewes, Phys. Rev. D 70, 031902(R) (2004) ADSGoogle Scholar
  51. 51.
    V.A. Kostelecky, M. Mewes, Phys. Rev. D 70, 076002 (2004) ADSGoogle Scholar
  52. 52.
    T. Katori, A. Kostelecky, R. Tayloe, Phys. Rev. D 74, 105009 (2006) ADSGoogle Scholar
  53. 53.
    R. Brustein, D. Eichler, S. Foffa, Phys. Rev. D 65, 105006 (2002) MathSciNetADSGoogle Scholar
  54. 54.
    Y. Grossman, C. Kilic, J. Thaler, D.G.E. Walker, Phys. Rev. D 72, 125001 (2005) ADSGoogle Scholar
  55. 55.
    L.B. Auerbach et al., Phys. Rev. D 72, 076004 (2005) ADSGoogle Scholar
  56. 56.
    D. Hooper, D. Morgan, E. Winstanley, Phys. Rev. D 72, 065009 (2005) ADSGoogle Scholar
  57. 57.
    M. Lubo, Phys. Rev. D 71, 047701 (2005) ADSGoogle Scholar
  58. 58.
    M.N. Barreto, D. Bazeia, R. Meneses, Phys. Rev. D 73, 065015 (2006) ADSGoogle Scholar
  59. 59.
    H. Belich, T. Costa-Soares, M.M. Ferreira Jr., J.A. Helay ël-Neto, M.T.D. Orlando, Phys. Lett. B 639, 678 (2006) ADSGoogle Scholar
  60. 60.
    H. Belich, E.O. Silva, M.M. Ferreira Jr., M.T.D. Orlando, Phys. Rev. D 83, 125025 (2011) ADSGoogle Scholar
  61. 61.
    K. Bakke, H. Belich, Eur. Phys. J. Plus 127, 102 (2012) Google Scholar
  62. 62.
    K. Bakke, H. Belich, E.O. Silva, Ann. Phys. 523, 910 (2011) Google Scholar
  63. 63.
    K. Bakke et al., J. Math. Phys. 52, 063505 (2011) MathSciNetADSGoogle Scholar
  64. 64.
    K. Bakke, H. Belich, J. Phys. G, Nucl. Part. Phys. 39, 085001 (2012) ADSGoogle Scholar
  65. 65.
    K. Bakke, E.O. Silva, H. Belich, J. Phys. G, Nucl. Part. Phys. 39, 055004 (2012) ADSGoogle Scholar
  66. 66.
    H. Belich et al., Phys. Rev. D 86, 125037 (2012) ADSGoogle Scholar
  67. 67.
    O. Gagnon, G.D. Moore, Phys. Rev. D 70, 065002 (2004) ADSGoogle Scholar
  68. 68.
    J.W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003) MathSciNetADSMATHGoogle Scholar
  69. 69.
    F.W. Stecker, S.T. Scully, Astropart. Phys. 23, 203 (2005) ADSGoogle Scholar
  70. 70.
    F.W. Stecker, S.L. Glashow, Astropart. Phys. 16, 97 (2001) ADSGoogle Scholar
  71. 71.
    E.O. Iltan, Eur. Phys. J. C 40, 269 (2005) ADSGoogle Scholar
  72. 72.
    E.O. Iltan, Mod. Phys. Lett. A 19, 327 (2004) ADSMATHGoogle Scholar
  73. 73.
    E.O. Iltan, J. High Energy Phys. 0306, 016 (2003) Google Scholar
  74. 74.
    V.A. Kostelecky, R. Lehnert, Phys. Rev. D 63, 065008 (2001) MathSciNetADSGoogle Scholar
  75. 75.
    R. Lehnert, Phys. Rev. D 68, 085003 (2003) MathSciNetADSGoogle Scholar
  76. 76.
    H. Belich, M.A. De Andrade, M.A. Santos, Mod. Phys. Lett. A 20, 2305 (2005) ADSMATHGoogle Scholar
  77. 77.
    H. Belich, T. Costa-Soares, M.M. Ferreira Jr., J.A. Helayël-Neto, M.T.D. Orlando, Int. J. Mod. Phys. A 21, 2415 (2006) ADSGoogle Scholar
  78. 78.
    A.P. Baeta Scarpelli, J.A. Helayel-Neto, Phys. Rev. D 73, 105020 (2006) ADSGoogle Scholar
  79. 79.
    N.M. Barraz Jr., J.M. Fonseca, W.A. Moura-Melo, J.A. Helayel-Neto, Phys. Rev. D 76, 027701 (2007) ADSGoogle Scholar
  80. 80.
    H. Belich et al., Phys. Lett. A 370, 126–130 (2007) ADSGoogle Scholar
  81. 81.
    R. Casana, M.M. Ferreira, J.S. Rodrigues, Phys. Rev. D 78, 125013 (2008) ADSGoogle Scholar
  82. 82.
    R. Casana et al., Phys. Rev. D 78, 105014 (2008) ADSGoogle Scholar
  83. 83.
    R. Casana et al., Phys. Rev. D 78, 025030 (2008) ADSGoogle Scholar
  84. 84.
    R. Casana et al., Phys. Rev. D 80, 125040 (2009) MathSciNetADSGoogle Scholar
  85. 85.
    R. Casana et al., Phys. Rev. D 80, 085026 (2009) MathSciNetADSGoogle Scholar
  86. 86.
    R. Casana et al., Eur. Phys. J. C 62, 573–578 (2009) ADSMATHGoogle Scholar
  87. 87.
    S.R. Coleman, S.L. Glashow, Phys. Rev. D 59, 116008 (1999) ADSGoogle Scholar
  88. 88.
    V.A. Kostelecky, M. Mewes, Phys. Rev. Lett. 87, 251304 (2001) ADSGoogle Scholar
  89. 89.
    V.A. Kostelecky, M. Mewes, Phys. Rev. D 66, 056005 (2002) ADSGoogle Scholar
  90. 90.
    J. Lipa et al., Phys. Rev. Lett. 90, 060403 (2003) ADSGoogle Scholar
  91. 91.
    R. Bluhm, V.A. Kostelecky, N. Russell, Phys. Rev. Lett. 79, 1432 (1997) ADSGoogle Scholar
  92. 92.
    R. Bluhm, V.A. Kostelecky, N. Russell, Phys. Rev. D 57, 3932 (1998) ADSGoogle Scholar
  93. 93.
    R. Bluhm, V.A. Kostelecky, C.D. Lane, N. Russell, Phys. Rev. Lett. 88, 090801 (2002) ADSGoogle Scholar
  94. 94.
    R. Bluhm, V.A. Kostelecky, Phys. Rev. Lett. 84, 1381 (2000) ADSGoogle Scholar
  95. 95.
    R. Bluhm, R. Bluhm, V.A. Kostelecky, C.D. Lane, Phys. Rev. Lett. 84, 1098 (2000) ADSGoogle Scholar
  96. 96.
    V.A. Kostelecky, N. Russell, Phys. Rev. Lett. 82, 2254 (1999) ADSGoogle Scholar
  97. 97.
    V.A. Kostelecky, C. Lane, Phys. Rev. D 60, 116010 (1999) ADSGoogle Scholar
  98. 98.
    V.A. Kostelecky, C.D. Lane, J. Math. Phys. 40, 6245 (1999) MathSciNetADSMATHGoogle Scholar
  99. 99.
    R. Lehnert, J. Math. Phys. 45, 3399 (2004) MathSciNetADSMATHGoogle Scholar
  100. 100.
    M.M. Ferreira Jr., F.M.O. Moucherek, Int. J. Mod. Phys. A 21, 6211 (2006) ADSMATHGoogle Scholar
  101. 101.
    M.M. Ferreira Jr., F.M.O. Moucherek, Nucl. Phys. A 790, 635 (2007) ADSGoogle Scholar
  102. 102.
    S. Chen, B. Wang, R. Su, Class. Quantum Gravity 23, 7581 (2006) MathSciNetADSMATHGoogle Scholar
  103. 103.
    O.G. Kharlanov, V.Ch. Zhukovsky, J. Math. Phys. 48, 092302 (2007) MathSciNetADSGoogle Scholar
  104. 104.
    M. Frank, I. Turan, I. Yurdusen, 0709.4276 [hep-th]
  105. 105.
    H. Muller, C. Braxmaier, S. Herrmann, A. Peters, Phys. Rev. D 67, 056006 (2003) ADSGoogle Scholar
  106. 106.
    H. Müller, A. Saenz, A. Peters, C. Lämmerzahl, Phys. Rev. D 68, 116006 (2003) ADSGoogle Scholar
  107. 107.
    H. Müller, Phys. Rev. D 71, 045004 (2005) ADSGoogle Scholar
  108. 108.
    N. Russell, Phys. Scr. 72, C38 (2005) Google Scholar
  109. 109.
    D.F. Phillips, M.A. Humphrey, E.M. Mattison, R.E. Stoner, R.F.C. Vessot, R.L. Walsworth, Phys. Rev. D 63, 111101 (2001) ADSGoogle Scholar
  110. 110.
    D. Bear, R.E. Stoner, R.L. Walsworth, V.A. Kostelecky, C.D. Lane, Phys. Rev. Lett. 85, 5038 (2000). Erratum-ibid. 89, 209902 (2002) ADSGoogle Scholar
  111. 111.
    M.A. Humphrey, D.F. Phillips, R.L. Walsworth, Phys. Rev. A 68, 063807 (2003) ADSGoogle Scholar
  112. 112.
    D. Colladay, P. MacDonald, Phys. Rev. D 83, 025021 (2011) ADSGoogle Scholar
  113. 113.
    M.S. Berger, V.A. Kostelecky, Phys. Rev. D 65, 091701 (2002) ADSGoogle Scholar
  114. 114.
    C.F. Farias, A.C. Lehum, J.R. Nascimento, A.Yu. Petrov, Phys. Rev. D 86, 065035 (2012) ADSGoogle Scholar
  115. 115.
    P.A. Bolokhov, S. Nibbelink Groot, M. Pospelov, Phys. Rev. D 72, 015013 (2005) ADSGoogle Scholar
  116. 116.
    A. Katz, Y. Shadmi, Phys. Rev. D 74, 115021 (2006) ADSGoogle Scholar
  117. 117.
    S. Groot Nibbelink, M. Pospelov, Phys. Rev. Lett. 94, 081601 (2005) MathSciNetADSGoogle Scholar
  118. 118.
    J.A. Helayël-Neto, H. Belich, G.S. Dias, F.J.L. Leal, W. Spalenza, A discussion on the role of fermionic supersymmetric partners in Lorentz-symmetry breaking, in Proceedings of Science, PoS—ICFI2010 (2010), p. 032 Google Scholar
  119. 119.
    D. Redigolo, Phys. Rev. D 85, 085009 (2012) ADSGoogle Scholar
  120. 120.
    E.T. Tomboulis, Phys. Rev. D 85, 024042 (2012) ADSGoogle Scholar
  121. 121.
    P. Gaete, E. Spallucci, Phys. Lett. B 675, 145 (2009) ADSGoogle Scholar
  122. 122.
    P. Gaete, J.A. Helayel-Neto, Phys. Lett. B 683, 211 (2010) MathSciNetADSGoogle Scholar
  123. 123.
    S. Carroll, G. Field, R. Jackiw, Phys. Rev. D 41, 1231 (1990) ADSGoogle Scholar
  124. 124.
    P. Gaete, E. Spallucci, Phys. Rev. D 77, 027702 (2008) MathSciNetADSGoogle Scholar
  125. 125.
    P. Gaete, E. Spallucci, J. Phys. A, Math. Theor. 41, 185401 (2008) MathSciNetGoogle Scholar
  126. 126.
    A.P. Baeta Scarpelli, H. Belich, J.L. Boldo, L.P. Colatto, J.A. Helayël-Neto, A.L.M.A. Nogueira, Nucl. Phys. B, Proc. Suppl. 127, 105–109 (2004) ADSGoogle Scholar
  127. 127.
    P. Gaete, I. Schmidt, Phys. Rev. D 61, 125002 (2000) ADSGoogle Scholar
  128. 128.
    P. Gaete, Phys. Rev. D 59, 127702 (1999) ADSGoogle Scholar
  129. 129.
    P. Gaete, Z. Phys. C 76, 355 (1997) Google Scholar
  130. 130.
    P. Dirac, Can. J. Phys. 33, 650 (1955) MathSciNetADSMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • H. Belich
    • 1
  • L. D. Bernald
    • 2
  • Patricio Gaete
    • 3
  • J. A. Helayël-Neto
    • 2
  1. 1.Departamento de Física e QuímicaUniversidade Federal do Espírito SantoVitóriaBrasil
  2. 2.Centro Brasileiro de Pesquisas FísicasRio de JaneiroBrasil
  3. 3.Departmento de Física and Centro Científico-Tecnológico de ValparaísoUniversidad Técnica Federico Santa MaríaValparaísoChile

Personalised recommendations