Advertisement

Beautiful mathematics for beauty-full and other multi-heavy hadronic systems

  • K. Azizi
  • A. R. Olamaei
  • S. Rostami
Regular Article - Theoretical Physics
  • 30 Downloads

Abstract.

In most non-perturbative methods in hadron physics the calculations are started with a correlation function in terms of some interpolating and transition currents in x -space. For simplicity, the calculations are then transformed to the momentum space by a Fourier transformation. To suppress the contributions of the higher states and continuum, and enhance the ground state contribution, the Borel transformation as well as continuum subtraction are applied with the help of quark-hadron duality assumption. In the present study we work out the mathematics required for these processes in the case of light and multi-heavy hadrons. We address a well-known problem in the subtraction of the effects of the higher states and continuum and discuss how we find finite results without any divergence by using an appropriate representation of the modified Bessel functions, appearing in the heavy quark propagator, and successive applications of the Borel transformations, which lead to more suppression of the higher states and continuum contributions. The results obtained can be used in the determination of the spectroscopic and decay properties of the multi-heavy standard and non-conventional (exotic) systems in many non-perturbative methods, especially the QCD sum rules.

References

  1. 1.
    T.M. Aliev, K. Azizi, H. Sundu, Eur. Phys. J. C 78, 396 (2018) arXiv:1804.02656 [hep-ph]ADSCrossRefGoogle Scholar
  2. 2.
    T.M. Aliev, K. Azizi, H. Sundu, On the nature of $\Xi_c(2930)$, arXiv:1803.04002 [hep-ph]Google Scholar
  3. 3.
    K. Azizi, N. Er, Nucl. Phys. A 970, 422 (2018) arXiv:1801.02168 [hep-ph]ADSCrossRefGoogle Scholar
  4. 4.
    S.S. Agaev, K. Azizi, H. Sundu, Eur. Phys. J. C 77, 395 (2017) arXiv:1704.04928 [hep-ph]ADSCrossRefGoogle Scholar
  5. 5.
    SELEX Collaboration (M. Mattson et al.), Phys. Rev. Lett. 89, 112001 (2002) arXiv:hep-ex/0208014CrossRefGoogle Scholar
  6. 6.
    SELEX Collaboration (A. Ocherashvili et al.), Phys. Lett. B 628, 18 (2005) arXiv:hep-ex/0406033ADSCrossRefGoogle Scholar
  7. 7.
    LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 119, 112001 (2017) arXiv:1707.01621 [hep-ex]ADSCrossRefGoogle Scholar
  8. 8.
    R.L. Jaffe, Phys. Rev. D 15, 267 (1977)ADSCrossRefGoogle Scholar
  9. 9.
    R.L. Jaffe, Phys. Rev. D 15, 281 (1977)ADSCrossRefGoogle Scholar
  10. 10.
    N. Isgur, J.E. Paton, Phys. Rev. D 31, 2910 (1985)ADSCrossRefGoogle Scholar
  11. 11.
    A. De Rujula, H. Georgi, S.L. Glashow, Phys. Rev. Lett. 38, 317 (1977)ADSCrossRefGoogle Scholar
  12. 12.
    R.L. Jaffe, Phys. Rep. 409, 1 (2005) arXiv:hep-ph/ 0409065ADSCrossRefGoogle Scholar
  13. 13.
    R.L. Jaffe, K. Johnson, Phys. Lett. B 60, 201 (1976)ADSCrossRefGoogle Scholar
  14. 14.
    Belle Collaboration (S.K. Choi et al.), Phys. Rev. Lett. 91, 262001 (2003) arXiv:hep-ex/0309032CrossRefGoogle Scholar
  15. 15.
    LHCb Collaboration (R. Aaij et al.), Phys. Rev. Lett. 115, 072001 (2015) arXiv:1507.03414 [hep-ex]ADSCrossRefGoogle Scholar
  16. 16.
    K. Azizi, Y. Sarac, H. Sundu, Phys. Lett. B 782, 694 (2018) arXiv:1802.01384 [hep-ph]ADSCrossRefGoogle Scholar
  17. 17.
    S.S. Agaev, K. Azizi, H. Sundu, Phys. Lett. B 781, 279 (2018) arXiv:1711.11553 [hep-ph]ADSCrossRefGoogle Scholar
  18. 18.
    S.S. Agaev, K. Azizi, H. Sundu, Phys. Rev. D 93, 114036 (2016) arXiv:1605.02496 [hep-ph]ADSCrossRefGoogle Scholar
  19. 19.
    T.M. Aliev, A. Ozpineci, M. Savci, V.S. Zamiralov, Phys. Rev. D 80, 016010 (2009) arXiv:0905.4664 [hep-ph]ADSCrossRefGoogle Scholar
  20. 20.
    T.M. Aliev, K. Azizi, M. Savci, Phys. Rev. D 82, 096006 (2010) arXiv:1007.3389 [hep-ph]ADSCrossRefGoogle Scholar
  21. 21.
    T.M. Aliev, K. Azizi, M. Savci, Phys. Lett. B 696, 220 (2011) arXiv:1009.3658 [hep-ph]ADSCrossRefGoogle Scholar
  22. 22.
    T.M. Aliev, K. Azizi, M. Savci, Nucl. Phys. A 870-871, 58 (2011) arXiv:1102.5460 [hep-ph]ADSCrossRefGoogle Scholar
  23. 23.
    S.S. Agaev, K. Azizi, H. Sundu, Phys. Rev. D 96, 094011 (2017) arXiv:1708.07348 [hep-ph]ADSCrossRefGoogle Scholar
  24. 24.
    W. Roberts, M. Pervin, Int. J. Mod. Phys. A 23, 2817 (2008) arXiv:0711.2492 [nucl-th]ADSCrossRefGoogle Scholar
  25. 25.
    A. Valcarce, H. Garcilazo, J. Vijande, Eur. Phys. J. A 37, 217 (2008) arXiv:0807.2973 [hep-ph]ADSCrossRefGoogle Scholar
  26. 26.
    S.S. Agaev, K. Azizi, H. Sundu, Phys. Rev. D 93, 074024 (2016) arXiv:1602.08642 [hep-ph]ADSCrossRefGoogle Scholar
  27. 27.
    Q.F. Lü, Y.B. Dong, Phys. Rev. D 94, 094041 (2016) arXiv:1603.06417 [hep-ph]ADSCrossRefGoogle Scholar
  28. 28.
    Z.G. Wang, Eur. Phys. J. C 68, 479 (2010) arXiv:1001.1652 [hep-ph]ADSCrossRefGoogle Scholar
  29. 29.
    Z.G. Wang, Phys. Lett. B 685, 59 (2010) arXiv:0912.1648 [hep-ph]ADSCrossRefGoogle Scholar
  30. 30.
    S.S. Agaev, K. Azizi, H. Sundu, EPL 118, 61001 (2017) arXiv:1703.07091 [hep-ph]ADSCrossRefGoogle Scholar
  31. 31.
    D. Ebert, R.N. Faustov, V.O. Galkin, Phys. Rev. D 84, 014025 (2011) arXiv:1105.0583 [hep-ph]ADSCrossRefGoogle Scholar
  32. 32.
    T.M. Aliev, K. Azizi, M. Savci, Nucl. Phys. A 895, 59 (2012) arXiv:1205.2873 [hep-ph]ADSCrossRefGoogle Scholar
  33. 33.
    T.M. Aliev, K. Azizi, M. Savc, Phys. Lett. B 715, 149 (2012) arXiv:1205.6320 [hep-ph]ADSCrossRefGoogle Scholar
  34. 34.
    T.M. Aliev, K. Azizi, M. Savci, J. Phys. G 40, 065003 (2013) arXiv:1208.1976 [hep-ph]ADSCrossRefGoogle Scholar
  35. 35.
    T.M. Aliev, K. Azizi, M. Savci, JHEP 04, 042 (2013) arXiv:1212.6065 [hep-ph]ADSCrossRefGoogle Scholar
  36. 36.
    T.M. Aliev, K. Azizi, M. Savc, J. Phys. G 41, 065003 (2014) arXiv:1404.2091 [hep-ph]ADSCrossRefGoogle Scholar
  37. 37.
    D. Ebert, R.N. Faustov, V.O. Galkin, A.P. Martynenko, Phys. Rev. D 66, 014008 (2002) arXiv:hep-ph/0201217ADSCrossRefGoogle Scholar
  38. 38.
    K.W. Wei, B. Chen, X.H. Guo, Phys. Rev. D 92, 076008 (2015) arXiv:1503.05184 [hep-ph]ADSCrossRefGoogle Scholar
  39. 39.
    Y.J. Shi, W. Wang, Y. Xing, J. Xu, Weak decays of doubly heavy baryons: Multi-body decay channels, arXiv:1712.03830 [hep-ph]Google Scholar
  40. 40.
    C.Y. Wang, C. Meng, Y.Q. Ma, K.T. Chao, NLO effects for doubly heavy baryon in QCD sum rules, arXiv:1708.04563 [hep-ph]Google Scholar
  41. 41.
    M.N. Anwar, J. Ferretti, F.K. Guo, E. Santopinto, B.S. Zou, arXiv:1710.02540 [hep-ph]Google Scholar
  42. 42.
    Altuğ Özpineci, Application of light cone QCD sum rules to hadron physics, PhD Thesis, Graduate School of Natural and Applied Sciences, Middle East Technical University (2001)Google Scholar
  43. 43.
    M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 385 (1979)ADSCrossRefGoogle Scholar
  44. 44.
    I.I. Balitsky, V.M. Braun, A.V. Kolesnichenko, Nucl. Phys. B 312, 509 (1989)ADSCrossRefGoogle Scholar
  45. 45.
    I.I. Balitsky, V.M. Braun, Nucl. Phys. B 311, 541 (1989)ADSCrossRefGoogle Scholar
  46. 46.
    L.J. Reinders, H. Rubinstein, S. Yazaki, Phys. Rep. 127, 1 (1985)ADSCrossRefGoogle Scholar
  47. 47.
    F.X. Lee, X.y. Liu, Phys. Rev. D 66, 014014 (2002) arXiv:nucl-th/0203051ADSCrossRefGoogle Scholar
  48. 48.
    U. Ozdem, K. Azizi, Phys. Rev. D 96, 074030 (2017) arXiv:1707.09612 [hep-ph]ADSCrossRefGoogle Scholar
  49. 49.
    P. Ball, JHEP 01, 010 (1999) arXiv:hep-ph/9812375ADSCrossRefGoogle Scholar
  50. 50.
    P. Ball, V.M. Braun, A. Lenz, JHEP 05, 004 (2006) arXiv:hep-ph/0603063ADSCrossRefGoogle Scholar
  51. 51.
    P. Ball, R. Zwicky, Phys. Rev. D 71, 014015 (2005) arXiv:hep-ph/0406232ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsDoğuş UniversityIstanbulTurkey
  2. 2.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.Department of PhysicsJahrom UniversityJahromIran
  4. 4.Young Researchers and Elites Club, South Tehran BranchIslamic Azad UniversityTehranIran

Personalised recommendations