Advertisement

Numerically computing QCD Laplace sum-rules using pySecDec

  • Steven Esau
  • Derek HarnettEmail author
Special Article - New Tools and Techniques
  • 19 Downloads

Abstract.

pySecDec is a program that numerically calculates dimensionally regularized integrals. We use pySecDec to compute QCD Laplace sum-rules for pseudoscalar (i.e., \( J^{PC}=0^{-+}\)) charmonium hybrids, and compare the results to sum-rules computed using analytic results for dimensionally regularized integrals. We find that the errors due to the use of numerical integration methods are negligible compared to the uncertainties in the sum-rules stemming from the uncertainties in the parameters of QCD, e.g., the coupling constant, quark masses, and condensate values. Also, we demonstrate that numerical integration methods can be used to calculate finite-energy and Gaussian sum-rules in addition to Laplace sum-rules.

References

  1. 1.
    M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 448 (1979)ADSCrossRefGoogle Scholar
  2. 2.
    M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 147, 385 (1979)ADSCrossRefGoogle Scholar
  3. 3.
    L.J. Reinders, H. Rubinstein, S. Yazaki, Phys. Rep. 127, 1 (1985)ADSCrossRefGoogle Scholar
  4. 4.
    S. Narison, QCD as a Theory of Hadrons, Vol. 17 (Cambridge University Press, 2007)Google Scholar
  5. 5.
    K.G. Wilson, Phys. Rev. 179, 1499 (1969)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    P. Pascual, R. Tarrach, QCD: Renormalization for the Practitioner (Springer, 1984)Google Scholar
  7. 7.
    E.E. Boos, A.I. Davydychev, Theor. Math. Phys. 89, 1052 (1991)CrossRefGoogle Scholar
  8. 8.
    A.I. Davydychev, J. Math. Phys. 33, 358 (1992)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    D.J. Broadhurst, J. Fleischer, O.V. Tarasov, Z. Phys. C 60, 287 (1993) arXiv:hep-ph/9304303v1ADSCrossRefGoogle Scholar
  10. 10.
    J.A.M. Vermaseren, arXiv:math-ph/0010025 (2000)Google Scholar
  11. 11.
    J. Kuipers, T. Ueda, J.A.M. Vermaseren, Comput. Phys. Commun. 189, 1 (2015) arXiv:1310.7007ADSCrossRefGoogle Scholar
  12. 12.
    B. Ruijl, T. Ueda, J. Vermaseren, arXiv:1707.06453 (2017)Google Scholar
  13. 13.
    M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi, GNU Scientific Library Reference Manual, 3rd edition (Network Theory Ltd., 2009)Google Scholar
  14. 14.
    T. Hahn, Comput. Phys. Commun. 168, 78 (2005) arXiv:hep-ph/0404043ADSCrossRefGoogle Scholar
  15. 15.
    T. Hahn, J. Phys. Conf. Ser. 608, 012066 (2015) arXiv:1408.6373CrossRefGoogle Scholar
  16. 16.
    S. Borowka, G. Heinrich, S. Jahn, S.P. Jones, M. Kerner, J. Schlenk, T. Zirke, Comput. Phys. Commun. 222, 313 (2018) arXiv:1703.09692ADSCrossRefGoogle Scholar
  17. 17.
    J. Govaerts, L.J. Reinders, J. Weyers, Nucl. Phys. B 262, 575 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    R. Berg, D. Harnett, R.T. Kleiv, T.G. Steele, Phys. Rev. D 86, 034002 (2012) arXiv:1204.0049ADSCrossRefGoogle Scholar
  19. 19.
    G. Launer, S. Narison, R. Tarrach, Z. Phys. C 26, 433 (1984)ADSCrossRefGoogle Scholar
  20. 20.
    S. Narison, Phys. Lett. B 693, 559 (2010) 705ADSCrossRefGoogle Scholar
  21. 21.
    D. Binosi, L. Theussl, Comput. Phys. Commun. 161, 76 (2004) arXiv:hep-ph/0309015ADSCrossRefGoogle Scholar
  22. 22.
    S. Narison, E. de Rafael, Phys. Lett. B 103, 57 (1981)ADSCrossRefGoogle Scholar
  23. 23.
    Particle Data Group (C. Patrignani et al.), Chin. Phys. C 40, 100001 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    R. Shankar, Phys. Rev. D 15, 755 (1977)ADSCrossRefGoogle Scholar
  25. 25.
    R.A. Bertlmann, G. Launer, E. de Rafael, Nucl. Phys. B 250, 61 (1985)ADSCrossRefGoogle Scholar
  26. 26.
    J. Ho, R. Berg, W. Chen, D. Harnett, T.G. Steele, Phys. Rev. D 98, 096020 (2018) arXiv:1806.02465ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of the Fraser ValleyAbbotsfordCanada

Personalised recommendations