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The European Physical Journal C

, Volume 68, Issue 3–4, pp 683–685 | Cite as

Addendum to: A new numerical method for obtaining gluon distribution functions G(x,Q 2)=xg(x,Q 2), from the proton structure function \(F_{2}^{\gamma p}(x,Q^{2})\)

  • Martin M. BlockEmail author
Addendum

Abstract

Since publication of M.M. Block in Eur. Phys. J. C 65, 1 (2010), we have discovered that the algorithm of Block (2010) does not work if g(s)→0 less rapidly than 1/s, as s→∞. Although we require that g(s)→0 as s→∞, it can approach 0 as \({1\over s^{\beta}}\), with 0<β<1, and still be a proper Laplace transform. In this note, we derive a new numerical algorithm for just such cases, and test it for \(g(s)={\sqrt{\pi}\over \sqrt{s}}\), the Laplace transform of \({1\over\sqrt{v}}\).

Keywords

Gluon Distribution Closed Contour Fractional Accuracy Complex Conjugate Pair Arbitrary Accuracy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M.M. Block, Eur. Phys. J. C 65, 1 (2010) CrossRefADSGoogle Scholar
  2. 2.
    Mathematica 7, a computing program from Wolfram Research, Inc., Champaign, IL, USA, www.wolfram.com, 2009
  3. 3.
    M.M. Block, L. Durand, P. Ha, D.W. McKay, to be published (2010). arXiv:1004.1440 [hep-ph]

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of Physics and AstronomyNorthwestern UniversityEvanstonUSA

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