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Sivers Function

Below we supply grid files, interpolation routines, and sample calculations for both the up and down quark Sivers function of the proton. Here we supply the implementation of evolution for the Torino and Bochum fits to the Sivers function, using (Eur.Phys. J. A39,89(2009)) and (Phys.Rev.D73,094023 (2006)) for the non-perturbative input needed for the CSS evolution. See the README file and arXiv:1110.6428v1 [hep-ph] for more explanation.

Example Figure: Up quark TMD PDF for x=0.09

Example Figure: Negative of the Up quark Sivers Function for x=0.1

Note that the implementation of the evolution of the Torino fits uses the unpolarized collinear PDFs. Therefore, in order Torino fits to work correctly, the standard integrated PDF sets need to be installed. Find the MSTW PDF sets here.

Direct Implementation of Evolution in Torino and Bochum Fits.

  • Up Quark Sivers Function Mathemematica 7 (from Torino fits).
  • Down Quark Sivers Function Mathemematica 7 (from Torino fits).
  • Up Quark Sivers Function Mathemematica 7 (from Bochum fits).
  • Gaussian fits to the evolved Torino and Bochum Sivers functions, valid for low kT.

    Table 1 from arXiv:1110.6428v1 [hep-ph]. The first column is Q in GeV, the second column is the Gaussian slope parameter b in GeV-2, the third column is the normalization a in GeV-3.


  • Torinotable: Gaussian fit to evolved Torino up quark Sivers function.
  • Bochumtable: Gaussian fit to evolved Bochum up quark Sivers function.
  • Mathematica package for Gaussian fits.


  • Simple Mathematica 7 package for Gaussian fits.
  • Example calculation using Mathematica package.
  • Fortran and C++ codes for Gaussian fits.


    Collection of Fortran 77 and C++ routines and example calculations for the Gaussian fits.

    Type 'make' to compile the routines and the example codes.