Here we describe the mathematica notebooks and the Fortran and C++
routines we prepared for the QCD evolution of the Sivers function.


Direct Implementation of Evolution
====================================

Bochum.nb : Direct implementation of the evolution for the 
up quark Sivers function using Bochum fits.

TorinoUp.nb : Direct implementation of the evolution for the 
up quark Sivers function using Torino fits.

TorinoDown.nb : Direct implementation of the evolution for the 
down quark Sivers function using Torino fits.



GAUSSIAN FITS FOR THE SIVERS FUNCTION
=====================================

====================================

IMPORTANT : 

THE GAUSSIAN FITS IN THE FOLLOWING PACKAGES ARE VALID FOR
SMALL VALUES OF TRANSVERSE MOMENTA KT AS
EXPLAINED IN ARXIV:1110.6428. WE ADVISE THE USERS TO BE
AWARE OF THE LIMITATIONS OF THE GAUSSIAN APPROXIMATION
WHILE USING THESE PACKAGES.

====================================


Mathematica Implementations
===========================

Sivers.nb : Mathematica package implementing the up and down quark
Sivers function using Bochum and Torino fits.

BochumUpSivers[xx,kk,qq] returns the up quark Sivers function in GeV^-2 with
xx=Bjorken-x
kk=transverse quark momentum in GeV
qq=hard scale in GeV


BochumDownSivers[xx,kk,qq] returns the down quark Sivers function in GeV^-2 with
xx=Bjorken-x
kk=transverse quark momentum in GeV
qq=hard scale in GeV
 
TorinoUpSivers[xx,kk,qq] returns the up quark Sivers function in GeV^-2 with
xx=Bjorken-x
kk=transverse quark momentum in GeV
qq=hard scale in GeV


TorinoDownSivers[xx,kk,qq] returns the down quark Sivers function in GeV^-2 with
xx=Bjorken-x
kk=transverse quark momentum in GeV
qq=hard scale in GeV

Torinotable.dat : Data file for the Table 1 of arXiv:1110.6428. 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 parameter a in GeV^-3.

Bochumtable.dat : Data file for the Table 1 of arXiv:1110.6428. 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 parameter a in GeV^-3.


Fortran and C++ Implementations
===============================

sivers.tar.gz:

This package contains Gaussian Fits for the QCD evolved
Sivers Function using Torino and Bochum extractions of 
references (Eur.Phys. J. A39,89(2009)) and (Phys.Rev.D73,094023 (2006)).

For both the Fortran and C++ implementations the following functions
are defined:

BochumSivers(x,kt,q,fl) returns the Sivers function in GeV^-2 with
x=Bjorken-x
kt=transverse quark momentum in GeV
q=hard scale in GeV
fl=flavor 1=up and 2=down quark.

TorinoSivers(x,kt,q,fl) returns the Sivers function in GeV^-2 with
x=Bjorken-x			    
kt=transverse quark momentum in GeV
q=hard scale in GeV 
fl=flavor 1=up and 2=down quark.


INSTALLATION AND EXECUTABLES:

make : compiles the fortran and c++ codes.

example_cpp : c++ example that demonstrates the use of 
BochumSivers and TorinoSivers functions. Returns the up and down
quark Bochum and Torino Sivers functions for
x=0.1, kt=1 GeV and q=sqrt(2.4) GeV.

example_f : fortran example that demonstrates the use of
BochumSivers and TorinoSivers functions. Returns the up and down
quark Bochum and Torino Sivers functions for
x=0.1, kt=1 GeV and q=sqrt(2.4) GeV.