Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>F</c:mi><c:mn>2</c:mn></c:msub><c:mo stretchy="false">(</c:mo><c:mi>x</c:mi><c:mo>,</c:mo><c:msup><c:mi>Q</c:mi><c:mn>2</c:mn></c:msup><c:mo stretchy="false">)</c:mo></c:math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>b</g:mi></g:math>-jet production at the LHC is given.