Scale dependence of open $c\bar{c}$ and $b\bar{b}$ production in the low $x$ region

Abstract

The `optimal' factorization scale $\mu_0$ is calculated for open heavy quark production. We find that the optimal value is $\mu_F=\mu_0\simeq 0.85\sqrt{p^2_T+m_Q^2} $; a choice which allows us to resum the double-logarithmic, $(\alpha_s\ln\mu^2_F\ln(1/x))^n$ corrections (enhanced at LHC energies by large values of $\ln(1/x)$) and to move them into the incoming parton distributions, PDF$(x,\mu_0^2)$. Besides this result for the single inclusive cross section (corresponding to an observed heavy quark of transverse momentum $p_T$), we also determined the scale for processes where the acoplanarity can be measured; that is, events where the azimuthal angle between the quark and the antiquark may be determined experimentally. Moreover, we discuss the important role played by the $2\to 2$ subprocesses, $gg\to Q\bar{Q}$ at NLO and higher orders. In summary, we achieve a better stability of the QCD calculations, so that the data on $c\bar{c}$ and $b\bar{b}$ production can be used to further constrain the gluons in the small $x$, relatively low scale, domain, where the uncertainties of the global analyses are large at present.