Conventional versus single-ladder-splitting contributions to double parton scattering production of two quarkonia, two Higgs bosons, andcc¯cc¯

Abstract

The double parton distributions (dPDF), both conventional (i.e. double ladder) and those corresponding to $1\ensuremath{\rightarrow}2$ ladder splitting, are calculated and compared for different two-parton combinations. The conventional and splitting dPDFs have very similar shape in ${x}_{1}$ and ${x}_{2}$. We make a first quantitative evaluation of the single-ladder-splitting contribution to double parton scattering (DPS) production of two S- or P-wave quarkonia, two Higgs bosons and $c\overline{c}c\overline{c}$. The ratio of the single-ladder-splitting to conventional (i.e. double ladder against double ladder) contributions is discussed as a function of center-of-mass energy, mass of the produced system and other kinematical variables. Using a simple model for the dependence of the conventional two-parton distribution on transverse parton separation (Gaussian and independent of ${x}_{i}$ and scales), we find that the single-ladder-splitting (or 2v1) contribution is as big as the conventional (or 2v2) contribution discussed in recent years in the literature. In many experimental studies of DPS, one extracts the quantity $1/{\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}^{\mathrm{DPS}}/({\ensuremath{\sigma}}^{\mathrm{SPS},1}{\ensuremath{\sigma}}^{\mathrm{SPS},2}$), with ${\ensuremath{\sigma}}^{\mathrm{SPS},1}$ and ${\ensuremath{\sigma}}^{\mathrm{SPS},2}$ being the single scattering cross sections for the two subprocesses in the DPS process. Many past phenomenological studies of DPS have only considered the conventional contribution and have obtained values a factor of $\ensuremath{\sim}2$ too small for $1/{\ensuremath{\sigma}}_{\mathrm{eff}}$. Our analysis shows that it is important also to consider the ladder-splitting mechanism, and that this might resolve the discrepancy (this was also pointed out in a recent study by Blok et al.). The differential distributions in rapidity and transverse momenta calculated for conventional and single-ladder-splitting DPS processes are however very similar which causes their experimental separation to be rather difficult, if not impossible. The direct consequence of the existence of the two components (conventional and splitting) is the energy and process dependence of the empirical parameter ${\ensuremath{\sigma}}_{\mathrm{eff}}$. This is illustrated in our paper for the considered processes.