Ratios of differential cross sections of heavy-flavour hadron production with ALICE

Measurements of heavy-flavour hadrons in pp collisions are important to test pertubative Quantum ChromoDynamics and as a reference for measurements in heavy-ion collisions. ALICE has measured several observables in this sector, e.g. p_T-differential cross-sections of prompt D mesons and semi-electronic decays of beauty and charm hadrons at different energies. These measurements are compared to theoretical calculations, like General-Mass Variable Flavour Number Scheme (GM-VFNS) and Fixed-Order plus Next-to-Leading-Logarithms (FONLL), which are affected by large uncertainties caused by renormalisation scale, factorization scale and the heavy quark mass. Because of low statistics, the pp reference spectra for PbPb data are often obtained by extrapolation of data taken at different centre-of-mass energies. This procedure is guided by theory and also affected by large systematic uncertainties. The FONLL authors proposed to consider ratios of cross-sections at different centre-of-mass energies for a substantial reduction of the systematic uncertainties. Therefore, ratios of p_T-differential cross-sections were studied to investigate the possibility to reduce theoretical uncertainties. Such ratios could benefit from the possibility to cancel some systematic errors on the measured data. Simulations with POWHEG are performed to provide an additional theory-based reference. By comparing calculated and measured ratios, sensitivity to the gluon distribution function may be obtained.