$\overline{\mathrm{M}\mathrm{S}}$ parton densities with NNLO heavy flavor matching conditions

A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\overline{\mathrm{M}\mathrm{S}}$ three-flavor density set, where the scale $\mu <m_c$, and using the recently derived two-loop matching conditions, we provide a new set of four-flavor parton densities where $m_c\le \mu <m_b$ and five-flavor densities where $\mu \ge m_b$. The effect of the next-to-next-to-leading order matching conditions on the evolution equations is important for scales just above the transition regions. This includes the small $x$ and small $Q^2$ domain studied by the H1 and ZEUS experiments at HERA. At small $x$ the effects of the matching conditions never die away even for large ${\mu }^2$.