$\bar{\rm MS}$ parton densities with NNLO heavy flavor matching conditions

TL;DR

This paper develops improved $ar{ m MS}$ parton density sets incorporating NNLO heavy flavor matching conditions, crucial for accurate predictions at small $x$ and near flavor transition scales in high-energy physics experiments.

Contribution

It introduces a new set of four- and five-flavor parton densities using two-loop matching conditions, enhancing precision near flavor thresholds in QCD evolution.

Findings

NNLO matching conditions significantly affect parton densities near flavor thresholds.

Effects persist at small $x$ even for large scales.

Provides improved parton densities for HERA-related kinematic regions.

Abstract

A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\bar{\rm MS}$ 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 $\mu^2$.