NNLO compatibility between pQCD theory and phenomenology in determination of the $b$-quark pole and \MSbar running masses

TL;DR

This paper compares theoretical pQCD predictions and experimental phenomenology at NNLO to determine the $b$-quark masses, assessing their compatibility and implications for proton PDFs and the Standard Model.

Contribution

It provides a detailed comparison of NNLO pQCD calculations with phenomenological data for $b$-quark masses, highlighting their consistency and impact on proton structure functions.

Findings

Good compatibility between pQCD and phenomenology at NNLO.

The $b$-quark mass influences the uncertainty in proton PDFs.

Refined $b$-quark mass values improve Standard Model parameter estimates.

Abstract

This contribution attempts to determine the $b$-quark pole mass $M_b$ and \MSbar running mass $\overline{m}_b$ with two different approaches at the next-to-next-to-leading order (NNLO) corrections. At the first approach, we derive a relation between the $b$-quark pole mass $M_b$ and its \MSbar running mass $\overline{m}_b$ at the NNLO corrections based on the perturbative Quantum Chromo Dynamics (pQCD) predictions. At the second approach, we extract numerical values of the $b$-quark pole and \MSbar running masses based on the NNLO phenomenology of H1 and ZEUS Collaborations combined beauty vertex production experimental data. Then we discuss about the compatibility between the pQCD theory results and phenomenology approach in determination of the $b$-quark pole and \MSbar running masses at the NNLO corrections. Also, we investigate the role and influence of the $b$-quark mass as an extra degree of freedom added to the input parameters of the Standard Model Lagrangian, on the improvement of the uncertainty band of the proton parton distribution functions (PDFs) and particularly on the gluon distribution.