  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.
