  Recently the renormalization of the band gap $m$, in both WSe$_2$ and
MoS$_2$, has been experimentally measured as a function of the carrier
concentration $n$. The main result establishes a decreasing of hundreds of meV,
in comparison with the bare band gap, as the carrier concentration increases.
These materials are known as transition metal dichalcogenides and their
low-energy excitations are, approximately, described by the massive Dirac
equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the
electromagnetic interaction between these quasiparticles and from
renormalization group analysis, we obtain that the renormalized mass describes
the band gap renormalization with a function given by
$m(n)/m_0=(n/n_0)^{C_\lambda/2}$, where $m_0=m(n_0)$ and $C_\lambda$ is a
function of the coupling constant $\lambda$. We compare our theoretical results
with the experimental findings for WSe$_2$ and MoS$_2$, and we conclude that
our approach is in agreement with these experimental results for reasonable
values of $\lambda$. In addition we introduced a Gross-Neveu (GN) interaction
which could simulate an disorder/impurity-like microscopic interaction. In this
case, we show that there exists a critical coupling constant, namely,
$\lambda_c \approx 0,66$ in which the beta function of the mass vanishes,
providing a stable fixed point in the ultraviolet limit. For
$\lambda>\lambda_c$, the renormalized mass decreases while for
$\lambda<\lambda_c$ it increases with the carrier concentration.
