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The file \textsf{ex.red} contains the \textsf{REDUCE} procedures
\textsf{e1}, \textsf{e2}, \textsf{e3},
which expand 1-, 2-, and 3-loop results obtained by \textsf{Grinder}
in $\varepsilon$ (denoted by \textsf{E}).

The bare HQET heavy-quark propagator in $d$-dimensional space-time
in an arbitrary covariant gauge has the form
\begin{equation}
\left[\omega \tilde{S}(\omega)\right]^{-1} = 1 + \mathcal{A} C_F I_1 \Sigma^{(1)}
+ \mathcal{A}^2 \sum C^{(2)}_i B^{(2)}_j \Sigma^{(2)}_{ij}
+ \mathcal{A}^3 \sum C^{(3)}_i B^{(3)}_j \Sigma^{(3)}_{ij}
+ \cdots
\label{pd}
\end{equation}
where
\[
\mathcal{A} = \frac{g_0^2(-2\omega)^{-2\varepsilon}}{(4\pi)^{d/2}}\,,
\]
the 2-loop colour structures are $C^{(2)}_i=C_F\times(C_F,C_A,T_F n_l)$,
the basis integrals are $B^{(2)}_j=I_1^2,I_2$;
the 3-loop colour structures are
$C^{(2)}_i=C_F\times(C_F^2,C_F C_A,C_A^2,C_F T_F n_l, C_A T_F n_l,(T_F n_l)^2)$,
and the basis integrals $B^{(3)}_j$ are discussed in Sect.~2.
The coefficients $\Sigma^{(l)}$ are in the file \textsf{pd.red};
they are called \textsf{S1}, \textsf{S2}, \textsf{S3},
and expressed via $d$ and $\xi=1-a_0$
(the bare gluon propagator is $\left(g_{\mu\nu}-\xi p_\mu p_\nu/p^2\right)/p^2$).
The same inverse propagator~(\ref{pd}) expanded in $\varepsilon$
is given in the file \textsf{pe.red}, as an expansion in
\[
A = \frac{g_0^2(-2\omega)^{-2\varepsilon}e^{-\gamma\varepsilon}}%
{(4\pi)^{d/2}\varepsilon}\,.
\]

The bare proper-vertex function $\Gamma(\omega,p)$
is calculated at the light-quark momentum $p=0$.
Its structure is similar to~(\ref{pd});
the coefficients $V^{(l)}$ are in the file \textsf{vd.red}.
Its expansion in $\varepsilon$ is given in the file \textsf{ve.red}.

The file \textsf{adim.red} contains the anomalous dimensions
$\tilde{\gamma}_Q$~(10), $\gamma_q$, $\tilde{\gamma}_j$~(13)
and the corresponding renormalization factors,
as well as two procedures to convert an anomalous dimension
to the corresponding renormalization factor and back
at three loops.
The anomalous dimensions are truncated expansions in $\mathsf{As}=\alpha_s/(4\pi)$,
and the anomalous dimensions in $\mathsf{Ae}=\alpha_s/(4\pi\varepsilon)$.

The file \textsf{ren.red} contains the renormalized propagator
in the momentum space (formula~(11)) and in the coordinate space
(formula~(12)).

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