  To reveal and understand astrophysical processes responsible for the Gamma
Ray Burst (GRB) phenomenon, it is crucial to discover and understand relations
between their observational properties. The presented study is performed in the
GRB rest frames and it uses a sample of 62 long GRBs from our sample of 77
Swift GRBs with known redshifts. Following the earlier analysis of the
afterglow {\it characteristic luminosity $L^*_a$ -- break time $T^*_a$}
correlation for a sample of long GRBs \citep{Dainotti2010} we extend it to
correlations between the afterglow and the prompt emission GRB physical
parameters. We reveal a tight physical scaling between the mentioned afterglow
luminosity $ L^*_a$ and the prompt emission {\it mean} luminosity $<L^*_p>_{45}
\equiv E_{iso}/T^*_{45}$. The distribution, with the Spearman correlation
coefficient reaching 0.95 for the data subsample with most regular light
curves, can be fitted with approximately $L^*_a \propto {<L^*_p>_{45}}^{0.7}$.
We also analyzed correlations of $L^*_a$ with several other prompt emission
parameters, including the isotropic energy $E_{iso}$, the peak energy in the
$\nu F_{\nu}$ spectrum, $E_{peak}$, and the variability parameter, $V$, defined
by \cite{N000}. As a result, we reveal significant correlations also between
these quantities, with an exception of the variability parameter. The main
result of the present study is the discovery that the highest correlated GRB
subsample in the \citet{Dainotti2010} afterglow analysis, for the GRBs with
canonical X\,-\,ray light curves, leads also to the highest {\it
prompt-afterglow} correlations and such events can be considered to form a
sample of standard GRBs for astrophysics and cosmology.
