  Overwhelming diversity of long gamma-ray bursts (LGRBs), discovered after the
launch of {\it Swift} satellite, is a major obstacle to LGRB studies. Recently,
it is shown that the prompt emission of LGRBs is classified into three
subclasses: Type I, Type II LGRBs populating separate fundamental planes in a
3D space defined by the peak luminosity, the duration, and the spectral peak
energy, and outliers not belonging to either of the planes. Here we show that
Type I LGRBs (LGRBs I) exhibit different shapes of light curves from Type II
LGRBs (LGRBs II). Furthermore, we demonstrate that this classification has
uncovered a new scaling law in the light curves of LGRBs II spanning 8 orders
of magnitude from the prompt to late X-ray afterglow emission. The scaled light
curve has four distinct phases. The first phase has a characteristic time scale
while the subsequent three phases exhibit power law behaviors with different
exponents. We discuss its possible interpretation in terms of the emission from
an optically thick fireball propagating in the cricumstellar matter at
relativistic speeds and argue that the observed four phases correspond to its
hydrodynamical phases. Our classification scheme can pin down the intrinsic
luminosities of LGRBs II through the scaling law from a sample of polymorphic
GRBs. Further refinement of this scheme and scaling law will make a subclass of
LGRBs a standard candle as reliable and accurate as Type Ia supernovae in the
more distant universe than supernovae can reach.
