  The spectra of gamma-ray bursts (GRBs) in a wide energy range can usually be
well described by the Band function, which is a two smoothly jointed power laws
cutting at a breaking energy. Below the breaking energy, the Band function
reduces to a cut-off power law, while above the breaking energy it is a simple
power law. However, for some detectors (such as the Swift-BAT) whose working
energy is well below or just near the breaking energy, the observed spectra can
be fitted to cut-off power law with enough precision. Besides, since the energy
band of Swift-BAT is very narrow, the spectra of most GRBs can be fitted well
even using a simple power law. In this paper, with the most up-to-date sample
of Swift-BAT GRBs, we study the effect of different spectral models on the
empirical luminosity correlations, and further investigate the effect on the
reconstruction of GRB Hubble diagram. We mainly focus on two luminosity
correlations, i.e., the Amati relation and Yonetoku relation. We calculate
these two luminosity correlations on both the case that the GRB spectra are
modeled by Band function and cut-off power law. It is found that both
luminosity correlations only moderately depend on the choice of GRB spectra.
Monte Carlo simulations show that Amati relation is insensitive to the
high-energy power-law index of the Band function. As a result, the GRB Hubble
diagram calibrated using luminosity correlations is almost independent on the
GRB spectra.
