  Emission mechanisms of the shell-type supernova remnant (SNR) RX J1713.7-3946
are studied with multi-wavelength observational data from radio, X-ray, GeV
$\gamma$-ray to TeV $\gamma$-ray band. A Markov Chain Monte Carlo method is
employed to explore the high-dimensional model parameter space systematically.
Three scenarios for the $\gamma$-ray emission are investigated: the leptonic,
the hadronic and a hybrid one. Thermal emission from the background plasma is
also included to constrain the gas density, assuming ionization equilibrium,
and a 2$\sigma$ upper limit of about 0.03 cm$^{-3}$ is obtained as far as
thermal energies account for a significant fraction of the dissipated kinetic
energy of the SNR shock. Although systematic errors dominate the $\chi^2$ of
the spectral fit of all models, we find that 1) the leptonic model has the best
constrained model parameters, whose values can be easily accommodated with a
typical supernova, but gives relatively poor fit to the TeV $\gamma$-ray data;
2) The hybrid scenario has one more parameter than the leptonic one and
improves the overall spectral fit significantly; 3) The hadronic one, which has
three more parameters than the leptonic model, gives the best fit to the
overall spectrum with relatively not-well-constrained model parameters and very
hard spectra of accelerated particles. The uncertainties of the model
parameters decrease significantly if the spectral indices of accelerated
electrons and protons are the same. The hybrid and hadronic models also require
an energy input into high-energy protons, which seems to be too high compared
with typical values of a supernova explosion. Further investigations are
required to reconcile these observations with SNR theories.
