Mapping the Galactic disk with the LAMOST and Gaia Red clump sample: I: precise distances, masses, ages and 3D velocities of $\sim$ 140000 red clump stars

We present a sample of $\sim$ 140,000 primary red clump (RC) stars of spectral signal-to-noise ratios higher than 20 from the LAMOST Galactic spectroscopic surveys, selected based on their positions in the metallicity-dependent effective temperature--surface gravity and color--metallicity diagrams, supervised by high-quality $Kepler$ asteroseismology data. The stellar masses and ages of those stars are further determined from the LAMOST spectra, using the Kernel Principal Component Analysis method, trained with thousands of RCs in the LAMOST-$Kepler$ fields with accurate asteroseismic mass measurements. The purity and completeness of our primary RC sample are generally higher than 80 per cent. For the mass and age, a variety of tests show typical uncertainties of 15 and 30 per cent, respectively. Using over ten thousand primary RCs with accurate distance measurements from the parallaxes of Gaia DR2, we re-calibrate the $K_{\rm s}$ absolute magnitudes of primary RCs by, for the first time, considering both the metallicity and age dependencies. With the the new calibration, distances are derived for all the primary RCs, with a typical uncertainty of 5--10 per cent, even better than the values yielded by the Gaia parallax measurements for stars beyond 3--4 kpc. The sample covers a significant volume of the Galactic disk of $4 \leq R \leq 16$ kpc, $|Z| \leq 5$ kpc, and $-20 \leq \phi \leq 50^{\circ}$. Stellar atmospheric parameters, line-of-sight velocities and elemental abundances derived from the LAMOST spectra and proper motions of Gaia DR2 are also provided for the sample stars. Finally, the selection function of the sample is carefully evaluated in the color-magnitude plane for different sky areas. The sample is publicly available.