  We analyze the collision of three particles with arbitrary mass ratio at zero
collision energy, assuming arbitrary short-range potentials, and generalize the
three-body scattering hypervolume $D$ first defined for identical bosons in
2008. We solve the three-body Schr\"{o}dinger equation asymptotically when the
three particles are far apart or one pair and a third particle are far apart,
deriving two asymptotic expansions of the wave function, and the parameter $D$
appears at the order $1/B^4$, where $B$ is the overall size of the triangle
formed by the particles. We then analyze the ground state energy of three such
particles with vanishing or negligible two-body scattering lengths in a large
periodic volume of side length $L$, where the three-body parameter contributes
a term of the order $D/L^6$. From this result we derive some properties of a
two-component Bose gas with negligible two-body scattering lengths: its energy
density at zero temperature, the corresponding generalized Gross-Pitaevskii
equation, the conditions for the stability of the two-component mixture against
collapse or phase separation, and the decay rates of particle densities due to
three-body recombination.
