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We construct a variational ground-state wave function of weakly interactingM-component Bose-Einstein condensates beyond the mean-field theory byincorporating the dynamical 3/2-body processes, where one of the two collidingparticles drops into the condensate and vice versa. Our numerical results withvarious masses and particle numbers show that the 3/2-body processes betweendifferent particles make finite contributions to lowering the ground-stateenergy, implying that many-body correlation effects between different particlesare essential even in the weak-coupling regime of the Bose--Einsteincondensates. We also consider the stability condition for $2$-componentmiscible states using the new ground-state wave function. Through thiscalculation, we obtain the relation $U^{2}_{AB}/U_{AA}U_{BB}<1+\alpha$, where$U_{ij}$ is the effective contact potential between particles $i$ and $j$ and$\alpha$ is the correction, which originates from the $3/2$-body and $2$-bodyprocesses.

Ground-State Wave Function with Interactions between Different Species in $M$-Component Miscible Bose-Einstein Condensates