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We prove stability bounds for local gauge-invariant scalar QCD quantummodels, with multiflavored bosons replacing (anti)quarks. We take a compact,connected gauge Lie group G, and concentrate on G=U(N),SU(N). Letd(N)=N^2,(N^2-1) be their Lie algebra dimensions. We start on a finitehypercubic lattice \Lambda\subset aZ^d, d=2,3,4, a\in(0,1], with L sites on aside, \Lambda_s=L^d sites, and free boundary conditions. The action is a sum ofa Bose-gauge part and a Wilson pure-gauge plaquette term. We employ a priorilocal, scaled scalar bosons with an a-dependent field-strength renormalization:a non-canonical scaling. The Wilson action is a sum over pointwise positiveplaquette actions with a pre-factor (a^{d-4}/g^2), and gauge coupling$0<g^2\leq g_0^2<\infty$. Sometimes we use an enhanced temporal gauge. Here,there are \Lambda_r\simeq (d-1)\Lambda_s retained bond variables. The unscaledpartition function is $Z^u_{\Lambda,a}\equivZ^u_{\Lambda,a,\kappa_u^2,m_u,g^2,d}$, where $\kappa_u^2>0$ is the unscaledhopping parameter and m_u are the boson bare masses. Letting $s_B\equiv[a^{d-2}(m_u^2a^2+2d\kappa_u^2)]^{1/2}$, $s_Y\equiv a^{(d-4)/2}/g$, we showthat the scaled partition function$Z_{\Lambda,a}=s_B^{N\Lambda_s}s_Y^{d(N)\Lambda_r} Z^u_{\Lambda,a}$ satisfiesthe stability bounds $e^{c_\ell d(N)\Lambda_s}\leq Z_{\Lambda,a}\leqe^{c_ud(N)\Lambda_s}$ with finite real $c_\ell, c_u$ independent of $L$ and thespacing $a$. We have extracted in $Z^u_{\Lambda,a}$ the dependence on \Lambdaand the exact singular behavior of the finite lattice free energy in thecontinuum limit $a\searrow 0$. For the normalized finite-lattice free energy$f_\Lambda^n=[d(N)\Lambda_s]^{-1}\ln Z_{\Lambda,a}$, we prove the existence of(at least, subsequentials) a thermodynamic limit for f_\Lambda^n and, next, ofa continuum limit.

On Thermodynamic and Ultraviolet Stability of Bosonic Lattice QCD Models in Euclidean Spacetime Dimensions $d=2,3,4$