We present a calculation of the B 0 −B 0 mixing matrix element in the framework of QCD sum rules for three-point functions. We compute αs corrections to a three-point function at the three-loop level in QCD perturbation theory, which allows one to extract the matrix element with next-to-leading order (NLO) accuracy. This calculation is imperative for a consistent evaluation of experimentallymeasured mixing parameters since the coefficient functions of the effective Hamiltonian for B 0 −B 0 mixing are known at NLO. We find that radiative corrections violate factorization at NLO; this violation is under full control and amounts to 10%.PACS numbers: 12.15. Lk, 13.35.Bv, 14.60.EfThe phenomenon of particle-antiparticle mixing, possible in systems of neutral mesons of different flavors, is the primary source of studies of CP violation (for review, see e.g. [1]). According to the Cabibbo-Kobayashi-Maskawa (CKM) picture, quarks of all three generations must be present in a transition for CP violation to occur. Historically, studies of K 0 −K 0 mixing provided first essential insights into the physics of heavy particles as well as tests of general concepts of quantum field theory. For a long time it was the only place where the effects of CP violation were clearly established (see e.g. [2]). Since weak couplings of s and d quarks to third generation quarks are small, experimental studies of CP violation in heavy mesons are considered more promising. While recent experimental results for heavy charmed mesons D(ūc) are encouraging, a full consistent theoretical description of this system is still lacking [3]. These considerations make the systems of B d (db) and B s (sb) mesons the most promising laboratory for a precision analysis of CP violation and mixing both experimentally and theoretically [4]. Hereafter we shall consider B d mesons. The generalization to B s mesons is straightforward.Phenomenologically the system of the B 0 −B 0 mesons is described by the effective mass operator (M − iΓ/2) ij , {i, j} = {1, 2} which in the presence of ∆B = 2 interactions acquires non-diagonal terms. The difference between the values of the mass eigenstates of B mesons ∆m = M heavy − M light ≈ 2 |M 12 | is an important observable which is precisely measured to be ∆m = 0.489 ± 0.005(stat) ± 0.007(syst) ps −1 [5]. With an adequate theoretical description, it can be used to extract top quark CKM parameters.In the standard model, the effective low-energy Hamiltonian describing ∆B = 2 transitions has been computed at next-to-leading order (NLO) in QCD perturbation theory (PT) [6]where η B = 0.55 ± 0.1 [7], J 5 = 1.627 in the naive dimensional regularization (NDR) scheme, S 0 (x t ) is the InamiLim function [8], andis a local four-quark operator at the normalization point µ.Note that the part of Eq. (1) in the second line is renormalization-group (RG) invariant. Mass splitting of heavy and light mass eigenstates can then be found to be2 . The largest uncertainty of about 30% in the theoretical calculation is introduced by the poorly known ...