Can the X(3872) be a 1++ four-quark state?

We use QCD spectral sum rules to test the nature of the meson X(3872), assumed to be an exotic four-quark (ccqq) state with J(PC)=1(++). For definiteness, we work with the diquark-antidiquark current proposed recently, at leading order in alpha(s), consider the contributions of higher dimension condensates and keep terms which are linear in the light quark mass m(q). We find M-X=(3925 +/- 127) MeV which is compatible, within the errors, with the experimental candidate X(3872), while the SU(3) breaking-terms lead to an unusual mass-splitting M-X(s)-M-X=-(61 +/- 30) MeV. The mass-difference between the neutral states due to isospin violation is about (2.6 similar to 3.9) MeV. For the b-quark, we predict M-Xb=(10144 +/- 106) MeV for the X-b(bbqq), which is much below the BB* threshold, and for the X-b(s)(bbss), a mass-splitting M-Xb(s)-M-Xb=-(121 +/- 182) MeV. Our analysis also indicates that the mass-splitting between the ground state and the radial excitation of about (225 similar to 250) MeV is much smaller than in the case of ordinary mesons and is (within the errors) flavor-independent. We also extract the decay constants, analogous to f(pi), of such mesons, which are useful for further studies of their leptonic and hadronic decay widths. The uncertainties of our estimates are mainly due to the ones from the c and b quark masses.