QCD spectral sum rules is used to test the nature of the meson X(3872), assumed to be an exotic four-quark $(c\bar{c}q\bar{q})$ state with J PC = 1++. For definiteness, the current proposed recently by Maiani et al [1] is used, at leading order in alphas, considering the contributions of higher dimension condensates. The value M X = (3.94±0.11) GeV is found which is compatible, within the errors, with the experimental candidate X(3872). The uncertainties of our estimates are mainly due to the one from the c quark mass.

In this work, we evaluate the D+sJ(2317), D(0)0(2308), D(0)0(2407) and D+0(2403) masses. These are scalar mesons recently discovered in the BABAR, BELLE and FOCUS Collaborations. The nature of these particles is intensely discussed nowadays. We treat them as a diquark-antidiquark configuration and treat the problem using the QCD sum rules (QCDSR) approach.

We review the existing mass and decay width determinations of pentaquarks with QCD Sum Rules (QCDSR). We give special attention to the intermediate assumptions and choices which we are obliged to do in this approach. As an example, we present the full calculation of the pentaquark mass with Borel sum rules and also with Finite Energy Sum Rules (FESR). We also work out the calculation of the theta decay width. We take the opportunity to comment our publications on this subject and include new and unpublished material.