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

Abstract

We use QCD spectral sum rules 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, we work with the current proposed recently by Maiani et al [1], 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 he 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 of about (2.6-3.9) MeV is much smaller than the value (8+-3) MeV proposed in [1]. For the b-quark, we predict M_{X_b}= (10144+-106) MeV for the X_b(b\bar{b}q \bar{q}), which is much below the {\bar B}B* threshold in contrast to the {\bar B}B* molecule prediction [2], and for the X_b^s(b\bar{b}s \bar{s}), a mass-splitting M_{X^s_{b}}-M_{X_b}=-(121+-182) MeV. Our analysis also indicates that the mass-splitting between the ground state and the radial excitation of about (225~250) MeV is much smaller than in the case of ordinary mesons and is (within the errors) flavour-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.