Can theX(3872)be a1++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 (ccqq) state with J P C = 1 ++ . For definiteness, we work with the current proposed recently by Maiani et al [1], at leading order in αs, consider the contributions of higher dimension condensates and keep terms which are linear in the light quark mass mq. We find MX = (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 MXs − MX = −(61 ± 30) MeV. The massdifference between the neutral states due to isospin violation of about (2.6 ∼ 3.9) MeV is smaller than the value (8±3) MeV proposed in [1]. For the b-quark, we predict MX b = (10144±106) MeV for the X b (bbqq), which is much below theBB * threshold in contrast to theBB * molecule prediction [2], and for the X s b (bbss), a mass-splitting M X s b − MX 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 fπ, 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.

The hidden-charm pentaquark and tetraquark states

“…The interpolating current J 4µ was also used to study the X(3872) as a tetraquark state in Refs. [575,576], where the extracted hadron masses were consistent with the result in Table 25. …”

Modification of theBmeson mass in a magnetic field from QCD sum rules

“…These values were chosen to mantain consistency with other QCDSR calculations [31,32]. The continuum threshold s 0 is a free parameter fixed using the phenomenological rule ðm H þ 400Þ MeV≲ ffiffiffiffi ffi s 0 p ≲ ðm H þ 800Þ MeV [31,38], which is an appropriate way of fixing s 0 when the s 0 -stable region falls outside the allowed M 2 window (explained below). This is the case for heavy-light mesons, as noted in Ref.…”

“…The inclusion of the effects from the magnetic field on the condensate terms is done by taking hqqi and hqσ 12 qi as functions of eB. The value used for the light quark chiral condensate in the absence of the magnetic field is hqqi 0 ¼ ð−0.23Þ 3 GeV 3 [31,32], while hQQi ∼ 0 for heavy quarks [9,33]. For the ratio ΣðeBÞ ≡ hqqiðeBÞ=hqqi 0 , we use two different parametrizations according to the intensity of the magnetic field.…”

Docc¯nn¯bound states exist?

“…Hogaasen et al [16] explained the mass and coupling properties of the X 3872 resonance as a 1 four-quark state using a chromomagnetic interaction once all spin-color configurations compatible with these quantum numbers were included. Matheus et al [17] used QCD spectral sum rules to test the nature of the X 3872 within a diquark-antidiquark scheme, identified as a possible 1 c cn n candidate.…”