XYZ-like spectra from Laplace sum rule at N2LO in the chiral limit

Abstract

We present new compact integrated expressions of QCD spectral functions of heavylight molecules and four-quark XY Z-like states at lowest order (LO) of perturbative (PT) QCD and up to d = 8 condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the XY Z-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11 to 14 and compared, in Section 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the XZ observed states are compatible with (almost) pure J P C = 1 +± , 0 ++ molecule or/and four-quark states. The ones of the 1 −± , 0 −± molecule / four-quark states are about 1.5 GeV above the Y c,b mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary D, B mesons (f DD ≈ 10 −3 f D ) and may behave numerically as 1/m 3/2 b (resp. 1/m b ) for the 1 + , 0 + (resp. 1 − , 0 − ) states which can stimulate further theoretical studies of these decay constants.

QCD sum rules approach to the X, Y and Z states

“…where the weak current J W µ is defined in (115) and the interpolating currents of the B and K pseudoscalar mesons are:…”

“…The contributions of the unknown order α 3 s (N3LO) correction are estimated from a geometric growth of the perturbative series [347] and are added as a source of systematic uncertainties in the truncation of the perturbative series. For a complete description on these NLO techniques in QCDSR, see [115,116] and references therein.…”

“…Using the fact that the final result must be independent of the arbitrary parameter µ (plateau / inflection point for the coupling and minimum for the 0.1 0.2 0.3 0.4 0.5 0.6 Table 9: Interpolating currents with a definite C-parity describing theDD-andD s D s -like molecular states for J PC = 0 ++ , 1 Table 8; b) The same as a) but for a given value of s 0 = 32 GeV 2 , and for different truncation of the perturbative series. Figures taken from [115]. mass), we consider as an optimal result the one at µ 4.5 GeV, where we deduce the result at N2LO, M DD = (3898 ± 36) MeV, and f DD = (170 ± 15), keV (258) which is included in Table 10.…”

“…This weak impact on the results from LO to N2LO is verified for the other tetraquark states too (see Refs. [115,116]). 7.5.…”

Pentaquarks with anticharm or beauty revisited

“…There is a renewed interest in the spectroscopy of exotic hadrons containing one or two heavy constituents. For a review, see, e.g., [1][2][3][4]. New configurations are studied, and exotic states suggested in the 70s or 80s are revisited.…”