XYZ-like Spectra from Laplace Sum Rule at N2LO in the Chiral Limit

TL;DR

This paper refines QCD spectral sum rule calculations for heavy-light exotic states, incorporating higher-order corrections and comparing results with experimental data to better understand their masses and couplings.

Contribution

It introduces new compact expressions for spectral functions and includes N2LO corrections, improving previous sum rule results for XYZ-like states with systematic error estimates.

Findings

Masses of observed XZ states align with pure molecule or four-quark configurations.

Heavier states are about 1.5 GeV above Y_{c,b} mesons.

Exotic couplings are weaker than ordinary mesons, scaling with inverse powers of heavy quark mass.

Abstract

We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-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 $XYZ$-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 $J^{PC}=1^{+\pm}, 0^{++}$ molecule or/and four-quark states. The ones of the $1^{-\pm}, 0^{-\pm}$ 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 ($f_{DD}\approx 10^{-3}f_D$) and may behave numerically as $1/ \bar m_b^{3/2}$ (resp. $1/ \bar m_b$) for the $1^{+},0^{+}$ (resp. $1^{-}, 0^{-}$) states which can stimulate further theoretical studies of these decay constants.