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Register a new userNature of the X(5568) : a critical Laplace sum rule analysis at N2LO
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R. Albuquerque
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We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)bar(bd) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (tau-sum rule variable, t_c continuum threshold and subtraction constant mu). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results + the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173sim 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavours (buds), do not support some previous interpretations of the D0 candidate[1], X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2thetaapprox 0.15. One can also scan the region (2327~ 2444) MeV (where the D*_{s0}(2317) might be a good candidate) and the one (5173~ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or pi+hadrons decays.
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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.
These talks review and summarize our results in [1,2] on $XYZ$-like spectra obtained from QCD Laplace Sum Rules in the chiral limit at next-to-next-leading order (N2LO) of perturbation theory (PT) and including leading order (LO) contributions of dimensions $dleq 6-8$ non-perturbative condensates. We conclude that the observed $XZ$ states are good candidates for $1^{+}$ and $0^+$ molecules or / and four-quark states while the predictions for $1^-$ and $0^-$ states are about 1.5 GeV above the $Y_{c,b}$ experimental candidates and hadronic thresholds. We (numerically) find that these exotic molecules couple weakly to the corresponding interpolating currents than ordinary $D,B$ heavy-light mesons while we observe that these couplings decrease faster [$1/m_b^{3/2}$ (resp. $1/m_b$) for the $1^+,0^+$ (resp. $1^-,0^-)$ states] than $1/m_b^{1/2}$. Our results do not also confirm the existence of the $X(5568)$ state in agreement with LHCb findings.
This talk reviews and summarizes some of our results in [1] on XYZ- SU3 Breakings obtained from QCD Laplace Sum Rules (LSR) at next-to-next-leading order (N2LO) of perturbative (PT) theory and including next-to-leading order (NLO) SU3 breaking corrections and leading order (LO) contributions of dimensions d< (6 - 8) non-perturbative condensates. We conclude that the observed X states are good candidates for being 1^++ and 0^++ molecules states. We find that the SU3 breakings are relatively small for the masses (< 10 (resp. 3) %) for the charm (resp. bottom) channels while they are large (< 20 %) for the couplings. Like in the chiral limit case, the couplings decrease faster: 1/m_b^3/2 than 1/m_b^1/2 of HQET. Our approach cannot clearly separate ( within the errors ) some molecule states from the four-quark ones with the same quantum numbers.
We review our results in Refs.[1,2] for the masses and couplings of heavy-light DD(BB)-like molecules and (Qq)(Qq)-like four-quark states from relativistic QCD Laplace sum rules (LSR) where next-to-next-to-leading order (N2LO) PT corrections in the chiral limit, next-to-leading order (NLO) SU3 PT corrections and non-perturbative contributions up to dimension d=6-8 are included. The factorization properties of molecule and four-quark currents have been used for the estimate of the higher order PT corrections. New integrated compact expressions of the spectral functions at leading order (LO) of perturbative QCD and up to dimensions d< (6 - 8) non-perturbative condensates are presented. The results are summarized in Tables 5 to 10, from which we conclude, within the errors, that the observed XZ states are good candidates for being 1^{++} and 0^{++} molecules or/and four-quark states, contrary to the observed Y states which are too light compared to the predicted 1^{-pm} and 0^{-pm} states. We find that the SU3 breakings are relatively small for the masses (< 10(resp. 3)%) for the charm (resp. bottom) channels while they are large (< 20%) for the couplings which decrease faster (1/m_{b}^{3/2}) than 1/m_{b}^{1/2} of HQET. QCD spectral sum rules (QSSR) approach cannot clearly separate (within the errors) molecules from four-quark states having the same quantum numbers. Results for the BK (DK)-like molecules and (Qq)(us)-like four-quark states from [3] are also reviewed which do not favour the molecule or/and four-quark interpretation of the X(5568). We suggest to scan the charm (2327 ~ 2444) MeV and bottom (5173 ~ 5226) MeV regions for detecting the (unmixed)(cu)ds and (bu)ds states. We expect that future experimental data and lattice results will check our predictions.
We present new compact integrated expressions of SU3 breaking corrections to 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 OPE. Including N2LO PT corrections in the chiral limit and NLO SU3 PT corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results for the XYZ-like masses and decay constants from QCD spectral sum rules. Systematic errors are estimated from a geometric growth of the higher order PT corrections and from some partially known d=8 non-perturbative contributions. Our optimal results, based on stability criteria, are summarized in Tables 18 to 21 and compared with some LO results in Table 22. In most channels, the SU3 corrections on the meson masses are tiny: < 10% (resp. <3%) for the c (resp. b)-quark channel but can be large for the couplings (< 20%). Within the lowest dimension currents, most of the 0^{++} and 1^{++} states are below the physical thresholds while our predictions cannot discriminate a molecule from a four-quark state. A comparison with the masses of some experimental candidates indicates that the 0^{++} X(4500) might have a large D^*_{s0}D^*_{s0} molecule component while an interpretation of the 0^{++} candidates as four-quark ground states is not supported by our findings. The 1^{++} X(4147) and X(4273) are compatible with the D^*_{s}D_{s}, bar D^*_{s0}D_{s1} molecules and/or with the axial-vector A_c four-quark ground state. Our results for the 0^{-pm}, 1^{-pm} and for different beauty states can be tested in the future data. Finally, we revisit our previous estimates [1] for the D^*_{0}D^*_{0} and D^*_{0}D_{1} and present new results for the D_1D_1.
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