Abstract
We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid’s constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract hybrid mass predictions for all JP ∈ {0±, 1±}, as well as explore possible mixing effects with conventional quark-antiquark mesons. Within theoretical uncertainties, our results are consistent with a degeneracy between the heavy-nonstrange and heavy-strange hybrids in all JP channels. We find a similar mass hierarchy of 1+, 1−, and 0+ states (a 1+ state lighter than essentially degenerate 1− and 0+ states) in both the charm and bottom sectors, and discuss an interpretation for the 0− states. If conventional meson mixing is present the effect is an increase in the hybrid mass prediction, and we estimate an upper bound on this effect.
Highlights
JHEP05(2017)149 the X(5568) has been studied as abdsu tetraquark [35])
Ground state masses of bottom-charm hybrids were recently computed using QCD sum-rules in [36]; we focus on a QCD sum-rules analysis of open-flavour heavylight hybrids i.e., hybrids containing one heavy quark and one light quark
We determine the bounds of our Borel scale by examining two conditions: the convergence of the operator product expansion (OPE), and the pole contribution to the overall mass prediction, mirroring our previous work done in charmonium and bottomonium systems [26]
Summary
Following GRW, we define open-flavour heavy-light hybrid interpolating currents jμ. where gs is the strong coupling and λa are the Gell-Mann matrices. (Note that there is no Diagram IV in figure 1 because, in [19], Diagram IV corresponds to an OPE contribution stemming from 6d quark condensates that is absent in the open-flavour heavy-light systems.) The MS-scheme with the D = 4 + 2 convention is used, and μ is the corresponding renormalization scale. The first term on the right-hand side of (2.14) corresponds to the diagrams of figure 1 whereas the last two terms give rise to new, renormalization-induced contributions to the OPE. The only exceptions are those containing the 5d mixed condensate (2.9); these give rise to the pair of diagrams depicted in figure 2 Both of these tree-level diagrams contain a heavy quark propagator with momentum q and are multiplied by a factor of 1 in (2.14), precisely what is needed to cancel the non-local divergence (2.11). 36(7 + z) 12(21 + 19z) −12(21 + 19z) 12(51 − 19z) −12(51 − 19z) f3(qGq)(z) 9(26 + 27z − 21z2) −9(26 + 27z − 21z2) −3(162 − 351z + 29z2) 3(162 − 351z + 29z2) −(162 + 369z + 205z2) 162 + 369z + 205z2 78 − 999z + 569z2 −(78 − 999z + 569z2)
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