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arXiv 1710.03067hep-ph
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QCD中的奇异多夸克态及其性质

Exotic polyquark states and their properties in QCD

Dmitri Melikhov

摘要:

我们制定了严格的标准,选择图考虑到潜在的多夸克(四或五)极在QCD的分析。这些准则的中心点是要求相关格林函数的费曼图包含四夸克(或在五夸克情况下分别包含五夸克)中间态和相应的切割。它表明,一些图表,“视觉上”似乎包含四夸克削减,原来是免费的这些奇异性,因此不应考虑在计算四夸克的性质。然后我们考虑大- $N_c$ QCD,它在许多情况下提供了强子性质的定性正确的图像,并详细讨论了四夸克态。对于“直接”和“重组”四点格林函数,这可能包含四夸克极点,我们制定大- $N_c$一致性条件,强烈限制的行为的四夸克到普通介子的过渡振幅。最后,这些条件使我们能够得到在大的$N_c$的潜在的四夸克态的宽度的限制。我们报告说,无论是风味异国情调和cryptoexotic(即,如果存在相应的极点,则味非奇异的)四夸克具有$O(1/N_c^2)$级的宽度,即,与具有$O(1/N_c)$级宽度的普通$\bar qq$介子相比,它们应该在参数上更窄。此外,对于味奇异态,大$N_c$一致性条件需要两个窄味奇异态,每个态主要耦合到一个特定的介子-介子通道。

英文摘要:

We formulate rigorous criteria for selecting diagrams to be taken into account in the analysis of potential polyquark (tetra or penta) poles in QCD. The central point of these criteria is the requirement that the Feynman diagrams for the relevant Green functions contain four-quark (or, respectively, five-quark in the pentaquark case) intermediate states and the corresponding cuts. It is shown that some diagrams which "visually" seem to contain the four-quark cuts, turn out to be free of these singularities and therefore should not be taken into account when calculating the tetraquark properties. We then consider large-$N_c$ QCD which in many cases provide qualitatively correct picture of hadron properties and discuss in detail the tetraquark states. For the "direct" and the "recombination" four-point Green functions, which may potentially contain the tetraquark poles, we formulate large-$N_c$ consistency conditions which strongly restrict the behaviour of the tetraquark-to-ordinary meson transition amplitudes. In the end, these conditions allow us to obtain constraints on width of the potential tetraquark states at large $N_c$. We report that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if the corresponding poles exist, have a width of order $O(1/N_c^2)$, i.e. they should be parametrically narrower compared to the ordinary $\bar qq$ mesons with a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the large-$N_c$ consistency conditions require two narrow flavor-exotic states, each of these states coupling dominantly to one specific meson-meson channel.

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