Abstract
It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of completely compact multiquark bound states. Multiquark operators still play a crucial role in the description of exotic states in regions of configuration space where the hadronic clusters are close to each other. Our proof gives a foundation for a unified viewpoint, where the multiquark-type and the molecular-type approaches play complementary roles, at the gauge-invariant nonlocal operator level.
Highlights
IntroductionAn indication that multiquark states are not of the completely confined type arises from the observation that interpolating local currents, that might couple to them, can always, by Fierz rearrangements, be brought into forms where they appear as combinations of products of colorsinglet quark bilinear and/or trilinear local operators [2,3]
The possibility of the existence of multiquark states [1,2], i.e., of states containing more than a pair of valence quark-antiquark for mesons and more than three valence quarks for baryons, called exotic states, raises in QCD the following question: can QCD produce, by the sole confining forces, multiquark bound states in the same way as it produces ordinary hadrons?An indication that multiquark states are not of the completely confined type arises from the observation that interpolating local currents, that might couple to them, can always, by Fierz rearrangements, be brought into forms where they appear as combinations of products of colorsinglet quark bilinear and/or trilinear local operators [2,3]
The cluster reducibility property of multiquark operators provides a general proof of the nonexistence of completely confined or compact multiquark states
Summary
An indication that multiquark states are not of the completely confined type arises from the observation that interpolating local currents, that might couple to them, can always, by Fierz rearrangements, be brought into forms where they appear as combinations of products of colorsinglet quark bilinear and/or trilinear local operators [2,3]. Correlation functions of such currents become dominated by disconnected diagrams, representing free hadron propagators, while the connected diagrams depict interactions among hadrons, which are of the nonconfining type. One expects to exhibit more their confined nature by means of their bound-state spectrum, which should show up through a tower of states lying at non-negligible distances from the multiquark thresholds, in analogy with the ordinary-hadron cases. A realization of the Y-shapedtype interactions is provided by the diquark picture [6,7,8]
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