Compositeness of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>(</mml:mo><mml:mn>3872</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> by considering decay and coupled-channels effects

Abstract

The compositeness of weakly bound states is discussed using the effective field theory from the viewpoint of the low-energy universality. We introduce a model with coupling of the single-channel scattering to the bare state, and study the compositeness of the bound state by varying the bare state energy. In contrast to the naive expectation that the near-threshold states are dominated by the molecular structure, we demonstrate that a noncomposite state can always be realized even with a small binding energy. At the same time, however, it is shown that a fine tuning is necessary to obtain the noncomposite weakly bound state. In other words, the probability of finding a model with the composite dominant state becomes larger with the decrease of the binding energy, in accordance with the low-energy universality. For the application to exotic hadrons, we then discuss the modification of the compositeness due to decay and coupled-channels effects. We quantitatively show that these contributions suppress the compositeness, because of the increase of the fraction of other components. Finally, as examples of near-threshold exotic hadrons, the structures of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub></a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>X</b:mi><b:mo>(</b:mo><b:mn>3872</b:mn><b:mo>)</b:mo></b:mrow></b:math> are studied by evaluating the compositeness. We find the importance of the coupled-channels and decay contributions for the structures of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>T</c:mi><c:mrow><c:mi>c</c:mi><c:mi>c</c:mi></c:mrow></c:msub></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>X</d:mi><d:mo>(</d:mo><d:mn>3872</d:mn><d:mo>)</d:mo></d:mrow></d:math>, respectively. Published by the American Physical Society 2024

Topics & Concepts