Possible molecular states of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math>) and new exotic states <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>X</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2900</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2900</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:mrow><mml:mi>a</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>2900</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mn>0</mml:mn></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:mrow><mml:mi>a</mml:mi></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>2900</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math>

Abstract

Two isosinglet hadron states ${X}_{0}(2900)$ and ${X}_{1}(2900)$ with $J=0$ and 1, respectively, discovered by the LHCb collaboration in 2020, are identified as molecular bound states of ${\overline{D}}^{*}{K}^{*}$. Recently two structures ${T}_{cs0}^{a}(2900{)}^{0}$ and ${T}_{cs0}^{a}(2900{)}^{++}$ have been observed at the hadron spectra, and one would suspect if they also are molecular states of ${D}^{*}$ and ${K}^{*}$. As long as they are of the molecular structures of ${D}^{*}{K}^{*}$, the hadron states must be in an isovector, namely ${T}_{cs0}^{a}(2900{)}^{0}$ and ${T}_{cs0}^{a}(2900{)}^{++}$ are ${I}_{3}=\ensuremath{-}1$, 1 components of the isovector. If it is the case, then the corresponding ${T}_{cs0}^{a}(2900{)}^{+}$ of $I=1,{I}_{3}=0$, and ${T}_{cs0}^{\ensuremath{'}a}(2900{)}^{+}$ of $I=0,{I}_{3}=0$ so far have evaded experimental observation, but should be found by the future experiments. To testify this ansatz, in this paper we study the possible molecular structures of ${\overline{D}}^{*}{K}^{*}$ and ${D}^{*}{K}^{*}$ within the Bethe-Salpeter framework. With reasonable input parameters it is found that ${\overline{D}}^{*}{K}^{*}$ isoscalar systems with ${J}^{P}={0}^{+}$ and ${1}^{+}$ have solutions. The result supports the ansatz of ${X}_{0}(2900)$ and ${X}_{1}(2900)$ being molecular states of ${\overline{D}}^{*}{K}^{*}$. Whereas for the system of ${D}^{*}{K}^{*}$ with $I=1$ the corresponding Bethe-Salpeter equation has no solution. Thus we can draw a clear conclusion that ${T}_{cs0}^{a}(2900{)}^{0}$ and ${T}_{cs0}^{a}(2900{)}^{++}$ should not be bound states of ${D}^{*}$ and ${K}^{*}$. The two structures observed by the LHCb collaboration may be caused by dynamics, such as the well-recognized triangle anomalies or other mechanisms.

Topics & Concepts