Hadronic molecule model for the doubly charmed state $$ {T}_{cc}^{+} $$

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>The mass, current coupling, and width of the doubly charmed four-quark meson <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {T}_{cc}^{+} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> are explored by treating it as a hadronic molecule <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {M}_{cc}^{+}\equiv {D}^0{D}^{\ast +} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo>≡</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>. The mass and current coupling of this molecule are calculated using the QCD two-point sum rule method by including into analysis contributions of various vacuum condensates up to dimension 10. The prediction for the mass <jats:italic>m</jats:italic> = (4060 <jats:italic>±</jats:italic> 130) MeV exceeds the two-meson <jats:italic>D</jats:italic><jats:sup>0</jats:sup><jats:italic>D</jats:italic><jats:sup>∗+</jats:sup> threshold 3875<jats:italic>.</jats:italic>1 MeV, which makes decay of the molecule <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {M}_{cc}^{+} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> to a pair of conventional mesons <jats:italic>D</jats:italic><jats:sup>0</jats:sup><jats:italic>D</jats:italic><jats:sup>∗+</jats:sup> kinematically allowed process. The strong coupling <jats:italic>G</jats:italic> of particles at the vertex <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {M}_{cc}^{+}{D}^0{D}^{\ast +} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> is found by applying the QCD three-point sum rule approach, and used to evaluate the width of the decay <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {M}_{cc}^{+}\to {D}^0{D}^{\ast +} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:msup> <mml:mi>D</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>. Obtained result for the width Γ = (3<jats:italic>.</jats:italic>8 <jats:italic>±</jats:italic> 1<jats:italic>.</jats:italic>7) MeV demonstrates that <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {M}_{cc}^{+} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> is wider than the resonance <jats:inline-formula><jats:alternatives><jats:tex-math>$$ {T}_{cc}^{+} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>cc</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>