Revisiting the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow><mml:mi>D</mml:mi><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:math> chiral interactions with the local momentum-space regularization up to the third order and the nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>
Bo Wang, Lu Meng
Abstract
We revisit the $D{D}^{*}$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $D{D}^{*}$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different than the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from the HAL QCD method, but appearing in the longer distance rather than $1<r<2\text{ }\text{ }\mathrm{fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of ${T}_{cc}^{+}$.