Résumé
We evaluate the masses and decay constants of the 0<sup loc="post">+</sup> and 1<sup loc="post">−</sup> open-charm (<math altimg="si1.svg"><mover accent="true"><mrow><mi>c</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>u</mi><mi>s</mi><mo stretchy="false">)</mo></math> tetraquarks and molecular states from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR). This method takes into account the stability criteria where the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the D<sup loc="post">−</sup>K<sup loc="post">+</sup> invariant mass recently reported by LHCb from B<sup loc="post">+</sup> → D<sup loc="post">+</sup>(D<sup loc="post">−</sup>K<sup loc="post">+</sup>) decays. We expect that the resonance near the D<sup loc="post">−</sup>K<sup loc="post">+</sup> threshold can be originated from the 0<sup loc="post">++</sup>(D<sup loc="post">−</sup>K<sup loc="post">+</sup>) molecule and/or D<sup loc="post">−</sup>K<sup loc="post">+</sup> scattering. The X0(2900) scalar state and the resonance XJ(3150) (if J = 0) can emerge from a minimal mixing model, with a tiny mixing angle θ0 ≃ (5.2 ± 1.9)<sup loc="post">0</sup>, between a scalar Tetramole (<math altimg="si2.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi mathvariant="script">M</mi><mn>0</mn></mrow></msub></math>) (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers), having a mass <math altimg="si3.svg"><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi mathvariant="script">M</mi><mn>0</mn></mrow></msub></mrow></msub><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>2743</mn><mo stretchy="false">(</mo><mn>18</mn><mo stretchy="false">)</mo><mspace width="0.25em"/><mtext>MeV</mtext></math>, and the first radial excitation of the D<sup loc="post">−</sup>K<sup loc="post">+</sup> molecule with mass M(DK)1 = 3678(310) MeV. In an analogous way, the X1(2900) and the XJ(3350) (if J = 1) could be a mixture between the vector Tetramole (<math altimg="si4.svg"><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi mathvariant="script">M</mi><mn>1</mn></mrow></msub></math>), with a mass <math altimg="si5.svg"><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi mathvariant="script">M</mi><mn>1</mn></mrow></msub></mrow></msub><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>2656</mn><mo stretchy="false">(</mo><mn>20</mn><mo stretchy="false">)</mo><mspace width="0.25em"/><mtext>MeV</mtext></math>, and its first radial excitation having a mass <math altimg="si6.svg"><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi mathvariant="script">T</mi></mrow><mrow><mi mathvariant="script">M</mi><mn>1</mn></mrow></msub></mrow></msub><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>4592</mn><mo stretchy="false">(</mo><mn>141</mn><mo stretchy="false">)</mo><mspace width="0.25em"/><mtext>MeV</mtext></math> with an angle θ0 ≃ (9.1 ± 0.6)<sup loc="post">0</sup>. A (non)-confirmation of these statements requires experimental findings of the quantum numbers of the resonances at 3150 and 3350 MeV.