<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.or

We have carried out an evaluation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>π</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi>π</a:mi> <a:mo>−</a:mo> </a:msup> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msubsup> <c:mi>D</c:mi> <c:mi>s</c:mi> <c:mo>+</c:mo> </c:msubsup> <c:msup> <c:mi>π</c:mi> <c:mo>+</c:mo> </c:msup> </c:math> mass distributions in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>D</e:mi> <e:mrow> <e:mi>s</e:mi> <e:mn>1</e:mn> </e:mrow> </e:msub> <e:mo stretchy="false">(</e:mo> <e:mn>2536</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> decay to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi>D</i:mi> <i:mi>s</i:mi> <i:mo>+</i:mo> </i:msubsup> <i:msup> <i:mi>π</i:mi> <i:mo>+</i:mo> </i:msup> <i:msup> <i:mi>π</i:mi> <i:mo>−</i:mo> </i:msup> </i:math> , from the perspective that the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>D</k:mi> <k:mrow> <k:mi>s</k:mi> <k:mn>1</k:mn> </k:mrow> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mn>2536</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> is a molecular state, mostly made from <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msup> <o:mi>K</o:mi> <o:mo>*</o:mo> </o:msup> <o:mi>D</o:mi> </o:math> in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>I</q:mi> <q:mo>=</q:mo> <q:mn>0</q:mn> </q:math> . We are able to obtain not only the mass distributions, but also the branching ratio of this decay. The shape of the mass distributions differs appreciably from those of the analogous reaction <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>D</s:mi> <s:mrow> <s:mi>s</s:mi> <s:mn>1</s:mn> </s:mrow> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mn>2460</s:mn> <s:mo stretchy="false">)</s:mo> <s:mo stretchy="false">→</s:mo> <s:msubsup> <s:mi>D</s:mi> <s:mi>s</s:mi> <s:mo>+</s:mo> </s:msubsup> <s:msup> <s:mi>π</s:mi> <s:mo>+</s:mo> </s:msup> <s:msup> <s:mi>π</s:mi> <s:mo>−</s:mo> </s:msup> </s:math> , which has been measured by the LHCb Collaboration and analyzed theoretically from the perspective that the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>D</x:mi> <x:mrow> <x:mi>s</x:mi> <x:mn>1</x:mn> </x:mrow> </x:msub> <x:mo stretchy="false">(</x:mo> <x:mn>2460</x:mn> <x:mo stretchy="false">)</x:mo> </x:math> is a molecular state of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mi>D</bb:mi> <bb:mo>*</bb:mo> </bb:msup> <bb:mi>K</bb:mi> </bb:math> , showing good agreement with the data. In spite of the analogy with the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>D</db:mi> <db:mrow> <db:mi>s</db:mi> <db:mn>1</db:mn> </db:mrow> </db:msub> <db:mo stretchy="false">(</db:mo> <db:mn>2460</db:mn> <db:mo stretchy="false">)</db:mo> </db:math> decay, the dynamical differences in the decay mechanism are important, since now the <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>f</hb:mi> <hb:mn>0</hb:mn> </hb:msub> <hb:mo stretchy="false">(</hb:mo> <hb:mn>500</hb:mn> <hb:mo stretchy="false">)</hb:mo> </hb:math> resonance is not generated, while it was the dominant mechanism in the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:msub> <lb:mi>D</lb:mi> <lb:mrow> <lb:mi>s</lb:mi> <lb:mn>1</lb:mn> </lb:mrow> </lb:msub> <lb:mo stretchy="false">(</lb:mo> <lb:mn>2460</lb:mn> <lb:mo stretchy="false">)</lb:mo> <lb:mo stretchy="false">→</lb:mo> <lb:msubsup> <lb:mi>D</lb:mi> <lb:mi>s</lb:mi> <lb:mo>+</lb:mo> </lb:msubsup> <lb:msup> <lb:mi>π</lb:mi> <lb:mo>+</lb:mo> </lb:msup> <lb:msup> <lb:mi>π</lb:mi> <lb:mo>−</lb:mo> </lb:msup> </lb:math> decay. Nonetheless, we find striking differences in the mass distributions compared with phase space as a consequence of the decay mechanism. The branching ratio obtained is an order of magnitude bigger than the one of the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msub> <qb:mi>D</qb:mi> <qb:mrow> <qb:mi>s</qb:mi> <qb:mn>1</qb:mn> </qb:mrow> </qb:msub> <qb:mo stretchy="false">(</qb:mo> <qb:mn>2460</qb:mn> <qb:mo stretchy="false">)</qb:mo> <qb:mo stretchy="false">→</qb:mo> <qb:msubsup> <qb:mi>D</qb:mi> <qb:mi>s</qb:mi> <qb:mo>+</qb:mo> </qb:msubsup> <qb:msup> <qb:mi>π</qb:mi> <qb:mo>+</qb:mo> </qb:msup> <qb:msup> <qb:mi>π</qb:mi> <qb:mo>−</qb:mo> </qb:msup> </qb:math> reaction, mostly due to the larger available phase space. We also show that the shape of the distributions obtained from the molecular picture is quite different from those obtained based on a <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>q</vb:mi> <vb:mover accent="true"> <vb:mi>q</vb:mi> <vb:mo stretchy="false">¯</vb:mo> </vb:mover> </vb:math> picture. We conclude that measuring the shape of the mass distributions and the total strength of the decay mode should be very valuable to learn about the structure of the