Estimate of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-wave <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

It is shown that the Belle and LHCb data on the interference of the amplitudes of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>D</c:mi></c:mrow></c:math> partial waves in the decays <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:msup><e:mo stretchy="false">)</e:mo><e:mo>+</e:mo></e:msup><e:mo stretchy="false">→</e:mo><e:msup><e:mi>D</e:mi><e:mrow><e:mo>*</e:mo><e:mo>+</e:mo></e:mrow></e:msup><e:msubsup><e:mi>K</e:mi><e:mi>S</e:mi><e:mn>0</e:mn></e:msubsup></e:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>D</j:mi><j:mrow><j:mi>s</j:mi><j:mn>1</j:mn></j:mrow></j:msub><j:mo stretchy="false">(</j:mo><j:mn>2536</j:mn><j:msup><j:mo stretchy="false">)</j:mo><j:mo>−</j:mo></j:msup><j:mo stretchy="false">→</j:mo><j:msup><j:mover accent="true"><j:mi>D</j:mi><j:mo stretchy="false">¯</j:mo></j:mover><j:mrow><j:mo>*</j:mo><j:mn>0</j:mn></j:mrow></j:msup><j:msup><j:mi>K</j:mi><j:mo>−</j:mo></j:msup></j:math> allow us to obtain an estimate of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mi>S</q:mi></q:mrow></q:math>-wave <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>D</s:mi><s:mo>*</s:mo></s:msup><s:mi>K</s:mi></s:math> scattering length in the channel with isospin <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>I</u:mi><u:mo>=</u:mo><u:mn>0</u:mn></u:math>: <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mo stretchy="false">|</w:mo><w:msubsup><w:mi>a</w:mi><w:mrow><w:msup><w:mi>D</w:mi><w:mo>*</w:mo></w:msup><w:mi>K</w:mi></w:mrow><w:mrow><w:mo stretchy="false">(</w:mo><w:mn>0</w:mn><w:mo stretchy="false">)</w:mo></w:mrow></w:msubsup><w:mo stretchy="false">|</w:mo><w:mo>=</w:mo><w:mo stretchy="false">(</w:mo><w:mn>0.94</w:mn><w:mo>±</w:mo><w:mn>0.06</w:mn><w:mo stretchy="false">)</w:mo><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>fm</w:mi></w:math>. The possibility of explaining the found value by the contribution of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>D</eb:mi><eb:mrow><eb:mi>s</eb:mi><eb:mn>1</eb:mn></eb:mrow></eb:msub><eb:mo stretchy="false">(</eb:mo><eb:mn>2460</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math> resonance is discussed. The decay of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>B</ib:mi><ib:mrow><ib:mi>s</ib:mi><ib:mn>1</ib:mn></ib:mrow></ib:msub><ib:mo stretchy="false">(</ib:mo><ib:mn>5830</ib:mn><ib:mo stretchy="false">)</ib:mo><ib:mo stretchy="false">→</ib:mo><ib:msup><ib:mi>B</ib:mi><ib:mo>*</ib:mo></ib:msup><ib:mover accent="true"><ib:mi>K</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover></ib:math> is also briefly discussed.