Phenomenological description of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow>

For coupled channels <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msup> <a:mrow> <a:mi>D</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msup> <a:msup> <a:mrow> <a:mi>K</a:mi> </a:mrow> <a:mrow> <a:mo>+</a:mo> </a:mrow> </a:msup> </a:mrow> </a:math> , <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>D</c:mi> <c:mo>+</c:mo> </c:msup> <c:msup> <c:mi>K</c:mi> <c:mn>0</c:mn> </c:msup> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>D</e:mi> <e:mi>s</e:mi> <e:mo>+</e:mo> </e:msubsup> <e:mi>η</e:mi> </e:math> , and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msubsup> <g:mi>D</g:mi> <g:mi>s</g:mi> <g:mo>+</g:mo> </g:msubsup> <g:msup> <g:mi>π</g:mi> <g:mn>0</g:mn> </g:msup> </g:math> , the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>S</i:mi> </i:math> -wave scattering amplitudes are constructed taking into account the mixing of the isoscalar resonance <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi>D</k:mi> <k:mrow> <k:mi>s</k:mi> <k:mn>0</k:mn> </k:mrow> <k:mo>*</k:mo> </k:msubsup> <k:mo stretchy="false">(</k:mo> <k:mn>2317</k:mn> <k:msup> <k:mo stretchy="false">)</k:mo> <k:mo>+</k:mo> </k:msup> </k:math> with nonresonance amplitudes with isospin <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>I</o:mi> <o:mo>=</o:mo> <o:mn>1</o:mn> </o:math> . The phenomenological approach we use allows us to quite simply clear up the general structure of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msubsup> <q:mi>D</q:mi> <q:mrow> <q:mi>s</q:mi> <q:mn>0</q:mn> </q:mrow> <q:mo>*</q:mo> </q:msubsup> <q:mo stretchy="false">(</q:mo> <q:mn>2317</q:mn> <q:msup> <q:mo stretchy="false">)</q:mo> <q:mo>+</q:mo> </q:msup> <q:mo stretchy="false">→</q:mo> <q:msubsup> <q:mi>D</q:mi> <q:mi>s</q:mi> <q:mo>+</q:mo> </q:msubsup> <q:msup> <q:mi>π</q:mi> <q:mn>0</q:mn> </q:msup> </q:math> decay amplitude violating isospin. We show that the phase of this amplitude coincides with the phase of the nonresonanct <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msubsup> <v:mi>D</v:mi> <v:mi>s</v:mi> <v:mo>+</v:mo> </v:msubsup> <v:msup> <v:mi>π</v:mi> <v:mn>0</v:mn> </v:msup> </v:math> scattering amplitude in agreement with the Watson theorem. Its modulus squared, as it should be, determines the width of the resonance peak in the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msubsup> <x:mi>D</x:mi> <x:mi>s</x:mi> <x:mo>+</x:mo> </x:msubsup> <x:msup> <x:mi>π</x:mi> <x:mn>0</x:mn> </x:msup> </x:math> channel. Taking into account the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msup> <z:mi>π</z:mi> <z:mn>0</z:mn> </z:msup> <z:mo>−</z:mo> <z:mi>η</z:mi> </z:math> mixing in internal lines up to the second order inclusively ensures that the unitarity condition is fulfilled. The presented analysis complements the description of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msubsup> <bb:mi>D</bb:mi> <bb:mrow> <bb:mi>s</bb:mi> <bb:mn>0</bb:mn> </bb:mrow> <bb:mo>*</bb:mo> </bb:msubsup> <bb:mo stretchy="false">(</bb:mo> <bb:mn>2317</bb:mn> <bb:msup> <bb:mo stretchy="false">)</bb:mo> <bb:mo>+</bb:mo> </bb:msup> <bb:mo stretchy="false">→</bb:mo> <bb:msubsup> <bb:mi>D</bb:mi> <bb:mi>s</bb:mi> <bb:mo>+</bb:mo> </bb:msubsup> <bb:msup> <bb:mi>π</bb:mi> <bb:mn>0</bb:mn> </bb:msup> </bb:math> decay based on the coupled channel unitarized chiral perturbation theory. The numerical estimates obtained by us for the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msubsup> <gb:mi>D</gb:mi> <gb:mrow> <gb:mi>s</gb:mi> <gb:mn>0</gb:mn> </gb:mrow> <gb:mo>*</gb:mo> </gb:msubsup> <gb:mo stretchy="false">(</gb:mo> <gb:mn>2317</gb:mn> <gb:msup> <gb:mo stretchy="false">)</gb:mo> <gb:mo>+</gb:mo> </gb:msup> <gb:mo stretchy="false">→</gb:mo> <gb:msubsup> <gb:mi>D</gb:mi> <gb:mi>s</gb:mi> <gb:mo>+</gb:mo> </gb:msubsup> <gb:msup> <gb:mi>π</gb:mi> <gb:mn>0</gb:mn> </gb:msup> </gb:math> decay width do not contradict those available in the literature.