Study of the B−→K−ηηc decay due to the <mml:math …

We study the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>B</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msup><a:mi>K</a:mi><a:mo>−</a:mo></a:msup><a:mi>η</a:mi><a:msub><a:mi>η</a:mi><a:mi>c</a:mi></a:msub></a:math> decay by taking into account the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>S</d:mi></d:math>-wave contributions from the pseudoscalar meson-pseudoscalar meson interactions within the unitary coupled-channel approach, where the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>D</f:mi><f:mover accent="true"><f:mi>D</f:mi><f:mo stretchy="false">¯</f:mo></f:mover></f:math> bound state is dynamically generated. In addition, the contribution from the intermediate resonance <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msubsup><j:mrow><j:mi>K</j:mi></j:mrow><j:mrow><j:mn>0</j:mn></j:mrow><j:mrow><j:mo>*</j:mo></j:mrow></j:msubsup><j:mo stretchy="false">(</j:mo><j:mn>1430</j:mn><j:msup><j:mrow><j:mo stretchy="false">)</j:mo></j:mrow><j:mrow><j:mo>−</j:mo></j:mrow></j:msup></j:mrow></j:math>, with <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msubsup><n:mi>K</n:mi><n:mn>0</n:mn><n:mo>*</n:mo></n:msubsup><n:mo stretchy="false">(</n:mo><n:mn>1430</n:mn><n:msup><n:mo stretchy="false">)</n:mo><n:mo>−</n:mo></n:msup><n:mo stretchy="false">→</n:mo><n:msup><n:mi>K</n:mi><n:mo>−</n:mo></n:msup><n:mi>η</n:mi></n:math>, is also considered. Our results show that there is a clear peak around 3720 MeV in the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>η</s:mi><s:msub><s:mi>η</s:mi><s:mi>c</s:mi></s:msub></s:math> invariant mass distribution, which could be associated with the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>D</u:mi><u:mover accent="true"><u:mi>D</u:mi><u:mo stretchy="false">¯</u:mo></u:mover></u:math> bound state. The future precise measurements of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>B</y:mi><y:mo>−</y:mo></y:msup><y:mo stretchy="false">→</y:mo><y:msup><y:mi>K</y:mi><y:mo>−</y:mo></y:msup><y:mi>η</y:mi><y:msub><y:mi>η</y:mi><y:mi>c</y:mi></y:msub></y:math> process at the Belle II and LHCb experiments could be, therefore, used to check the existence of the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi>D</bb:mi><bb:mover accent="true"><bb:mi>D</bb:mi><bb:mo stretchy="false">¯</bb:mo></bb:mover></bb:math> bound state, and to deepen our understanding of the hadron-hadron interactions.