Five-body <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>V</mml:mi></mml:math> semileptonic decays

Our main objective is to derive the decay rate for the semileptonic decays <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mo stretchy="false">→</a:mo><a:mi>V</a:mi><a:msup><a:mo>ℓ</a:mo><a:mo>+</a:mo></a:msup><a:msub><a:mi>ν</a:mi><a:mo>ℓ</a:mo></a:msub><a:mo stretchy="false">(</a:mo><a:mo>ℓ</a:mo><a:mo>=</a:mo><a:mi>e</a:mi><a:mo>,</a:mo><a:mi>μ</a:mi><a:mo stretchy="false">)</a:mo></a:math>, where <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>V</f:mi></f:math> represents a vector particle. In these decays, the vector particle <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>V</h:mi></h:math> decays into three pseudoscalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>D</j:mi><j:mo stretchy="false">→</j:mo><j:mi>ω</j:mi><j:msup><j:mo>ℓ</j:mo><j:mo>+</j:mo></j:msup><j:msub><j:mi>ν</j:mi><j:mo>ℓ</j:mo></j:msub></j:math>, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>ω</m:mi></m:math> subsequently decays into <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>π</o:mi><o:mo>+</o:mo></o:msup><o:msup><o:mi>π</o:mi><o:mo>−</o:mo></o:msup><o:msup><o:mi>π</o:mi><o:mn>0</o:mn></o:msup></o:math>, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>D</q:mi><q:mo stretchy="false">→</q:mo><q:mi>ω</q:mi></q:math> form factors. These measurements can be performed using data obtained from BESIII. Published by the American Physical Society 2024