Analysis of three-body decays B→D(V→)PP under the factorization-assisted topological-amplitude approach

Motivated by the accumulated experimental results on three-body charmed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi></a:math> decays with resonance contributions in , LHCb, and Belle (II), we systematically analyze <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>B</c:mi><c:mrow><c:mo stretchy="false">(</c:mo><c:mi>s</c:mi><c:mo stretchy="false">)</c:mo></c:mrow></c:msub><c:mo stretchy="false">→</c:mo><c:msub><c:mi>D</c:mi><c:mrow><c:mo stretchy="false">(</c:mo><c:mi>s</c:mi><c:mo stretchy="false">)</c:mo></c:mrow></c:msub><c:mo stretchy="false">(</c:mo><c:mi>V</c:mi><c:mo stretchy="false">→</c:mo><c:mo stretchy="false">)</c:mo><c:msub><c:mi>P</c:mi><c:mn>1</c:mn></c:msub><c:msub><c:mi>P</c:mi><c:mn>2</c:mn></c:msub></c:math> decays with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>V</m:mi></m:math> representing a vector resonance (<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>ρ</o:mi><o:mo>,</o:mo><o:msup><o:mi>K</o:mi><o:mo>*</o:mo></o:msup><o:mo>,</o:mo><o:mi>ω</o:mi></o:math>, or <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ϕ</q:mi></q:math>) and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>P</s:mi><s:mrow><s:mn>1</s:mn><s:mo>,</s:mo><s:mn>2</s:mn></s:mrow></s:msub></s:math> as a light pseudoscalar meson (pion or kaon). The intermediate subprocesses <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>B</u:mi><u:mrow><u:mo stretchy="false">(</u:mo><u:mi>s</u:mi><u:mo stretchy="false">)</u:mo></u:mrow></u:msub><u:mo stretchy="false">→</u:mo><u:msub><u:mi>D</u:mi><u:mrow><u:mo stretchy="false">(</u:mo><u:mi>s</u:mi><u:mo stretchy="false">)</u:mo></u:mrow></u:msub><u:mi>V</u:mi></u:math> are calculated with the factorization-assisted topological-amplitude (FAT) approach and the intermediate resonant states <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi>V</bb:mi></bb:math> described by the relativistic Breit-Wigner distribution successively decay to <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi>P</db:mi><db:mn>1</db:mn></db:msub><db:msub><db:mi>P</db:mi><db:mn>2</db:mn></db:msub></db:math> via strong interaction. Taking all lowest resonance states (<fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>ρ</fb:mi><fb:mo>,</fb:mo><fb:msup><fb:mi>K</fb:mi><fb:mo>*</fb:mo></fb:msup><fb:mo>,</fb:mo><fb:mi>ω</fb:mi><fb:mo>,</fb:mo><fb:mi>ϕ</fb:mi></fb:math>) into account, we calculate the branching fractions of these decay modes as well as the Breit-Wigner-tail effects for <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>B</hb:mi><hb:mrow><hb:mo stretchy="false">(</hb:mo><hb:mi>s</hb:mi><hb:mo stretchy="false">)</hb:mo></hb:mrow></hb:msub><hb:mo stretchy="false">→</hb:mo><hb:msub><hb:mi>D</hb:mi><hb:mrow><hb:mo stretchy="false">(</hb:mo><hb:mi>s</hb:mi><hb:mo stretchy="false">)</hb:mo></hb:mrow></hb:msub><hb:mo stretchy="false">(</hb:mo><hb:mi>ρ</hb:mi><hb:mo>,</hb:mo><hb:mi>ω</hb:mi><hb:mo stretchy="false">→</hb:mo><hb:mo stretchy="false">)</hb:mo><hb:mi>K</hb:mi><hb:mi>K</hb:mi></hb:math>. Our results agree with the data by , LHCb, and Belle (II). Among the predictions that are still not observed, there are some branching ratios of order <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msup><rb:mn>10</rb:mn><rb:mrow><rb:mo>−</rb:mo><rb:mn>6</rb:mn></rb:mrow></rb:msup><rb:mi>–</rb:mi><rb:msup><rb:mn>10</rb:mn><rb:mrow><rb:mo>−</rb:mo><rb:mn>4</rb:mn></rb:mrow></rb:msup></rb:math> which are hopeful to be measured by LHCb and Belle II. Our approach and the perturbative QCD approach (PQCD) adopt the compatible theme to deal with the resonance contributions. What is more, our data for the intermediate two-body charmed <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi>B</tb:mi></tb:math>-meson decays in FAT approach are more precise. As a result, our results for branching fractions have smaller uncertainties, especially for color-suppressed emission diagram dominated modes.