Enhanced quark-loop contribution to pure annihilation nonleptonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-meson decays in the PQCD approach

In this study, we conduct an enhanced investigation of pure annihilation-type charmless hadronic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>B</a:mi></a:math> decays within the framework of the perturbative QCD approach. Specifically, we account for the quark-loop enhanced contribution to various decay processes at the next-to-leading order (NLO) in the strong coupling constant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>α</c:mi><c:mi>s</c:mi></c:msub></c:math>. The NLO amplitudes possess large imaginary parts that have signs opposite to those of the leading-order amplitudes. This cancellation effect implies that the NLO contribution does not significantly influence the branching ratios of the processes under consideration. However, the NLO effect explored in this work constitutes an important source of the strong phases in the weak-annihilation nonleptonic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mover accent="true"><e:mi>B</e:mi><e:mo stretchy="false">¯</e:mo></e:mover><e:mi>q</e:mi></e:msub></e:math>-meson decay amplitudes. As a result, it can have a substantial impact on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math>-violating observables such as the direct <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>C</k:mi><k:mi>P</k:mi></k:math> asymmetry <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi mathvariant="script">A</m:mi><m:mrow><m:mi>C</m:mi><m:mi>P</m:mi></m:mrow><m:mrow><m:mi>dir</m:mi></m:mrow></m:msubsup></m:math> and mixing-induced <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>C</p:mi><p:mi>P</p:mi></p:math> asymmetry <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi mathvariant="script">A</r:mi><r:mrow><r:mi>C</r:mi><r:mi>P</r:mi></r:mrow><r:mrow><r:mi>mix</r:mi></r:mrow></r:msubsup></r:math>. The numerical result evidently revealed that NLO QCD correction significantly enhances both <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi mathvariant="script">A</u:mi><u:mrow><u:mi>C</u:mi><u:mi>P</u:mi></u:mrow><u:mrow><u:mi>dir</u:mi></u:mrow></u:msubsup></u:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msubsup><x:mi mathvariant="script">A</x:mi><x:mrow><x:mi>C</x:mi><x:mi>P</x:mi></x:mrow><x:mrow><x:mi>mix</x:mi></x:mrow></x:msubsup></x:math> of the pure annihilation-type <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>B</ab:mi></ab:math> decay processes.