Decay-angular-distribution correlated CP violation in heavy hadron cascade decays

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> violation in baryon decay processes is still undiscovered to date. We present a general analysis of the decay-angular distributions and the corresponding <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mi>P</c:mi></c:math> asymmetries in cascade decays of the type <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="double-struck">H</e:mi><e:mo stretchy="false">→</e:mo><e:mi>R</e:mi><e:mo stretchy="false">(</e:mo><e:mo stretchy="false">→</e:mo><e:mi>a</e:mi><e:mi>b</e:mi><e:mo stretchy="false">)</e:mo><e:mi>c</e:mi></e:math>, where <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi mathvariant="double-struck">H</l:mi></l:math> is a heavy hadron that decays through weak interactions <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="double-struck">H</o:mi><o:mo stretchy="false">→</o:mo><o:mi>R</o:mi><o:mi>c</o:mi></o:math> and the resonance <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>R</s:mi></s:math> decays strongly via <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>R</u:mi><u:mo stretchy="false">→</u:mo><u:mi>a</u:mi><u:mi>b</u:mi></u:math>. Based on the analysis, we propose to search for <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>C</x:mi><x:mi>P</x:mi></x:math> violation in the decay-angular distributions in the cascade decay processes <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi mathvariant="double-struck">B</z:mi><z:mo stretchy="false">→</z:mo><z:mi mathvariant="script">B</z:mi><z:mi>M</z:mi></z:math>, with <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi mathvariant="script">B</eb:mi></eb:math> or <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>M</hb:mi></hb:math> subsequently decaying through strong interactions, where <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi mathvariant="double-struck">B</jb:mi></jb:math> is the mother baryon, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi mathvariant="script">B</mb:mi></mb:math> and <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mi>M</pb:mi></pb:math> are the daughter baryon and meson, respectively, and <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>M</rb:mi></rb:math> has to be spin nonzero. We also present some typical decay channels in which the search for such kinds of <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi>C</tb:mi><tb:mi>P</tb:mi></tb:math> asymmetries can be performed.