CP violation in two-body hadronic Λb decays in the PQCD approach

We systematically investigate the <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>-averaged branching ratios and <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> violations (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>C</e:mi><e:mi>P</e:mi><e:mi>V</e:mi><e:mi mathvariant="normal">s</e:mi></e:mrow></e:math>) for the two-body hadronic decays <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi mathvariant="normal">Λ</h:mi><h:mi>b</h:mi></h:msub><h:mo stretchy="false">→</h:mo><h:mi>p</h:mi><h:mi>h</h:mi></h:math>, where <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>h</l:mi></l:math> runs through the mesons <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi>π</n:mi><n:mo>−</n:mo></n:msup></n:math>, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi>ρ</p:mi><p:mo>−</p:mo></p:msup></p:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi>a</r:mi><r:mn>1</r:mn><r:mo>−</r:mo></r:msubsup><r:mo stretchy="false">(</r:mo><r:mn>1260</r:mn><r:mo stretchy="false">)</r:mo></r:math>, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>K</v:mi><v:mo>−</v:mo></v:msup></v:math>, <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>K</x:mi><x:mrow><x:mo>*</x:mo><x:mo>−</x:mo></x:mrow></x:msup></x:math>, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msubsup><z:mi>K</z:mi><z:mn>1</z:mn><z:mo>−</z:mo></z:msubsup><z:mo stretchy="false">(</z:mo><z:mn>1270</z:mn><z:mo stretchy="false">)</z:mo></z:math>, and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msubsup><db:mi>K</db:mi><db:mn>1</db:mn><db:mo>−</db:mo></db:msubsup><db:mo stretchy="false">(</db:mo><db:mn>1400</db:mn><db:mo stretchy="false">)</db:mo></db:math>, in the perturbative QCD approach to order <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msubsup><hb:mi>α</hb:mi><hb:mi>s</hb:mi><hb:mn>2</hb:mn></hb:msubsup></hb:math> in the strong coupling. Various topological amplitudes are obtained by incorporating subleading-twist hadron distribution amplitudes, which exhibit reasonable hierarchical patterns, sizable strong phases, and non-negligible higher-power corrections. The predicted direct <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:mi>C</jb:mi><jb:mi>P</jb:mi><jb:mi>V</jb:mi><jb:mi mathvariant="normal">s</jb:mi></jb:mrow></jb:math> in <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi mathvariant="normal">Λ</mb:mi><mb:mi>b</mb:mi></mb:msub><mb:mo stretchy="false">→</mb:mo><mb:mi>p</mb:mi><mb:msup><mb:mi>π</mb:mi><mb:mo>−</mb:mo></mb:msup><mb:mo>,</mb:mo><mb:mi>p</mb:mi><mb:msup><mb:mi>K</mb:mi><mb:mo>−</mb:mo></mb:msup></mb:math>, different from those in similar <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>B</qb:mi></qb:math> meson decays, are as small as the current data. The low <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>C</sb:mi><sb:mi>P</sb:mi><sb:mi>V</sb:mi></sb:math> in <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msub><ub:mi mathvariant="normal">Λ</ub:mi><ub:mi>b</ub:mi></ub:msub><ub:mo stretchy="false">→</ub:mo><ub:mi>p</ub:mi><ub:msup><ub:mi>π</ub:mi><ub:mo>−</ub:mo></ub:msup></ub:math> results from the cancelation between the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>S</yb:mi></yb:math>- and <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>P</ac:mi></ac:math>-wave <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mrow><cc:mi>C</cc:mi><cc:mi>P</cc:mi><cc:mi>V</cc:mi><cc:mi mathvariant="normal">s</cc:mi></cc:mrow></cc:math>, while the one in <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msub><fc:mi mathvariant="normal">Λ</fc:mi><fc:mi>b</fc:mi></fc:msub><fc:mo stretchy="false">→</fc:mo><fc:mi>p</fc:mi><fc:msup><fc:mi>K</fc:mi><fc:mo>−</fc:mo></fc:msup></fc:math> is determined by the tiny <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mi>S</jc:mi></jc:math>-wave <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:mi>C</lc:mi><lc:mi>P</lc:mi><lc:mi>V</lc:mi></lc:math>. However, individual partial-wave <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:mrow><nc:mi>C</nc:mi><nc:mi>P</nc:mi><nc:mi>V</nc:mi><nc:mi mathvariant="normal">s</nc:mi></nc:mrow></nc:math> can exceed 10%, consistent with direct <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mrow><qc:mi>C</qc:mi><qc:mi>P</qc:mi><qc:mi>V</qc:mi><qc:mi mathvariant="normal">s</qc:mi></qc:mrow></qc:math> in <tc:math xmlns:tc="http://www.w3.org/1998/Math/MathML" display="inline"><tc:mi>B</tc:mi></tc:math> meson decays. The <vc:math xmlns:vc="http://www.w3.org/1998/Math/MathML" display="inline"><vc:mrow><vc:mi>C</vc:mi><vc:mi>P</vc:mi><vc:mi>V</vc:mi><vc:mi mathvariant="normal">s</vc:mi></vc:mrow></vc:math> in the <yc:math xmlns:yc="http://www.w3.org/1998/Math/MathML" display="inline"><yc:msub><yc:mi mathvariant="normal">Λ</yc:mi><yc:mi>b</yc:mi></yc:msub><yc:mo stretchy="false">→</yc:mo><yc:mi>p</yc:mi><yc:msubsup><yc:mi>K</yc:mi><yc:mn>1</yc:mn><yc:mo>−</yc:mo></yc:msubsup><yc:mo stretchy="false">(</yc:mo><yc:mn>1270</yc:mn><yc:mo stretchy="false">)</yc:mo><yc:mo>,</yc:mo><yc:mi>p</yc:mi><yc:msubsup><yc:mi>K</yc:mi><yc:mn>1</yc:mn><yc:mo>−</yc:mo></yc:msubsup><yc:mo stretchy="false">(</yc:mo><yc:mn>1400</yc:mn><yc:mo stretchy="false">)</yc:mo></yc:math> channels are relatively larger. In particular, <gd:math xmlns:gd="http://www.w3.org/1998/Math/MathML" display="inline"><gd:mrow><gd:mi>C</gd:mi><gd:mi>P</gd:mi><gd:mi>V</gd:mi><gd:mi mathvariant="normal">s</gd:mi></gd:mrow></gd:math> above 20% appear in the up-down asymmetries associated with the final-state angular distributions of <jd:math xmlns:jd="http://www.w3.org/1998/Math/MathML" display="inline"><jd:msub><jd:mi mathvariant="normal">Λ</jd:mi><jd:mi>b</jd:mi></jd:msub><jd:mo stretchy="false">→</jd:mo><jd:mi>p</jd:mi><jd:msubsup><jd:mi>K</jd:mi><jd:mn>1</jd:mn><jd:mo>−</jd:mo></jd:msubsup><jd:mo stretchy="false">(</jd:mo><jd:mn>1270</jd:mn><jd:mo stretchy="false">)</jd:mo><jd:mo>,</jd:mo><jd:mi>p</jd:mi><jd:msubsup><jd:mi>K</jd:mi><jd:mn>1</jd:mn><jd:mo>−</jd:mo></jd:msubsup><jd:mo stretchy="false">(</jd:mo><jd:mn>1400</jd:mn><jd:mo stretchy="false">)</jd:mo></jd:math>, followed by the secondary <rd:math xmlns:rd="http://www.w3.org/1998/Math/MathML" display="inline"><rd:msub><rd:mi>K</rd:mi><rd:mn>1</rd:mn></rd:msub><rd:mo stretchy="false">→</rd:mo><rd:mi>K</rd:mi><rd:mi>π</rd:mi><rd:mi>π</rd:mi></rd:math> decays. These observables offer promising prospects for firmly establishing baryon <ud:math xmlns:ud="http://www.w3.org/1998/Math/MathML" display="inline"><ud:mrow><ud:mi>C</ud:mi><ud:mi>P</ud:mi><ud:mi>V</ud:mi><ud:mi mathvariant="normal">s</ud:mi></ud:mrow></ud:math>. The decay asymmetry parameters of <xd:math xmlns:xd="http://www.w3.org/1998/Math/MathML" display="inline"><xd:msub><xd:mi mathvariant="normal">Λ</xd:mi><xd:mi>b</xd:mi></xd:msub><xd:mo stretchy="false">→</xd:mo><xd:mi>p</xd:mi><xd:mi>h</xd:mi></xd:math> are also predicted for future experimental confrontations.