Implications of recent LHCb data on CP violation in b -baryon four-body decays

Motivated by the recent <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 observation, we investigate the <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> violation of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>b</e:mi></e:math>-baryon charmless four-body decays under the U-spin symmetry. However, we find that only U-spin symmetry cannot provide effective predictions, particularly for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi mathvariant="normal">Λ</g:mi><g:mi>b</g:mi></g:msub></g:math> decays. For giving more useful predictions, we also give a simple dynamic analysis. By counting the power (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mi>λ</j:mi><j:mo>=</j:mo><j:msqrt><j:mrow><j:mfrac><j:mrow><j:msub><j:mrow><j:mi mathvariant="normal">Λ</j:mi></j:mrow><j:mrow><j:mi>QCD</j:mi></j:mrow></j:msub></j:mrow><j:mrow><j:msub><j:mrow><j:mi>m</j:mi></j:mrow><j:mrow><j:mi>b</j:mi></j:mrow></j:msub></j:mrow></j:mfrac></j:mrow></j:msqrt></j:mrow></j:math>) of each topological diagram, we find that for the specific decay <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msubsup><m:mrow><m:mi>B</m:mi></m:mrow><m:mrow><m:mi>b</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msubsup><m:mo stretchy="false">→</m:mo><m:mi>R</m:mi><m:mo stretchy="false">(</m:mo><m:msubsup><m:mrow><m:mi>B</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msubsup><m:msup><m:mrow><m:mi>M</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup><m:msup><m:mrow><m:mi>M</m:mi></m:mrow><m:mrow><m:mover accent="true"><m:mrow><m:mn>2</m:mn></m:mrow><m:mrow><m:mo stretchy="false">¯</m:mo></m:mrow></m:mover></m:mrow></m:msup><m:mo stretchy="false">)</m:mo><m:msup><m:mrow><m:mi>M</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup></m:mrow></m:math>, only one U-spin amplitude can contribute in the leading power, while for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:msubsup><t:mrow><t:mi>B</t:mi></t:mrow><t:mrow><t:mi>b</t:mi></t:mrow><t:mrow><t:mn>2</t:mn></t:mrow></t:msubsup><t:mo stretchy="false">→</t:mo><t:mi>R</t:mi><t:mo stretchy="false">(</t:mo><t:msubsup><t:mrow><t:mi>B</t:mi></t:mrow><t:mrow><t:mn>1</t:mn></t:mrow><t:mrow><t:mn>2</t:mn></t:mrow></t:msubsup><t:msup><t:mrow><t:mi>M</t:mi></t:mrow><t:mrow><t:mn>2</t:mn></t:mrow></t:msup><t:mo stretchy="false">)</t:mo><t:mi>R</t:mi><t:mo stretchy="false">(</t:mo><t:msup><t:mrow><t:mi>M</t:mi></t:mrow><t:mrow><t:mover accent="true"><t:mrow><t:mn>2</t:mn></t:mrow><t:mrow><t:mo stretchy="false">¯</t:mo></t:mrow></t:mover></t:mrow></t:msup><t:msup><t:mrow><t:mi>M</t:mi></t:mrow><t:mrow><t:mn>2</t:mn></t:mrow></t:msup><t:mo stretchy="false">)</t:mo></t:mrow></t:math>, only two U-spin amplitudes can contribute in this leading power. Then the most effective prediction can be given as Considering the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi mathvariant="normal">Λ</cb:mi><cb:mi>b</cb:mi></cb:msub></cb:math> can effectively be produced in LHCb, we strongly encourage a more precise experimental investigation of it.