Evidence of the low-lying baryon Σ*(1/2−) in the process <mml:math xmlns:mml…

Motivated by the Belle measurements of the process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi mathvariant="normal">Λ</a:mi><a:mi>c</a:mi><a:mo>+</a:mo></a:msubsup><a:mo stretchy="false">→</a:mo><a:mi>η</a:mi><a:msup><a:mi>π</a:mi><a:mo>+</a:mo></a:msup><a:mi mathvariant="normal">Λ</a:mi></a:math>, we investigate this process by considering the contributions from the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi mathvariant="normal">Λ</f:mi><f:mo stretchy="false">(</f:mo><f:mn>1670</f:mn><f:mo stretchy="false">)</f:mo></f:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>a</k:mi><k:mn>0</k:mn></k:msub><k:mo stretchy="false">(</k:mo><k:mn>980</k:mn><k:mo stretchy="false">)</k:mo></k:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Σ</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1385</o:mn><o:mo stretchy="false">)</o:mo></o:math>. In addition, we also consider the predicted low-lying baryon <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi mathvariant="normal">Σ</t:mi><t:mo>*</t:mo></t:msup><t:mo stretchy="false">(</t:mo><t:mn>1</t:mn><t:mo>/</t:mo><t:msup><t:mn>2</t:mn><t:mo>−</t:mo></t:msup><t:mo stretchy="false">)</t:mo></t:math>. Our results involving the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi mathvariant="normal">Σ</y:mi><y:mo>*</y:mo></y:msup><y:mo stretchy="false">(</y:mo><y:mn>1</y:mn><y:mo>/</y:mo><y:msup><y:mn>2</y:mn><y:mo>−</y:mo></y:msup><y:mo stretchy="false">)</y:mo></y:math> are favored by fitting to the Belle data of the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>η</db:mi><db:mi mathvariant="normal">Λ</db:mi></db:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>π</gb:mi><gb:mo>+</gb:mo></gb:msup><gb:mi mathvariant="normal">Λ</gb:mi></gb:math> invariant mass distributions. Furthermore, we predict the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi>η</jb:mi><jb:msup><jb:mi>π</jb:mi><jb:mo>+</jb:mo></jb:msup></jb:math> invariant mass distribution and the angular distribution <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi>d</lb:mi><lb:mi mathvariant="normal">Γ</lb:mi><lb:mo>/</lb:mo><lb:mi>d</lb:mi><lb:mi>cos</lb:mi><lb:mi>θ</lb:mi></lb:math>, which are significantly different depending on whether or not the contribution from the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msup><ob:mi mathvariant="normal">Σ</ob:mi><ob:mo>*</ob:mo></ob:msup><ob:mo stretchy="false">(</ob:mo><ob:mn>1</ob:mn><ob:mo>/</ob:mo><ob:msup><ob:mn>2</ob:mn><ob:mo>−</ob:mo></ob:msup><ob:mo stretchy="false">)</ob:mo></ob:math> is considered. Finally, we show that, with the contribution from the <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msup><tb:mi mathvariant="normal">Σ</tb:mi><tb:mo>*</tb:mo></tb:msup><tb:mo stretchy="false">(</tb:mo><tb:mn>1</tb:mn><tb:mo>/</tb:mo><tb:msup><tb:mn>2</tb:mn><tb:mo>−</tb:mo></tb:msup><tb:mo stretchy="false">)</tb:mo></tb:math>, the calculated Dalitz plot agrees with the Belle measurements. Future precise measurements of the process <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msubsup><yb:mi mathvariant="normal">Λ</yb:mi><yb:mi>c</yb:mi><yb:mo>+</yb:mo></yb:msubsup><yb:mo stretchy="false">→</yb:mo><yb:mi>η</yb:mi><yb:msup><yb:mi>π</yb:mi><yb:mo>+</yb:mo></yb:msup><yb:mi mathvariant="normal">Λ</yb:mi></yb:math> could shed further light on the existence of the low-lying <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:msup><dc:mi mathvariant="normal">Σ</dc:mi><dc:mo>*</dc:mo></dc:msup><dc:mo stretchy="false">(</dc:mo><dc:mn>1</dc:mn><dc:mo>/</dc:mo><dc:msup><dc:mn>2</dc:mn><dc:mo>−</dc:mo></dc:msup><dc:mo stretchy="false">)</dc:mo></dc:math>.