Roles of Λ resonances in the K − p → γ Σ reaction

We investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>K</a:mi> <a:mo>−</a:mo> </a:msup> <a:mi>p</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>γ</a:mi> <a:mi mathvariant="normal">Σ</a:mi> </a:math> reaction using an effective Lagrangian approach within an isobar model framework. The model includes contributions from <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>s</e:mi> </e:math> -channel hyperon and hyperon resonance, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>t</g:mi> </g:math> -channel <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>K</i:mi> </i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>K</k:mi> <k:mo>*</k:mo> </k:msup> </k:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>u</m:mi> </m:math> -channel proton and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi mathvariant="normal">Δ</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>1232</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> exchanges, and a phenomenological contact term. Our analysis focuses on the roles of various <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi mathvariant="normal">Λ</t:mi> </t:math> resonances. The results indicate that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi mathvariant="normal">Λ</w:mi> <w:mo stretchy="false">(</w:mo> <w:mn>1600</w:mn> <w:mo stretchy="false">)</w:mo> </w:math> resonance is crucial for describing the experimental data at lower energies. At higher energies, the inclusion of either the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi mathvariant="normal">Λ</bb:mi> <bb:mo stretchy="false">(</bb:mo> <bb:mn>1670</bb:mn> <bb:mo stretchy="false">)</bb:mo> </bb:math> or the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi mathvariant="normal">Λ</gb:mi> <gb:mo stretchy="false">(</gb:mo> <gb:mn>1690</gb:mn> <gb:mo stretchy="false">)</gb:mo> </gb:math> resonance significantly improves the agreement with data. However, the current data are insufficient to distinguish between these two scenarios. We suggest that future measurements at higher beam energies and the measurement of the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi mathvariant="normal">Σ</lb:mi> </lb:math> polarization are needed to identify the roles of the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi mathvariant="normal">Λ</ob:mi> <ob:mo stretchy="false">(</ob:mo> <ob:mn>1670</ob:mn> <ob:mo stretchy="false">)</ob:mo> </ob:math> and <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:mi mathvariant="normal">Λ</tb:mi> <tb:mo stretchy="false">(</tb:mo> <tb:mn>1690</tb:mn> <tb:mo stretchy="false">)</tb:mo> </tb:math> resonances.