Two-photon production of f0 and a0 resonances as hadronic molecules composed of two vector mesons

Ascribed as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ρ</a:mi><a:mi>ρ</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>K</c:mi><c:mo>*</c:mo></c:msup><c:msup><c:mover accent="true"><c:mi>K</c:mi><c:mo stretchy="false">¯</c:mo></c:mover><c:mo>*</c:mo></c:msup></c:math> molecular states, respectively, isoscalar <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>f</g:mi><g:mn>0</g:mn></g:msub><g:mo stretchy="false">(</g:mo><g:mn>1500</g:mn><g:mo stretchy="false">)</g:mo></g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>f</k:mi><k:mn>0</k:mn></k:msub><k:mo stretchy="false">(</k:mo><k:mn>1710</k:mn><k:mo stretchy="false">)</k:mo></k:math> states are expected to have isovector partners, potentially identified as <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>a</o:mi><o:mn>0</o:mn></o:msub><o:mo stretchy="false">(</o:mo><o:mn>1450</o:mn><o:mo stretchy="false">)</o:mo></o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>a</s:mi><s:mn>0</s:mn></s:msub><s:mo stretchy="false">(</s:mo><s:mn>1710</s:mn><s:mo stretchy="false">)</s:mo></s:math>. The predicted dominant decay modes for these two <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>a</w:mi><w:mn>0</w:mn></w:msub></w:math> resonances are <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>a</y:mi><y:mn>0</y:mn></y:msub><y:mo stretchy="false">(</y:mo><y:mn>1450</y:mn><y:mo stretchy="false">)</y:mo><y:mo stretchy="false">→</y:mo><y:mi>ω</y:mi><y:mi>π</y:mi><y:mi>π</y:mi></y:math> and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi>a</db:mi><db:mn>0</db:mn></db:msub><db:mo stretchy="false">(</db:mo><db:mn>1710</db:mn><db:mo stretchy="false">)</db:mo><db:mo stretchy="false">→</db:mo><db:mi>ω</db:mi><db:mi>π</db:mi><db:mi>π</db:mi><db:mo>,</db:mo><db:mi>ϕ</db:mi><db:mi>π</db:mi><db:mi>π</db:mi></db:math>. We estimate cross sections for two-photon production of these four resonances within hadronic molecular picture, and demonstrate that SuperKEKB’s luminosity is sufficient for their observation and more precise parameter measurements.