Extending the bridge connecting chiral Lagrangians and QCD Gaussian sum rules for low-energy hadronic physics

It has previously been demonstrated that the mesonic fields in chiral Lagrangians can be related to the quark-level operators of QCD sum-rules via energy-independent (constant) scale factor matrices constrained by chiral symmetry. This leads to universal scale factors for each type of chiral nonet related to quark-antiquark (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>q</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>) operators and four-quark (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>q</e:mi><e:mi>q</e:mi><e:mover accent="true"><e:mi>q</e:mi><e:mo stretchy="false">¯</e:mo></e:mover><e:mover accent="true"><e:mi>q</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math>) operators. Motivated by these successful demonstrations of scale-factor universality for the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>K</k:mi><k:mn>0</k:mn><k:mo>*</k:mo></k:msubsup></k:math> isodoublet and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>a</m:mi><m:mn>0</m:mn></m:msub></m:math> isotriplet scalar mesons, a revised Gaussian QCD sum rule methodology is developed that enables the extension to higher-dimensional isospin sectors, including the possibility of mixing with glueball components. Moreover, to extract nonperturbative information about a resonance stemming from the final state interactions of its decay products, a background-resonance interference approximation is developed and shown to provide an excellent description of both <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>π</o:mi><o:mi>K</o:mi></o:math> scattering amplitude data and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>π</q:mi><q:mi>η</q:mi></q:math> scattering calculations. This background-resonance interference approximation inspires new resonance models as ingredients in the scale-factor analysis connecting chiral Lagrangians and QCD Gaussian sum rules. Using the revised Gaussian QCD sum rule methodology, key properties of the scale factors are examined for the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msubsup><s:mi>K</s:mi><s:mn>0</s:mn><s:mo>*</s:mo></s:msubsup></s:math> isodoublet and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>a</u:mi><u:mn>0</u:mn></u:msub></u:math> isotriplet scalar mesons for a sequence of increasingly sophisticated resonance models. Gaussian sum rules are demonstrated to have sufficient resolution to distinguish between different resonance models, and it is shown that the background-resonance interference approximation not only describes <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mo stretchy="false">{</w:mo><w:mi>π</w:mi><w:mi>K</w:mi><w:mo>,</w:mo><w:mi>π</w:mi><w:mi>η</w:mi><w:mo stretchy="false">}</w:mo></w:math> scattering, but leads to the best universality and energy-independence properties of the scale factors.