QCD sum rule study of excited light meson operators

We apply the QCD sum rule method to systematically study excited light meson operators and calculate their decay constants. These operators are constructed by explicitly adding one covariant derivative to the quark-antiquark pair. In total, twelve such operators are constructed, among which ten are subjected to detailed numerical analyses. The considered quark contents include <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>q</a:mi></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mover accent="true"><e:mi>q</e:mi><e:mo stretchy="false">¯</e:mo></e:mover><e:mi>s</e:mi></e:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mover accent="true"><i:mi>s</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mi>s</i:mi></i:math> (<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>q</m:mi><m:mo>=</m:mo><m:mi>u</m:mi><m:mo>/</m:mo><m:mi>d</m:mi></m:math>), allowing the formation of various <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>S</o:mi><o:mi>U</o:mi><o:mo stretchy="false">(</o:mo><o:mn>3</o:mn><o:mo stretchy="false">)</o:mo></o:math> flavor nonets. For instance, our results support the interpretation that the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>a</s:mi><s:mn>2</s:mn></s:msub><s:mo stretchy="false">(</s:mo><s:mn>1320</s:mn><s:mo stretchy="false">)</s:mo></s:math>, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>f</w:mi><w:mn>2</w:mn></w:msub><w:mo stretchy="false">(</w:mo><w:mn>1270</w:mn><w:mo stretchy="false">)</w:mo></w:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi>f</ab:mi><ab:mn>2</ab:mn><ab:mo>′</ab:mo></ab:msubsup><ab:mo stretchy="false">(</ab:mo><ab:mn>1525</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math>, and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mi>K</eb:mi><eb:mn>2</eb:mn><eb:mo>*</eb:mo></eb:msubsup><eb:mo stretchy="false">(</eb:mo><eb:mn>1430</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math> states constitute a flavor nonet with quantum numbers <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msup><ib:mi>J</ib:mi><ib:mrow><ib:mi>P</ib:mi><ib:mo stretchy="false">(</ib:mo><ib:mi>C</ib:mi><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup><ib:mo>=</ib:mo><ib:msup><ib:mn>2</ib:mn><ib:mrow><ib:mo>+</ib:mo><ib:mo stretchy="false">(</ib:mo><ib:mo>+</ib:mo><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup></ib:math>. In addition, we predict several excited meson states, whose masses and decay constants are determined using the QCD sum rule method.