Unraveling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1690</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> as a pseudoscalar <mml:math xmlns:mml="

The recently observed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>K</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1690</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> has been identified as a supernumerary pseudoscalar resonance signal in the strange-meson spectrum predicted by quark model calculations. It is the best candidate of a strange cryptoexotic state. In this work, we systematically study the hadron masses of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>u</e:mi> <e:mi>d</e:mi> <e:mover accent="true"> <e:mi>d</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mover accent="true"> <e:mi>s</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> tetraquark states with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>J</k:mi> <k:mi>P</k:mi> </k:msup> <k:mo>=</k:mo> <k:msup> <k:mn>0</k:mn> <k:mo>−</k:mo> </k:msup> </k:math> in the method of QCD sum rules. For ten interpolating currents, we calculate the correlation functions up to dimension-8 nonperturbative condensates. To calculate the trigluon condensate, we comprehensively consider the contributions from different operators with and without covariant derivatives. The infrared safety can be guaranteed for the completely calculated trigluon condensate by properly addressing the IR divergences in Feynman diagrams. It is demonstrated that the trigluon condensate provides significant contributions to the sum-rule analyses in these light tetraquark systems. Our results support the interpretation of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>K</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>1690</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> resonance to be a pseudoscalar <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>u</q:mi> <q:mi>d</q:mi> <q:mover accent="true"> <q:mi>d</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> <q:mover accent="true"> <q:mi>s</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> </q:math> tetraquark state.