Absence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>η</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1855</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mat

Inspired by the experimental discoveries of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>X</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3872</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>c</e:mi> <e:mover accent="true"> <e:mi>q</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mi>q</e:mi> <e:mover accent="true"> <e:mi>c</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> </e:math> ) and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mrow> <k:mi>c</k:mi> <k:mi>c</k:mi> </k:mrow> </k:msub> </k:math> ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>c</m:mi> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mi>c</m:mi> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> </m:math> ), we systematically study their orbitally excited strange partners, i.e., the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>K</s:mi> <s:msub> <s:mover accent="true"> <s:mi>K</s:mi> <s:mo stretchy="false">¯</s:mo> </s:mover> <s:mn>1</s:mn> </s:msub> </s:math> ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>q</w:mi> <w:mover accent="true"> <w:mi>s</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> <w:mi>s</w:mi> <w:mover accent="true"> <w:mi>q</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> </w:math> ) system, which may be related to the recently observed <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>η</cb:mi> <cb:mn>1</cb:mn> </cb:msub> <cb:mo stretchy="false">(</cb:mo> <cb:mn>1855</cb:mn> <cb:mo stretchy="false">)</cb:mo> </cb:math> , and the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>K</gb:mi> <gb:msub> <gb:mi>K</gb:mi> <gb:mn>1</gb:mn> </gb:msub> </gb:math> ( <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>q</ib:mi> <ib:mover accent="true"> <ib:mi>s</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> <ib:mi>q</ib:mi> <ib:mover accent="true"> <ib:mi>s</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> </ib:math> ) system. Within the framework of an accurate few-body calculation method, we employ the chiral quark model to investigate both the molecular and diquark structures of these two multiquark systems in addition to channel coupling effects. Our results show that the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi>K</ob:mi> <ob:msub> <ob:mover accent="true"> <ob:mi>K</ob:mi> <ob:mo stretchy="false">¯</ob:mo> </ob:mover> <ob:mn>1</ob:mn> </ob:msub> </ob:math> system remains a scattering state, although we have considered two different sets of parameters in our calculations to avoid the influence of parameters. On the other hand, due to the presence of a good-diquark structure in the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:mi>K</sb:mi> <sb:msub> <sb:mi>K</sb:mi> <sb:mn>1</sb:mn> </sb:msub> </sb:math> system, we obtain a very shallow bound state in the coupled-channel calculation, where the one-gluon, the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mi>η</ub:mi> </ub:math> -meson, <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msub> <wb:mi>f</wb:mi> <wb:mn>0</wb:mn> </wb:msub> </wb:math> -meson, and <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi>σ</yb:mi> </yb:math> -meson exchanges play crucial roles. The interquark distance and component analysis also suggest that it is a loosely bound molecular state.