<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-meson decays to vector charmoniumlike states and a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></m

A series of vector charmonium(like) states, accompanied by a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>K</a:mi></a:math> meson, have been observed in the decays of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>B</c:mi></c:mrow></c:math> meson. These processes are color-suppressed at the quark level, as inferred from topological diagram analysis. In this work, we calculate the branching fractions of the decays <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>B</e:mi><e:mo stretchy="false">→</e:mo><e:mi>ψ</e:mi><e:mi>K</e:mi></e:math>, where <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>ψ</h:mi></h:math> denotes the charmonium(like) states <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>ψ</j:mi><j:mo stretchy="false">(</j:mo><j:mn>1</j:mn><j:mi>S</j:mi><j:mo stretchy="false">)</j:mo></j:math>, <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ψ</n:mi><n:mo stretchy="false">(</n:mo><n:mn>2</n:mn><n:mi>S</n:mi><n:mo stretchy="false">)</n:mo></n:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>ψ</r:mi><r:mo stretchy="false">(</r:mo><r:mn>4040</r:mn><r:mo stretchy="false">)</r:mo></r:math>, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>ψ</v:mi><v:mo stretchy="false">(</v:mo><v:mn>3770</v:mn><v:mo stretchy="false">)</v:mo></v:math>, and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>ψ</z:mi><z:mo stretchy="false">(</z:mo><z:mn>4160</z:mn><z:mo stretchy="false">)</z:mo></z:math>. Our analysis incorporates both short-distance (naive factorization approach) and long-distance (final-state interactions) contributions. Within reasonable parameters, our results align with experimental data except for the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>ψ</db:mi><db:mo stretchy="false">(</db:mo><db:mn>4160</db:mn><db:mo stretchy="false">)</db:mo></db:math>, suggesting its possible exotic nature. Furthermore, we find that long-distance contributions dominate these decay processes, highlighting the crucial role of final-state interactions in the productions of charmonium(like) states in <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>B</hb:mi></hb:math> decays.