Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo stretchy="false">→</mml:mo> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:math>

Motivated by systematic observations of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>B</a:mi> <a:mi>c</a:mi> </a:msub> </a:math> decays at LHCb, we analyze <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msubsup> <c:mi>B</c:mi> <c:mi>c</c:mi> <c:mo>+</c:mo> </c:msubsup> <c:mo stretchy="false">→</c:mo> <c:mi>J</c:mi> <c:mo>/</c:mo> <c:mi>ψ</c:mi> <c:mo stretchy="false">(</c:mo> <c:mi>A</c:mi> <c:mo>,</c:mo> <c:mi>T</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> decays [where <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>A</h:mi> </h:math> denotes axial-vector mesons <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi>a</j:mi> <j:mn>1</j:mn> </j:msub> <j:mo stretchy="false">(</j:mo> <j:mn>1260</j:mn> <j:msup> <j:mo stretchy="false">)</j:mo> <j:mo>+</j:mo> </j:msup> </j:math> , <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>b</n:mi> <n:mn>1</n:mn> </n:msub> <n:mo stretchy="false">(</n:mo> <n:mn>1235</n:mn> <n:msup> <n:mo stretchy="false">)</n:mo> <n:mo>+</n:mo> </n:msup> </n:math> , and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>T</r:mi> </r:math> denotes tensor mesons <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msub> <t:mi>a</t:mi> <t:mn>2</t:mn> </t:msub> <t:mo stretchy="false">(</t:mo> <t:mn>1320</t:mn> <t:msup> <t:mo stretchy="false">)</t:mo> <t:mo>+</t:mo> </t:msup> </t:math> , <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msubsup> <x:mi>K</x:mi> <x:mn>2</x:mn> <x:mo>*</x:mo> </x:msubsup> <x:mo stretchy="false">(</x:mo> <x:mn>1430</x:mn> <x:msup> <x:mo stretchy="false">)</x:mo> <x:mo>+</x:mo> </x:msup> </x:math> ] within the perturbative QCD (pQCD) factorization framework. The framework employs light-cone distribution amplitudes to regulate nonperturbative dynamics, utilizing Sudakov suppression to control endpoint divergences. Our predictions indicate branching ratios of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mn>10</bb:mn> <bb:mrow> <bb:mo>−</bb:mo> <bb:mn>3</bb:mn> </bb:mrow> </bb:msup> <bb:mi>–</bb:mi> <bb:msup> <bb:mn>10</bb:mn> <bb:mrow> <bb:mo>−</bb:mo> <bb:mn>2</bb:mn> </bb:mrow> </bb:msup> </bb:math> for <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msubsup> <db:mi>B</db:mi> <db:mi>c</db:mi> <db:mo>+</db:mo> </db:msubsup> <db:mo stretchy="false">→</db:mo> <db:mi>J</db:mi> <db:mo>/</db:mo> <db:mi>ψ</db:mi> <db:mi>A</db:mi> </db:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msup> <gb:mn>10</gb:mn> <gb:mrow> <gb:mo>−</gb:mo> <gb:mn>5</gb:mn> </gb:mrow> </gb:msup> <gb:mi>–</gb:mi> <gb:msup> <gb:mn>10</gb:mn> <gb:mrow> <gb:mo>−</gb:mo> <gb:mn>4</gb:mn> </gb:mrow> </gb:msup> </gb:math> for <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msubsup> <ib:mi>B</ib:mi> <ib:mi>c</ib:mi> <ib:mo>+</ib:mo> </ib:msubsup> <ib:mo stretchy="false">→</ib:mo> <ib:mi>J</ib:mi> <ib:mo>/</ib:mo> <ib:mi>ψ</ib:mi> <ib:mi>T</ib:mi> </ib:math> decays, which seem to be in the reach of future experiments. We also provide predictions for the polarization fractions of these decays. Based on quark helicity analysis, the longitudinal polarization amplitudes are expected to dominate the branching ratios.