Unveiling the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1270</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> double-pole structure in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:…

By looking at the pseudoscalar-vector meson spectra in $\bar{B}\to J/\psi \rho\bar{K}$ and \bar{K}^*\pi$ weak decays, we theoretically investigate double-pole structure of $K_1(1270)$ resonance by using Chiral Unitary approach to account for final state interactions between pseudoscalar vector mesons. The appears as dynamically generated through these coupled channels influence shape invariant mass distributions under consideration. We show how those shapes are affected confront results from our model with future experiments that might $PV$ decays.