Polarization and quantum entanglement effects in B^± c→ J/ψ +π ^± +π ⁰ process

Motivated by the very recent observation of the B⁺c→ J/ψ +π ⁺ +π ⁰ B c + → J / ψ + π + + π 0 decay using proton–proton collision data by the LHCb collaboration, we study the four-body angular distributions and the quantum entanglement effects in the B⁺c→ J/ψ +π ⁺ +π ⁰ B c + → J / ψ + π + + π 0 associated with J/ψ → μ ⁺+μ ⁻. J / ψ → μ + + μ - . The helicity angular distributions are given in the QCD effective theory and the von Neumann entropy is obtained in B^± c→ J/ψ (→ μ ⁺μ ⁻)+ρ ^± (→ π ^± π ⁰) B c ± → J / ψ ( → μ + μ - ) + ρ ± ( → π ± π 0 ) decay process.