Weak annihilation contribution to angular observables in B₂^+ D^*+ ^+ ^- decays

Abstract We analyze the rare semileptonic decays B₂^+ D^*+ (P₁ P₂) ^+ ^- B c + → D ∗ + (→ P 1 P 2) ℓ + ℓ -, with P₁ P₂ = D^+ ⁰ P 1 P 2 = D + π 0 or D⁰ ^+ D 0 π +, and =, ℓ = μ, τ. We focus on the impact of weak annihilation contributions alongside penguin, box, and long-distance effects. Using the effective Hamiltonian for b d ^+ ^- b → d ℓ + ℓ - transitions and Bc D^* B c → D ∗ form factors from covariant confined quark model inputs, we compute the differential branching ratios, forward–backward asymmetry, longitudinal helicity fraction of the D^* D ∗, and various normalized angular coefficients. The results of the observables show that weak annihilation effects are sizable, particularly at low q² q 2, significantly modifying several observables and shifting zero-crossings. Resonance effects dominate at high q² q 2, restricting reliable analysis windows. We conclude that the inclusion of weak annihilation is essential for precise Standard Model predictions and for isolating possible New Physics effects in Bc^+ D^*+ ^+ ^- <m