Five-body D→ V Semileptonic Decays

Our main objective is to derive the decay rate for the semileptonic decays D→ Vℓ^+ν_ℓ (ℓ=e,μ), where V represents a vector particle. In these decays, the vector particle V decays into three pseudo-scalar particles. To accomplish this, we evaluate the phase-space factor for the five-body decay with a set of eight independent variables which uniquely define a point in the phase space. We further conduct a detailed investigation of the D→ωℓ^+ν_ℓ, where ω subsequently decays into π^+π^-π^0, within the Standard Model and in a general effective field theory description of the weak interactions at low energies. The outcomes of this study have potential applications in the measurement of D→ω form factors. These measurements can be performed using data obtained from BESIII.