Up-down Asymmetries and Angular Distributions in $D\to K_{1}(\to Kππ)\ell^+ν_{\ell}$

Abstract

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for the decay cascade D → K1(1270, 1400)ℓ + ν ℓ → (Kππ)ℓ + ν ℓ (ℓ = e, µ), in which the electron and muon mass is explicitly included. Using a set of phenomenological results for D → K1 form factors, we calculate partial decay widths and branching fractions for D 0 → K − 1 ℓ + ν ℓ and D + → K 0 1 ℓ + ν ℓ , but find that results for B(D → K1(1270)e + νe) are larger than recent BESIII measurements by about a factor 1.5. We further demonstrate that the measurement of up-down asymmetry in D → K1e + νe → (Kππ)e + νe and angular distributions in D → K1ℓ + ν ℓ → (Kππ)ℓ + ν ℓ can help to determine the hadronic amplitude requested in B → K1(→ Kππ)γ. Based on the Monte-Carlo simulation with the LHCb geometrical acceptance, we find that the angular distributions of MC events can be well described.

Feasibility study of measuring $b\to sγ$ photon polarisation in $D^0\rightarrow K_1(1270)^- e^+ν_e$ at STCF

“…In the fit, the 2-D signal shape is described by the MC-simulated shape extracted from the signal MC events while the 2-D background shape is modeled by those derived from the inclusive MC sample. The smooth 2-D probability density functions of signal and background are modeled by using RooNDKeysPdf [27,28].…”