Abstract
Using the helicity amplitude technique, we derive differential decay widths and angular distributions for the decay cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which the electron and muon mass is explicitly included. Using a set of phenomenological results for $D\to K_1$ form factors, we calculate partial decay widths and branching fractions for $D^0\to K_1^-\ell^+\nu_{\ell}$ and $D^+\to K_1^0\ell^+\nu_{\ell}$, but find that results for ${\cal B}(D\to K_1(1270)e^+\nu_{e})$ are larger than recent BESIII measurements by about a factor 1.5. We further demonstrate that the measurement of up-down asymmetry in $D\to K_{1}e^+\nu_e\to (K\pi\pi)e^+\nu_{e}$ and angular distributions in $D\to K_{1}\ell^+\nu_\ell\to (K\pi\pi)\ell^+\nu_{\ell}$ can help to determine the hadronic amplitude requested in $B\to K_1(\to K\pi\pi)\gamma$. Based on the Monte-Carlo simulation with the LHCb geometrical acceptance, we find that the angular distributions of MC events can be well described.
Highlights
Nowadays searching for new physics (NP) beyond the standard model (SM) is a most primary objective in particle physics
We further demonstrate that the measurement of up-down asymmetry in D → K1eþνe → ðKππÞeþνe and angular distributions in D → K1lþνl → ðKππÞlþνl can help to determine the hadronic amplitude requested in
Weak decays of heavy quarks have played an important role in testing standard model and probing new physics beyond
Summary
Nowadays searching for new physics (NP) beyond the standard model (SM) is a most primary objective in particle physics. This can in principle proceed in two distinct directions. The NP particles can affect various low-energy observables by modifying the coupling strength or introducing new interaction forms and a high precision study of these observables is likely to indirectly access the NP. In the SM, the charged weak interaction has the V − A chirality and thereby the photon in b → sγ is predominantly left-handed. A representative scenario of this type is the left-right symmetric model [4,5], in which the photon can acquire a significant right-handed component
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