Abstract
The semileptonic decay of heavy flavor mesons offers a clean environment for extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, which describes the CP-violating and flavor changing process in the Standard Model. The involved form factors where the dynamical information is encoded play an essential role in achieving any conclusive statement. That is, the knowledge of the form factors should be under good control, requiring one to examine more observables in addition to the branching fraction. In this paper, we provide the mean value and the q2-dependent shape for further observables [differential decay distribution (dΓ/dq2), forward-backward asymmetry left({mathcal{A}}_{FB}^{ls}right) , longitudinal left({P}_L^lright) and transverse left({P}_T^lright) polarization of a charged lepton, longitudinal polarization of a vector meson in the final state left({F}_L^l(V)right) , leptonic convexity parameter left({C}_F^lright) , and trigonometric moments left({W}_i^lright) in the decay of D(s) and B(s) to P/Vl+νl (l = e, μ or τ)], based on the predictions of the relevant form factors from the covariant light-front quark model. P and V denote the pseudoscalar and vector meson, respectively. As a comparison, we find a good agreement with the results from the covariant confining quark model and the relativistic quark model in the literature. As it has been observed that the {P}_L^l and {F}_L^l(V) are crucial quantities to discriminate various New Physics models, the reexamination of these observables from a different method is also essential and necessary.
Highlights
JHEP02(2021)179 the covariant light-front quark model (CLFQM) was proposed [14], where all four-momentum of each vertex is conserved, and the constituent quarks are offshell
We provide the mean value and the q2-dependent shape for further observables [differential decay distribution, forward-backward asymmetry (AlF B), longitudinal (PLl ) and transverse (PTl ) polarization of a charged lepton, longitudinal polarization of a vector meson in the final state (FLl (V )), leptonic convexity parameter (CFl ), and trigonometric moments (Wil) in the decay of D(s) and B(s) to P/V l+νl (l = e, μ or τ )], based on the predictions of the relevant form factors from the covariant light-front quark model
The observables are expressed by the combination of form factors via helicity amplitudes, including the differential decay rate, forward-backward asymmetry, longitudinal (PLl ) and transverse (PTl ) polarization of the charged lepton (PLl ), longitudinal polarization of vector in the final state (FLl (V )), and trigonometric moments (Wil)
Summary
We take the decay process of D as an example to demonstrate our derivation for the relevant equations. The hadronic part can be parameterized by the invariant form factors, which are a function of the momentum transfer squared (q2), between the initial and final meson. In the rest frame of the initial meson D, one has the explicit representations [36] of the polarization four-vectors μ(λW ): μ(t) =. Q0 is the energy and |p2| is the momentum of the Woff-shell in the D rest frame In this frame (see figure 2), pμ1 = (m1, 0, 0, 0) , pμ2 = (E2, 0, 0, −|p2|) , qμ = (q0, 0, 0, |p2|) ,. In the D rest frame, the explicit representations of the polarization four-vectors for the final vector meson ν 2. We define θ as the polar angle of the lepton in the l+νl center-of-mass frame with respect to the Woff-shell line of flight in the D rest frame. Eq (2.24) agrees with eq (37) in ref. [32], except for some extra factors that will be compensated in the final result
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