Abstract
A new model-independent parametrization is proposed for the hadronic form factors in the semileptonic $\bar{B}\to D\ell\bar{\nu}_\ell$ decay. By a combined consideration of the recent experimental and lattice QCD data, we determine precisely the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|=41.01(75)\times 10^{-3}$ and the ratio $\mathcal{R}_D=\frac{\mathcal{BR}(\bar{B}\to D \tau \bar{\nu}_\tau)}{\mathcal{BR}(\bar{B}\to D \ell \bar{\nu}_\ell)}=0.301(5)$. The coefficients in this parametrization, related to phase shifts by sumrulelike dispersion relations and hence called phase moments, encode important scattering information of the $\bar{B}\bar{D}$ interactions which are poorly known so far. Thus, we give strong hints about the existence of at least one bound and one virtual $\bar B \bar D$ $S$-wave $0^+$ states, subject to uncertainties produced by potentially sizable inelastic effects. This formalism is also applicable for any other semileptonic processes induced by the weak $b\to c$ transition.
Highlights
One of the most primary goals in flavor physics currently is to precisely determine the elements of the CabibboKobayashi-Maskawa (CKM) matrix, since they afford a sharp probe of physics beyond the standard model (SM) as inputs of the CKM unitarity triangle
To determine the phase moments Ain introduced in Eq (5), we perform a combined fit to the recent experimental data measured by Belle [8] together with the lattice QCD (LQCD) results of the vector and scalar form factors at nonzero recoil obtained by the HPQCD [10] and FL-MILC [11] collaborations
We have proposed a new modelindependent parametrization for the form factors in the semileptonic B → Dlν decays
Summary
One of the most primary goals in flavor physics currently is to precisely determine the elements of the CabibboKobayashi-Maskawa (CKM) matrix, since they afford a sharp probe of physics beyond the standard model (SM) as inputs of the CKM unitarity triangle. Experimental and theoretical efforts are extensively devoted to study both inclusive and exclusive semileptonic decays of bottom hadrons For the latter ones, different ways have been proposed to parametrize the hadronic form factors involved, the most commonly used of which are the Boyd-GrinsteinLebed (BGL) [1] and Caprini-Lellouch-Neubert (CLN) [2] parametrizations. The Belle Collaboration measured the differential decay rates of the exclusive B → Dlνl [8] and B → DÃlνl reactions [9] using Their full data set; and there have been lattice QCD (LQCD) results on the form factors at nonzero recoils for B → Dlνl obtained by the HPQCD [10] and Fermilab Lattice plus. Our new parametrization, bringing information from semileptonic decays to the scattering problem, will definitely shed light on those newly predicted/discovered states
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