$V_{cb}$ from the semileptonic decay $B\to D\ell {\bar{\nu }}_{\ell }$ and the properties of the $D$ meson distribution amplitude

Abstract

The improved QCD light-cone sum rule (LCSR) provides an effective way to deal with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the improved LCSR approach to deal with the $B\to D$ TFF $f^{+}(q^2)$ up to twist-4 accuracy. Due to the elimination of the most uncertain twist-3 contribution and the large suppression of the twist-4 contribution, the obtained LCSR shall provide us a good platform for testing the $D$-meson leading-twist DA. For the purpose, we suggest a new model for the $D$-meson leading-twist DA (${\varphi }_{3D}$), whose longitudinal behavior is dominantly determined by a parameter $B$. Moreover, we find its second Gegenbauer moment $a_2^D\sim B$. Varying $B$ within certain region, one can conveniently mimic the $D$-meson DA behavior suggested in the literature. Inversely, by comparing the estimations with the experimental data on the $D$-meson involved processes, one can get a possible range for the parameter $B$ and a determined behavior for the $D$-meson DA. Secondly, we discuss the $B\to D$ TFF at the maximum recoil region and present a detailed comparison of it with the pQCD estimation and the experimental measurements. Thirdly, by applying the LCSR on $f^{+}(q^2)$, we study the CKM matrix element $\Vcb$ together with its uncertainties by adopting two types of processes, i.e. the $B^0/{\bar{B}}^0$-type and the $B^{\pm }$-type. It is noted that a smaller $B\precsim 0.20$ shows a better agreement with the experimental value on $\Vcb$. For example, for the case of $B=0.00$, we obtain $|V_{cb}|(B^0/{\bar{B}}^0-\mathrm{type})=(41.28{}_{-4.82}^{+5.68}{}_{-1.16}^{+1.13})\times 10^{-3}$ and $|V_{cb}|(B^{\pm }-\mathrm{type})=(40.44{}_{-4.72}^{+5.56}{}_{-1.00}^{+0.98})\times 10^{-3}$, whose first (second) uncertainty comes from the squared average of the mentioned theoretical (experimental) uncertainties.

13 pages, 10 figures. Reference updated and discussion improved. To be published in Nucl.Phys.B

References in corpus (8)

• The B -> D* l nu form factor at zero recoil from three-flavor lattice QCD: A model independent determination of |V_cb|
• Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb|
• Quenched lattice calculation of the B --> D l nu decay rate
• Accurate bottom-quark mass from Borel QCD sum rules for $f_B$ and $f_{B_s}$
• Measurement of the Moments of the Photon Energy Spectrum in B -> X_s gamma Decays and Determination of |V_cb| and m_b at Belle
• Form Factor for $B\to Dl\tilde{\nu }$ in Light-Cone Sum Rules With Chiral Current Correlator
• Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data
• Chiral extrapolation of lattice data for B-meson decay constant

Cited by in corpus (10)

• Perturbative corrections to $B\to D$ form factors in QCD
• The Ratio $\mathcal{R}(D)$ and the $D$-meson Distribution Amplitude
• The $D_s$-meson leading-twist distribution amplitude within the QCD sum rules and its application to the $B_s\to D_s$ transition form factor
• Heavy and light meson wavefunctions
• The $D\to \rho$ semileptonic and radiative decays within the light-cone sum rules
• Uncertainties of the $B\to D$ transition form factor from the $D$-Meson Leading-Twist Distribution Amplitude
• $a_0(980)$-meson twist-2 distribution amplitude within the QCD sum rules and investigation of $D\to a_0(980)(\to \eta \pi )e^{+}{\nu }_e$
• Heavy Pseudoscalar Twist-3 Distribution Amplitudes within QCD Theory in Background Fields
• Properties of the ${\eta }_q$ leading-twist distribution amplitude and its effects to the $B/D^{+}\to {\eta }^{(\prime )}{\ell }^{+}{\nu }_{\ell }$ decays
• Footprint in fitting $B\to D$ vector form factor and determination for $D$-meson leading-twist LCDA