Form factors $f_{+}^{B\to \pi }(0)$ and $f_{+}^{D\to \pi }(0)$ in $QCD$ and determination of $|V_{ub}|$ and $|V_{cd}|$

Abstract

We present a QCD study on $B,D\to \pi$ semileptonic transitions at zero momentum transfer and an estimate of magnitudes of the associated CKM matrix elements. Light cone sum rules (LCSRs) with chiral correlator are applied to calculate the form factors $f_{+}^{B\to \pi }(0)$ and $f_{+}^{D\to \pi }(0)$. We show that there is no twist-3 and-5 component involved in the light-cone expansions such that the resulting sum rules have a good convergence and offer an understanding of these form factors at twist-5 level. A detailed $\mathcal{O}({\alpha }_s)$ computation is carried out in leading twist-2 approximation and the $\overline{MS}$ masses are employed for the underlying heavy quarks. With the updated inputs and experimental data, we have $f_{+}^{B\to \pi }(0)=0.28_{-0.02}^{+0.05}$ and $|V_{ub}|=(3.4_{-0.6}^{+0.2}\pm 0.1\pm 0.1)\times 10^{-3}$; $f_{+}^{D\to \pi }(0)=0.62\pm 0.03$ and $|V_{cd}|=0.244\pm 0.005\pm 0.003\pm 0.008$. As a by-product, a numerical estimate for the decay constant $f_D$ is yielded as $f_D=190_{-11}^{+12}\mathrm{MeV}$.

23 pages, 4 figures, 3 tables, published in JHEP

References in corpus (9)

• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Heavy Quark Masses from Sum Rules in Four-Loop Approximation
• Light-cone sum rules for $B\to \pi$ form factors revisited
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• Twist-4 Distribution Amplitudes of the K${}^{\ast }$ and $\varphi$ Mesons in QCD
• Charm and Bottom Quark Masses from Perturbative QCD
• Testing QCD Sum Rules on the Light-Cone in D->(pi,K) l nu Decays
• Visualization of semileptonic form factors from lattice QCD
• Radiative Corrections on the $B\to P$ Form Factors with Chiral Current in the Light-Cone Sum Rules

Cited by in corpus (9)

• Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory
• The $\rho$-meson longitudinal leading-twist distribution amplitude within QCD background field theory
• Semileptonic and leptonic $B$ decays, circa 2016
• $B\to \rho$ transition form factors within the QCD light-cone sum rules and the $\rho$-meson leading-twist distribution amplitude
• Investigating the ratio of CKM matrix elements $|V_{ub}|/|V_{cb}|$ from semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and kaon twist-2 distribution amplitude
• Recent Developments on the CKM Matrix
• The $B\to \pi \ell {\nu }_{\ell }$ semileptonic decay within the LCSR approach under heavy quark effective field theory
• Revisiting $D$-meson twist-2, 3 distribution amplitudes
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules