New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules

TL;DR

This paper delivers an improved, $O(\alpha_s)$-accurate light-cone sum-rule calculation of $B\to\pi,K,\eta$ decay formfactors $f_+^P$, $f_0^P$, and $f_T^P$, including twist-2 and twist-3 radiative corrections and leading-order twist-4 effects. By a careful fixing of the sum-rule parameters, a detailed treatment of hadronic inputs (notably the Gegenbauer moments $a_{1,2,4}$) and SU(3) breaking, and a three-parameter, analytically-consistent parametrization of $q^2$-dependence, the authors provide precise predictions at $q^2=0$ and reliable extrapolations to the full kinematic range $0\le q^2\le (m_B-m_P)^2$. The results support precise determinations of CKM elements and nonleptonic $B$-decay analyses, while emphasizing the potential gains from lattice determinations of the Gegenbauer moments, particularly $a_1^K$. Overall, the work updates and refines the LCSR framework for heavy-to-light decays, delivering a practical, lattice-friendly set of form factors with quantified uncertainties.

Abstract

We present an improved calculation of $B\to$ light pseudoscalar formfactors from light-cone sum rules, including one-loop radiative corrections to twist-2 and twist-3 contributions, and leading order twist-4 corrections. The total theoretical uncertainty of our results at zero momentum transfer is 10 to 13% and can be improved, at least in part, by reducing the uncertainty of hadronic input parameters, in particular those describing the twist-2 distribution amplitudes of the pi, K and eta. We present our results in a way which details the dependence of the formfactors on these parameters and facilitates the incorporation of future updates of their values from e.g. lattice calculations.

Figures (7)

• Figure 1: Perturbative contributions to the correlation function $\Pi$. The external quarks are on-shell with momenta $up$ and $(1-u)p$, respectively.
• Figure 2: $a_2(1\,{\rm GeV})$ and $a_4(1\,{\rm GeV})$ as determined from the constraints (\ref{['phionehalf']}) and (\ref{['eq:constraint2']}). Solid line: central values, dashed lines: uncertainties. The black square labeled BZ denotes the central values used in this paper, Eq. (\ref{['eq:center']}), BMS the prediction of the nonlocal condensate model, Eq. (\ref{['stefanis']}), rescaled to $\mu=1\,$GeV, and BF is the central value obtained in Ref. wavefunctions.
• Figure 3: Central values of the formfactors $f(0)$ and uncertainties $\Delta$. Numbers from Tab. \ref{['tab:final']}.
• Figure 6: Dependence of $f_+^\pi(0)$ on (a) the Borel parameter $M^2$ and (b) the continuum threshold $s_0$. Input parameters: set 2 in Tab. \ref{['tab:fB']}.
• Figure 8: $f_+$ (solid lines), $f_0$ (short dashes) and $f_T$ (long dashes) as functions of $q^2$ for $\pi$, $K$ and $\eta$. The renormalisation scale of $f_T$ is chosen to be $m_b$. Input parameters: set 2 in Tab. \ref{['tab:fB']}.