Semileptonic charm decaysD→πlνlandD→Klνlfrom QCD light-cone sum rules

Abstract

We present a new calculation of the D ! and D ! K form factors from QCD light-cone sum rules. The MS scheme for the c-quark mass is used and the input parameters are updated. The results are f þ D ð0Þ ¼ 0:67 þ0:10 À0:07 , f þ DK ð0Þ ¼ 0:75 þ0:11 À0:08 , and f þ D ð0Þ=f þ DK ð0Þ ¼ 0:88 AE 0:05. Combining the calculated form factors with the latest CLEO data, we obtain jV cd j ¼ 0:225 AE 0:005 AE 0:003 þ0:016 À0:012 and jV cd j=jV cs j ¼ 0:236 AE 0:006 AE 0:003 AE 0:013 where the first and second errors are of experimental origin and the third error is due to the estimated uncertainties of our calculation. We also evaluate the form factors f À D and f À DK and predict the slope parameters at q 2 ¼ 0. Furthermore, calculating the form factors from the sum rules at q 2 < 0, we fit them to various parametrizations. After analytic continuation, the shape of the D ! , K form factors in the whole semileptonic region is reproduced, in a good agreement with experiment.

Perturbative corrections to B → D form factors in QCD

“…The determination of the sum rule parameters ω M and ω s can be achieved by implementing the standard procedure described in [15] and applying the same strategies leads to 6) which are in agreement with the intervals adopted in [10,61].…”

“…In addition, QCD factorization for the correlation function (2.1) is fully applicable at space-like momentum transfer on the basis of the power counting analysis. It is then distinctly that the B-meson LCSR for the form factors of B → D ν derived in (4.10) can be trusted at q 2 min ≤ q 2 ≤ q 2 max = 2 GeV 2 , where a moderate value q 2 min = −3 GeV 2 will be employed (see also [61]) in the following analysis for the sake of adopting the same intervals of the sum rules parameters shown in (5.6). In order to access the information of B → D form factors in the whole kinematic region, we…”

“…Following the arguments of [32,61], we will take advantage of the z-series parametrization, in line with the analytical properties and perturbative QCD scaling behaviours of B → D form factors, which can be readily introduced by mapping the cut complex q 2 -plane onto the unit disk |z(q 2 , t 0 ) ≤ 1| according to the conformal transformation [64] z(q 2 , t 0 ) = t + − q 2 − √ t + − t 0…”

“…Taking into account the near-threshold behaviour from angular momentum conservation leads to the suggested parametrization [32,61] …”

B s → Kℓν ℓ and B (s) → π(K)ℓ + ℓ − decays at large recoil and CKM matrix elements

“…In LCSRs, parameters of the pion and kaon twist-2 DA's include the decay constants, and the Gegenbauer moments a π 2,4 and a K 1,2 . Normalization of the twist-3 DAs is determined by µ π,K , where the ChPT relations [20] between light-quark masses are used (see e.g., [18]). The remaining parameters of the JHEP08(2017)112 Table 2.…”