Abstract
In this paper, we calculate the helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable region, we investigate the -meson two-body decays and semi-leptonic decays , where stand for light pseudoscalar and vector mesons, respectively. The branching fractions can be derived using the CKM matrix element and the lifetime from the Particle Data Group, and we obtain , , , , and . We then obtain and , which agree with the LHCb measured value within -error. We also obtain , which like other theoretical predictions, is consistent with the LHCb measured value within -error. These imply that the HFFs under the LCSR approach are also applicable to the meson two-body decays and semi-leptonic decays , and the HFFs obtained using LCSR in a new way implies that there may be new physics in the semi-leptonic decays.
Highlights
The Bc-meson that consists of two different heavy quarks was first observed by CDF collaboration [1] in year 1998
II, we present the calculation technology of the Bc → J/ψ helicity form factors (HFFs) and the branching fractions for Bc+ → J/ψ + (P, V, l+νl) decays
Since we used a usual current in the calculation, the HFFs will include all the Twist-2,3,4 light-cone distribution amplitudes (LCDAs), see subsection III A, which will maintain the accuracy of light-cone sum rules (LCSR) to a large extent
Summary
The Bc-meson that consists of two different heavy quarks was first observed by CDF collaboration [1] in year 1998. Many ratios of different branching fraction associated with Bc → J/ψ have been measured by the LHCb collaboration, such as Rπ+/μ+νμ = B(Bc+ → J/ψπ+)/B(Bc+ → J/ψμ+νμ) = 0.0469 ± 0.0028(stat.) ± 0.0046(syst.) [5], RK+/π+ = B(Bc+ → J/ψK+)/B(Bc+ → J/ψπ+) = 0.069 ± 0.019(stat.) ± 0.005(syst.) [6], which is updated to RK+/π+ = 0.079 ± 0.007(stat.) ± 0.003(syst.) [7], and RJ/ψ = B(Bc+ → J/ψτ +ντ )/B(Bc+ → J/ψμ+νμ) = 0.71 ± 0.17(stat.) ± 0.18(syst.) [8], where “stat.” is the statistical error and “syst.” is the systematic error. We shall study the Bc → J/ψ helicity form factors (HFFs) instead of traditional TFFs by applying the LCSR approach.
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