Abstract
The measured branching ratio of the D meson semileptonic decay D rightarrow rho e^+ nu _e, which is based on the 0.82~{mathrm{fb}^{-1}} CLEO data taken at the peak of psi (3770) resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the Drightarrow rho transition form factors A_{1,2}(q^2) and V(q^2). After extrapolating the LCSR predictions of these TFFs to whole q^2-region, we obtain 1/|V_{mathrm{cd}}|^2 times Gamma (D rightarrow rho e nu _e) =(55.45^{+13.34}_{-9.41})times 10^{-15}~mathrm{GeV}. Using the CKM matrix element and the D^0(D^+) lifetime from the Particle Data Group, we obtain mathcal{B} (D^0rightarrow rho ^- e^+ nu _e) = (1.749^{+0.421}_{-0.297}pm 0.006)times 10^{-3} and mathcal{B} (D^+ rightarrow rho ^0 e^+ nu _e) = (2.217^{+0.534}_{-0.376}pm 0.015)times 10^{-3}, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two D meson radiative processes and obtain mathcal{B}(D^0rightarrow rho ^0 gamma )= (1.744^{+0.598}_{-0.704})times 10^{-5} and mathcal{B}(D^+ rightarrow rho ^+ gamma ) = (5.034^{+0.939}_{-0.958})times 10^{-5}, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the D meson decays.
Highlights
Belle, LHCb, BES and PANDA, the D meson semileptonic decays provide a good platform for the precision test of standard model (SM) and for searching of new physics (NP) beyond the SM
We present the predictions from various approaches in Table 3, i.e. from the CLEO collaboration [3], the 3PSR [6], the heavy quark effective field theory (HQEFT) [7,8], relativistic harmonic oscillator potential model (RHOPM) [9], the quark model (QM) [10, 11], the light-front quark model (LFQM) [12], the HMχ T [13], and the Lattice QCD
We have investigated the D → ρ transition form factors (TFFs) within the lightcone sum rules (LCSR) approach
Summary
LHCb, BES and PANDA, the D meson semileptonic decays provide a good platform for the precision test of standard model (SM) and for searching of new physics (NP) beyond the SM. The QCD SR approach is applicable in both small and intermediate q2-region, which provides a bridge between the pQCD and lattice QCD predictions, and a more accurate QCD SR prediction is helpful for a better understanding of the TFFs. In the paper, as a new QCD SR analysis, we take the improved version of QCD SR approach, i.e. the lightcone sum rules (LCSR) [18,19,20], to recalculate the D → ρ TFFs. The LCSR avoids the problems of the conventional SVZ SR by making a partial resummation of the operator product expansion (OPE) to all orders and reorganize the OPE expansion in terms of the twists of relevant operators rather than their dimensions.
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