Four-body semileptonic charm decays D? P1P2l+?l based on SU(3) flavor analysis

Motivated by the significant experimental progress in probing semileptonic decays D -> P1P2e thorn nu e oe 1/4 mu; e thorn , we analyze the branching ratios of the D -> P1P2e thorn nu e decays with the nonresonant, the light scalar meson resonant, and the vector meson resonant contributions in this work. We obtain the hadronic amplitude relations between different decay modes by the SU(3) flavor analysis, and then predict relevant branching ratios of the D -> P1P2e thorn nu e decays by the present experimental data with 2 sigma errors. Most of our predicted branching ratios are consistent with present experimental data within 2 sigma error bars, and others are consistent with the data within 3 sigma error bars. We find that the branching ratios of the nonresonant decays D0 -> pi- over bar K0e thorn nu e;pi 0K-e thorn nu e;D thorn ->pi thorn K-e thorn nu e;pi 0 over bar K0e thorn nu e;pi thorn pi- e thorn nu e;pi 0 pi 0e thorn nu e, and D thorn s -> K thorn K-e thorn nu e; K0 over bar K0e thorn nu e are on the order of Oo10-3-10-4 thorn . The vector meson resonant contributions are dominant in the D0 ->pi- over bar K0e thorn nu e;pi 0K-e thorn nu e;pi 0 pi-e thorn nu e;D thorn ->pi thorn K-e thorn nu e;pi 0 over bar K0e thorn nu e;pi thorn pi-e thorn nu e, and D thorn s -> K thorn K-e thorn nu e; K0 over bar K0e thorn nu e;K thorn pi-e thorn nu e;K0 pi 0e thorn nu e decays. The nonresonant, the vector meson resonant, and the scalar resonant contributions are all important in the D0 -> eta pi-e thorn nu e decays. The D0 -> K-K0e thorn nu e;eta 0 pi-e thorn nu e and D thorn -> over bar K0K0e thorn nu e;pi 0 pi 0e thorn nu e; eta pi 0e thorn nu e;eta 0 pi 0e thorn nu e decays only receive both the nonresonant and the scalar resonant contributions, and both contributions are important in their branching ratios. According to our predictions, many decay modes could be observed in the experiments like BESIII, LHCb, and Belle II, and some decay modes might be measured in these experiments in the near future.

Automated summary

Motivated by experimental progress in semileptonic decays D -> P1P2e thorn nu e oe 1/4 mu; e thorn, this study analyzes the branching ratios of these decays with nonresonant, light scalar meson resonant, and vector meson resonant contributions. By applying SU(3) flavor analysis, the hadronic amplitude relations between different decay modes are obtained and relevant branching ratios are predicted based on current experimental data with 2 sigma errors. Most of the predicted branching ratios are consistent with present experimental data within 2 sigma error bars, while others are within 3 sigma error bars. Many decay modes could be observed in experiments like BESIII, LHCb, and Belle II, and some may be measured in the near future.