# Analysis of $D^+\to\bar K^0e^+\nu_e$ and $D^+\to\pi^0e^+\nu_e$ Semileptonic Decays

## TL;DR

This paper measures the branching fractions and form factors of specific semileptonic D+ decays using BESIII data, providing precise tests of CKM matrix elements and form factor calculations.

## Contribution

It provides new precise measurements of branching fractions and form factors for D+ semileptonic decays, and extracts CKM matrix elements using experimental data and lattice QCD inputs.

## Key findings

- Branching fraction for D+ to K0e+nu_e: (8.60±0.06±0.15)%
- Branching fraction for D+ to pi0e+nu_e: (3.63±0.08±0.05)%
- Determined CKM elements |V_cs| and |V_cd| with uncertainties

## Abstract

Using 2.93~fb$^{-1}$ of data taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we study the semileptonic decays $D^+ \to \bar K^0e^+\nu_e$ and $D^+ \to \pi^0 e^+\nu_e$. We measure the absolute decay branching fractions $\mathcal B(D^+ \to \bar K^0e^+\nu_e)=(8.60\pm0.06\pm 0.15)\times10^{-2}$ and $\mathcal B(D^+ \to \pi^0e^+\nu_e)=(3.63\pm0.08\pm0.05)\times10^{-3}$, where the first uncertainties are statistical and the second systematic. We also measure the differential decay rates and study the form factors of these two decays. With the values of $|V_{cs}|$ and $|V_{cd}|$ from Particle Data Group fits assuming CKM unitarity, we obtain the values of the form factors at $q^2=0$, $f^K_+(0) = 0.725\pm0.004\pm 0.012$ and $f^{\pi}_+(0) = 0.622\pm0.012\pm 0.003$. Taking input from recent lattice QCD calculations of these form factors, we determine values of the CKM matrix elements $|V_{cs}|=0.944 \pm 0.005 \pm 0.015 \pm 0.024$ and $|V_{cd}|=0.210 \pm 0.004 \pm 0.001 \pm 0.009$, where the third uncertainties are theoretical.