We present an analysis of the decay $D^{+} \to K^{-} \pi^+ e^+ \nu_e$ based on data collected by the BESIII experiment at the $\psi(3770)$ resonance. Using a nearly background-free sample of 18262 events, we measure the branching fraction $\mathcal{B}(D^{+} \to K^{-} \pi^+ e^+ \nu_e) = (3.71 \pm 0.03 \pm 0.08)\%$. For $0.8<m_{K\pi}<1.0$ GeV/$c^{2}$ the partial branching fraction is $\mathcal{B}(D^{+} \to K^{-} \pi^+ e^+ \nu_e)_{[0.8,1]} = (3.33 \pm 0.03 \pm 0.07)\%$. A partial wave analysis shows that the dominant $\bar K^{*}(892)^{0}$ component is accompanied by an \emph{S}-wave contribution accounting for $(6.05\pm0.22\pm0.18)\%$ of the total rate and that other components are negligible. The parameters of the $\bar K^{*}(892)^{0}$ resonance and of the form factors based on the spectroscopic pole dominance predictions are also measured. We also present a measurement of the $\bar K^{*}(892)^{0}$ helicity basis form factors in a model-independent way.
The $S$-wave phase $\delta_{S}$ measured in the 12 $m_{K\pi}$ bins with statistical and systematic uncertainties. The systematic uncertainties include: (I) background fraction, (II) background shape, (III) the $\bar K_{0}^{*}(1430)^{0}$ mass and width, (IV) additional resonances, (V) tracking efficiency correction, (VI) PID efficiency correction.
Average form-factor products in the $K^{*}$-dominated region.
The energy dependence of the K L 0 -K S 0 transmission regeneration amplitudes on deuterons and neutrons in the momentum region 10–50 GeV/ c is determined. The moduli of the modified transmission amplitudes are momentum dependent. These dependences are fitted by the expression A j p − nj , where A j and n j ( j = d, n) are constants: A d =2.88 ±0.04 mb , n d =0.546±0.030, for deuterons , A n =1.97 ±0.14 mb , n n =0.530±0.019, for neutrons , The amplitude phases do not depend on the kaon momentum and are equal to ϕ d = (−130.9 ± 2.7)° ϕ n = (−132.3 ± 1.7)°. The mean value of the ratio of the total cross-section differences for K 0 and K 0 interactions with neutrons and protons is determined. The residues of the partial ω and ϱ amplitudes, which contribute to the kaon-nucleon interaction amplitudes, are also obtained.
FORWARD CROSS SECTION, AMPLITUDE AND PHASE FOR K0 REGENERATION.
(AK0 - K0) TOTAL CROSS SECTION DIFFERENCES.
The modulus and the phase of the K L o −K S o regeneration amplitude on carbon have been measured. In a momentum range of 16–40 GeV/ c the phase is constant within experimental error bars and coincides with the regeneration phase on hydrogen. Both the modulus and the phase of the regeneration amplitude on carbon are in agreement with optical model predictions.
ASSUMING A CONSTANT PHASE INDEPENDENT OF MOMENTUM, THE CARBON REGENERATION AMPLITUDE HAS A PHASE OF -130 +- 17 DEG.
None
THE AVERAGE PHASE IS -130.9 +- 2.7 DEG (NO EXPLICIT MOMENTUM DEPENDENCE). USING ABS(ETA+-) = 2.3*10**-3.
REGENERATION AMPLITUDE ASSUMING MOMENTUM INDEPENDENT CONSTANT PHASE.
CROSS SECTION DIFFERENCES ASSUMING MOMENTUM INDEPENDENT CONSTANT PHASE.
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