Analysis of the dynamics of the decay D + → K S 0 π 0 e + ν e $$ {D}^{+}\to {K}_S^0{\pi}^0{e}^{+}{\nu}_e $$

Abstract The branching fraction of D + → K S 0 π 0 e + ν e $$ {D}^{+}\to {K}_S^0{\pi}^0{e}^{+}{\nu}_e $$ is measured for the first time using 7.93 fb −1 of e + e − annihilation data collected at the center-of-mass energy s $$ \sqrt{s} $$ = 3.773 GeV with the BESIII detector operating at the BEPCII collider, and is determined to be B D + → K S 0 π 0 e + ν e = 0.881 ± 0.017 stat . ± 0.016 syst . % $$ \mathcal{B}\left({D}^{+}\to {K}_S^0{\pi}^0{e}^{+}{\nu}_e\right)=\left(0.881\pm {0.017}_{\textrm{stat}.}\pm {0.016}_{\textrm{syst}.}\right)\% $$ . Based on an analysis of the D + → K S 0 π 0 e + ν e $$ {D}^{+}\to {K}_S^0{\pi}^0{e}^{+}{\nu}_e $$ decay dynamics, we observe the S-wave and P-wave components with fractions of f S-wave = (6.13 ± 0.27stat. ± 0.30syst. )% and f K ¯ ∗ 892 0 = 93.88 ± 0.27 stat . ± 0.29 syst . % $$ {f}_{{\overline{K}}^{\ast }{(892)}^0}=\left(93.88\pm {0.27}_{\textrm{stat}.}\pm {0.29}_{\textrm{syst}.}\right)\% $$ , respectively. From these results, we obtain the branching fractions B D + → K S 0 π 0 S − wave e + ν e = 5.41 ± 0.35 stat . ± 0.37 syst . × 10 − 4 $$ \mathcal{B}\left({D}^{+}\to {\left({K}_S^0{\pi}^0\right)}_{S-\textrm{wave}}{e}^{+}{\nu}_e\right)=\left(5.41\pm {0.35}_{\textrm{stat}.}\pm {0.37}_{\textrm{syst}.}\right)\times {10}^{-4} $$ and B D + → K ¯ ∗ 892 0 e + ν e = 4.97 ± 0.11 stat . ± 0.12 syst . % $$ \mathcal{B}\left({D}^{+}\to {\overline{K}}^{\ast }{(892)}^0{e}^{+}{\nu}_e\right)=\left(4.97\pm {0.11}_{\textrm{stat}.}\pm {0.12}_{\textrm{syst}.}\right)\% $$ . In addition, the hadronic form-factor ratios of D + → K ¯ ∗ 892 0 e + ν e $$ {D}^{+}\to {\overline{K}}^{\ast }{(892)}^0{e}^{+}{\nu}_e $$ at q 2 = 0, assuming a single-pole dominance parameterization, are determined to be r V = V 0 A 1 0 = 1.43 ± 0.07 stat . ± 0.03 syst . $$ {r}_V=\frac{V(0)}{A_1(0)}=1.43\pm {0.07}_{\textrm{stat}.}\pm {0.03}_{\textrm{syst}.} $$ and r 2 = A 2 0 A 1 0 = 0.72 ± 0.06 stat . ± 0.02 syst . $$ {r}_2=\frac{A_2(0)}{A_1(0)}=0.72\pm {0.06}_{\textrm{stat}.}\pm {0.02}_{\textrm{syst}.} $$ .