Study of $\phi\to K\bar{K}$ in the amplitude analysis of $D^{+}\to K_{S}^{0}K_{L}^{0}\pi^{+}$

TL;DR

This paper reports the first amplitude analysis and branching fraction measurement of the decay D+ to KS0KL0pi+, revealing a lower-than-expected relative branching ratio for phi to K0K0 versus K+K- channels, consistent with isospin symmetry.

Contribution

It provides the first detailed amplitude analysis and precise branching fraction measurement for D+ to KS0KL0pi+ decay, including the phi meson coupling to neutral kaons.

Findings

Measured branching fraction of (5.780 ± 0.085 ± 0.052)×10^{-3} for D+ to KS0KL0pi+

Determined the relative branching ratio of phi to K0K0 versus K+K- as 0.628 ± 0.022 ± 0.015 ± 0.017

Result aligns with isospin expectations and differs from previous world averages.

Abstract

We present the first amplitude analysis and branching fraction measurement of $D^{+} \rightarrow K_{S}^{0}K_{L}^{0}\pi^{+}$ decay. The analysis uses a dataset corresponding to an integrated luminosity of 20.3~$\rm fb^{-1}$, which was recorded at a center-of-mass energy 3.773~GeV by the BESIII detector. The measured branching fraction is $\mathcal{B}(D^{+} \rightarrow K_{S}^{0}K_{L}^{0}\pi^{+})=(5.780\pm0.085\pm 0.052)\times10^{-3}$, where the first uncertainty is statistical and the second is systematic. Using the known value of ${\cal B}(D^+ \to \phi \pi^+,\,\phi \to K^+K^-)$, we determine the relative branching fraction between $\phi \to K_{S}^0K_{L}^0$ and $\phi \to K^+K^-$ to be $\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K_{S}^0K_{L}^0)/\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K^+K^-)= 0.628\pm0.022\pm 0.015\pm0.017$, where the third uncertainty is related to $\mathcal{B}(D^{+} \to \phi \pi^{+}, \phi \to K^+K^-)$. This result is significantly lower than the previous world average and is consistent with the isospin expectation for the $\phi$ meson's coupling to charged and neutral kaon pairs.