Cross section and parametrization of charmonium decay

TL;DR

Addressing charmonium quasi two‑body decays in the nonperturbative regime, the paper develops a unified current‑formalism framework to compute cross sections and parametrize decays into vector–pseudoscalar (VP) final states. It derives the two‑body differential cross sections in the CMS for PP, PV, PA, and PT channels, and shows how the same method extends to SS, SV, SA, and ST final states, with explicit angular dependences. The VP parametrization is built on SU(3) flavor symmetry with spurion‑type symmetry breaking, yielding amplitudes $A_f(s)=a_{3g}(s)+a_{γ}(s)+a_c(s)$ and separating strong/electromagnetic pieces into $X_f$ and $Y_f$ that depend on meson mixing angles $θ_P$, $θ_V$. Form factors are treated via radiative‑transition physics, linking production and decay form factors through a quark‑structure factor $G(μ_u,μ_d,μ_s)$ and an energy‑dependent function $g(s)$, enabling resonance and continuum contributions through $B(s)$. The framework provides a practical tool for BESIII data analyses, illuminating meson mixing, SU(3) breaking, and internal quark structure, while being extendable to other two‑body charmonium decays.

Abstract

The parametrization forms of charmonium quasi two body decays are discussed in detail in this paper. The symmetry analysis and magnetic transition description are utilized to provide the multi-aspect comprehension of the decay dynamics, including the meson mixing angle, form factor, and $SU(3)$ symmetry breading effect. As the prerequisite, the electromagnetic cross sections involving scalar and pseudoscalar, are calculated for eight final states based on the approach of current algebra. Moreover, the mathematical manipulations of calculation for four kinds of final states are spelled out to illuminate the technique strategy.

Figures (6)

• Figure 1: Feynman diagram of $e^+e^- \to PP$ process.
• Figure 2: Feynman diagram of $e^+e^- \to PV$ process.
• Figure 3: Feynman diagram of $e^+e^- \to PA$ process.
• Figure 4: Feynman diagram of $e^+e^- \to PT$ process.
• Figure 5: The three classes of diagrams of $e^+e^-\rightarrow light\, \, hadrons$ at charmonium resonance. The charmonium state is represented by a charm quark loop.