Light meson decays at BESIII

Abstract. The BESIII experiment has accumulated the world’s largest data samples of 1.3 billion J/ψ events and 0.45 billion ψ(3686) events, which provide a unique opportunity to investigate light meson decays. The η and η′ decays are sensitive tools for investigations of π − π and η − π interactions, symmetry breaking, and serve as a test of chiral perturbation theory. In recent years considerable results on η and η′ decays were achieved at the BESIII experiment. In this proceeding, we present the significant progresses on amplitude analyses of Dalitz decays η′ → 3π, η′ → ηππ, and radiative decay η′ → γπ+π−, η′ → γγπ0. Additionally, the a0(980)f0(980) mixing is an important probe to the nature of those two lightest scalar mesons. The first observation of a0(980)f0(980) mixing is also presented, which will help to improve the understanding of the nature of a0(980) and f0(980).


Introduction
Light meson decays play a crucial role in examining and understanding the Quantum Chromodynamics (QCD) theory in non-pertubative energy region. The η meson is well established and its main decay modes are fairly well known [1]. However, η decay dynamics remains a subject of extensive theoretical studies aiming at extensions of the chiral perturbation theory (ChPT).
In addition, the scalar mesons a 0 0 (980) and f 0 (980) are difficult to accommodate into the traditional quark-antiquark model [2]. In theory, they are explained as tetra-quarks [3], KK molecule [4], or quark-antiquark gluon hybrid [5] and so on. The mixing mechanism in the system of a 0 0 (980)-f 0 (980), is thought to be an essential approach to clarify the nature of these two mesons.
The BESIII detector has accumulated the world's largest data samples of 1.3 billion J/ψ events and 0.45 billion ψ(3686) events, which provides a unique opportunity to investigate light meson physics through J/ψ and ψ(3686) decays. In this presentation, we will introduce some recent results from BESIII Collaboration that are related to light meson decays.
With the branching fractions of η → ππη taken from the PDG [1], r ± and r 0 are calculated to be (8.77 ± 1.19) × 10 −3 and (15.86 ± 1.33) × 10 −3 , respectively. The observed substantial Pand S -wave resonant contributions have to be properly considered by theory before attempting to determine light quark masses from r ± and r 0 .
In this proceeding, the most precise measurements of the matrix element for the η → ηπ + π − and η → ηπ 0 π 0 decays are presented based on J/ψ radiative decay [17]. Both the general and the linear representations are used to determine the Dalitz plot parameters, the fit results are shown in Fig. 2. The Dalitz plot parameters for both decays are in reasonable agreement and more precise than the previous measurements [12][13][14][15].

Precision study of η → γπ + π − decay dynamics
In the vector meson dominance (VMD) model [18], the radiative decay η → γπ + π − is dominated by the decay η → γρ(770). In the past, the dipion mass distribution was studied by several experiments [19][20][21][22]. A peak shift of about +20 MeV/c 2 for the ρ 0 meson with respect to the expected position was observed. This discrepancy could be attributed to a higher term of the Wess-Zumino-Witten anomaly, known as the box anomaly, in the chiral perturbation theory (ChPT) Lagrangian [23].  In this proceeding, we present a precision measurement of the dipion mass distribution for the η → γπ + π − process originating from the radiative decays J/ψ → γη [24]. Both modeldependent and model-independent approaches are used to investigate the decay dynamics,  23 the fit results are shown in Fig. 3. The ω contribution is observed for the first time in the dipion mass spectrum. The model-dependent fit indicates that only the components of ρ 0 and ω as well as the corresponding interference fail to describe the data, and an extra significant contribution, i.e. the box anomaly or ρ + , is found to be necessary. The model independent approach provides a satisfactory parametrization of the dipion invariant mass spectrum.

Observation of the doubly radiative decay η → γγπ 0
Recently, the doubly radiative decay η → γγπ 0 was studied in the frameworks of the linear σ model (LσM) [25] and the VMD model [26], which demonstrated that the contributions from the VMD are dominant. Experimentally, only an upper limit of the nonresonant branching fraction of B(η → γγπ 0 ) NR < 8 × 10 −4 at the 90% confidence level has been determined by the GAMS-2000 experiment [27].   The invariant mass of M γγπ 0 and the M 2 γγ dependent partial widths are shown in Fig. 4  (a) and (b), respectively. The branching fraction of the inclusive decay is measured for the first time to be B(η → γγπ 0 ) Incl. = (3.20 ± 0.07(stat) ± 0.23(sys)) × 10 −3 . In addition, the branching fraction for the nonresonant decay is determined to be B(η → γγπ 0 ) NR = (6.16 ± 0.64(stat) ± 0.67(sys)) × 10 −4 , which agrees with the upper limit measured by the GAMS-2000 experiment [27]. The invariant mass of M γπ 0 is shown as in Fig. 4 (c), and the product branching fraction with the omega intermediate state involved is obtained to be B(η → γω) · B(ω → γπ 0 ) = (2.37 ± 0.14(stat) ± 0.18(sys)) × 10 −3 . These results are useful to test QCD calculations on the transition form factor, and provide valuable inputs to the theoretical understanding of the light meson decay mechanisms.
3 Observation of a 0 0 (980)-f 0 (980) mixing The nature of the scalar mesons a 0 0 (980) and f 0 (980) have been controversial for several decades. In theory, these two states are difficult to accommodate in the traditional quarkantiquark model [2], and many alternative formulations have been proposed to explain their internal structure, including tetra-quarks [2,3], KK molecule [4], or quark-antiquark gluon hybrid [5].
The mixing mechanism of a 0 0 (980)-f 0 (980), which was first proposed in the late 1970s [28], is thought to be an essential approach to clarify the nature of these two mesons. The mixing mechanism predicts a narrow peak of about 8 MeV/c 2 in width between the charged and neutral KK mass thresholds, while the normal widths of a 0 0 (980) and f 0 (980)  23 should be 50 − 100 MeV/c 2 [1]. The mixing intensities, ξ f a and ξ a f , are important experimental probes for the nature of a 0 0 (980) and f 0 (980), as they are sensitive to the coupling constants in the processes of a 0 0 (980) → KK and f 0 (980) → KK, respectively. A direct measurement of the mixing intensities would provide crucial constraints in models of a 0 0 (980) and f 0 (980) internal structure.
In this proceeding, we present a study of a 0 0 (980)-f 0 (980) mixing with the decays of J/ψ → φηπ 0 (η → γγ and η → π + π − π 0 , φ → K + K − ) and ψ(3686) → γχ c1 → γπ 0 π + π − [29]. The signals of a 0 0 (980)-f 0 (980) mixing are observed with a statistical significance of larger than 5σ for the first time, and the corresponding branching fractions and mixing intensities are summarized in Table 1.    Figure 5. The statistical significance of the signal scanned in the two-dimensional space of g a 0 K + K − and g f 0 K + K − . The regions with higher statistical significance indicate larger probability for the emergence of the two coupling constants. The markers indicate predictions from various illustrative theoretical models.
Since a 0 0 (980)-f 0 (980) mixing is sensitive to the coupling constants of a 0 0 (980) → KK and f 0 (980) → KK, we obtain the statistical significance of the mixing signal by scanning the two coupling constants g a 0 K + K − and g f 0 K + K − . The statistical significance of the signal scanned in the two-dimensional space of g a 0 K + K − and g f 0 K + K − is shown in Fig. 5. For the distribution, the regions with higher statistical significance indicate larger probability for the emergence of the two coupling constants. The predicted coupling constants from various models [30] are displayed as well (color markers), but the theoretical uncertainties on the models are not considered here.

Summary
With the largest data samples of 1.3 billion J/ψ events and 0.45 billion ψ(3686) events, the BESIII Collaboration has made significant progresses on light meson decays. Firstly, η  23 hadronic Dalitz decays η → 3π, η → ηππ, and η radiative decays η → γπ + π − as well as the double radiative decay η → γγπ 0 are investigated, which deepen our knowledge about η decay dynamics. Secondly, the a 0 0 (980)-f 0 (980) mixing is observed with the statistical significance of large than 5σ for the first time. The corresponding branching fractions and mixing intensities are measured. The constraint regions on the coupling constants, g a 0 K + K − and g f 0 K + K − , are also estimated. The results will help to improve the understanding of the nature of a 0 0 (980) and f 0 (980).