Puzzle of Anomalously Large Isospin Violations inη(1405/1475)→3π

Abstract

The BES-III Collaboration recently reported the observation of anomalously large isospin violations in J/ψ→γη(1405/1475)→γπ(0)f(0)(980)→γ+3π, where the f(0)(980) in the ππ invariant mass spectrum appears to be much narrower (~10 MeV) than the peak width (~50 MeV) measured in other processes. We show that a mechanism, named as triangle singularity (TS), can produce a narrow enhancement between the charged and neutral KK¯ thresholds, i.e., 2m(K(±))~2m(K(0)). It can also lead to different invariant mass spectra for η(1405/1475)→a(0)(980)π and KK ¯*+c.c., which can possibly explain the long-standing puzzle about the need for two close states η(1405) and η(1475) in ηππ and KK¯π, respectively. The TS could be a key to our understanding of the nature of η(1405/1475) and advance our knowledge about the mixing between a(0)(980) and f(0)(980).

Threshold and Kinematic Effects for the Exotic Resonance-Like Structures

“…Another interesting observation is that the width of f 0 (980) is just about 10 MeV which is much narrower than that of about 40 ∼ 100 MeV observed in other processes [11]. These unusual results inspired the study of the isospin violation mechanism for η(1405) → 3π where the ATS mechanism was identified and found to play a key role in accounting for the anomalously large isospin violation effects [12]. In a followed up analysis [13] a mixture of f 1 (1420) was found in J/ψ → γ3π apart from the dominant η(1405) contribution.…”

“…[12,13] that the processes η(1405)/η(1475) and f 1 (1420) decaying into 3π are ideal places to recognize the ATS condition. The intermediate KK * + c.c.…”

“…Note that so far the high-statistics experimental analyses at BESIII only see one pseudoscalar meson (either η(1405) or η(1475)) in each exclusive decay channel, there could be only one state (we tentatively quote it as the historical η(1440)) in this mass region. This possibility will solve the mysterious problem of how to understand that the Lattice QCD predicted pseudoscalar glueball has a mass of about 2.4∼2.6 GeV, while the candidate of η(1405) is so light [12,13].…”

Observation of the isospin-violating decayJ/ψ→ϕπ0f0(980Ablikim1, Ачасов2, Ai3 et al. 2015Phys. Rev. D204100View full textAdd to dashboardCite

“…In this study, the f 0 (980) width was found to be 9.5 ± 1.1 MeV/c 2 . One proposed explanation for this anomalously narrow width and the observed large isospin violation, which cannot be caused by a 0 0 (980) − f 0 (980) mixing, is the triangle singularity mechanism [5,6].…”

Mechanisms of the isospin-breaking decayf1(1285)→f0(980Achasov1, Кожевников2, Shestakov3 2016Phys. Rev. D250540View full textAdd to dashboardCite

“…Recently, the results of the first experiments on its discovery in the reactions [30], (e) J/ψ → φf 0 (980)π 0 → φ 3π [31], (f) J/ψ → φf 1 (1285) → φf 0 (980)π 0 → φ 3π [31] have been obtained with the help of detectors VES in Protvino [27,28] and BESIII in Beijing [29][30][31]. The theoretical considerations concerning the BESIII data [30] * achasov@math.nsc.ru † kozhev@math.nsc.ru ‡ shestako@math.nsc.ru on the reaction (d), that is, on the decay η(1405) → f 0 (980)π 0 → 3π, were presented in [32][33][34][35]. Interest in the a 0 0 (980) − f 0 (980) mixing is primarily due to the fact that the amplitude of the isospin breaking transition a 0 0 (980) → (K + K − + K 0K 0 ) → f 0 (980), caused by the mass difference of the K + K − and K 0K 0 intermediate states, in the region between KK thresholds turns out to be of the order of (m K 0 − m K + )/m K 0 [1] [i.e.…”