RECORD
Amplitude analysis of the anomalous decay $\eta'\to\pi^+\pi^-\gamma$
High Energy Physics - Phenomenology · Submitted 6 Dec 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results show that the anomaly contribution is mandatory in order to explain the data.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In this paper we perform an amplitude analysis of $\eta'\to\pi^+\pi^-\gamma$ and confront it with the latest BESIII data. Based on the final-state interaction theorem, we represent the amplitude in terms of an Omn\'es function multiplied by a form factor that corresponds to the contributions from left-hand cuts and right-hand cuts in the inelastic channels. We also take into account the isospin violation effect induced by $\rho-\omega$ mixing. Our results show that the anomaly contribution is mandatory in order to explain the data. Its contribution to the decay width of $\Gamma(\eta'\to\pi\pi\gamma)$ is larger than that induced by isospin violation. Finally we extract the pole positions of the $\rho$ and $\omega$ as well as their corresponding residues.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we perform an amplitude analysis of $\eta'\to\pi^+\pi^-\gamma$ and confront it with the latest BESIII data. | contribution 1.00 | 0.94 | 0.04 | asserted 0.85 |
| s1 | Based on the final-state interaction theorem, we represent the amplitude in terms of an Omn\'es function multiplied by a form factor that corresponds to the contributions from left-hand cuts and right-hand cuts in the inelastic channels. | method 1.00 | 0.86 | 0.03 | asserted 1.00 |
| s2 | We also take into account the isospin violation effect induced by $\rho-\omega$ mixing. | method 0.94 | 0.84 | 0.03 | asserted 0.98 |
| s3 | Our results show that the anomaly contribution is mandatory in order to explain the data. | result 0.76 | 0.94 | 0.76 | asserted 1.00 |
| s4 | Its contribution to the decay width of $\Gamma(\eta'\to\pi\pi\gamma)$ is larger than that induced by isospin violation. | result 0.99 | 0.92 | 0.19 | asserted 1.00 |
| s5 | Finally we extract the pole positions of the $\rho$ and $\omega$ as well as their corresponding residues. | result 0.93 | 0.95 | 0.06 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v4
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In this paper we perform an amplitude analysis of $\eta'\to\pi^+\pi^-\gamma$ and confront it with the latest BESIII data. Based on the final-state interaction theorem, we represent the amplitude in terms of an Omn\'es function multiplied by a form factor that corresponds to the contributions from left-hand cuts and right-hand cuts in the inelastic channels. We also take into account the isospin violation effect induced by $\rho-\omega$ mixing. Our results show that the anomaly contribution is mandatory in order to explain the data. Its contribution to the decay width of $\Gamma(\eta'\to\pi\pi\gamma)$ is larger than that induced by isospin violation. Finally we extract the pole positions of the $\rho$ and $\omega$ as well as their corresponding residues.
Human review
How the literature uses it
9 arXiv papers cite this in 10 sentences
Papers whose main result relates to this one's
States the same result 1 paper
-
The analysis of the dipionic mass distribution in the decay \eta'->\gamma\pi^+\pi^- confirms the existence of a non-resonant contribution which is the box anomaly.
The box anomaly and radiative decays of \eta(\eta')-mesons · 0.91
Papers citing it · 6 sentences without a confident label
Compares with it 1 paper
-
All the values of $T^I_J(0)$ in Tab. [ref] are close to the prediction of $χ$PT or our earlier analyses [ref] .
A study on the correlation between poles and cuts in $\pi\pi$ scattering · Fits · 0.96
Cites it as background 3 papers
-
Recent studies of some of the aforementioned decays include Refs. [ref] for $η→3π$, Ref. [ref] for $η^(')→4π$, Refs. [ref] for $η^(')→π^+π^-γ$, Ref. [ref] for $η^'→π^0γγ$ and $η^'→ηγγ$, and Refs. [ref] for transition form factors and Dalitz decays.
$\eta^{\prime}\to\eta\pi\pi$ decays in unitarized resonance chiral theory · Introduction · 0.95
-
In principle, the left-hand cut (l.h.c.) contribution could also be considered [ref] .
Composite nature of $Z_b$ states from data analysis · Two-body scattering $t$-matrix element · 0.84
-
Note that in the literature, e.g., Ref. [ref] , the mixing angle $θ$ is often referred to the singlet-octet one, and $α= θ+ 54.7^∘$.
Semileptonic $B$ and $B_s$ decays involving scalar and axial-vector mesons · Results and discussion · 0.89
What it cites · 46 sentences without a confident label
Uses the method or tool of 6 papers
-
The relevant chiral Lagrangian can be written as [ref] : [equation] The part $L^_(4)$ containing the LO operators of the chiral anomaly is [ref] [equation] where $F≈92.2$ MeV is the pion decay constant in the chiral limit and $Φ$ is a nonet matrix collecting the pseudoscalar Goldstone bosons: Φ= ( [ π^0√(2) +η_8√(6) π^+ K^+; π^- -π^0√(2) +η_8√(6) K^0; K^- K^0 -2 η_8√(6); ] )+1/√(3)η_0 .
Odd-intrinsic-parity processes within the Resonance Effective Theory of QCD · Formalism of R$χ$T · 0.83
-
The $ρ-ω$ mixing is taken into account following Ref. [ref] .
1305.57511 · Formalism of R$χ$T · 1.00
-
Notice that the width is rather small and thus we can ignore its energy dependence[In a more dedicated way, one can use the standard Breit-Wigner formalism to represent the $ππ→ω→ππ$ amplitude [ref] : T^1_P_ω=g_2(s)^2/ M^2-s-i ρ_1(s)g_1^2(s)-i ρ_2(s)g_2^2(s)-i ρ_3(s)g_3^2(s) .Here 1, 2, 3 represents the $πγ$, $ππ$ and $πππ$ channels, respectively.
1403.75141 · Couplings of $g_η'Vγ$ · 0.92
Uses data or values from 6 papers
-
In this section, we fit to the invariant di-pion mass spectrum by BESIII [ref] .
Precision Study of $\eta^\prime\rightarrow\gamma\pi^+\pi^-$ Decay Dynamics · Fit to experimental data · 1.00
-
Thus, we fix $θ_P$ at $-21.37^∘$ [ref] and set $α_0$ free.
1305.57511 · Fit to experimental data · 0.83
-
The function $φ^1_1$(s) denotes the phase of $P$-wave elastic $ππ→ππ$ amplitude, which was given in a previous amplitude analysis of $ππ$ scattering [ref] .
A new method to study the number of colors in the final-state interactions of hadrons · Final state interaction · 0.98
Compares with 10 papers
-
However, the resulting decay widths involving $η'$, $Γ_η'→ργ$, $Γ_η'→ωγ$ and $Γ_ϕ→η'γ$, are now deviated about 30-60 percents from the previous determinations in Ref. [ref] .
1305.57511 · Fit to experimental data · 0.97
-
A good fit can be obtained with $θ_P≈-10.9±0.5^∘$, which is compatible with the determinations in Refs. [ref] .
Measurement of the pseudoscalar mixing angle and $\eta^{\prime}$ gluonium content with KLOE detector · Fit to experimental data · 0.96
-
A good fit can be obtained with $θ_P≈-10.9±0.5^∘$, which is compatible with the determinations in Refs. [ref] .
Anomalous decay and scattering processes of the eta meson · Fit to experimental data · 0.96
Cites as support 1 paper
-
Nonetheless, the CB data is not precise enough to disentangle the effect of $ρ-ω$ interference from others in the line shape, as shown, e.g., by Ref. [ref] .
0907.40470 · Introduction · 0.97
Cites as background 6 papers
-
The mixing of the $η_8$ and $η_0$ with an angle $θ_P$ yields the physical $η$ and $η'$ states[We notice that more complicated schemes for $η-η'$ mixing involving two mixing angles have been studied in e.g., Refs. [ref] , which is commonly used to describe the two-photon decays well [ref] . ].
On the 1/N expansion in chiral perturbation theory · Formalism of R$χ$T · 0.90
-
The mixing of the $η_8$ and $η_0$ with an angle $θ_P$ yields the physical $η$ and $η'$ states[We notice that more complicated schemes for $η-η'$ mixing involving two mixing angles have been studied in e.g., Refs. [ref] , which is commonly used to describe the two-photon decays well [ref] . ].
Scrutinizing the eta-eta' mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory · Formalism of R$χ$T · 0.90
-
The mixing of the $η_8$ and $η_0$ with an angle $θ_P$ yields the physical $η$ and $η'$ states[We notice that more complicated schemes for $η-η'$ mixing involving two mixing angles have been studied in e.g., Refs. [ref] , which is commonly used to describe the two-photon decays well [ref] . ].
Pseudoscalar decay constants at large N_c · Formalism of R$χ$T · 0.90
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.