Measurement of the branching ratio for $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$ decay

Measurement of the branching ratio for $η \to π^{0} γ γ$ decay

S. Prakhov et al. (Crystal Ball Collaboration)

Phys. Rev. C 72, 025201 – Published 18 August 2005

Abstract

The branching ratio (BR) for the rare decay $η \to π^{0} γ γ$ was measured with the Crystal Ball multiphoton spectrometer. The result, BR $(η \to π^{0} γ γ) = (3.5 \pm 0 . 7_{stat} \pm 0 . 6_{syst}) \times 10^{- 4}$ , is in agreement with calculations of chiral perturbation theory to third order. We have used a sample of 28 million η mesons produced at the BNL Alternating Gradient Synchrotron using the $π^{-} p \to η n$ reaction close to threshold. We detail the intricate extraction of the signal, which has about 1.6 thousand $η \to π^{0} γ γ$ events, from the overwhelming background of $η \to 3 π^{0}$ decays and from the $π^{-} p \to π^{0} π^{0} n$ reaction.

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Received 19 October 2004

DOI:https://doi.org/10.1103/PhysRevC.72.025201

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Vol. 72, Iss. 2 — August 2005

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Figure 1
Comparison of data (solid triangles) and MC (circles) distributions. For the two-cluster events satisfying the $π^{-} p \to η n \to γ γ n$ hypothesis we show (a) the CB energy threshold, (b) the two-photon invariant mass, (c) the c.m. η-production angle, and (d) the vertex $z$ coordinate. For the six-cluster events satisfying the $π^{-} p \to η n \to 6 γ n$ hypothesis we show (e) the CB energy threshold and (f) the six-photon invariant mass. For the six-cluster events satisfying the $π^{-} p \to η n \to 3 π^{0} n \to 6 γ n$ hypothesis we show (g) the $χ^{2}$ probability of a 4-C kinematic fit, (h) the c.m. η-production angle, and (i) the $3 π^{0}$ invariant mass. The vertical line in the invariant-mass spectra (b), (f), and (i) shows the η mass, which is 0.547 GeV/ $c^{2}$ [21].
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Figure 2
Comparison of the data and MC distributions for reaction $π^{-} p \to π^{0} π^{0} n$ : (a) Dalitz plot of the data, (b) Dalitz plot of the MC simulation, (c) the $π^{0} n$ invariant mass squared, and (d) the $π^{0} π^{0}$ invariant mass squared. The MC invariant mass spectra are normalized to the data.
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Figure 3
The probability distributions for four-cluster events that survived the $2 π^{0}$ cut and passed the 2% CL cut for the 1-C hypothesis $π^{-} p \to π^{0} γ γ n \to 4 γ n$ : (a) experimental LH $_{2}$ data, (b) experimental empty-target data, (c) MC simulation for $4 \times 10^{5}$ $π^{-} p \to η n \to π^{0} γ γ n$ events, (d) MC for $3 \times 10^{7}$ $π^{-} p \to η n \to 3 π^{0} n$ events, (e) MC for $4 \times 10^{7}$ $π^{-} p \to π^{0} π^{0} n$ events, (f) MC for $1 \times 10^{7}$ $π^{-} p \to η n \to γ γ n$ events, and (g) MC for $6 \times 10^{6}$ $π^{-} p \to π^{0} n$ events.
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Figure 4
Two-dimensional distributions of the vertex $z$ coordinate versus the $π^{0} γ γ$ invariant mass, where both of the parameters are obtained from the output of the kinematic fit to the hypothesis $π^{-} p \to π^{0} γ γ n \to 4 γ n$ : (a) experimental LH $_{2}$ data, (b) experimental empty-target data, (c) MC simulation for $π^{-} p \to η n \to π^{0} γ γ n$ , (d) MC for $π^{-} p \to η n \to 3 π^{0} n$ , (e) MC for $π^{-} p \to π^{0} π^{0} n$ , (f) MC for $π^{-} p \to η n \to γ γ n$ , and (g) MC for $π^{-} p \to π^{0} n$ .
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Figure 5
Two-dimensional plots of the parameter ρ versus the cluster energy of each of the two photons from η-decay obtained for events selected as $π^{-} p \to π^{0} γ γ n \to 4 γ n$ candidates: (a) experimental LH $_{2}$ data, (b) experimental empty-target data, (c) MC simulation for $π^{-} p \to η n \to π^{0} γ γ n$ , (d) MC for $π^{-} p \to η n \to 3 π^{0} n$ , (e) MC for $π^{-} p \to π^{0} π^{0} n$ , (f) MC for $π^{-} p \to η n \to γ γ n$ , and (g) MC for $π^{-} p \to π^{0} n$ . The curves in the plots show the cuts on ρ. The cuts require discarding all events in which at least one value of ρ lies above the curve. The numbers that label the curves increase with tighter cut criteria.
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Figure 6
Same as Fig. 5 when both photons are from the $π^{0}$ decay.
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Figure 7
Change of the $π^{0} γ γ$ invariant-mass spectrum upon applying different ρ cuts: (a) experimental LH $_{2}$ data, (b) MC simulation for $π^{-} p \to η n \to π^{0} γ γ n$ , (c) MC for $π^{-} p \to η n \to 3 π^{0} n$ , and (d) MC for $π^{-} p \to π^{0} π^{0} n$ . The spectra shown by the solid line (labeled No. 0) are obtained without any cut on ρ. The numbers that label the three other spectra correspond to the ρ-cut numbers shown in Figs. 5 and 6.
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Figure 8
Two-dimensional plots of the maximal $m (π^{0} γ)$ invariant mass (from the two possible ones) versus $m (π^{0} γ γ)$ for events selected as $π^{-} p \to π^{0} γ γ n \to 4 γ n$ candidates: (a) experimental LH $_{2}$ data, (b) experimental empty-target data, (c) MC simulation for $π^{-} p \to η n \to π^{0} γ γ n$ , (d) MC for $π^{-} p \to η n \to 3 π^{0} n$ , (e) MC for $π^{-} p \to π^{0} π^{0} n$ , (f) MC for $π^{-} p \to η n \to γ γ n$ , and (g) MC for $π^{-} p \to π^{0} n$ . The lines in the plots show the cuts on $m_{\max} (π^{0} γ)$ . The cuts require discarding all events in which $m_{\max} (π^{0} γ)$ lies above the line. The number that labels the lines in (a) increases when the cut criteria are tighter.
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Figure 9
Change of the $π^{0} γ γ$ invariant-mass spectrum upon applying different $m_{\max} (π^{0} γ)$ cuts: (a) experimental LH $_{2}$ data, (b) MC simulation for $π^{-} p \to η n \to π^{0} γ γ n$ , (c) MC for $π^{-} p \to π^{0} π^{0} n$ , and (d) MC for $π^{-} p \to η n \to γ γ n$ . The spectra shown by the solid line (labeled No. 0) are obtained without any cut on $m_{\max} (π^{0} γ)$ . The numbers that label the three other spectra correspond to the $m_{\max} (π^{0} γ)$ -cut numbers of Fig. 8.
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Figure 10
Fit of the $m (π^{0} γ γ)$ spectra for the $π^{-} p \to π^{0} γ γ n$ candidates selected at the 2% CL, with the vertex $z$ coordinate within $\pm 6$ cm, and after applying cut No. 2 on the ρ parameter. (a) MC simulation for $3 \times 10^{7}$ $π^{-} p \to η n \to 3 π^{0} n$ events, (b) MC for $4 \times 10^{7}$ $π^{-} p \to π^{0} π^{0} n$ events, (c) empty-target data, (d) MC for $1 \times 10^{7}$ $π^{-} p \to η n \to γ γ n$ events, (e) MC for $6 \times 10^{6}$ $π^{-} p \to π^{0} n$ events (not used in the fit), (f) MC for $4 \times 10^{5}$ $π^{-} p \to η n \to π^{0} γ γ n$ events, (g) experimental LH $_{2}$ data before (spectrum No. 1) and after the $η \to 3 π^{0}$ and the $π^{0} π^{0}$ background subtraction (spectrum No. 2 is the $η \to 3 π^{0}$ subtraction only, spectrum No. 3 is after subtraction of both background contributions), (h) the remaining distribution after subtraction of the empty-target background from spectrum No. 3, and (i) final spectrum after subtraction of the $η \to γ γ$ background. The MC-simulation spectrum for $η \to π^{0} γ γ$ , shown in (i) by the solid line, is normalized to the number of events for this process obtained from the fit.
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Figure 11
Same as Fig. 10 except that a 20% CL is applied in the kinematic fit.
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Figure 12
Same as Fig. 11 except that cut No. 1 on $m_{\max} (π^{0} γ)$ has been applied.
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Figure 13
Same as Fig. 11 except that cut No. 2 on $m_{\max} (π^{0} γ)$ has been applied.
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Figure 14
The $m (γ γ)$ spectra (above the $π^{0}$ -meson mass) obtained for events that satisfy the 2-C kinematic fit to the $π^{-} p \to η n \to π^{0} γ γ n$ hypothesis at the 20% CL. The events were preselected by testing the 1-C $π^{-} p \to π^{0} γ γ n$ hypothesis at the 20% CL, with the vertex $z$ coordinate within $\pm 8$ cm, after applying cut No. 2 on the parameter ρ, and cut No. 2 on $m_{\max} (π^{0} γ)$ . (a) experimental LH $_{2}$ data, (b) MC simulation for $3 \times 10^{7}$ $π^{-} p \to η n \to 3 π^{0} n$ events, (c) MC for $4 \times 10^{7}$ $π^{-} p \to π^{0} π^{0} n$ events, (d) empty-target data, (e) MC for $1 \times 10^{7}$ $π^{-} p \to η n \to γ γ n$ events, and (f) experimental LH $_{2}$ spectrum after subtraction of only the $η \to 3 π^{0}$ background (open circles), and after subtraction of both the $η \to 3 π^{0}$ and the $π^{0} π^{0}$ background contributions (solid triangles); the $η \to π^{0} γ γ$ MC-simulation spectrum (solid line) is normalized to the number of $η \to π^{0} γ γ$ events obtained by the maximum-likelihood fit. The $η \to 3 π^{0}$ background is subtracted according to its fixed weight factor. The subtraction of the $π^{0} π^{0}$ background is made according to the results of the same maximum-likelihood fit. The empty-target and the $η \to γ γ$ background contributions are not subtracted in (f).
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Figure 15
Same as Fig. 14 except that cut No. 3 on $m_{\max} (π^{0} γ)$ has been applied.
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Physical Review C

covering nuclear physics

Measurement of the branching ratio for $η \to π^{0} γ γ$ decay

S. Prakhov et al. (Crystal Ball Collaboration)

Phys. Rev. C 72, 025201 – Published 18 August 2005

Abstract

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Physical Review C

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Measurement of the branching ratio for η→π0γγ decay

S. Prakhov et al. (Crystal Ball Collaboration)

Phys. Rev. C 72, 025201 – Published 18 August 2005

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Measurement of the branching ratio for $η \to π^{0} γ γ$ decay