Phys. Rev. D 76, 092005 (2007) - The ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2({\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}){\ensuremath{\pi}}^{0}$, $2({\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{\eta}$, ${K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ and ${K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ cross sections measured with initial-state radiation

The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation

B. Aubert et al. (BABAR Collaboration)

Phys. Rev. D 76, 092005 – Published 20 November 2007; Erratum Phys. Rev. D 77, 119902 (2008)

Abstract

We study the processes $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0} γ$ , $2 (π^{+} π^{-}) η γ$ , $K^{+} K^{-} π^{+} π^{-} π^{0} γ$ and $K^{+} K^{-} π^{+} π^{-} η γ$ with the hard photon radiated from the initial state. About 20 000, 4300, 5500, and 375 fully reconstructed events, respectively, are selected from $232 {fb}^{- 1}$ of BABAR data. The invariant mass of the hadronic final state defines the effective $e^{+} e^{-}$ center-of-mass energy, so that the obtained cross sections from the threshold to about 5 GeV can be compared with corresponding direct $e^{+} e^{-}$ measurements, currently available only for the $η π^{+} π^{-}$ and $ω π^{+} π^{-}$ submodes of the $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ channel. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from $e^{+} e^{-} \to ω (782) π^{+} π^{-}$ and study the $ω (1420)$ and $ω (1650)$ resonances. In the charmonium region, we observe the $J / ψ$ in all these final states and several intermediate states, as well as the $ψ (2 S)$ in some modes, and we measure the corresponding branching fractions.

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Received 21 August 2007

DOI:https://doi.org/10.1103/PhysRevD.76.092005

Erratum

Erratum: The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation [Phys. Rev. D 76, 092005 (2007)]

B. Aubert et al.

Phys. Rev. D 77, 119902 (2008)

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Vol. 76, Iss. 9 — 1 November 2007

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Figure 1
Distribution of $χ^{2}$ from the five-constraint fit for $2 (π^{+} π^{-}) π^{0}$ candidates in the data (points) after subtracting the $e^{+} e^{-} \to q \bar{q}$ background (hatched histogram). The open histogram is the distribution for simulated signal events, normalized as described in the text. The dashed histogram is the estimated backgrounds from other ISR channels, as described in the text.
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Figure 2
Invariant mass distribution for selected $2 (π^{+} π^{-}) π^{0}$ events in the data (points). The hatched and open histograms represent the non-ISR background and sum of all backgrounds, respectively. The smooth line approximates the non-ISR background, as described in the text.
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Figure 3
(a) Invariant mass distributions for simulated $2 (π^{+} π^{-}) π^{0}$ events in the phase space model, reconstructed in the signal (open) and control (hatched) regions of Fig. 1. (b) Net reconstruction and selection efficiency as a function of mass obtained from this simulation. The curve represents a 3rd order polynomial fit.
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Figure 4
The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ cross section as a function of $e^{+} e^{-}$ c.m. energy measured with ISR data. Only statistical errors are shown.
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Figure 5
(a) The smallest $π^{+} π^{-} π^{0}$ mass in each selected $2 (π^{+} π^{-}) π^{0}$ event versus the five-pion mass. (b) The full $π^{+} π^{-} π^{0}$ mass distribution (four entries per event) in these events. The crosshatched histogram represents the estimated non-ISR background.
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Figure 6
Scatter plots of (a) each $π^{+} π^{-}$ mass versus the mass of the remaining $π^{+} π^{-} π^{0}$ and (b) each $π^{\pm} π^{0}$ mass versus the mass of the remaining $π^{+} π^{-} π^{\mp}$ for the selected $2 (π^{+} π^{-}) π^{0}$ candidates (four entries per plot per event).
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Figure 7
Distribution of the $π^{+} π^{-} π^{0}$ mass closest to the $η$ mass in the data (points). The histograms represent the distributions from simulated $η ρ$ (open), $ω π^{+} π^{-}$ (dashed), and $u d s$ events (hatched), normalized as described in the text. The inner (inner and outer) vertical lines delimit the $η π^{+} π^{-}$ signal (sideband) region.
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Figure 8
Invariant mass distribution for events in the $η π^{+} π^{-}$ signal (open histogram) and sideband (dashed) regions (see Fig. 7). The points represent the background obtained from the $χ_{4 π π^{0}}^{2}$ control region, and the hatched histogram is that from $u d s$ events. The inset shows the low end of the mass distribution, where direct $e^{+} e^{-} \to η^{'} γ$ events are visible.
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Figure 9
Invariant mass distribution of the $π^{+} π^{-}$ pair not from the $η$ in selected $η π^{+} π^{-}$ events in the data (points) and in simulated $η ρ$ events (histogram).
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Figure 10
(a) Invariant mass distribution for selected simulated $η ρ$ events, and (b) the detection efficiency versus mass, including the $η \to π^{+} π^{-} π^{0}$ branching fraction.
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Figure 11
The $e^{+} e^{-} \to η π^{+} π^{-}$ cross section as a function of c.m. energy obtained via ISR at BABAR. The direct measurements from DM2, ND, and CMD2 are also shown. Only statistical errors are shown.
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Figure 12
Distribution of the $π^{+} π^{-} π^{0}$ mass closest to the $ω$ mass in the data (points) after subtraction of $u d s$ and ISR-type backgrounds. The histogram is the distribution for simulated $ω π^{+} π^{-}$ events. The inner (inner and outer) vertical lines delimit the $ω$ signal (sideband) region.
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Figure 13
Invariant mass distribution for events in the $ω π^{+} π^{-}$ signal region (points) and sidebands (hatched histogram).
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Figure 14
The $e^{+} e^{-} \to ω π^{+} π^{-}$ cross section as a function of c.m. energy obtained via ISR at BABAR. The direct measurements from DM1, DM2, and CMD2 are also shown. Only statistical errors are shown.
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Figure 15
(a) Invariant mass distribution of the $π^{+} π^{-}$ pair not from the $ω$ in selected $ω π^{+} π^{-}$ events in the data (points) and in simulated events (histogram). The vertical lines delimit the $f_{0} (980)$ signal region and sidebands. (b) The $e^{+} e^{-} \to ω f_{0} (980)$ cross section.
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Figure 16
The $e^{+} e^{-} \to ω π^{+} π^{-}$ cross section excluding the $ω f_{0} (980)$ contribution (points). The curve shows the result of the fit of the $ω (1420)$ and $ω (1650)$ resonances described in the text (Fit 3 in Table 6).
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Figure 17
The background-subtracted invariant mass distributions for all $π^{+} π^{-}$ pairs (open histogram, four entries per event), $π^{\pm} π^{0}$ pairs (points, four entries per event), and $π^{+} π^{+}$ and $π^{-} π^{-}$ pairs (hatched histogram, two entries per event), for events with no $η$ or $ω \to π^{+} π^{-} π^{0}$ candidates.
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Figure 18
(a) The invariant mass distributions for $π^{+} π^{-} π^{0}$ (triangles) and $π^{+} π^{-} π^{\pm}$ (squares) combinations for events in which the other $π^{+} π^{-}$ or $π^{\pm} π^{0}$ pair is in the $ρ$ signal region. The hatched histogram is an estimate of the combinatorial background. (b) The average of the triangles and squares in (a) minus the combinatorial background. The line is the result of a Breit-Wigner fit.
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Figure 19
(a) The total $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ cross section (circles) and the contributions from $ω π^{+} π^{-}$ (squares) and $η π^{+} π^{-}$ (triangles). (b) The cross section obtained as the difference between the total and the latter two contributions, which is dominated by the $e^{+} e^{-} \to ρ (770) X$ process.
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Figure 20
Distribution of $χ^{2}$ from the 5C fit for $2 (π^{+} π^{-}) η$ candidates in the data (points). The open and hatched histograms are the distribution for simulated signal events and non-ISR background, respectively, normalized as described in the text.
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Figure 21
Invariant mass distribution for selected $2 (π^{+} π^{-}) η$ events in the data (points). The hatched and open histograms represent the non-ISR background and the sum of all backgrounds, respectively.
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Figure 22
The $e^{+} e^{-} \to 2 (π^{+} π^{-}) η$ cross section as a function of c.m. energy measured with ISR data. Only statistical errors are shown.
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Figure 23
(a) Background-subtracted invariant mass distribution for the four pions recoiling against the $η$ in $2 (π^{+} π^{-}) η$ events. (b) Invariant mass distribution for all $π^{+} π^{-} η$ combinations (four entries per event) in selected $2 (π^{+} π^{-}) η$ candidates (open histogram) and the estimated non-ISR background (hatched).
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Figure 24
(a) Distribution of the $π^{+} π^{-} η$ mass closest to the $η^{'}$ mass in the data (open histogram), along with the estimated non-ISR background contribution (hatched). The vertical lines indicate the $η^{'} (958)$ signal and sideband regions. (b) The $e^{+} e^{-} \to η^{'} (958) π^{+} π^{-}$ cross section obtained via ISR. The line is the result of the Breit-Wigner fit described in the text.
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Figure 25
(a) Distribution of the $π^{+} π^{-} η$ invariant mass in the $1 - 1.5 GeV / c^{2}$ region for the data (points). The line represents the result of the fit described in the text, with the shaded region representing the background component. (b) The $e^{+} e^{-} \to f_{1} (1285) π^{+} π^{-}$ cross section obtained via ISR. The line is the result of the Breit-Wigner fit described in the text.
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Figure 26
Distribution of $χ^{2}$ from the 5C fit for $K^{+} K^{-} π^{+} π^{-} π^{0}$ candidates in the data (points). The open histogram is the distribution for simulated signal events, normalized as described in the text. The hatched and dashed histograms are the backgrounds from non-ISR events and ISR $K^{+} K^{-} π^{+} π^{-}$ events, respectively, estimated as described in the text.
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Figure 27
Invariant mass distribution for selected $K^{+} K^{-} π^{+} π^{-} π^{0}$ candidates in the data (points). The hatched and open histograms represent the non-ISR background and the sum of all backgrounds, respectively.
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Figure 28
(a) Invariant mass distribution for simulated $K^{+} K^{-} π^{+} π^{-} π^{0}$ events in the signal (open) and control (hatched) regions of Fig. 26. (b) Net reconstruction and selection efficiency as a function of mass obtained from this simulation; the curve represents a third order polynomial fit.
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Figure 29
The $e^{+} e^{-} \to K^{+} K^{-} π^{+} π^{-} π^{0}$ cross section as a function of $e^{+} e^{-}$ c.m. energy measured with ISR data. The errors are statistical only.
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Figure 30
(a) The $π^{+} π^{-} π^{0}$ mass versus two-kaon-three-pion mass, and (b) the $π^{+} π^{-} π^{0}$ mass projection for selected $K^{+} K^{-} π^{+} π^{-} π^{0}$ candidates. The hatched histogram represents the estimated non-ISR background.
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Figure 31
(a) The $π^{+} π^{-} π^{0}$ mass versus the $K^{+} K^{-}$ mass and (b) the $K^{+} K^{-}$ mass projection for selected $K^{+} K^{-} π^{+} π^{-} π^{0}$ candidates. The hatched histogram represents the estimated non-ISR background.
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Figure 32
(a) The $π^{+} π^{-} π^{0}$ mass distribution in the region below $700 MeV / c^{2}$ for events with a $K^{+} K^{-}$ mass within $15 MeV / c^{2}$ of the $ϕ$ mass (points). The histogram is the distribution for the ISR $ϕ η$ simulation. (b) The $e^{+} e^{-} \to ϕ η$ cross section measured here in the $K^{+} K^{-} π^{+} π^{-} π^{0}$ final state (large dots), compared with the previous BABAR measurement in the ISR $K^{+} K^{-} γ γ$ final state [26].
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Figure 33
(a) Expanded view of the $π^{+} π^{-} π^{0}$ invariant mass distribution [Fig. 30] in the region near the $ω (782)$ for all selected events in the data (open histogram) and the estimated non-ISR background (hatched). The vertical lines delimit the $ω$ signal region and sidebands. (b) The $e^{+} e^{-} \to ω (782) K^{+} K^{-}$ cross section obtained via ISR.
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Figure 34
Distribution of $χ^{2}$ from the 5C fit for $K^{+} K^{-} π^{+} π^{-} η$ candidates in the data (points). The open histogram is the distribution for simulated signal events, and the hatched histogram is the estimated background from non-ISR events.
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Figure 35
The $e^{+} e^{-} \to K^{+} K^{-} π^{+} π^{-} η$ cross section as a function of c.m. energy measured with ISR data. Only statistical errors are shown.
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Figure 36
(a) The $π^{+} π^{-} η$ mass versus the $K^{+} K^{-} π^{+} π^{-} η$ mass, and (b) the $π^{+} π^{-} η$ mass projection for selected $K^{+} K^{-} π^{+} π^{-} η$ candidates. The hatched histogram represents the estimated non-ISR background.
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Figure 37
(a) The $π^{+} π^{-} η$ mass versus the $K^{+} K^{-}$ mass and (b) the $K^{+} K^{-}$ mass projection for selected $K^{+} K^{-} π^{+} π^{-} η$ candidates. The hatched histogram represents the estimated non-ISR background.
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Figure 38
Raw invariant mass distribution for all selected $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ events in the charmonium region. The line represents the result of the fit described in the text.
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Figure 39
Raw invariant mass distribution for all selected $e^{+} e^{-} \to 2 (π^{+} π^{-}) η$ events in the charmonium region. The line represents the result of the fit described in the text.
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Figure 40
Raw invariant mass distribution for all selected $e^{+} e^{-} \to K^{+} K^{-} π^{+} π^{-} π^{0}$ events in the charmonium region. The line represents the result of the fit described in the text.
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Figure 41
Raw invariant mass distribution for all selected $e^{+} e^{-} \to K^{+} K^{-} π^{+} π^{-} η$ events in the charmonium region. The line represents the result of the fit described in the text.
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Figure 42
(a) The $π^{+} π^{-} π^{0}$ mass closest to $J / ψ$ mass versus the five-pion mass for selected $2 (π^{+} π^{-}) π^{0}$ events. (b) The five-pion mass for events with a three-pion mass within 50 MeV of the $J / ψ$ mass.
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Figure 43
Background-subtracted $2 (π^{+} π^{-}) π^{0}$ invariant mass distributions in the charmonium region for events with a $π^{+} π^{-} π^{0}$ mass in the (a) $η$ and (b) $ω (782)$ mass region.
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Physical Review D

covering particles, fields, gravitation, and cosmology

The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation

B. Aubert et al. (BABAR Collaboration)

Phys. Rev. D 76, 092005 – Published 20 November 2007; Erratum Phys. Rev. D 77, 119902 (2008)

Abstract

Erratum

Erratum: The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation [Phys. Rev. D 76, 092005 (2007)]

B. Aubert et al.

Phys. Rev. D 77, 119902 (2008)

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Physical Review D

covering particles, fields, gravitation, and cosmology

The e+e−→2(π+π−)π0, 2(π+π−)η, K+K−π+π−π0 and K+K−π+π−η cross sections measured with initial-state radiation

B. Aubert et al. (BABAR Collaboration)

Phys. Rev. D 76, 092005 – Published 20 November 2007; Erratum Phys. Rev. D 77, 119902 (2008)

Abstract

Erratum

Erratum: The e+e−→2(π+π−)π0, 2(π+π−)η, K+K−π+π−π0 and K+K−π+π−η cross sections measured with initial-state radiation [Phys. Rev. D 76, 092005 (2007)]

B. Aubert et al.

Phys. Rev. D 77, 119902 (2008)

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The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation

Erratum: The $e^{+} e^{-} \to 2 (π^{+} π^{-}) π^{0}$ , $2 (π^{+} π^{-}) η$ , $K^{+} K^{-} π^{+} π^{-} π^{0}$ and $K^{+} K^{-} π^{+} π^{-} η$ cross sections measured with initial-state radiation [Phys. Rev. D 76, 092005 (2007)]