Φ Radiative decays at KLOE

Nuclear Physics B (Proc. Suppl.) 162 (2006) 108–113 www.elsevierphysics.com

Φ Radiative decays at KLOE C. Di Donatoa∗ for the KLOE Collaboration† a

Universit´ a e Sezione I.N.F.N. di Napoli, Dip. Scienze Fisiche, Complesso Universitario M.S.A., Via Cintia Ed.G, 80126 Napoli,Italy We present results from the KLOE experiment about the φ → f0 (980)γ → π + π − γ, the φ → f0 (980)γ → π 0 π 0 γ, the measurement of the η mass and the branching fractions BR(φ → η  γ)/BR(φ → ηγ) with the π + π − 7γ final state.

1. Introduction The KLOE experiments are performed at the Frascati φ-factory DaΦNE, an e+ e− collider oper√ ating at s ∼ 1020 MeV. The analysis described here have been performed on the data collected in 2001 and 2002, for an integrated luminosity of ∼ 450pb−1. 2. Scalar meson at a φ-factory A φ-factory can contribute to understanding the scalar mesons. The lighter mesons f0 (980) and a0 (980) are accessible through the φ(1020) → Sγ radiative decays, which study can answer the questions about the structure of these scalar ∗ e-mail

address: [email protected] Kloe Collaboration: F. Ambrosino, A. Antonelli, M. Antonelli, C. Bacci, P. Beltrame, G. Bencivenni, S. Bertolucci, C. Bini, C. Bloise, S. Bocchetta, V. Bocci, F. Bossi, D. Bowring, P. Branchini, R. Caloi, P. Campana, G. Capon, T. Capussela, F. Ceradini, S. Chi, G. Chiefari, P. Ciambrone, S. Conetti, E. De Lucia, A. De Santis, P. De Simone, G. De Zorzi, S. Dell’Agnello, A. Denig, A. Di Domenico, C. Di Donato, S. Di Falco, B. Di Micco, A. Doria, M. Dreucci, G. Felici, A. Ferrari, M. L. Ferrer, G. Finocchiaro, S. Fiore, C. Forti, P. Franzini, C. Gatti, P. Gauzzi, S. Giovannella, E. Gorini, E. Graziani, M. Incagli, W. Kluge, V. Kulikov, F. Lacava, G. Lanfranchi, J. Lee-Franzini, D. Leone, M. Martini, P. Massarotti, W. Mei, S. Meola, S. Miscetti, M. Moulson, S. M¨ uller, F. Murtas, M. Napolitano, F. Nguyen, M. Palutan, E. Pasqualucci, A. Passeri, V. Patera, F. Perfetto, L. Pontecorvo, M. Primavera, P. Santangelo, E. Santovetti, G. Saracino, B. Sciascia, A. Sciubba, F. Scuri, I. Sfiligoi, T. Spadaro, M. Testa, L. Tortora, P. Valente, B. Valeriani, G. Venanzoni, S. Veneziano, A. Ventura, R. Versaci, G. Xu † The

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mesons. KLOE has already published results on φ decays to f0 (980)γ and a0 (980)γ, with fully neutral final state, based on an integrated luminosity of 16pb−1 collected in 2000. Here we present the published studies [1] on φ decays to f0 (980)γ with f0 (980) → π + π − , and preliminary results on φ decays to f0 (980)γ with f0 (980) → π 0 π 0 , based on data collected in 2001-2002. In these works we fit the π + π − invariant mass spectrum to disentangle the contribution from the scalar meson; we use three different approaches in the description of the scalar amplitude: • Kaon-loop model (KL) [2]: the φ meson couples to the scalar through a loop of K + K − ; the quantities gSππ , gSKK ,MS are free parameters in the fit; • No-Structure model (NS) [3]: a direct coupling of the φ to the f0 is assumed, with a subsequent coupling of the f0 to the ππ pair. The f0 amplitude is a Breit-Wigner with a mass dependent width; • Model of Scattering-Amplitudes (SA) [4]: the amplitude is the sum of the scattering amplitudes ππ → ππ and ππ → KK with shape fixed by experimental input. 2.1. φ → f0 (980)γ → π + π − γ The main contribution to the decay under study comes from e+ e− → π + π − γ events with a photon from initial state (ISR), dominating for small photon polar angles θγ , or final state (FSR) radiation. In the low mass region, 400 <

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C. Di Donato / Nuclear Physics B (Proc. Suppl.) 162 (2006) 108–113

Table 1 The KL-NS fit results:Interval of maximal variations for the f0 parameters resulting from the systematic uncertainties studies done on both fits Parameter KL NS mf0 (M eV ) 980-987 973-981 5.0-6.3 1.6-2.3 gf0 K + K − (GeV ) gf0 π+ π− (GeV ) 3.0-4.2 0.9-1.1 2.6-4.4 R = gf20 K + K − /gf20 π+ π− 2.2-2.8 1.2-2.0 gφf0 γ (GeV −1 ) gives marginal agreement. Finally, we analysed the forward-backward asymmetry as a function of m, comparing the behaviour with a simulation including the f0 contribution besides the ISR and FSR. The f0 γ term is essential to have acceptable agreement in the region of the f0 peak and also

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mπ+ π− < 600 MeV, there is a small contribution from φ → ρ± π ± with ρ± → π ± γ (ρπ term); a possible contribution from φ → f0 (600)γ is also considered. We search for the f0 (980) signal as a deviation from the expected shape. The function to fit the mπ+ π− spectrum takes into account the following term: ISR + F SR+ρπ+scalar±interf erence(scalar, F SR)+ residualbackground. A sizeable interference term between FSR and f0 decay is expected in the m spectrum, because of the quantum numbers of the π + π − pair; they are the same if the production is through FSR and f0 decay (J P C = 0++ for FSR and f0 , J P C = 1−− for ISR). We fit the data in the region 420 < mπ+ π− < 1010 MeV using bins 1.2 MeV wide, Figure 1. Concerning the fits KL and NS, the peak around 980 MeV is well interpreted as due to the φ → f0 (980)γ contribution, with a destructive interference with FSR; the non-scalar part is well described by the parametrization used, while we are not sensitive to the ρπ term. The f0 signal appears as an excess of events in the region between 900 and 1000 MeV. In the KL fit the contribution from f0 (600) (the σ) is unnecessary to describe the spectrum. The results of the fits suggest the f0 to be strongly coupled to kaons and to the φ. In Table 1 we show intervals of maximal variations for the f0 parameters resulting from the systematic uncertainties done on both fits. The SA fit

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Figure 1. Results of KL fit (a)-(b)-(c) and of the NS (d)-(e)-(f). (a)-(d) Data spectrum compared with the fitting function (upper curve following data points) and with the estimated non-scalar part of the function (lower curve); (b)-(e) fit residuals as a function of m; (c)-(f) the fitting function is compared to the spectrum obtained subtracting to the measured data the non-scalar part of the function in the f0 region.

in the low mass region, see Figure 2. 2.2. φ → f0 (980)γ → π 0 π 0 γ In this analysis we extract the light meson parameters in the π 0 π 0 γ channel studying a sample of Lint = 450 pb−1 , the high statistics allows us to study the density in the Dalitz plot, mπ0 π0 versus mπ0 γ , Figure 3. The process under study is e+ e− → π 0 π 0 γ and the two main contributions are: • e+ e− → ωπ 0 → π 0 π 0 γ (ωπ); • φ → Sγ → π 0 π 0 γ (Sγ);

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Figure 2. The forward-backward asymmetry data (full circles) compared to the Monte Carlo expectations based on the non-scalar plus f0 part obtained from the KL amplitude (open squares). The right plot shows the detail of the comparison in the f0 region

where S √is f0 (600) + f0 (980). We found a reasonable s dependence of the cross section for the two processes. In order to study the interference between the ωπ and Sγ channels we do not divide the events in categories and we just fit the whole Dalitz. We present preliminary results about the fit to the Dalitz plot with improved KL parametrization [5]: with a KK scattering phase; new parametrization of ππ scattering phase; scalar contributions from f0 (980) and f0 (600). The combined fit to the ππ scattering data and to already published KLOE data on φ → Sγ produces six differents sets of parameters able to describe both distributions [5]. In the KL fit we live as free parameters the mass of f0 , the couplings gf0 π+ π− and gf0 K+K − , the VMD description; we fixed the ππ/KK phase and the f0 (600) to the results of Achasov. The preliminary results indicate a strong coupling of the f0 (980) to kaons, in agreement with our own measurement in the π + π − γ final state, see Table 2. The presence of a f0 (600) is needed to

Figure 3. Dalitz plot for data clearly shows the presence of Sγ (top band) and ωπ processes (bottom-left band)

accurately describe the data. The fit with the NS approach is in progress. 3. Pseudoscalar meson at a φ-factory 3.1. Measurement of the η mass KLOE is performing a new η mass measurement using an approach completely different from the one used in the past. This has been done because there is a large discrepancy between the two most precise measurements: the GEM collaboration [6] obtained a value 0.5 MeV below the one by NA48 [7]. We measured the mass by studying the decay φ → ηγ, η → γγ. To improve the energy response of the calorimeter, a kinematic fit is performed with constraints from energy-momentum conservation. A cut in the Dalitz plot of the 3γ final state is performed in order to reduce the background. The data sample, collected in 2001-2002, has been divided into eight periods, each corresponding to about 50 pb−1 , for

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each point we perform a measurement and a fit to the eight points gives the value and the statistical error of the mass, see Figure 4.

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Table 2: The KL fit results: Parameter values are from the best fit; the first error is statistical from the fit, the second one reflects the changes related to the other fit variants with acceptable χ2 f0 (980) + f0 (600) (Mf0 (600) fixed) f0 (980) + f0 (600) (Mf0 (600) free) f0 (980) → π + π − Mf0 (980) (M eV ) 976.8 ± 0.3 ± 10.5 974.8 ± 0.6 ± 12.5 980 − 987 gf0 (980)K + K − (GeV ) 3.76 ± 0.04 ± 1.16 3.49 ± 0.08 ± 0.57 3.9 − 6.5 gf0 (980)π+ π− (GeV ) −1.43 ± 0.01 ± 0.60 −1.29 ± 0.04 ± 0.77 2.8 − 3.8 Mf0 (600) (M eV ) 461 − 543 551 ± 15 − 76 χ2 /ndf 2753/2676 2734/2675 P (χ2 ) 14.5% 20.8%

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Figure 4. The η mass measurement in several periods, the box shows the systematic error √ The main source of systematics is due to a s miscalibration. Studying the line shape of the meson we find a φ mass 110 keV below the value reported by the CMD-2√ collaboration [8]. We apply a correction to the s of +110 keV, with an error of 110 keV, to be conservative and this is translated in a correction of +57 keV on the value of the η mass. We get the preliminary result: mη = (547822 ± 5sta ± 69syst ) keV The π 0 mass measurement, using the decay φ → π 0 γ, has been done as a check of the method; we get: mπ0 = (134990 ± 6sta ± 30syst ) keV which is fully in agreement with the official value DG from PDG mP = (134976.6 ± 0.6) keV. The π0

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KLOE measurement differs from the NA48 meaA48 surement (mN = (547843±30sta±41syst ) keV) η by only 0.24 standard deviations and disagrees = (547311 ± 28sta ± with the GEM one (mGEM η 32syst ) keV) by seven standard deviations. 3.2. BR(φ → η  γ)/BR(φ → ηγ) The branching ratio of the decay φ → η  γ is particularly interesting since its value can probe the s¯ s and gluonium contents of the η  . The ratio BR(φ → η  γ)/BR(φ → ηγ) is related to the η − η  mixing angle. We present a preliminary KLOE measurement of the R ratio using the 2001-2002 data collection. φ → η  γ, with π + π − 7γ final state, can be produced in two different decay chains: φ → η  γ, η  → π + π − η, η → 3π 0 φ → η  γ, η  → π 0 π 0 η, η → π + π − π 0 φ → ηγ, with the 7γ final state, can be produced by: φ → ηγ, η → π 0 π 0 π 0 The following requirements are used to isolate all signal events: • seven clusters in the calorimeter with |tclu − rclu /c| < 5σt , and θγ > 21◦ with respect to the beam direction. For a charged final state we also ask: • one charged vertex in a cylinder with a 4 cm radius and a 16 cm height around the interaction point. All events identified as a KS KL pair are rejected. A kinematic fit is performed with energymomentum conservation imposed, and the χ2 is used as selection variable. From the analysis of 427 pb−1 we select 3750 candidate events for φ → η  γ; the background, as estimated from Monte Carlo simulation of all physical processes that can be identified as a signal, is 345 Nsig = Nobs − Nbackg. = 3405 ± 65stat ± 28syst Combining the previous measurement with the study of φ → ηγ decays (Nη→3π0 = 1665000 ±

1300) we can calculate the ratio of the two branching ratios: R=

εηγ BRηγ Nη  γ · Kρ chr + εneu BRneu Nηγ εchr BR  η γ η γ η γ η γ

 + − 0 BRηchr  γ = BR(η → π π η) · BR(η → 3π ) neu  0 0 + − 0 BRη γ = BR(η → π π η) · BR(η → π π π )

The factor Kρ is a correction of the observed decay rate for the interference between φ → η(η  )γ and ρ → η(η  )γ. The main source of systematic error comes from the uncertainty on the η  → π + π − η and η  → π 0 π 0 η branching ratios (3%). Using the expression for R we obtain the preliminary result: R = (4.74 ± 0.09stat ± 0.20sys ) · 10−3 Using the current PDG [9] value for BR(φ → ηγ) we extract the: BR(φ → η  γ) = (6.17±0.12stat ±0.28sys)·10−5 The value obtained for R can be related directly to the pseudoscalar mixing angle in the flavour basis. Using the approach by Bramon et al.[10], where the SU(3) breaking is taken into account ¯ and takvia constituent quark mass ratio ms /m, ing into account the correction induced by the OZI-rule, which reduces the VP wave-function overlaps [11], via the two parameters ZN S and ZS , we get: BR(φ → η  γ) = BR(φ → ηγ)  2  3 ms ZN S tanϕV pη  2 cot ϕP 1 − m ¯ ZS sin2ϕP pη

R=

where ϕV = 3.4◦ is the deviation from ideal mixing for vector mesons and pη(η ) is the radiative photon momentum in the φ center of mass. We find the following results: ϕP = (41.5 ± 0.3stat ± 0.7sys ± 0.6th )◦ This ϕP value is equivalent to the mixing angle of θP = −13.2◦ in the octet-singlet basis. The mixing angle value has been obtained neglecting possible gluonium contents of the η  meson. A gluonium component of the η  can be parametrized

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as follows 1 s> u + dd¯ > +Yη |s¯ |η  >= Xη  |u¯ (2) + Zη |gluonium > via the Zη parameter. The normalization gives: Xη2 + Yη2 + Zη2 = 1 A possible gluonium content of the η  is revealed by Zη2 > 0 ⇔ Xη2 + Yη2 < 1 Constraints based on simple SU (3) ideas can be used to check the assumption of no gluonium contents of the η  meson. If Zη = 0 one has Yη = cosϕP , which is a resonable approximation if the gluonium component is small. In Figure 5 we plot a band corresponding to SU (3) constraints and our measurement of cosϕP , in the Xη , Yη plane. The circumference Xη2 + Yη2 = 1 corresponds to zero gluonium in the η  . We find Xη2 + Yη2 = 0.92 ± 0.06 REFERENCES 1. F. Ambrosino et al., Phys. Lett. B 634 (2006) 148-154. 2. N.N. Achasov and V.N. Ivanchenko, Nucl. Phys. B 315 (1989) 465. 3. G. Isidori, L. Maiani and S. Pacetti, private communication. 4. M. Boglione, M.R. Pennington, Eur. Phys. J. C 30 (2003) 503. 5. N.N. Achasov and A.V. Kiselev, hepph/0512047. 6. M. Abdel-Bary et al., Phys. Lett. B 619 (2005) 281. 7. A. Lai et al., Phys. Lett. B 533 (2002) 196. 8. R.R. Akhmetsin et al., Phys. Lett. B 578 (2004) 285. 9. Review of Particle Physics 2005, http://pdg.web.cern.ch/pdg. 10. A. Bramon, R. Escribano, M.D. Scadron, Eur. Phys. J. C 7 (1999) 271. 11. A. Bramon, R. Escribano and M.D. Scadron, Phys. Lett. B 503, (2001) 271.

Figure 5. Bounds on X and Y from SU (3) calculations and experimental branching fractions. The Γ(η  →γγ) Γ(η  →ργ) Γ(φ→η  γ) three constraints: Γ(π 0 →γγ) ; Γ(ω→π 0 γ) ; Γ(φ→ηγ) .