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Studies of φ meson radiative decays with KLOE

The KLOE Collaboration∗

Presented by P.Gauzzia†

aDipartimento di Fisica, Universita degli Studi di Roma “La Sapienza” and INFN Sezione di Roma,P.le A.Moro 2, 00185 - Rome (Italy)

A sample of 5.3 × 107φ mesons, produced at the Frascati φ-factory DAΦNE, has been used by the KLOECollaboration to study the φ radiative decays. The decays φ → ηπ0γ and φ → π0π0γ have been exploited tostudy the scalar mesons a0(980) and f0(980). Furthermore a new determination of the η − η′ mixing angle hasbeen obtained from the measurement of the ratio of the decay rates of φ → η′γ to φ → ηγ.

1. Introduction

The Frascati φ-factory DAΦNE is an e+e− col-lider working at the peak of the φ(1020) reso-nance. The peak cross section is σφ ≈ 3300 nb.The KLOE experiment has collected an inte-grated luminosity of 25 pb−1, corresponding to7.5 × 107φ, during the 2000 data taking, and 190pb−1, corresponding to 5.7 × 108φ, during the2001 one. The results reported in this paper havebeen obtained from the analysis of a sample of 16

∗The KLOE Collaboration: A. Aloisio, F. Ambrosino,A. Antonelli, M. Antonelli, C. Bacci, G. Bencivenni,S. Bertolucci, C. Bini, C. Bloise, V. Bocci, F. Bossi,P. Branchini, S. A. Bulychjov, R. Caloi, P. Cam-pana, G. Capon, G. Carboni, M. Casarsa, V. Casavola,G. Cataldi, F. Ceradini, F. Cervelli, F. Cevenini, G. Chie-fari, P. Ciambrone, S. Conetti, E. De Lucia, G. De Rober-tis, P. De Simone, G. De Zorzi, S. Dell’Agnello, A. Denig,A. Di Domenico, C. Di Donato, S. Di Falco, A. Doria,M. Dreucci, O. Erriquez, A. Farilla, G. Felici, A. Fer-rari, M. L. Ferrer, G. Finocchiaro, C. Forti, A. Franceschi,P. Franzini, C. Gatti, P. Gauzzi, S. Giovannella, E. Gorini,F. Grancagnolo, E. Graziani, S. W. Han ,M. Incagli, L. In-grosso, W. Kluge, C. Kuo, V. Kulikov, F. Lacava, G. Lan-franchi, J. Lee-Franzini, D. Leone, F. Lu, M.Martemianov,M. Matsyuk, W. Mei, L. Merola, R. Messi, S. Miscetti,M. Moulson, S. Muller, F. Murtas, M. Napolitano, A. Ne-dosekin, F. Nguyen, M. Palutan, E. Pasqualucci, L. Pas-salacqua, A. Passeri, V. Patera, E. Petrolo, L. Pontecorvo,M. Primavera, F. Ruggieri, P. Santangelo, E. Santovetti,G. Saracino, R. D. Schamberger, B. Sciascia, A. Sciubba,F. Scuri, I. Sfiligoi, T. Spadaro, E. Spiriti, G. L. Tong,L. Tortora, E. Valente, P. Valente, B. Valeriani, G. Ve-nanzoni, S. Veneziano, A. Ventura, G. Xu, G. W. Yu†E-mail: Paolo.Gauzzi@roma1.infn.it

pb−1 from the year 2000 data. The analysis ofthe 2001 data is in progress. More details on theanalyses presented here can be found in refs.[1].

2. φ →S(0++)γ (S=f0, a0)

The nature of the scalar mesons (JPC=0++)f0(980) and a0(980) is not well established. Theyare not easily interpreted as ordinary qq mesons,belonging to the 3P0 nonet, alternative hypothe-ses have been proposed: qqqq states[2] or KKbound states[3]. According to the theory thebranching ratios of φ → f0γ and φ → a0γ, aswell as the f0 and a0 mass shapes, are sensitiveto the structure of these particles[4].

Concerning the f0, the decay f0 → π0π0

has been measured, by selecting events withoutcharged tracks and with exactly five prompt pho-tons in the detector. The same final state hasbeen used to study the decay φ → a0γ, witha0 → ηπ0 and η → γγ. These two processeshave been previously measured by the experi-ments SND and CMD-2 at VEPP-2M in Novosi-birsk[5]. In addition another final state, consist-ing of two charged pions and five prompt photons,was also used to study the decay φ → a0γ, cor-responding to a0 → ηπ0 and η → π+π−π0. Thislast decay chain has been observed by KLOE forthe first time.The processes that are expected to contribute tothe five photon final state, besides the signals,are: (i) φ → σ(500)γ with σ → π0π0 (σ(500) is

ELSEVIERProceedings of ICHEP 2002, pp. 677–680

S. Bentvelsen, P. de Jong, J. Koch and E. Laenen (Editors) 31st INTERNATIONALCONFERENCEONHIGH ENERGY PHYSICS AMSTERDAM

c© 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0920-5632(02)02189-8

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the other scalar meson expected in the mass re-gion below 1 GeV, recently observed at FNAL bythe E791 Collaboration[6]), (ii) φ → ρ0π0 withρ → π0γ, ηγ, (iii) e+e− → ωπ0 with ω → π0γ.Some contamination is expected from events withthree ((iv) φ → ηγ, η → γγ and φ → π0γ) andseven ((v) φ → ηγ, η → π0π0π0) prompt pho-tons, wrongly reconstructed as five photon ones.A kinematic fit is performed, by requiring the4-momentum conservation to reject events from(iv) and (v), then the best photon pairing issearched for, by associating pairs of photons toπ0 and η, to discriminate between φ → π0π0γand φ → ηπ0γ. The ωπ0 background is reducedby rejecting events with π0γ invariant mass com-patible with the ω mass.

The final sample for φ → π0π0γ consists of

m (MeV)

dBR

/dm

x 1

08 (M

eV-1

)

φ→(f0+σ)γ

φ→f0γ

φ→σγ

Interference

-25

0

25

50

75

300 400 500 600 700 800 900 1000

Figure 1. Differential decay rate for φ → π0π0γ;the solid line is the result of Fit B, individualcontributions are also shown.

3102 events with a 20% contamination (evaluatedby Monte Carlo (MC)). The total detection effi-ciency for the signal is 40%. By normalizing tothe number of φ produced the following branch-ing ratio can be obtained: Br(φ → π0π0γ) =(1.09± 0.03± 0.05)× 10−4 in agreement with theNovosibirsk measurements[5], with much smalleruncertainties.

0

25

50

75

100

700 750 800 850 900 950 1000Mηπ (MeV)

Eve

nts

(a)

0

20

40

60

700 750 800 850 900 950 1000Mηπ (MeV)

Eve

nts

(b)

0

2

4

6

700 750 800 850 900 950 1000Mηπ (MeV)

dBR

/dM

ηπ

(x10-7 MeV-1)

(c)

Figure 2. ηπ0 invariant mass spectra: (a) fivephoton sample; (b) π+π− plus five photon sam-ple. (c) Theoretical curve obtained from the com-bined fit.

For φ → ηπ0γ, 916 events have been selectedwith 30% contamination (MC), and 32% over-all efficiency. By normalizing to the number ofφ produced, KLOE obtains Br(φ → ηπ0γ) =(8.51±0.51±0.57)×10−5, also in agreement withthe Novosibirsk measurements[5].The final state of φ → ηπ0γ and η → π+π−π0

consists of two charged tracks coming from the in-teraction point and five prompt photons; this sig-nature is unique among the possible final states,so that the background comes from events withtwo tracks and three (φ → ηγ, η → π+π−π0),four (e+e− → ωπ0, ω → π+π−π0; φ →KLKS ,KS → π0π0 and KL → πlν) or six (φ →KLKS →π+π−π0π0π0, with prompt KL decay) promptphotons. The analysis scheme is similar to thatof the five photon sample: 197 events have been

678 P. Gauzzi

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selected with 4 ± 4 background events and with19% efficiency. From this decay chain the Br(φ →ηπ0γ) = (7.96±0.60±0.47)×10−5 is extracted, ingood agreement with the result of the five photonsample.

In order to disentangle the various contribu-

Table 1Fit results.f0 Fit A Fit Bχ2/ndf 109.5/34 43.2/33Mf0 (MeV) 962 ± 4 973 ± 1g2

f0KK/(4π) (GeV2) 1.29 ± 0.14 2.79 ± 0.12g2

f0KK/g2f0ππ 3.22 ± 0.29 4.00 ± 0.14

gφσγ - 0.060 ± 0.008a0

χ2/ndf 27.2/25g2

a0KK/(4π) (GeV2) 0.40 ± 0.04ga0ηπ/ga0KK 1.35 ± 0.09Br(φ → ρ0π0 → ηπ0γ) (0.5 ± 0.5) × 10−5

tions, the data have been fitted to theoreticalmass spectra obtained from the following model:(a) the coupling of φ to S(0++)γ is assumed to oc-cur through a charged kaon loop[4], (b) the scalarpropagator with finite width corrections is used,(c) the φ → ρ0π0 parametrization is taken fromVDM calculations[7].Two different fits have been tried on the π0π0

mass spectrum, after background subtraction:without (Fit A) and with (Fit B) φ → σ(500)γ;the σ(500) has been parametrized as a fixed widthBreit-Wigner (Mσ = 478 MeV, Γσ = 324 MeV[6])and a point-like φ − σγ coupling has been as-sumed. The free parameters of the fits are:the f0 mass, the coupling g2

f0KK/(4π), the ratiog2

f0KK/g2f0ππ, the Br(φ → ρ0π0 → π0π0γ) and

gφσγ (only for Fit B).The parameter values are listed in tab.1, theφ → ρ0π0 contribution turns out to be negligi-ble for both fits. Fit A gives a large χ2, while FitB shows a good agreement with the experimentaldata. In fig.1 the differential decay rate is plotted,together with the various contributions from FitB; the depletion of the mass spectrum below 700MeV is produced by a large negative interferencebetween f0 and σ.For φ → ηπ0γ, a combined fit of the two mass

spectra, after background subtraction, has beenperformed, by fixing their relative normalizationto the ratio Br(η → γγ)/Br(η → π+π−π0). Thefree parameters are: the coupling g2

a0KK/(4π),the ratio ga0ηπ/ga0KK and Br(φ → ρ0π0 → ηπ0γ)(tab.1). The mass of the a0 is not free, it hasbeen fixed to the PDG value Ma0=984.8 MeV.The results are shown in fig.2; by integrating thetheoretical curve the a0 contribution can be eval-uated: Br(φ → a0γ → ηπ0γ) = (7.4±0.7)×10−5.In tab.2 the fit results are compared to the predic-tions of the K+K− loop model for some possiblestructures of the scalar mesons. The f0 param-eters are compatible with the qqqq model, whilethe a0 ones disagree with that model.

3. φ → η′γ/φ → ηγ

The mass eigenstates η and η′ are related tothe SU(3) octet-singlet states through the pseu-doscalar mixing angle. Even in the case for twomixing angles which appears in extended chiralperturbation theory, as well as from phenomeno-logical analyses, it has been argued that the twomixing parameters in the quark flavour basis areequal, apart from small terms which violate theOZI rule[8]. It is then possible to parametrize themixing with only one angle ϕP , which can be ex-tracted from the ratio R=Br(φ → η′γ)/Br(φ →ηγ)[9].Moreover the large Br(B→Kη′) value ob-served[10], also raises interest about the gluo-nium contents of the η′[11]. This gluonium con-tents can be tested with a precise measurementof Br(φ → η′γ).The same final state, π+π− and three promptphotons, has been choosen for both decays. Thisfinal state proceeds through the chains: φ → ηγ,η → π+π−π0, π0 → γγ (Br≈ 3 × 10−3) andφ → η′γ, η′ → ηπ+π−, η → π0π0 (Br≈ 2×10−5).φ → ηγ decays are easily selected with smallbackground; 50210 events have been counted with37% efficiency. Since this decay chain is about 100times more probable than the η′ decay, it is alsothe main source of background for φ → η′γ. Af-ter all background removal, 120± 12± 5 φ → η′γevents have been selected, with 23% efficiency.Thus R = (4.70±0.47±0.31)×10−3 is obtained.

Studies of ÷ meson radiative decays with KLOE 679

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Table 2KLOE results compared to K+K− loop predictions[4].f0 KLOE ss(uu+dd)/

√2 (uu+dd)/

√2 ss

g2f0KK/(4π) (GeV2) 2.79 ± 0.12 2.3 0.15 0.3

gf0ππ/g2f0KK 0.50 ± 0.01 0.3 – 0.5 2 0.5

Br(φ → π0π0γ)×104 1.08 ± 0.07 ∼ 1 ∼ 0.15 ∼ 0.2a0 ss(uu-dd)/

√2 (uu-dd)/

√2

g2a0KK/(4π) (GeV2) 0.40 ± 0.04 2.3 0.15

ga0ηπ/ga0KK 1.35 ± 0.09 0.91 1.53Br(φ → a0γ)×104 0.74 ± 0.07 ∼ 2 ∼ 0.2

Y

X

η,

η,

KLOE

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

(2)

(1)

Figure 3. Bounds on Xη′ and Yη′ from SU(3) cal-culations and experimental branching fractions.

From this ratio the mixing angle in the quarkflavour basis can be extracted: ϕP = (41.8+1.9

−1.6)◦,

that is equivalent to θP = (−12.9+1.9−1.6)

◦ in theoctet-singlet basis, in the picture with only onemixing angle. By using the current PDG valueBr(φ → ηγ) = (1.297 ± 0.003)%, it followsBr(φ → η′γ) = (6.10 ± 0.61 ± 0.43) × 10−5; thisis the most accurate determination up to now.The above values have been obtained neglectingany gluonium contents of η and η′. If one allowsfor gluonium:

|η〉 = Xη

∣∣uu + dd

⟩ √2 + Yη |ss〉 + Zη |glue〉

|η′〉 = Xη′∣∣uu + dd

⟩ √2 + Yη′ |ss〉 + Zη′ |glue〉

A consistency check can be performed: if Zη′ = 0,then |Yη′ | = cosϕP ; other constraints on Xη′ andYη′ can be obtained from (1) Γ(η′ → ργ)/Γ(ω →π0γ) and (2) Γ(η′ → γγ)/Γ(π0 → γγ). Then in

the Xη′ , Yη′ plane (fig.3) the overlap region ofthe three allowed bands is consistent within onestandard deviation with no gluonium contents inthe η′, in fact: X2

η′ + Y 2η′ = 0.94+0.06

−0.09.

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