Radiative and other rare ρ, ω, φ – decays from VEPP-2M Tatyana Dimova BINP, Novosibirsk International Workshop on e+e- collisions from Phi to Psi’08 hfghfgh

VEPP-2M e+ e- collider VEPP-2M collider: 0.36-1.4 GeV in c.m., L31030 1/cm2s at 1 GeV Detectors CMD-2 and SND: 60 pb-1 collected in 1993-2000 hfghfgh

Spherical Neutral Detector (SND) 1 –beam pipe, 2 –drift chambers, 3 –scintillation counter, 4 –lightguides, 5 –PMTs, 6 –NaI(Tl) crystals, 7 – vacuum phototriodes, 8 – iron absorber, 9 –streamer tubes, 10 – 1 cm iron plates, 11 –scintillation counters, 12 and 13 –collider magnets.

Cryogenic Magnet Detector - 2 (CMD-2) 1 – vacuum chamber, 2 – drift chamber, 3 – Z-chamber, 4 – superconducting solenoid, 5 – compensating solenoid, 6 – BGO endcap calorimeter, 7 – CsI(Tl,Na) barrel calorimeter, 8 – muon range system, 9 – iron yoke, 10- storage ring lenses

Available data near ρ, ω, φ – resonances Energy region Integrated luminosity (SND/CMD-2) ω,ρ – resonances 10 pb-1/8pb-1 φ – resonance 13 pb-1/ 16pb-1 List of considered radiative and rare decays V→P0P0 φ→ π0 π0, φ→η π0, → π0π0, ρ→ π0 π0 V→P0 φ→η'  , φ→η , φ→ π0 , →η, → π0, ρ → η, ρ → π0 rare hadron decays  0, π+π−, π+π− π+π− ρ  π+π−0, π+π− π+π− → π+π−

V → P0 P0 decays Vector Dominance Model (V → V′ P →P P  ) Coupling of φ – meson into scalars (a0, f0) through K±-loops was suggested by Achasov, Ivanchenko (1989) Parameters of decays depend on structure of scalars ( qq or 2(qq) ) Extension of Chiral Perturbation Theory for V→P0P0 decays developed by Bramon et al (1992)

V → P0 P0 decays Experiments: GAMS (first measurement, ω → π0π0) (1994) SND, CMD-2 (φ → π0π0 ; φ → η π0; ω,ρ→ π0π0 )(1997,2000) KLOE (φ → π0π0 ; φ → η π0) After decays parameters ( branching fractions, invariant mass spectra MPP) were measured further theory development occurred: Chiral Perturbation Theory [2,3] UχPT (Unitarized ChPT) [1] Linear Sigma Model (LσM), [2,3] Kaon Loops [4] Direct Coupling (No Structure)[5] 1. E. Marco et al., Phys.Lett.B470 (1999) 20; 2.A.Bramon et al., Phys. Rev. D69(2004)074008; 3. R.Escribano, Nucl. Phys. Proc. Suppl. 126 (2004) 204; 4. N.N.Achasov and A.V.Kiselev, Phys. Rev. D73(2006)054029; 5. G.Isidori et al., J.High Energy Phys. 05(2006)049; And many others.

Study of φ → π0π0 decay Experimental results and theoretical calculations of branching fraction of φ → π0π0 decay: Experiment B(φ → π0π0) ·104 (ωπ° subtracted) SND (1.158±0.093±0.052) CMD-2 (1.08±0.17±0.09) SND&CMD-2 (1.14 ± 0.095) KLOE (1.07 ± 0.06) Models B(φ → π0π0) VDM (φ→ρ0π0→π0π0 ) 1.2·10−5 ChPT 5.1·10-5 VDM+ChPT (6.1-6.4)·10-5 LσM 1.16·10-4 (Mf0,ΦS) VDM+LσM 1.19·10-4 Achasov (qq) / (qq)2 (4.5-5.4) ·10-5 / 2.5·10-4

π0π0 invariant mass spectra fits SND Comparison of invariant mass Mππ spectra for SND, CMD-2 and KLOE detectors. CMD-2 VDM predicts too small value of φ → π0π0 branching fraction Scalar meson contributions are needed to describe Mππ spectrum SND and CMD-2 data are described with only one scalar f0(980) but KLOE spectrum shows that 2 scalars ( f0 and σ ) are necessary KLOE study also shows that data can be fitted by several models

Study of φ → η π0 decay Experiment Experimental results and theoretical calculations of branching fraction of φ → η π0 decay: Experiment B(φ → η π0) ·104 SND 0.88±0.14±0.09 CMD-2 0.90±0.24±0.10 SND&CMD-2 0.89±0.15 KLOE 0.695±0.026 Models B(φ → η π0) VDM 5.4·10-6 ChPT 3.0·10-5 VDM+ChPT (3.4-3.6)·10-5 LσM (7.5-9.5)·10-5 (Ma0,Φρ) Achasov (qq) / (qq)2 2.4·10-5 / 2.0·10-4

ηπ0 invariant mass spectra fits SND KLOE VDM predicts too small value of branching fraction Scalar meson contribution is needed to describe Mηπ spectrum SND and CMD-2 data are described with one scalar a0(980) as well as KLOE data KLOE study also shows that data can be fitted by several models

Study of ω,ρ → π0π0 decays Models B(ρ→ π0π0) VDM 1.1·10-5 (via ωπ ) Experiment B(ω → π0π0) ·105 B(ρ→ π0π0) ·105 SND CMD-2 SND&CMD-2 Models B(ω → π0π0) B(ρ→ π0π0) VDM 3.2·10-5 1.1·10-5 (via ωπ ) ChPT 5.1·10-5 9.5·10-6 VDM+ChPT (4.7±1.1)·10-5 2.6·10-5 VDM+ LσM (4.5±1.1)·10-5 3.8·10-5 Fitted cross section for e+e−→ π0π0 , red line – without contribution of ρ → σ .

Study of ω,ρ → π0π0 decays Measured values of branching fractions B (ω → π0π0) and B(ρ→ π0π0) significantly exceed VDM predictions. For ρ→ π0π0 decay the difference can be explained by contribution of σ(600) transition through π±-loops. But for 00 the mechanism with - and K-loops is expected to be small because of small value of ρ- mixing. One can see that the angular spectrum does not allow to separate different mechanisms of 00 decay with available statistics. Angle of the photon in π0π0 rest frame. Solid line – pure ω → ρπ0, dashed - mixture of ρπ0 and σ states.

Study of magnetic dipole V → P0 decays SND CMD-2 SND&CMD-2 Other B(φ → η)·10-2 1.364 ±0.023± 0.029 1.338 ± 0.012 ± 0.052 1.373 ± 0.010 ± 0.085 1.287 ± 0.013 ± 0.063 1.18 ± 0.03 ± 0.06 1.325 ± 0.025 1.2 ± 0.06 (PDG96) B(ω → η)·10-4 4.33 ±0.44 ± 0.13 4.44 ± 2.29 ± 0.28 5.10 ± 0.72 ± 0.34 4.52 ± 0.39 6.5 ± 1.0 (PDG96) B(ρ → η)·10-4 2.82 ±0.30 ± 0.18 3.21 ± 1.39 ± 0.20 3.28 ± 0.37 ± 0.23 3.01 ± 0.27 2.4+0.8-0.9 (PDG96) B(φ → π0)·10-3 1.34 ±0.07 ± 0.07 1.226± 0.036± 0.096 1.258 ± 0.037 ± 0.077 1.285 ± 0.072 1.31 ± 0.13 (PDG96) B(ω → π0)·10-2 9.34 ±0.15 ±0.31 8.45 ± 0.09 ±0.25 9.06 ± 0.20 ± 0.57 8.55 ± 0.24 8.5 ± 0.5 (PDG96) B(ρ → π0)·10-4 5.15 ±1.16 ±0.73 5.32 ±0.63 ±0.50 6.21 ± 1.28 ± 0.39 5.56 ± 0.69 6.8 ± 1.79 (PDG96) B(φ → η′)·10-5 6.7 ± 5.0 ± 1.5 6.7 ± 2.8 ± 0.8 8.2 ± 2.1 ± 1.1 4.9 ± 2.2 ± 0.6 6.49 +1.38-1.20 6.23 ± 0.27 ± 0.12 (KLOE06)

Example of coupling constant Fit to V → P0 data Model described in Escribano, Nadal, hep-ph/0703187 Measured values of coupling constants |η > =Xη |ηq> +Yη |ηs> + Zη |G> |η'> =Xη'|ηq> +Yη' |ηs> + Zη' |G> decays gVP (GeV-1) φ → η 0.211 ± 0.002 ω → η 0.135 ± 0.006 ρ → η 0.480 ± 0.022 φ → π0 0.041 ± 0.001 ω → π0 0.703 ± 0.010 ρ → π0 0.243 ± 0.015 φ → η' 0.221 ± 0.023 φ → η′ (KLOE) 0.216 ± 0.005 In the absence of gluonium in η and η΄ states Zη = Zη' =0, and mixing parameterization has standard form: |η > =cos ΦP |ηq> - sin ΦP |ηs>, |η' > =sin ΦP |ηq> + cos ΦP |ηs>, For vector states: |ω > =cos ΦV|ωq> - sin ΦV|ωs>, |φ > =sin ΦV |ω q> + cos ΦV|ωs>, If Zη or Zη' ≠0, additional mixing angles appear: ΦηG or Φη'G . Ratios of VP wave-function overlap integrals (zq=Cq/Cπ, zs=Cs/Cπ) are also fitted. So we have the following set of parameters to be fitted: g, ΦV, ΦP, zq, zs· m/ms , ΦηG , Φη'G . Example of coupling constant parameterization:

Result of fit of V → P0 data The fits are based on following decays: φ,ω,ρ→π0, φ,ω,ρ→ η (SND+CMD-2) , φ → η′(KLOE), η′ → ω  ,ρ (PDG): Fit 1: ΦηG = Φη'G = 0: g = 0.705 ± 0.010 GeV-1;ΦV =(3.34 ± 0.09)°; ΦP=(42.00 ± 0.65)°; Zq=0.87 ± 0.03; Zs·m/ms =0.64 ± 0.01; χ2=2.7/4 Fit 2: ΦηG = 0: ΦP=(41.7 ± 1.0)°; Zq=0.87 ± 0.03; Zs·m/ms=0.65 ± 0.02; |Φη'G|= (−10±12)°; χ2=2.5/3 Fit 3: Φ η'G = 0: Zs·m/ms=0.64 ± 0.01; |ΦηG|= (0 ±13)°; χ2=2.7/3 decays gVP (GeV-1) experiment gVP (GeV-1) FIT 2 φ → π0 0.041 ± 0.001 0.041 ω → π0 0.703 ± 0.010 0.704 ρ → π0 0.243 ± 0.015 0.235 φ → η 0.211 ± 0.002 0.211 ω → η 0.135 ± 0.006 0.140 ρ → η 0.480 ± 0.022 0.457 η′ → ω (PDG) 0.139 ±0.015 0.146 η′ → ρ 0.41 ± 0.03 0.400 φ → η′ (KLOE) 0.216 ± 0.005 0.216 Using Φη'G from FIT 2, we calculated admixture of gluonium in η′ : |Zη'|2 = 0.03+0.05−0.03

OZI and G parity suppressed decays: φ → ωπ0 As there is non resonance process e+e− → ρ,ρ′ → ωπ0, decay φ → ωπ0 can be observed only through interference pattern, which looks as a dip in cross section energy dependence. SND SND: B(φ → ωπ0) = (5.5 +1.6−1.4 ± 0.3)· 10−5 In ω → π+π−π0 mode parameters of interference are: Re Z = 0.108 ± 0.016 Im Z = −0.125 ± 0.020 KLOE: B(φ → ωπ0) = (5.63 ± 0.70)· 10−5 In same mode: Re Z = 0.097 ± 0.012 Im Z = −0.133 ± 0.009 Cross section of e+e− → ωπ0 process with interference pattern The models taking into account φ →ω →ρ and φ →*→ρ transitions cannot explain values of B(φ → ωπ0), Re Z and Im Z . Further theoretical study is needed.

OZI and G parity suppressed decays: φ → π+π−, π+π−π+π− SND SND: B(φ → π+π−) = (7.1 ± 1.4)· 10−5 Parameters of interference are: Re Z = 0.061 ± 0.006 Im Z = −0.041 ± 0.007 CMD-2: B(φ → π+π− π+π−) = (3.9 ± 2.8)· 10−5 Parameters of interference are: Re Z = 0.122 ± 0.040 Im Z = −0.003 ± 0.063 Cross section of e+e− →π+π− Similar to φ → ωπ0 decay theoretical models cannot describe measured parameters for φ → π+π− decay. While data for φ → π+π− π+π− decay is in good agreement with φ →*→ρ mechanism of φ – ρ mixing. CMD-2 Cross section of e+e− →π+π− π+π−

ρ–ω mixing and ω → π+π−, ρ → π+π−π0 decays Simple model of ρ–ω mixing can be written in the following way: (here ωI and ρI – pure states, Πρω – polarizations operator of ρ–ω mixing) Cross section of e+e− → π+π− process Pion form factor for e+e− → π+π− process was parameterized in the following way: Higher order resonances were also taken into account (ρ′, ρ′′). SND: B(ω → π+π−) = (1.71 ± 0.10)· 10−2 Φρω= (113.7 ± 2.4) ° Assuming that ω → π+π− proceeds only through ρ–ω mixing (gIωππ = 0) it was calculated that Φρω≈101°. For ρ → π+π−π0 this angle is expected to be Φρω= −90°. CMD-2: B(ω → π+π−) = (1.46 ± 0.12)· 10−2 (only ρ–ω mixing was taking into account)

ρ–ω mixing and ω → π+π−, ρ → π+π−π0 decays Cross section of e+e− → π+π−π0 was fitted as a sum of ρ,ω, ω,′ ω′′ resonances. Fit without ρ gives bad χ2. SND: B(ρ → π+π−π0) = (1.01+0.54−0.36 ± 0.034) ·10−4 Φρω= (−135+17−13 ± 9)° Value of angle Φρω has 2σ deviation from the expected one Φρω= −90°. Cross section of e+e− → π+π−π0 process for ω → π+π− decay mixing angle Φρω differs by 6σ from expected one in simple ρ–ω mixing model for ρ → π+π−π0 decay obtained value of Φρω doesn’t contradict simple model of ρ–ω mixing calculation of Φρω for ρ → π+π−π0 decay based on parameters of ρ–ω mixing obtained in e+e− → π+π− fit gives rather small value of Φρω~ −45° contradicting with experimental value. More theoretical input is needed.

Search for ρ → π+π−π+π− decay The yellow region corresponds to the extrapolation of the energy dependence of the cross section from the energy region above 1.05 GeV. It was assumed that the cross section is determined by *→ρ, ρ′→ a1 (1260) π → π+π−π+π− transition. To compare the obtained experimental data with existing theoretical predictions, it is useful to evaluate the cross section of the process at the cms energy corresponding to the ρ-meson mass. The cross section was determined in the energy range 0.75–0.8 GeV : σρ = (0.020 ± 0.010 ± 0.003) nb. This cross section corresponds to following value of branching fraction: CMD-2 Cross section of e+e− → π+π− π+π− process CMD-2: B(ρ → π+π− π+π−) = (1.8 ± 0.95)· 10−5

Conclusions From 1993 to 2000 SND and CMD-2 detectors collected about 60 pb-1 of data Several decays were observed for the first time: φ → π0π0, φ → η π0, ρ → π0π0, φ → η′, φ  ωπ0, etc. Branching fractions of many decays were measured with the best accuracy: φ → π0, φ → η , ω → π0, ω → η, ρ → π0, ρ → η, etc. Study of electric dipole decays of ρ, ω, φ-mesons showed that the main mechanism is transition to light scalars f0(980), a0(980) and σ. The data on magnetic dipole radiative transitions can be described in the frame of simple quark model. The gluonium admixture in η′ is compatible with zero OZI and G-parity suppressed decays φ  ωπ0, 2π, 4π were measured. Observed decay amplitudes for φ 2π and φ  ωπ0 cannot be explained by single photon transition mechanism. Branching fractions of ω → π+π−, ρ → π+π−π0 decays were measured. For ω → π+π− phase of ρ–ω mixing differs by 6 standard deviations from expected in simple ρ–ω mixing model. Indications of ρ → π+π−π+π− decay were obtained for the first time. More data are needed for a complete study.

Comparison of invariant mass Mππ and Mηπ spectra for SND and CMD-2 detectors Results of Mππ and Mηπ fits for SND and CMD-2 Data with Kaon Loop model (N.Achasov) ○ - SND ■ - CMD-2 Fit results SND CMD-2 Mf0 (MeV) 969.8 ± 4.5 977 ± 6.7 g2π π /4π (GeV2) 0.40 ± 0.06 g2K K /4π(GeV2) 2.44 ± 0.73 B(φ→f0)·104 g2K K / g2π π 4.6 ± 0.6 6.1 ± 2.0 ○ - SND ■ - CMD-2 Fit results SND CMD M a0(MeV) 995+52 -10 ----- g2η π /4π(GeV2) 0.77 +1.29 -0.20 g2K K /4π(GeV2) 1.4 +9.4 -0.9 B(φ→ a0)·104 0.88±0.17 0.90±0.26

ρ–ω mixing and ω → π+π−, ρ → π+π−π0 decays Pion formfactor for e+e− → π+π− process was fitted in the following way: SND High order resonances were also taken into account (ρ′, ρ′′). SND: B(ω → π+π−) = (1.71 ± 0.10)· 10−2 Φρω= (113.7 ± 2.4) ° Cross section of e+e− → π+π− process CMD-2: B(ω → π+π−) = (1.46 ± 0.12)· 10−2 (only ρ–ω mixing was taking into account) SND Cross section was fit as a sum of ρ,ω, ω,′ ω′′ resonances. Fit without ρ gives bad χ2. SND: B(ρ → π+π−π0) = (1.01+0.54−0.36 ± 0.034) ·10−4 Φρω= (−135 ± 1713 ± 9)° Value of cross section of ρ → π+π−π0 corresponds to standard ρ–ω mixing and angle differs 2σ deviation from expected one Φρω= −90° Cross section of e+e− → π+π−π0 process