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CVC test in e + e − →KK cross section and data on τ − →K − K 0 ν τ decay

International Workshop on e+e- collisions from Phi to Psi. CVC test in e + e − →KK cross section and data on τ − →K − K 0 ν τ decay. —. Konstantin Beloborodov Budker Institute of Nuclear Physics Novosibirsk, Russia. Laboratori Nazionali di Frascati, Italy, 7 - 10 April 2008. Outline.

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CVC test in e + e − →KK cross section and data on τ − →K − K 0 ν τ decay

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  1. International Workshop on e+e- collisions from Phi to Psi CVC test in e+e−→KK cross section and data on τ−→K−K0ντ decay — Konstantin Beloborodov Budker Institute of Nuclear Physics Novosibirsk, Russia Laboratori Nazionali di Frascati, Italy, 7 - 10 April 2008

  2. Outline • Introduction • Experimental data • VDM, relations, parameters • Fit results • CVC test • Conclusions

  3. Introduction • What is a goal of this work? • Do simultaneous fit of e+e–→K+K– and e+e–→KSKL cross sections in wide energy region (2E0=1.03÷2.2 GeV) • Test and improve cross section description, based on Vector Dominance Model. • Measure parameters of vector mesons • As a result of the fit, extract isovector and isoscalar parts of the amplitude: • Compare the isovector part of K-meson form factor and spectral function, obtained from τ decay

  4. Experimental data • * DM2 data was corrected by a factor of 1/0.7~1.4: • Correction parameter for DM2 cross section data was free and was obtained about 1.42±0.16 • Similar situation in the π+π–π0 channel: In the paper hep-ex/0201040 v2

  5. e+ K+ e+ KS gγV gVKK gγV gVKK γ* V γ* V e- K- e- KL Theoretical framework: Vector Dominance Model

  6. Parameters +,+ not used in total width + fixed from PDG + free parameters + gρωπ=gωρπ=16.8 GeV–1 V:MV and ΓV – fixed from PDG φ(1020): Mφ and Γφ – free parameters V‘, V“: MV and ΓV – free parameters within errors from PDG

  7. Relations Leptonic widths SU(2) – phases for charge and neutral channels are the same SU(3) LW+SU(3)

  8. Problems in the approximation of cross sections • Parameters of vector meson excitations are known very approximately • Energy dependence of total widths is not well known • SU(3) relations are not precise (violation ~20%) • Quark model ratios between leptonic widths are not exact • Mixing between vector mesons exists • Additional amplitude exists due to rescattering in the final states • Experimental data above 1.4 GeV have low precision • Technical problem: there are many solutions (local minima), up to 2N-1 in case of N resonances.

  9. Ambiguity of resonances parameters determination: solution of the problem • Find any possible solutions • In case of constant widths of the resonances find all 2N-1 solutions • Use these 2N-1 solutions as starting positions for minimization procedure • Choose a solution with smallest χ2 e-print (2007) 0710.5627 Data approximations: variants

  10. Data approximation: results

  11. Data approximation: results Variant 1 Variant 1 Variant 2 Variant 2 Variant 3 Variant 3 Variant 4 Variant 4 Variant 5 Variant 5 Variant 6 Variant 6 Variant 7 Variant 7 Variant 8 Variant 8 Variant 9 Variant 9

  12. Data approximation: systematic error Data • SND: e+e–→K+K– ▪ DM2: e+e–→K+K– ◦ SND: e+e–→KSKL ▫ DM1: e+e–→KSKL Systematic №2–№5 №8–№9 + №6,№7

  13. • SND: e+e–→K+K– ▪ DM2: e+e–→K+K– ◦ SND: e+e–→KSKL ▫ DM1: e+e–→KSKL ρ(770) ω(782) φ(1020) ρ'(1450) ω'(1420) φ'(1680) ρ''(1700) ω''(1650) Data approximation: cross section

  14. Data approximation: summary • In the charged channel there is a dip in the cross section in the energy range 1.05-1.15 GeV, which can be explained by an addition to the amplitude due to rescattering in the final state • Amplitudes of radial excitations of vector mesons have opposite sign with respect to the amplitudes of ρ, ω and φ vector mesons, as expected • Presence of ω mesons in the description is necessary • Presence of orbital excitations of vector mesons in the description is necessary • Experimental data above 1.7 GeV are not well described: it is evident from the data that there is an interference structure • Phases θV, deviate from 0, showing that more sophisticated model taking into account mixing between vector mesons and rescattering effects in final state should be used

  15. CVC: comparison of e+e−→ρ,ρ',ρ"→KK and τ−→K−K0ντ Data • CLEO: τ−→K−K0ντ Fit variants: №2–№5 №8–№9 №6 №7 Hep-ph/0409080 v2

  16. Conclusions • Simultaneous fit of e+e–→K+K– and e+e–→KSKL cross sections was performed in the framework of vector dominance model in a wide energy range (2E0=1.01÷2.2 GeV) • The following results were obtained: • dip in the e+e–→K+K– experimental cross section in the energy range from 1.05 to 1.15 GeV • phases of radial excitations of light vector mesons are close to prediction • Γφ'eeΓφ'KK/Γφ‘2=(0.37±0.08)·10–6 • Γω"eeΓω"KK/Γω“2=(0.4÷0.7)·10–7 • Range parameter R=2.0±0.2 GeV–1 • Isovector and isoscalar parts of the K-meson form factor were obtained • Comparison of isovector contribution and experimental data on spectral function, obtained from τ−→K−K0ντ decay, was done • More sophisticated VMD model, including mixing between vector mesons and amplitude corrections due to rescattering in final state, should be used

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