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H A D R O N IZATION OF Q C D CURRENTS: t  KK pn t

H A D R O N IZATION OF Q C D CURRENTS: t  KK pn t. Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés. Pablo Roig Pablo.Roig@ific.uv.es I nstituto de FÍ sica C orpuscular CSIC-UVEG València (Spain). SUMMARY:. Hadronic decays of the t lepton

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H A D R O N IZATION OF Q C D CURRENTS: t  KK pn t

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  1. HADRONIZATION OF QCD CURRENTS:tKKpnt Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés Pablo Roig Pablo.Roig@ific.uv.es Instituto de FÍsica Corpuscular CSIC-UVEG València (Spain)

  2. SUMMARY: • Hadronic decays of the t lepton • Kühn-Santamaría Model in TAUOLA • Tools : cPT, Large Nc , RcT • t-(2K p)- nt • Conclusions (Gómez Dumm, Pich, Portolés, R. to appear) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  3. HADRONIC DECAYS OF THE tLEPTON nt t- W - Tm=<Hadrons|(V-A)m eiSQCD|0>= =Si(Lorentz Structure)i Fi(Q2,sj) h1 . . . QCD Hadrons hn TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  4. HADRONIC DECAYS OF THE tLEPTON nt t- W - Tm=<Hadrons|(V-A)m eiSQCD|0>= =Si(Lorentz Structure)i Fi(Q2,sj) h1 . . . QCD Hadrons ? hn LQCD= LQCD (qi,Gma;gs,mi) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  5. HADRONIC DECAYS OF THE tLEPTON nt t- W - Tm=<Hadrons|(V-A)m eiSQCD|0>= =Si(Lorentz Structure)i Fi(Q2,sj) h1 . . . QCD Hadrons hn RcT TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  6. HADRONIC DECAYS OF THE tLEPTON nt t- W - h1 h2 QCD h3 Hadrons TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  7. KÜHN-SANTAMARÍA MODEL (Kühn-Santamaría ‘90) PT O(p2) PT O(p4) (Sakurai ’69, Kühn & Wagner ’84, Pich ’87) Vector Meson Dominance KS Asymptotic behaviour ruled by QCD (Brodsky-Farrar ’73, B-Lepage ‘80) ? (Gounaris-Sakurai ‘68) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  8. TOOLS: EFFECTIVE FIELD THEORIES QCD EFT PhT Low energy expansion Intermediate region cPT 1/Nc (Gasser & Leutwyler ’84, ’85) (‘t Hooft ’74, Witten ‘79)  # 0-width resonances Tree level diagrams Matching the OPE TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  9. TOOLS: EFFECTIVE FIELD THEORIES QCD EFT PhT Low energy expansion Intermediate region cPT 1/Nc RcT (Gasser & Leutwyler ’84, ’85) (‘t Hooft ’74, Witten ‘79) (Peris, Perrottet, de Rafael ‘98)  # 0-width resonances Only one nonet Off-shell width Tree level diagrams (Gómez-Dumm, Pich, Portolés ‘00) Matching the OPE TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  10. RcT APPLIED     F a m a m      V V GV, FV a m  a m      i V A a m    gi    ci di V V V V   v m v m v m v m       TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  11. RcT APPLIED   23 unknown couplings   F a m a m      V V GV, FV a m  a m      i V A a m    gi    ci di V V V V   v m v m v m v m       TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  12. t-(2K p)- nt The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) does not include all possible contributions for the exchanged resonances and depends noticeably on the excited resonance parameters. TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  13. t-(2K p)- nt The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) does not include all possible contributions for the exchanged resonances and depends noticeably on the excited resonance parameters. CLEO (Liu ’03, CLEO ‘04) could not fit their data using KS expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD). TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  14. t-(2K p)- nt BaBar has recently (BaBar ‘07) published very precise data on e+e- KK p/husing ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = 0.167+0.024 in t-(KK p)- nt. Under CVC one can relate e+e- data to the t decay. (Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  15. t-(2K p)- nt BaBar has recently (BaBar ‘07) published very precise data on e+e- KK p/husing ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = 0.167+0.024 in t-(KK p)- nt. Under CVC one can relate e+e- data to the t decay. (Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08) Assumptions of this procedure: SU(2) symmetry K* >> r,w,f Interferences are negligible TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  16. t-(2K p)- nt BaBar has recently (BaBar ‘07) published very precise data on e+e- KK p/husing ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = 0.167+0.024 in t-(KK p)- nt. Under CVC one can relate e+e- data to the t decay. (Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08) Assumptions of this procedure: SU(2) symmetry K* >> r,w,f Interferences are negligible TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  17. t-(2K p)- nt BaBar has recently (BaBar ‘07) published very precise data on e+e- KK p/husing ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = 0.167+0.024 in t-(KK p)- nt. Under CVC one can relate e+e- data to the t decay. (Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08) Assumptions of this procedure: SU(2) symmetry K* >> r,w,f Interferences are negligible Error of this simplification  30 % both in KS approach and in ours TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  18. t-(2K p)- nt BaBar has recently (BaBar ‘07) published very precise data on e+e- KK p/husing ISR events. Furthermore, their Dalitz-plot fit has allowed to separate cleanly the I=0,1 contributions. Assuming CVC and comparing to ALEPH ’99 allows to derive (GV/GT) = 0.167+0.024 in t-(KK p)- nt. Under CVC one can relate e+e- data to the t decay. (Davier, Descotes-Genon, Höcker, Malaescu, Zhang ‘08) Assumptions of this procedure: SU(2) symmetry K* >> r,w,f Interferences are negligible Error of this simplification  30 % both in KS approach and in ours (Apart from the error intrinsic to using Breit-Wigner function for resonance exchange) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  19. t-(2K p)- nt (Gómez Dumm, Pich, Portolés, R. to appear) Our work: • Computation of the involved process within RcT(23-8 =15couplings). • Brodsky-Lepage behaviour demanded to the Form Factors (15-9= 6couplings). • Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (6-3= 3couplings). • Axial-form factor fixed by t3p nt(3-1= 2couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04). • Vector-form factor fixed thanks to br (tK+K-p-nt) and br(tK-K0p0nt) (2-2= 0couplings). TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  20. t-(2K p)- nt (Gómez Dumm, Pich, Portolés, R. to appear) Our work: • Computation of the involved process within RcT(23-8 =15couplings). • Brodsky-Lepage behaviour demanded to the Form Factors (15-9= 6couplings). • Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (6-3= 3couplings). • Axial-form factor fixed by t3p nt(3-1= 2couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04). • Vector-form factor fixed thanks to br (tK+K-p-nt) and br(tK-K0p0nt) (2-2= 0couplings). Hence, we predict: i) the spectra of the KKp modes ii)(GV/GT)  0.66 TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  21. (Gómez Dumm, Pich, Portolés, R. to appear) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  22. (Gómez Dumm, Pich, Portolés, R. to appear) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  23. CONCLUSIONS • Current analyses of t-  (3p-,K+K-p-) ntdata using TAUOLA have shown theoretical inconsistencies. We would like to improve the hadronic matrix elements in TAUOLA. • We have studied these decays within RcT with a Large NC-inspired model guided by QCD. • We have improved our off-shell a1 width and revisited t-  3p- nt. • Using the available experimental data, we have been able to predict the spectra of all KKp charge channels. • Our expressions are easy to extend to the e+e- scattering below 2 GeV and thus may be of use for PHOKHARA. • Our results have been implemented in SHERPA (LHC and TEVATRON) and may be used by the B-factories. • LHC, BABAR, BELLE, BES-III…are promising facilities to test our predictions. • The future looks even more promising and exciting: Vus,msand, of course, hadronization of QCD currents. TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  24. BACKUP SLIDES

  25. K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  V A a m    V V v m   c,1R & 2R obtained from: TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  26. K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  Some allowed r0,-, K*0 contributions are lacking in the modes: K+K-p-,K-K0p0,K-p-p+,K0p0p- V A a m    V V v m   TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  27. cPT: The low-energy EFT of QCD (Gasser & Leutwyler ’84, ’85) Goldstone Bosons TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  28. Resonances+ Goldstone Bosons TOOLS : RcT (Ecker, Gasser, Pich, De Rafael ‘89) (Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89) Antisymmetric tensor formalism (Gómez Dumm, Pich, Portolés ’04) VMD (Ruiz-Femenía, Pich, Portolés ’03) (Gómez Dumm, Pich, Portolés, R. to appear) TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  29. Resonances+ Goldstone Bosons TOOLS : RcT (Ecker, Gasser, Pich, De Rafael ‘89) (Ecker, Gasser, Leutwyler, Pich, De Rafael ‘89) ,… V V V j v m a m j A j a m A V j V v m j V V j V j j j TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  30. PREVIOUS WORK: t- (p p p)- nt l0=11.9+0.4 TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  31. OUR WORK: t- (p p p)- nt (Gómez Dumm, Pich, Portolés, R. to appear) l0=0.10+0.03 Fixed: QCD prediction for <VAP> Ma1 = (1.17 + 0.01) GeV The only parameter of the fit!! Ga1 = (0.50 + 0.02) GeV TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  32. SU(2) AND INTERFERENCES K- K+ K*- K*+ v m vm K+ p0 K- p0 p+ K0 K*+ K*- v m v m p+ K- K- K0 TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  33. SU(2) AND INTERFERENCES K- K+ K*- K*+ - v m vm K+ p0 K- p0 p+ K0 K*+ K*- + v m v m p+ K- K- K0 TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  34. OFF-SHELL WIDTH OF MESON RESONANCES TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

  35. OUTLOOK: t-  (h1h2h3 )- nt h1h2h3 FA FV • 3p • 2K p • K 2p • 2p h • p K h • 3K Vus,ms Vus,ms Vus,ms TAU 08 BINP, Novosibirsk HADRONIZATION OF QCD CURRENTSPablo Roig (IFIC)

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