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A PROPOSAL FOR IMPROVING THE H A D R O N IZATION OF Q C D CURRENTS IN TAU OLA

A PROPOSAL FOR IMPROVING THE H A D R O N IZATION OF Q C D CURRENTS IN TAU OLA. Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés. See Phys.Rev.D69:073002,2004 ; AIP Conf.Proc.964:40-46,2007 ; Work to appear soon. PHI PSI 08 Frascati April 10th 2008. Pablo Roig

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A PROPOSAL FOR IMPROVING THE H A D R O N IZATION OF Q C D CURRENTS IN TAU OLA

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  1. A PROPOSAL FOR IMPROVING THE HADRONIZATION OF QCD CURRENTS IN TAUOLA Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés See Phys.Rev.D69:073002,2004 ; AIP Conf.Proc.964:40-46,2007 ; Work to appear soon PHIPSI08 Frascati April 10th 2008 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 • Outlook : (Gómez Dumm, Pich, Portolés, R. to appear) t-(h1h2h3) - nt IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  3. SUMMARY: • Hadronic decays of the t lepton • Kühn-Santamaría Model in TAUOLA • Tools : cPT, Large Nc , RcT • t-(2K p)- nt • Outlook : (Gómez Dumm, Pich, Portolés, R. to appear) t-(h1h2h3) - nt h1h2h3=3K,2p h, Kph IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  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 IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  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 LQCD= LQCD (qi,Gma;gs,mi) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  6. 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 PhT: RcT IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  7. HADRONIC DECAYS OF THE tLEPTON nt t- W - h1 h2 QCD h3 Hadrons (Kühn, Santamaría ’90)(KS) (Gómez-Cadenas, González-García, Pich ’90) (GGP) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  8. 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) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  9. KÜHN-SANTAMARÍA-like MODELS & TAUOLA (Decker, Mirkes, Sauer, Was ‘92) (Decker, Mirkes ‘92) (Decker, Finkemeier, Mirkes ’93) (Decker, Finkemeier ’93, ‘94) (Decker, Finkemeier, Heiliger, Jonsson ‘94) (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96) (Mirkes, Urech ‘97) (Kühn, Mirkes, Willibald ‘97) (Jadach, Was ’90, ‘93) (Jadach, Kühn, Was ‘90) (Jezabeck, Was, Jadach, Kühn ‘90) (Jadach, Was, Decker, Kühn ‘90) (Bondar, Eidelman, Milstein, Pierzchala, Root, Was, Worek ‘02) (Golonka, Kersevan, Pierzchala, Richter-Was, Was, Worek ‘06) (Kühn, Was ‘06) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  10. 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: IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  11. K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  Some allowed contributions are lacking: V A a m    V-exchanged missing in K+K-p- r0   V2m K*0 V1m K-K0p0 K*0 V1m r- V1m K-p-p+ K*0 V1m r- V1m K0p0p- IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  12. K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  V V v m   Our aim is to tackle an ambitious program for describing within a theoretical frameworkas close as possible to QCD the considered decays. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  13. 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 IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  14. 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 9 (SRA) Off-shell width Tree level diagrams (Gómez-Dumm, Pich, Portolés ‘00) Matching the OPE IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  15. cPT: The low-energy EFT of QCD (Gasser & Leutwyler ’84, ’85) PGB IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  16. Resonances+ PGB 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. in progress) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  17. Resonances+ PGB 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 A j a m A V j V v m j V V j V j j j IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  18. 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       IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  19. RcT APPLIED     F a m a m      V V GV, FV a m  a m      i V A 24 couplings a m    gi    ci di V V V V   v m v m v m v m       IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  20. t-(2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  21. t-(2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  22. t-(2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters. CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD). IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  23. t-(2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters. CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD). BaBar presented their data on these modes in TAU’06. However the plot of the spectral function vs. invariant mass of the hadronic system was not at the Proc. (Nugent ‘06) and they have not submitted the paper yet. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  24. t-(2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) The phenomenological approach of KS-like works (Finkemeier and Mirkes ’95, ‘96) do not include all possible contributions for the exchanged resonances and depend noticeably on the excited resonances parameters. CLEO (Liu ’03, CLEO ‘04) could not fit their data using FM expressions and reshaped the model violating the normalization of the WZ term (i.e. low-energy QCD). BaBar presented their data on these modes in TAU’06. However the plot of the spectral function vs. invariant mass of the hadronic system was not at the Proc. (Nugent ‘06) and they have not submitted the paper yet. 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) IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  25. t-(2K p)- nt (Gómez Dumm, Pich, Portolés, R. in progress) Our work: • Computation of the involved process within RcT(15 couplings). • Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings). • Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings). • Axial-form factor fixed by t3p nt(2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04). • Vector-form factor fixed thanks to BaBar data on e+e-(KKp)- nt and ALEPH’99’s full t spectrum. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  26. t-(2K p)- nt (Gómez Dumm, Pich, Portolés, R. in progress) Our work: • Computation of the involved process within RcT(15 couplings). • Brodsky-Lepage behaviour demanded to the Form Factors (6 couplings). • Computation and fit to Br(w3p) completing (Pich, Portolés, Ruiz-Femenía ‘03). Use of some constraints from this work for <VVP> (3 couplings). • Axial-form factor fixed by t3p nt(2 couplings). (Gómez-Dumm, Pich, Portolés ‘04) (Cirigliano, Ecker, Eidemüller, Pich, Portolés ‘04). • Vector-form factor fixed thanks to BaBar data on e+e-(KKp)- nt and ALEPH’99’s full t spectrum. Thus, we can concentrate on improving the most challenging aspect in t decays into three mesons: The axial-vector form factors and, specifically, the off-shell width of the a1. Easy to extend to the e+e- scattering below 2 GeV. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  27. OUTLOOK: t-  (h1h2h3 )- nt h1h2h3 FA FV • 3p • 2K p • K 2p • 2p h • p K h • 3K Vus,ms Vus,ms Vus,ms mnt IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

  28. 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 and PHOKARA. • We have studied these decays within RcT with a Large NC-inspired model guided by QCD. • We have used BaBar data on e+e-KKpto fix our free parametres on the Vector Current sector. We will improve our analysis once t-K+K-p- nt data are published. • We aim to improve our off-shell a1 width in order to revisit t-  3p- nt. • Our results have been implemented in SHERPA (LHC and TEVATRON) and may be used by the B-factories. • LHC, BABAR, BELLE, BES…are promising facilities to test our predictions. • The future looks even more promising and exciting: Vus,ms, mnt and, of course, hadronization of QCD currents. IMPROVING HADRONIZATION IN TAUOLAPablo Roig (IFIC) PHIPSI08 Frascati

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