Work done in collaboration with D. Gómez-Dumm, A. Pich, J. Portolés 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 PHI PSI 08 Frascati April 10th 2008 Pablo Roig Pablo.Roig@ific.uv.es Instituto de FÍsica Corpuscular CSIC-UVEG València (Spain)

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

HADRONIC DECAYS OF THE t LEPTON nt t- W - Tm=<Hadrons|(V-A)m eiSQCD|0>= =Si(Lorentz Structure)i Fi(Q2,sj) h1 . QCD Hadrons hn IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

HADRONIC DECAYS OF THE t LEPTON 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

HADRONIC DECAYS OF THE t LEPTON 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

HADRONIC DECAYS OF THE t LEPTON nt t- W - h1 h2 QCD h3 Hadrons (Kühn, Santamaría ’90)(KS) (Gómez-Cadenas, González-García, Pich ’90) (GGP) IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  A V a m    V V v m   c,1R & 2R obtained from: IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) K-S-like works & HADRONIZATION IN TAUOLA (Finkemeier, Mirkes ’95,’96) (Finkemeier, Kühn, Mirkes ‘96)  Some allowed contributions are lacking: A V 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 framework as close as possible to QCD the considered decays. IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

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) Tree level diagrams Off-shell width (Gómez-Dumm, Pich, Portolés ‘00) Matching the OPE IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

cPT: The low-energy EFT of QCD (Gasser & Leutwyler ’84, ’85) PGB IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) RcT APPLIED     F a m a m      V V GV, FV a m  a m      i A V a m    gi  ci  di  V V V V  v m v m  v m v m       IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) RcT APPLIED     F a m a m      V V GV, FV a m  a m      i A V 24 couplings a m    gi  ci  di  V V V V  v m v m  v m v m       IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) t-  (2K p)- nt First work on this already in ’90 (González-García, Gómez-Cadenas, Pich) IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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/h using 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) OUTLOOK: t-  (h1 h2 h3 )- nt h1 h2 h3 FA FV 3p 2K p K 2p 2p h p K h 3K Vus, ms Vus, ms Vus, ms mnt IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati

IMPROVING HADRONIZATION IN TAUOLA Pablo Roig (IFIC) CONCLUSIONS Current analyses of t-  (3p-, K+K-p-) nt data 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-  KKp to 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 TAUOLA Pablo Roig (IFIC) PHI PSI 08 Frascati