Hadronic decays ot the t lepton: t -  (2K p) - n t within Resonance Chiral Theory

1. Hadronic decays ot the t lepton: t-(2K p)-ntwithin Resonance Chiral Theory Pablo Roig1, Daniel Gómez-Dumm2, Antonio Pich1 and Jorge Portolés1 1IFIC (CSIC-Universitat de València), València (Spain) 2IFLP-CONICET, La Plata (Argentina) Abstract: The analysis of the t-K+ K- p-nt decays by the CLEO-III experiment has shown noticeable inconsistencies. We have studied this decay within the framework of Resonance Chiral Theory. Most of the unknown couplings of our Effective Lagrangian have been determined by requiring the asymptotic behaviour, ruled by QCD, both to the vector and axial-vector form factors. Our results have been implemented in the SHERPA Monte-Carlo, a tool to be used at LHC and Tevatron. Current and forthcoming experiments, either from B-factories like BaBar and Belle or from tau-charm factories like BES have an ambitious tau decay program that will be able to settle our study. 1.- Introduction: In addition to its intrinsic interest, hadronic decays of the tau lepton offer a clean way of testing the strong interactions and, in particular, its main open problem: the hadronization of QCD currents. These decays span an energy region in which QCD is clearly non-perturbative. Much better than relying on parameterisations or modelling phenomenological Lagrangians turns out to be the use of Effective Field Theories, that preserve the symmetries of the fundamental interaction and are written in terms of the suitable degrees of freedom for a given energy range. The crucial advantage in doing this way is that one does not only end up fitting the data but learns about QCD as well. Being Mt~1.8 GeV, it is not enough to use Chiral Perturbation Theory to describe these processes using only pseudo-Goldstone bosons (pGb’s). In fact, the dominant contribution comes from resonance exchange so that one needs an effective theory of QCD that accounts for both contributions. Resonance Chiral Theory is an appropriate framework to include them both. Fig. 1- In principle, there are 22 unknown couplings (in red) in our Lagrangian (those after F, FV, GV). am and vm stand for (axial-) vector currents. f for the pGb’s, and A and V for the (axial-)vector resonances. The strong vertices are depicted by a thick dot and the odd-intrinsic parity ones by a filled square. Explicit computation and imposing a Brodsky-Lepage-like behaviour to the (axial-)vector form factors yields just 6 of them free. Fig. 2- Published CLEO data corresponds to raw mass spectra. Their analysis violates QCD normalisation at low energies. Fig.3- BABAR showed preliminary data on this mode at TAU06. Their study is currently under completion. BELLE is also working on it. 2.- Resonance Chiral Theory (RcT) and large NC expansion: Chiral Perturbation Theory (cPT) is the Effective Field Theory of low-energy QCD. It describes the interactions among the octet of lightest pseudoscalar particles and it is based in an expansion in powers of p2/m2. Although it is not clear what is the expansion parameter at intermediate energies, 1/NC has been proposed to do this task. • Fig.4- OUR RESULT: • We have been able to determine all 6 and give a prediction for the spectral function fitting the BR: • l0VAP Green’s function • c1235 & d123VVP Green’s func. • 2g4+g5w  3p • c4  t-K- K0 p0nt • g4+g5  t-K+ K- p-nt • Unlike CLEO, we claim for Vector Current Dominance in these channels. LO in 1/NC amounts to consider tree level diagrams with meson exchange whose local interactions are given by an Effective Lagrangian. RcT enlarges the domain of applicability of cPT by including resonances as active degrees of freedom and it is large NC inspired. For convenience,we work in the antisymmetric tensor formalism: And similarly for axial-vector resonances (we rely on Vector Meson Dominance). 3.- t-(2K p)- ntdecays (RcT and other studies) Schematically, the different contributions to the process under study are sketched in the following diagrams: References: P. Roig, D. Gómez-Dumm, A.Pich and, J. Portolés, to appear D. Gómez-Dumm, A.Pich, J. Portolés Phys.Rev.D69:073002,2004 D. Gómez-Dumm, A.Pich, J. Portolés Phys.Rev.D62:054014,2000 P.D. Ruiz-Femenía , A.Pich, J. Portolés JHEP 0307:003,2003 Acknowledgements: P.R. Is supported by a FPU contract (MEC). This work has been supported in part by the EU MRTN-CT-2006-035482 (FLAVIAnet), by MEC (Spain) under grant FPA2004-00996 and by Generalitat Valenciana under grants ACOMP06/098 and GV05/015. This work has also been supported by CONICET and ANPCyT (Argentina), under grants PIP6009, PIP6084, PICT02-03-10718 and PICT04-03-25374.