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1
Hadronic decays ot the t lepton t- ? (2K p)- nt
within 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 Mt1.8 GeV, it is not enough to use Chiral
Perturbation Theory to describe these processes
using only pseudo-Goldstone bosons (pGbs). 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 pGbs, 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 Greens function
• c1235 d123 ? VVP Greens func.
• 2g4g5 ? w ? 3p
• c4 ? t- ? K- K0 p0 nt
• g4g5 ? 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)- nt decays (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.D69073002,2004 D. Gómez-Dumm,
A.Pich, J. Portolés Phys.Rev.D62054014,2000 P.D.
Ruiz-Femenía , A.Pich, J. Portolés JHEP
0307003,2003 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.