25-29 September 2017
Salamanca, Spain
Europe/Zurich timezone

## Chiral model for the $D^+ \to K^+ K^- K^+$ decay amplitude

28 Sep 2017, 17:35
20m
Auditorium

#### Auditorium

Talk Spectroscopy of mesons

### Speaker

M.R. Robilotta (Instituto de Física - Universidade de São Paulo)

### Description

Isobar models, successful as they are in providing fits for heavy meson decays,
rely on both parameters which are not physically transparent and sums
of Breit-Wigner functions.
As an alternative, we propose a Multi-Meson-Model (Triple-M) for the
$D^+ \to K^+ K^- K^+$ amplitude.
The decay is assumed to be dominated by the process
$D^+\to W^+ \to K^+ K^- K^+$ and, therefore,
driven by axial current matrix elements:
$\mathcal{A} =\langle (KKK)^+|A_{\mu}|0\rangle \langle 0|A^{\mu}|D^+\rangle$.
In the want of a complete unitary description of this amplitude, we consider the so called (2 + 1) approximation,
in which two-body unitarized amplitudes are coupled to spectator particles.
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In the Triple-M, we depart from lagrangians employed in chiral perturbation theory with resonances (R$\chi$PT),
which describe interactions of pseudoscalar mesons by means of both leading order (LO) contact terms
and next-to-leading order (NLO) resonance exchanges.
The NLO LECs are assumed to be saturated by resonances.
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We consider all channels in the $K^+K^-$ subsystem with spin $J = 1, 0$ and isospin $I = 1, 0$,
associated with the resonances $\rho$, $\phi$, $a_0$ and two $f$-scalar states,
corresponding to a singlet and to a member of an octet of $SU(3)$.
The physical $f_0(980)$ is then a linear combination of these scalar states.
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The unitarization of two-body amplitudes is performed by ressumming geometrical Dyson series,
based on interaction kernels and two-meson propagators,
involving $\pi\pi$, $KK$, $\eta\eta$ and $\eta\pi$ intermediate states.
The ensuing coupled channel systems give naturally rise to the widths of resonances and,
in the case of the
scalar-isoscalar channel, to an amplitude which is more consistent than a sum of Breit-Wigners.
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The main features of the Triple-M read:
\
{\bf 1.} it incorporates resonances and extends the isobar model;
\
{\bf 2.} it includes a non-resonant contribution, a consequence of chiral symmetry,
which is a real function, fully determined by theory;
\
{\bf 3.} all imaginary terms in the amplitude are completely determined by unitarity and
no free complex parameters are employed;
\
{\bf 4.} all free parameters represent either meson masses or coupling constants and, therefore,
have a rather transparent physical meaning.
\

A check of the Triple-M was made with the amplitude used in the analysis of the isobar model
and it will be tested directly against data, in the near future.

### Primary authors

R. Aoude (Centro Brasileiro de Pesquisas Físicas - CBPF) P.C. Magalhães (Centro Brasileiro de Pesquisas Físicas - CBPF) A.C. dos Reis (Centro Brasileiro de Pesquisas Físicas - CBPF) M.R. Robilotta (Instituto de Física - Universidade de São Paulo)