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


Talk Spectroscopy of mesons Spectroscopy of mesons


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


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.
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.
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.
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.
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)

Presentation Materials