3 research outputs found
Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics
We perform a non-perturbative chiral study of the masses of the lightest
pseudoscalar mesons. In the calculation of the self-energies we employ the
S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory
(UCHPT) that include the lightest nonet of scalar resonances. Values for the
bare masses of pions and kaons are obtained, as well as an estimate of the mass
of the \eta_8. The former are found to dominate the physical pseudoscalar
masses. We then match to the self-energies from Chiral Perturbation Theory
(CHPT) to O(p^4), and a robust relation between several O(p^4) CHPT
counterterms is obtained. We also resum higher orders from our calculated
self-energies. By taking into account values determined from previous chiral
phenomenological studies of m_s/\hat{m} and 3L_7+L^r_8, we determine a tighter
region of favoured values for the O(p^4) CHPT counterterms 2L^r_6-L^r_4 and
2L^r_8-L^r_5. This determination perfectly overlaps with the recent
determinations to O(p^6) in CHPT. We warn about a likely reduction in the value
of m_s/\hat{m} by higher loop diagrams and that this is not systematically
accounted for by present lattice extrapolations. We also provide a favoured
interval of values for m_s/\hat{m} and 3L_7+L^r_8.Comment: 26 pages, 9 figures. Original new material is included. Major
rewriting when comparing with lattice QC
Theoretical Study of the \gamma\gamma-->meson-meson Reaction
We present a unified picture which studies simultaneously the gamma
gamma-->pi^+ pi^-, pi^0 pi^0, K^+ K^-, K^0 bar{K}^0, pi^0 eta reactions up to
about sqrt(s)=1.4 GeV reproducing the experimental cross sections. The present
work implements in an accurate way the final state interactions of the
meson-meson system, which is shown to be essential in order to reproduce the
data, particularly the L=0 channel. This latter channel is treated here
following a recent theoretical work in which the meson-meson amplitudes are
well reproduced and the f_0, a_0, sigma resonances show up clearly as poles of
the t matrix. The present work, as done in earlier ones, also incorporates
elements of chiral symmetry and exchange of vector and axial resonances in the
crossed channels, as well as a direct coupling to the f_2(1270) and a_2(1320)
resonances. We also evaluate the decay width of the f_0(980) and a_0(980)
resonances into the gamma-gamma channel.Comment: 20 pages, 13 figures, LaTeX. Only significant change in the
calculation of \gamma\gamma-->pi^+ pi^- from the more careful treatment of
the tail of the f_2(1270) resonanc
N/D Description of Two Meson Amplitudes and Chiral Symmetry
The most general structure of an elastic partial wave amplitude when the
unphysical cuts are neglected is deduced in terms of the N/D method. This
result is then matched to lowest order, , Chiral
Perturbation Theory(PT) and to the exchange (consistent with chiral
symmetry) of resonances in the s-channel. The extension of the method to
coupled channels is also given. Making use of the former formalism, the
and (I=1/2) P-wave scattering amplitudes are described without
free parameters when taking into account relations coming from the 1/
expansion and unitarity. Next, the scalar sector is studied and good agreement
with experiment up to GeV is found. It is observed that the
, and resonances are meson-meson states
originating from the unitarization of the PT
amplitudes. On the other hand, the is a combination of a strong
S-wave meson-meson unitarity effect and of a preexisting singlet resonance with
a mass around 1 GeV. We have also studied the size of the contributions of the
unphysical cuts to the (I=0) and (I=1/2) elastic S-wave
amplitudes from PT and the exchange of resonances in crossed channels up
to MeV. The loops are calculated as in PT at next
to leading order. We find a small correction from the unphysical cuts to our
calculated partial waves.Comment: 32 pages, LaTeX, 9 Figures. Estimations of the unphysical cuts have
been done in a new section. Final versio