Gauged linear sigma model and pion-pion scattering

Abstract

A simple gauged linear sigma model with several parameters to take the symmetry breaking and the mass differences between the vector meson and the axial vector meson into account is considered here as a possibly useful template for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. An analytic procedure is first developed for relating the Lagrangian parameters to four well established (in the QCD application) experimental inputs. One simple equation distinguishes three different cases:1. QCD with axial vector particle heavier than vector particle, 2. possible technicolor model with vector particle heavier than the axial vector one, 3. the unphysical QCD case where both the KSRF and Weinberg relations hold. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) theglobal region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of bare sigma mass parameter for describing these two regions. If a reasonable globa fit is made, there is some loss of precision in the near threshold region.Comment: 19 pages, 9 figure

f2(1810) as a triangle singularity

“…Apart from the fit of the amplitude one wishes to see the meaning of the structure observed experimentally. One wishes to associate resonances to states stemming from the interaction of quarks and gluons [34][35][36] or from the interaction of hadrons making molecules [27,28,[37][38][39][40]. However, in the present case the structure observed comes from neither of these.…”

B0andBs0decays intoJ/Bayar1, Wu2, Oset3 2014Phys. Rev. D444520View full textAdd to dashboardCite

“…We can see a link of the quark pictures with the chiral unitary approach by recalling the interesting observation made in [51] that "the properties obtained within these quark models should be interpreted as being 'bare' properties, subject to a nontrivial renormalization due to effects which provide unitary corrections to the scattering amplitudes in which these particles appear as poles." These unitary corrections, incorporating meson-meson multiple scattering, are so huge that upon its implementation the width of the f 0 (500) appears of the order of 500 MeV, as seen in the work of [52]. Certainly, this effect of the meson-meson scattering adds necessarily meson-meson components to the wave function of the f 0 (500), that in terms of quarks could be interpreted as having largely a four-quark component, or a meson-meson component if we use a different basis to write the wave function.…”

$$f_0(500)$$ f 0 ( 500 ) , $$f_0(980)$$ f 0 ( 980 ) , and $$a_0(980)$$ a 0 ( 980 ) production in the $$\chi _{c1} \rightarrow \eta \pi ^+\pi ^-$$ χ c 1 → η π + π - reaction

“…Yet, other different approaches which start from a seed of qq for these resonances, also get a large meson-meson component for these states as soon as this seed is coupled to two mesons and the mesons are allowed to interact in a realistic scheme fulfilling unitarity [15][16][17][18]. A thorough recent review on these issues can be found in Ref.…”