arXiv subjects
Publications and source records attributed to Francesco Giacosa.
We discuss an Nf=3 linear sigma model with vector and axial-vector mesons (extended Linear Sigma Model - eLSM). We present first results regarding the masses of axial-vector mesons determined from the extended model.
It is explained why the interpretation of the resonances $f_{2}(1270),$ $a_{1}(1260)$ and $f_{0}(1370)$ as quark-antiquark states is legitimate. The result of the quark model and of recently performed Bethe-Salpeter studies are not (necessarily) in conflict and can be understood as two different approaches toward the description of the same quark-antiquark resonances.
We outline the extension of the globally chirally invariant Nf = 2 linear sigma model with vector and axial-vector degrees of freedom to Nf=3. We present preliminary results concerning the scalar meson masses.
We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions for the axial coupling constants of the nucleon, $g_{A}^{N}$, and its partner, $g_{A}^{N^{*}}$. Using experimental data for the decays $N^{*} \to N π$ and $a_{1} \toπγ$, as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0}\sim500$ MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay $N^{*} \to N η$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$.
We study the implications of a light tetraquark on the chiral phase transition at nonzero temperature $T$: The behavior of the chiral and four-quark condensates and the meson masses are studied in the scenario in which the resonance $f_{0}(600)$ is described as a predominantly tetraquark state. It is shown that the critical temperature is lowered and the transition softened. Interesting mixing effects between tetraquark, and quarkonium configurations take place.
We calculate low-energy meson decay processes and pion-pion scattering lengths in a globally chirally invariant two-flavour linear sigma model exploring the quark content of the scalar mesons f(0)(600) and a(0)(980), as well as f(0)(1370) and a(0)(1450). To this end, we investigate which one of these sets of fields is more likely to contain quark-antiquark states.
We present a two-flavour linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate pion-pion scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We investigate this question by assigning the quark-antiquark sigma and a0 states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the sigma, which turns out to be too small. We also study the alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the pion-pion scattering length $a_{0}^{0}$ is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.
A sigma-model with two linked Mexican hats is discussed. This scenario could be realized in low-energy QCD when the ground state and the first excited (pseudo)scalar mesons are included, and where not only in the subspace of the ground states, but also in that of the first excited states, a Mexican hat potential is present. This possibility can change some basic features of a low-energy hadronic theory of QCD. It is also shown that spontaneous breaking of parity can occur in the vacuum for some parameter choice of the model.
The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in the approach proposed by Korthals-Altes. This SU(2) calculation is based on a particular, effective two-loop correction to the pressure needed for the extraction of the hypothetic number density of isolated and screened magnetic monopoles or antimonopoles in the deconfining phase. By exponentiating the exchange of the tree-level massless but one-loop dressed mode within a quadratic spatial contour of side-length $L$ in the effective theory we demonstrate that for $L\to\infty$ the Wilson loop exhibits {\sl perimeter} law. This is in contrast to a rigorous {\sl lattice} result subject to the Wilson action and for this action valid at sufficiently high temperature. In the framework of the effective theory there is, however, a regime for small (spatially unresolved) $L$ were the exponent of the spatial Wilson loop possesses curvature as a function of $L$.
A definition of `dynamical generation', a hotly debated topic at present, is proposed and its implications are discussed. This definition, in turn, leads to a method allowing to distinguish in principle tetraquark and molecular states. The different concept of `dynamical reconstruction' is also introduced and applies to the generation of preexisting mesons (quark-antiquark, glueballs, >...) via unitarization methods applied to low-energy effective Lagrangians. Large $N_{c}$ arguments play an important role in all these investigations. A simple toy model with two scalar fields is introduced to elucidate these concepts. The large $N_{c}$ behavior of the parameters is chosen in order that the two scalar fields behave as quark-antiquark mesons. When the heavier field is integrated out, one is left with an effective Lagrangian with the lighter field only. A unitarization method applied to the latter allows to `reconstruct' the heavier `quarkonium-like' field, which was previously integrated out. It is shown that a Bethe-Salpeter (BS) analysis is capable to reproduce the preformed quark-antiquark state. However, when only the lowest term of the effective Lagrangian is retained, the large $N_{c}$ limit of the reconstructed state is not reproduced: instead of the correct large $N_{c}$ quarkonium limit, it fades out as a molecular state would do. Implications of these results are presented: it is proposed that axial-vector, tensor and (some) scalar mesons just above 1 GeV obtained via the BS approach from the corresponding low-energy, effective Lagrangian in which only the lowest term is kept, are quarkonia states, in agreement with the constituent quark model, although they might fade away as molecular states in the large $N_{c}$ limit.
We consider a globally invariant chiral Lagrangian that contains vector and axial-vector mesons. We compute the f0(600) decay width into two pions and pion-pion scattering lengths and compare with the corresponding results in which the (axial-)vector degrees of freedom decouple. We show that the role of vector mesons has a great impact on these quantities.
The decays of a light scalar meson into a vector meson and a photon ($S\to Vγ)$ are evaluated in the tetraquark and quarkonium assignments of the scalar states. A link with the radiative decays $ϕ\to Sγ$ is established: experimental results for $S\to Vγ$ will allow to understand if the direct, quark-loop contribution to $ϕ\to Sγ$ or the kaon-loop contribution is dominant. Also strong decays $S\to PP$ -where $P$ denotes a pseudoscalar meson- are investigated: the tetraquark assignment works better than the quarkonium one. It is then also discussed why the tetraquark assignment is favoured with respect to a loosely bound kaonic molecular interpretation of $a_{0}(980)$ and $f_{0}(980)$ mesons.
We reply to the preceding Comment by E. van Beveren et al., arXiv:0811.2589 [hep-ph].
Two-photon decays of light scalar mesons are discussed within the quarkonium and tetraquark asignements: in both cases the decay rate of the sigma resonances turns out to be smaller than 1 keV.
We investigate the implications of a tetraquark field on chiral symmetry restoration at nonzero temperature. In order for the chiral phase transition to be cross-over, as shown by lattice QCD studies, a strong mixing between scalar quarkonium and tetraquark fields is required. This leads to a light ($\sim0.4$ GeV), predominantly tetraquark state, and a heavy ($\sim1.2$ GeV), predominantly quarkonium state in the vacuum, in accordance with recently advocated interpretations of spectroscopy data. The mixing even increases with temperature and leads to an interchange of the roles of the originally heavy, predominantly quarkonium state and the originally light, predominantly tetraquark state. Then, as expected, the scalar quarkonium is a light state when becoming degenerate in mass with the pion as chiral symmetry is restored at nonzero temperature.
We calculate the pion-nucleon scattering lengths $a_{0}^{(\pm)}$ and the mass parameter $m_{0}$, which describes the nucleon mass in the chiral limit, at tree-level in the framework of a globally symmetric linear sigma model with parity-doubled nucleons. When recent lattice results [Takahashi] are used, we obtain $m_{0}\simeq300-600$ MeV. While $a_{0}^{(-)}$ is in fair agreement with experimental data, $a_{0}^{(+)}$ is too small because of the employed large scalar meson mass. This indicates the need to account for additional scalar degrees of freedom.
We study the line shapes of radiative $ϕ$-decays with a direct coupling of the $ϕ$ meson to the $f_{0}(980)$ and $a_{0}(980)$ scalar mesons. The latter couple via derivative interactions to $π_0 π_0$ and $π_0 η$, respectively. Although the kaon-loop mechanism is usually regarded as the dominant mechanism in radiative $ϕ$ decays, here we test a different possibility: we set the kaon-loop to zero and we fit the theoretical curves to the data by retaining only the direct coupling. Remarkably, satisfactory fits can be achieved, mainly due to the effects of derivative interactions of scalar with pseudoscalar mesons.
In this proceeding the emergence of a composite, adjoint-scalar field as an average over (trivial holonomy) calorons and anti-calorons is reviewed. This composite field acts as a background field to the dynamics of perturbative gluons, to which is coupled via an effective, gauge invariant Lagrangian valid for temperatures above the deconfinement phase transition. Moreover, also an Higgs mechanism is induced by the composite field: two gluons acquire a quasi-particle thermal mass. On the phenomenological side the composite field acts as a bag pressure which shows a linear dependence on the temperature. As a result the linear rise with temperature of the trace anomaly is obtained and is compared to recent lattice studies.