arXiv subjects

M. Modugno

Publications and source records attributed to M. Modugno.

61 records · Page 4Linked to original sources

arXiv1998

Pseudoscalar and scalar meson masses at finite temperature

The composite operator formalism is applied to QCD at finite temperature to calculate the masses of scalar and pseudoscalar mesons. In particular the ratio of the sigma mass to the pion mass is an interesting measure of the degree of chiral symmetry breaking at different temperatures. We calculate the temperature T* at which M_sigma(T) < 2M_pi(T), above which the sigma partial width into two pions vanishes. We find T*=0.95T_c (where T_c is the critical temperature for the chiral phase transition), within the full effective potential given by the formalism. We find that an expansion a-la Landau of the effective potential around the critical point in the limit of small quark mass provides for a very good determination of T*.

hep-ph↗

arXiv1997

Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N

We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions at order 1/N, where N is the number of fermion species. We make use of a general formula valid for four-fermion theories, previously applied to the model in 1+1 dimensions. We consider both the discrete and continuous symmetry versions of the model. We show that the pion-like excitations give the dominant contribution at low temperatures. The range of validity for such pion dominance is analyzed. The complete analysis from low to high temperatures also shows that in the critical region the role of composite states is relevant, even for quite large N, and that the free-component behaviour at high T starts at about twice the mean field critical temperature.

hep-ph↗

arXiv1997

Corrections to the Pagels-Stokar Formula for f_π

Within the composite operator formalism we derive a formula for the pion decay constant $f_π$, as defined directly from the residue at the pion pole of the meson propagator, rather than from the matrix element of the axial current. The calculation is performed under some simplifying assumptions, and we verify the complete consistency with soft-pion results, in particular with the Adler-Dashen relation. The formula one obtains for (the pole-defined) $f_π^2$ differs from the previous Pagels-Stokar expression by an additive term, and it still provides $f_π^2$ in terms of the quark self-energy. We make some numerical estimates leading to $(30 ÷40)%$ deviation for $f_π^2$ with respect to the Pagels-Stokar formula.

hep-ph↗

arXiv1996

Low Temperature Dominance of Pion-like Excitations in the Massive Gross-Neveu Model at Order 1/N

We perform a 1/N-expansion of the partition function of the massive Gross-Neveu model in 1+1 dimensions. The procedure allows for the inclusion of the contribution of scalar and pseudoscalar composites (of order 1/N) to the equation of state. The naive expectation that the bosonic fluctuations correct significantly the mean field approximation at low temperatures is confirmed by our calculations. Actually the relevant degrees of freedom of hadronic matter at low temperatures are found to be pion-like excitations, rather than the fundamental constituents.

hep-ph↗

arXiv1996

1/N_c expansion for the partition function in four fermion models

We present a derivation of the bosonic contribution to the thermodynamical potential of four fermion models by means of a $1/N_c$-expansion of the functional integral defining the partition function. This expansion turns out to be particularly useful to correct the mean field approximation expecially at low temperatures, where the relevant degrees of freedom are low-mass bosonic excitations (pseudogoldstones).

hep-ph↗

arXiv1995

Disoriented Chiral Condensates: A Dynamical Simulation in the (2+1)-Dimensional Gross-Neveu Model

We simulate the formation and growth of disoriented chiral condensate (DCC) regions which follow the expansion of a high energy density region into the ``cold'' vacuum. The numerical study is based on the one-loop effective potential for the massive 2+1-dimensional Gross-Neveu model. We pay attention to the setting of the initial conditions and to determining which parameters are relevant for a strong amplification of the pion field. We find that the size of the ``hot'' source plays a significant role. For large enough source radii, we observe strong correlation phenomena, corresponding to the growth of large regions where the pion field oscillates along a given direction. We give our results in terms of the $θ$ angle which defines the DCC disorientation, of the other $O(4)$ angles distributions, of the local ratios $R_{a}=π_{a}^{2}/{\vecπ}^2$ $(a=1,2,3)$, and of the energies associated with the fields at representative times.

hep-ph↗

arXiv1994

Thermodynamics of the Massive Gross-Neveu Model

We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large $N$ limit is discussed bearing attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in $4-$dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pion like state.

hep-th↗