Abstract:We obtain the constraints on the ruling parameters of the dense hadronic gas model at the critical temperature and propose the quasiuniversal ratios of the thermodynamic quantities. The possible appearence of thermodynamical instability is discussed.
“…At small T the effect, of course, is striking. One observes further that the minimum mass obtained from thermodynamics is now almost equal to the one from direct computation in (19) and that T c is only 10% above the temperature at which p = 0. Due to this closeness the derivatives are also larger and the peak in interaction measure even sharper.…”
Section: Fit Of Parameters and Their X F Dependencementioning
confidence: 73%
“…where ρ 0 is a dimensionless number. The degeneracy factor N 2 f of the m = 0 Goldstone bosons and the massive flavor nonsinglet states was factored out from (19). For the massive states with m > m 0 , we assume an exponential Hagedorn spectrum together with a power of m. Using this spectrum we get for the scaled hadron gas pressurê…”
Section: The Pressure At Low Temperature Modelled As a Hadron Gasmentioning
confidence: 99%
“…Some examples are as follows: Ref. [16] computes ρ(m) in the bag model, [17] writes "confining phase is consistent with effective string theory in which conformal symmetry and modular invariance play a significant role", [18] for the first time discusses a separate density for mesons and baryons, but believes that they should be equal to exponential accuracy, [19] tries to connect hadronic and plasma phases like here, [20]- [22] believes that the mesonic and baryonic densities should be different and fits both of them, [24] doubts the empirical validity of the exponential mass spectrum and [25] updates mass spectrum fits and includes the chemical potential in the hadron gas discussion. From all the work on ρ(m) it is obvious that there is no unique parametrisation for it.…”
Section: The Pressure At Low Temperature Modelled As a Hadron Gasmentioning
confidence: 99%
“…As a second step, the right panel of Fig. 5 shows numerical results for the 2nd log T derivative of the scaled pressure solution ( 35) of ( 28) at T 0 = 0.5 but now integrated over the exponential mass spectrum (19) ρ(m, b, a, m 0 ). A large negative value of a is needed, here a = −10.…”
Section: Third Order Transition With Excluded Volume Correctionsmentioning
confidence: 99%
“…The hadronic pressure will then vanish at T = 0. To see what this implies quantitatively, take the hadron mass spectrum in (19), use the toy model parameters in (26) and replace δ(m) → δ(m − m gb ) with m gb = 0.5 ≈ T c . The argument here is that for physical QCD T c is close to m π .…”
Section: Fit Of Parameters and Their X F Dependencementioning
We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit (N c → ∞, N f → ∞ with x f = N f /N c fixed) and calculate one string-loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions it may even become of third order. Operationally these computations imply modelling the low temperature chiral symmetry breaking phase with a hadron gas containing N 2 f massless Goldstone bosons and an exponential spectrum of massive hadrons. A third order transition is possible only if repulsive hadron interactions via the excluded volume effect are included.
“…At small T the effect, of course, is striking. One observes further that the minimum mass obtained from thermodynamics is now almost equal to the one from direct computation in (19) and that T c is only 10% above the temperature at which p = 0. Due to this closeness the derivatives are also larger and the peak in interaction measure even sharper.…”
Section: Fit Of Parameters and Their X F Dependencementioning
confidence: 73%
“…where ρ 0 is a dimensionless number. The degeneracy factor N 2 f of the m = 0 Goldstone bosons and the massive flavor nonsinglet states was factored out from (19). For the massive states with m > m 0 , we assume an exponential Hagedorn spectrum together with a power of m. Using this spectrum we get for the scaled hadron gas pressurê…”
Section: The Pressure At Low Temperature Modelled As a Hadron Gasmentioning
confidence: 99%
“…Some examples are as follows: Ref. [16] computes ρ(m) in the bag model, [17] writes "confining phase is consistent with effective string theory in which conformal symmetry and modular invariance play a significant role", [18] for the first time discusses a separate density for mesons and baryons, but believes that they should be equal to exponential accuracy, [19] tries to connect hadronic and plasma phases like here, [20]- [22] believes that the mesonic and baryonic densities should be different and fits both of them, [24] doubts the empirical validity of the exponential mass spectrum and [25] updates mass spectrum fits and includes the chemical potential in the hadron gas discussion. From all the work on ρ(m) it is obvious that there is no unique parametrisation for it.…”
Section: The Pressure At Low Temperature Modelled As a Hadron Gasmentioning
confidence: 99%
“…As a second step, the right panel of Fig. 5 shows numerical results for the 2nd log T derivative of the scaled pressure solution ( 35) of ( 28) at T 0 = 0.5 but now integrated over the exponential mass spectrum (19) ρ(m, b, a, m 0 ). A large negative value of a is needed, here a = −10.…”
Section: Third Order Transition With Excluded Volume Correctionsmentioning
confidence: 99%
“…The hadronic pressure will then vanish at T = 0. To see what this implies quantitatively, take the hadron mass spectrum in (19), use the toy model parameters in (26) and replace δ(m) → δ(m − m gb ) with m gb = 0.5 ≈ T c . The argument here is that for physical QCD T c is close to m π .…”
Section: Fit Of Parameters and Their X F Dependencementioning
We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit (N c → ∞, N f → ∞ with x f = N f /N c fixed) and calculate one string-loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions it may even become of third order. Operationally these computations imply modelling the low temperature chiral symmetry breaking phase with a hadron gas containing N 2 f massless Goldstone bosons and an exponential spectrum of massive hadrons. A third order transition is possible only if repulsive hadron interactions via the excluded volume effect are included.
The free energy analyzed in the framework of the quantum field theory in conjunction with the statistical model for a [Formula: see text] meson is found to undergo an expansion in the condensate wave function. The superconducting and fractal properties of the meson are found to originate from the branch-cut type of singularity in the wave function of the model in which the gauge symmetry breaking is manifest.
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