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For temperatures below (above) $^{T}$± = $^{c}$± T$_{H}$ (0 $^{< c}$± < 1) the most probable mass is negative (positive) and the spectrum (1) defines the low (high) temperature pressure p − ( p $^{+}$) 

<img src='content_image/381414.jpg'>

There are two remarkable facts concerning the low tem- perature pressure. First, for 〈 m 〉 ≤ 0 the resulting mass attenuation of the integrand in (1) decreases at fixed bag volume so rapidly that the only vicinity of M$_{0}$ contributes into the mass-volume spectrum. In other words, in this regime all heavy QGP bags are extremely suppressed and as a result only the smallest bags with the mass M$_{0}$ and the width about Γ( V$_{0}$ ) can contribute into the spectrum (1) [8]. Consequently, such QGP bags would not be distinguishable from the usual low-mass hadrons. Such a regime leads to the subthreshold suppression of the QGP bags at low temperatures even in finite systems and, hence, is able to explain the absence of heavy/large QGP bags and strangelets for $^{T < T}$± . Second, for the non-vanishing functions γ and B at low 

temperatures, i.e. γ$_{0}$ = γ ( T = 0) > 0 and B$_{0}$ = B ( T = 0) > 0, the QGP pressure at such temperatures should be negative and linear in temperature p − ( T → 0) ≈ − T B 2 0 2 γ 2 $_{0}$. Such a linear T -behavior of the QGP pressure at low temperatures, p$_{QGP}$ = σ$_{p}$T 4 − A$_{1}$T , is known for a long time [21] and was reported by several groups (see [9] for details). Using this fact and matching p + with p$_{QGP}$ it was possible to estimate the resonance width coefficient γ and the mass density B from the lattice QCD data [9] 

<img src='content_image/381410.jpg'>

where 3 σ$_{p}$ is the Stefan-Bolzmann constant of the QGP. Eqs. (11) and (12) allow one to determine $^{T}$± = 0 . 5 T$_{H}$ and show that the resonance width at zero temperature very weakly depends on the number of elementary de- grees of freedom in QGP, but strongly depends on the cross-over temperature T$_{co}$ 

where the constant C$_{γ}$ , depending on number of color and flavor states of QGP, varies between 1 . 22 and 1 . 3 [9]. The minimal width of the QGP bags strongly increases with temperature. For instance, at Hagedorn tempera- ture one obtains Γ$_{R}$( V$_{0}$, T = T$_{H}$ ) = √$_{12 Γ}$$_{R}$$_{(}$$_{V}$$_{0}$$_{, T}$ = 0). Therefore, for T$_{co}$ ∈ [170; 200] MeV the minimal width of the QGP bags is Γ$_{R}$( V$_{0}$, T = 0) ∈ [400; 600] MeV and Γ$_{R}$( V$_{0}$, T = T$_{H}$ ) ∈ [1400; 2000] MeV. These estimates clearly show us that, even without the subthreshold sup- pression, the heavy/large QGP bags cannot be directly observed at any temperature due to very short life-time. 

<img src='content_image/381413.jpg'>

Also one of the most remarkable features of the FWM is that its mass dependence of a mean resonance width can help to determine the Regge trajectories of QGP bags and to resolve a few problems related to them. 

## III. ASYMPTOTIC TRAJECTORIES OF QGP BAGS 

Nowadays there is great interest in the behavior of the Regge trajectories of higher resonances in the con- text of the 5-dimensional string theory holographically dual to QCD [20] which is known as anti-de-Sitter space/conformal field theory (AdS/CFT). However, as was mentioned earlier, the Regge trajectories are widely understood only as the linear relation between the reso- nance mass square and resonance spin or radial quantum number. We would like to determine the full Regge tra- jectories of QGP bags. In our analysis we follow Ref. [3] which is based on the following most general assump- tions: (I) α ( S ) is an analytical function, having only the physical cut from S = S$_{0}$ to S = ∞ ; (II) α ( S ) is polyno- mially restricted at the whole physical sheet; (III) there exists a finite limit of the phase trajectory at S → ∞ . Us- ing these assumptions, it was possible to prove [3] that for S → ∞ the upper bound of the Regge trajectory asymptotics at the whole physical sheet is 

where the function g 2 u > 0 should increase slower than any power in this limit and its phase must vanish at | S | → ∞ . On the other hand, in Ref. [3] it was also shown that, 

if in addition to (I)-(III) one requires that the transition amplitude T ( s, t ) is a polynomially restricted function of S for all nonphysical t > t$_{0}$ > 0, then the real part of the Regge trajectory does not increase at | S | → ∞ and the trajectory behaves as 

where g 2 l > 0 and C$_{l}$ are some constants. Moreover, (15) defines the lower bound for the asymptotic behavior of the Regge trajectory [3]. The expression (15) is a generalization of a well known Khuri result [2]. It means that for each family of hadronic resonances the Regge poles do not go beyond some vertical line in the complex spin plane. In other words, it means that in asymptotics S → + ∞ the resonances become infinitely wide, i.e. they are moving out of the real axis of the proper angular momentum J and, therefore, there is only a finite number of resonances in the corresponding transition amplitude. 

To compare the FWM results with the trajectories (14) and (15) we need to relate the mass and width of QGP bags, since they are independent variables in this model. Nevertheless, this can be done for their averaged values. 

To illustrate this statement, let’s recall our result on the mean Gaussian width of the free bags averaged with 

<img src='content_image/381411.jpg'>

<img src='content_image/381412.jpg'>

