Asymptotic Regge trajectories of non-strange mesons

Abstract

We analyze the asymptotic behavior of Regge trajectories of non-strange mesons. In contrast to an existing belief, it is demonstrated that for the asymptotically linear Regge trajectories the width of heavy hadrons cannot linearly depend on their mass. Using the data on masses and widths of ρ J −− , ω J −− , a J ++ and f J ++ mesons for the spin values J ≤ 6, we extract the parameters of the asymptotically linear Regge trajectory predicted by the finite width model of quark gluon bags. As it is shown the obtained parameters for the data set B correspond to the cross-over temperature lying in the interval 170.9-175.3 MeV which is consistent with the kinetic freeze-out temperature of early hadronizing particles found in relativistic heavy ion collisions at and above the highest SPS energy.Unexpectedly, a strong argument in favor of linear asymptotic behavior of Regge trajectories of free hadrons was given in [9] by the exactly solvable statistical model for quark gluon (QG) bags [10]. This model is named the finite width model (FWM) since it accounts for finite width of QG bags. Quite generally, the FWM demonstrates that free QG bags of mass M r ≥ M 0 ≈ 2.5 GeV that belong to the continuous mass-volume spectrum of the Hagedorn type [11] should have the mean width Γ r ∼ √ M r . Such a behavior can be provided by the asymptotically linear Regge trajectory [8,9] only. Moreover, the FWM shows that such a behavior of mean width of QG bags, but with the temperature dependent coefficient, remains valid at high temperatures.The main purpose of this work is to extract the parameters of the asymptotic Regge trajectory predicted by the FWM using the experimental data. For our analysis we take the data of ρ J −− , ω J −− , a J ++ and f J ++ mesons which are known with the highest accuracy for J ≤ 6. In contrast to the usual analysis which is restricted by searching for a connection between spin and mass of the trajectory members, we use the full Regge trajectory in the complex s-plane. This allows us to simultaneously describe the masses and widths of involved mesons. Such a task is very important nowadays since a great significance of the width of heavy resonances or bags for the realistic equation of state of strongly interacting matter [9,10,12] and for a description of the fast equilibration process of heavy baryons/antibaryons [13,14,15] and kaons/antikaons [15] in relativistic heavy ion collisions was realized only recently. Also our analysis is necessary for further development of the string model of hadrons and for improvement of such transport codes as the hadron string dynamics [16] and the UrQMD model [17] by including the finite width of heavy resonances. In addition here we would like to demonstrate that a widely spread belief [14,15,18] that the width of heavy hadronic resonances linearly depends on their mass is simply inconsistent with an existence of linear Regge trajectories.The work is organized as follows. Section 2 contains a brief analysis of the asymptotic Regge trajectory properties which demonstrates t...

Non-Smooth Chemical Freeze-Out and Apparent Width of Wide Resonances and Quark Gluon Bags in a Thermal Environment

“…The FWM [16,17] is able to successfully describe a variety of the lattice QCD thermodynamics data [71][72][73] at vanishing baryonic chemical potential. Also its predictions for the Regge trajectories of non-strange and strange mesons [27] were successfully confirmed by the thorough analysis of both the real and the imaginary parts of the leading Regge trajectories [37] of ρ J −− , ω J −− , a J ++ and f J ++ mesons for the spin values J ≤ 6 and the ones of K * J P mesons of isospin 1 2 , parity P = (−1) J and spin values J ≤ 5. One of the most important predictions of the FWM [16,17] is that at vanishing baryonic chemical potential the QG bags are strongly suppressed (by a factor of fifteen-sixteen order of magnitude) In other words, according to the FWM [16,17] at √ s N N = 4.9 GeV the QG bags can be formed.…”

“…Before analyzing the hadronic mass spectrum in a thermal environment it is necessary to remind that the question of whether the experimental mass spectrum of hadrons given in the Particle Data Group tables coincides with the spectrum suggested by R. Hagedorn is of great interest nowadays [29][30][31]. However, almost all discussions of the hadron mass spectrum simply ignore the width of resonances, whereas long ago it was found that the large resonance width may essentially modify the spectrum [16][17][18][32][33][34][35][36][37]. Therefore, it is important to study the effective mass spectrum of hadrons having a physical width.…”

“…IG. 2: Photoabsorption cross sections on nuclei [37,38,9,40,41,42] FIG. 3: Nucleon spectral function in hot hadronic matter under RHIC conditions; solid line: "chemical freezeout" with T =180MeV, N =0.68 0 (µN =333MeV), µπ=0; dashed line: "thermal freezeout" with T =100MeV, N =0.12 0 (µN =531MeV) and µπ=96MeV; the dotted line indicates the location of the free nucleon mass.…”

Simple solution to the Strangeness Horn description puzzle

“…Furthermore, in [8] the estimates based on the Hagedorn mass spectrum inclusion were done without accounting for the large resonance width and without knowing the branching ratios of these hypothetical resonances. Although the mass dependence of width of heavy resonances was found within the finite width model of quark gluon bags [46,47] and recently it was successfully verified on the Regge trajectories of heavy mesons [48], the possible channels of their decays and the corresponding branching ratios are completely unknown yet. However, the more serious issue is that the finite width model [46,47] explains that the huge deficit of the empirical hadronic spectrum compared to the Hagedorn one is due to the fact that the 'missing' hadrons with the masses above 2.5 GeV and with the large width are the quark gluon bags, which are extremely suppressed (by fifteen-sixteen orders of magnitude) compared to the stable hadrons up to the temperatures of about half of the Hagedorn temperature.…”

Can We Rigorously Define Phases in a Finite System?

“…Recently, however, the importance of finite width of heavy/large quark gluon plasma bags was realized [21][22][23]. Both the theoretical estimates [22,23] and the analysis of the asymptotic Regge trajectories of non-strange mesons [37] indicate that the width of the quark gluon bag of the volume V with the mass M being heavier than M 0 ≈ 2.5 GeV is Γ = γ(T ) V V0 (here V ≥ V 0 = 1 fm 3 ). Since even at T = 0 the value γ(T = 0) ≈ 400 MeV is large, we conclude that the short life time t lif e (V ) = 1/Γ(V ) of such bags can, in principle, modify our conclusions about the metastable states λ n>0 .…”