Evolution of Critical Correlations at the QCD Phase Transition

We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the distribution of isoscalar particles (sigmas) in configuration space. Non-equilibrium dynamics is induced through a sudden symmetry breaking leading gradually to the deformation of the initial fractal geometry. After constructing an ensemble of configurations describing the initial state of the isoscalar field we solve the equations of motion and show that remnants of the critical state and the associated fractal geometry survive for time scales larger than the time needed for the mass of the isoscalar particles to reach the two-pion threshold. This result is more transparent in an event-by-event analysis of the phenomenon. Thus, we conclude that the initial fractal properties can eventually be transferred to the observable pion-sector through the decay of the sigmas even in the case of a quench.

PROPAGATOR POLES AND AN EMERGENT STABLE STATE BELOW THRESHOLD: GENERAL DISCUSSION AND THE E(38) STATE

In the framework of a simple quantum field theory describing the decay of a scalar state into two (pseudo)scalar ones we study the pole(s) motion(s) of its propagator: besides the expected pole on the second Riemann sheet, we find — for a large enough coupling constant — a second, additional pole on the first Riemann sheet below threshold, which corresponds to a stable state. We then perform a numerical study for a hadronic system in which a scalar particle couples to pions. We investigate under which conditions a stable state below the two-pion threshold can emerge. In particular, we study the case in which this stable state has a mass of 38 MeV, which corresponds to the recently claimed novel scalar state E(38). Moreover, we also show that the resonance f0(500) and the stable state E(38) could be two different manifestations of the same "object". Finally, we also estimate the order of magnitude of its coupling to photons.

FORWARD PHYSICS AT THE LHC: ELASTIC SCATTERING

The following effects in the nearly forward ("soft") region of the LHC are proposed to be investigated: • At small |t| the fine structure of the cone (Pomeron) should be scrutinized: (a) a break of the cone near t ≈ -0.1 GeV 2, due to the two-pion threshold, and required by t-channel unitarity, and (b) possible small-period oscillations between t = 0 and the dip region. • In measuring the elastic pp scattering and total pp cross-section at the LHC, the experimentalists are urged to treat the total cross-section σt, the ratio ρ of real to imaginary part of the forward scattering amplitude, the forward slope B and the luminosity [Formula: see text] as free parameters, and to publish model-independent results on dN/dt. • Of extreme interest are the details of the expected diffraction minimum in the differential cross-section. Its position, expected in the interval 0.4 < -t < 1 GeV 2 at the level of about 10-2 mb · GeV -2–10-1 mb · GeV -2, cannot be predicted unambiguously, and its depth, i.e. the ratio of dσ/dt at the minimum to that at the subsequent maximum (about -t = 5 GeV 2, which is about 5) is of great importance. • The expected slow-down with increasing |t| of the shrinkage of the second cone (beyond the dip-bump), together with the transition from an exponential to a power decrease in -t, will be indicative of the transition from "soft" to "hard" physics. Explicit models are proposed to help in quantifying this transition. • In a number of papers a limiting behavior, or saturation of the black disk limit (BDL), was predicted. This controversial phenomenon shows that the BDL may not be the ultimate limit, instead a transition from shadow to antishadow scattering may by typical of the LHC energy scale.