Non-perturbative Region Research Articles

STRONG COULOMB COUPLING IN RELATIVISTIC QUANTUM CONSTRAINT DYNAMICS

We study, in the framework of relativistic quantum constraint dynamics, the bound state problem of two oppositely charged spin 1/2 particles, with masses m1 and m2, in mutual electromagnetic interaction. We search for the critical value of the coupling constant α for which the bound state energy reaches the lower continuum, thus indicating the instability of the heavier particle or of the strongly coupled QED vacuum in the equal mass case. Two different choices of the electromagnetic potential are considered, corresponding to different extensions of the substitution rule into the nonperturbative region of α: (i) the Todorov potential, already introduced in the quasipotential approach and used by Crater and Van Alstine in Constraint Dynamics; (ii) a second potential (potential II), characterized by a regular behavior at short distances. For the Todorov potential we find that for m2>m1 there is always a critical value αc of α, depending on m2/m1, for which instability occurs. In the equal mass case, instability is reached at αc=1/2 with a vanishing value of the cutoff radius, generally needed for this potential at short distances. For potential II, on the other hand, we find that instability occurs only for m2>2.16 m1.

Classical and quantum coherent state description of NN-bar annihilation at rest in the Skyrme model with omega mesons.

We model the $N\bar{N}$ system at rest as a baryon number zero lump in the Skyrme model including the $\omega$ field. We integrate the classical equations of motion from the highly non-perturbative annihilation region into the non-interacting radiation zone. Subsequent coherent state quantization of the radiation field gives a good description of the pion spectrum from annihilation at rest.

Study of hard scattering processes in multihadron production from ?? collisions at LEP

The production of multihadronic states in γγ collisions at LEP has been studied with the DELPHI detector. The analyzed data correspond to an integrated luminosity of about 32pb−1, collected in the LEP runs of 1990–1992. Minimum bias data and a sample of events with jets at highpT have been selected under the requirement that no scattered electron or positron is observed. The two data sets have been compared to Monte Carlo predictions. The non-perturbative contribution described by the vector meson dominance Model and direct\(q\bar q\) production from pointlike photons described by the quark parton model were found to be insufficient to reproduce the data. It has been necessary to include a third interaction component, which is due to perburbative hard scattering of the partonic constituents of the photon. Several parametrisations of the quark and gluon densities of the photon have been tested. The interplay with the cut in jet transverse momentum, which is necessary for the separation of the perturbative and non-perturbative regions, is discussed. The data favour parametrisations with rather soft partonic content of the photon.

Dissipative processes in an expanding massive gluon gas

The temperature dependence of the kinetic coefficients is obtained in the nonperturbative region with the help of Green-Kubo-type formulae in the model of massive gluon gas motivated by numerical results from simulations of lattice QCD. The entropy production rate is estimated using scaling hydrodynamics. It is shown that the increase in the viscosity coefficients leads to entropy generation in heavy ion collision processes which could be big, especially for temperatures close to the critical one.

The renormalization group in the local potential approximation and its applications to the O ( n) model

In the local potential approximation, the renormalization group is reduced to a semi-linear parabolic partial differential equation. We study the general properties ofthe equation and in particular we show that the flow is the gradient of a scalar function. Then, we apply this approximation to the O ( n) model and solve the equation numerically. The critical exponents in three dimensions are found to agree with the best known values. In two dimensions, we obtain asymptotic freedom for all values of n. We also study the flow in non-perturbative regions, where first-order transition occurs.

Solution of the GLR equation in the nonperturbative region

We discuss solutions to the nonlinear GLR evolution equations in the nonperturbative part of the low- x B region. A new definition of the critical line is obtained, and we conclude that there is only one solution which matches the perturbative Gribov-Lipatov-Altarelli-Parisi evolution.

Solutions to the Gribov-Levin-Ryskin equation in the nonperturbative region

We discuss solutions to the nonlinear GLR evolution equations in the nonperturbative part of the low- x B region. A new definition of the critical line is obtained, and we conclude that there is only one solution which matches the perturbative Gribov-Lipatov-Alterelli-Parisi evolution.

Gluon gas viscosity in the nonperturbative region

Using the Green-Kubo-type formula and the cut-off model motivated by Monte Carlo lattice gluodynamics simulations we find the temperature behaviour of the shear viscosity for a gluon gas in the region of the deconfinement phase transition.

Intermediate Range Force Contributions to Dynamical Chiral Symmetry Breaking in QCD11The project supported by National Natural Science Foundation of China

We propoee the intermediate range QCD force singular like by analysing the gluon propagator in the nonperturbative region from QCD sum rules. With the help of the Slavnov-Taylor-Ward identity we derive the equations for the nonperturbative quark propagator from the Schwinger-Dyson (SD) equation. Solutions for the quark propagator in two special cases are given. We find that the intermediate range force is also responsible for the chiral symmetry breaking in QCD.

Path integral for Yang-Mills theory in a non-perturbative region

The choice of physical variables in gauge theories is discussed. It is shown that the quantum description is independent of the choice of physical degrees of freedom if the physical variables are considered to be curvelinear in the path integral approach. Then, the conventional path with a gauge condition is modified. The path integral found is used for the quantum description of the Yang-Mills fields with an ambiguous gauge (Gribov's problem).

Resummation of the QCD perturbative series for hard processes

We study the region of inhibited radiation in hard hadronic processes, as for jet cross sections and heavy flavour production near threshold. The cases of deep inelastic scattering and Drell-Yan annihilation are explicitly considered. A general method to exponentiate leading and next-to-leading logarithms to all orders in perturbation theory is developed. A complete formula for the large N-moments is given and shown to agree with previous two-loop calculations. The resummation procedure suggests how to connect the perturbative and nonperturbative regions. The natural limit within the perturbative phase is shown to be the intrinsic transverse momentum.

Spectrometry of quark states in QCD and roots for effective lagrangians

The mass-like asymmetry of the quark spectrum in the gluon vacuum is investigated. The meaning of the spectral density for quark states is clarified and its connection with the gluon condensate is established. The concept of a non-perturbative low-energy region is applied to stabilize the low-energy fermion vacuum. The exact equation for the averaged quark spectrum is derived. It reveals the non-perturbative features of the dynamical quark mass.

Model of dynamical breaking of chiral symmetry and quark condensate

In the framework of the model proposed earlier to describe QCD in the nonperturbative region it is shown that the presence of a 1/k/sup 4/ singularity in the gluon propagator leads to dynamical breaking of the chiral symmetry and the occurrence of the quark condensate. A value of the quark condensate close to the phenomenological value is obtained.

Perturbative QCD effects in the non-perturbative low energy region

We show that a large body of phenomena in p p annihilation into hyperons, or into three mesons containing a pair of strange quarks, as well as K-P scattering with production of a strange quark pair (like K −p→ΦΛ), can be understood as a simple consequence of perturbative QCD dynamics. We give detailed predictions for ratios of cross section, poolarizations and some selection rules. When measured the predictions are well satisfied. LEAR experiments are indicated.

Spontaneous chiral symmetry breaking in particle physics

The effective potential for q q condensation is examined also taking account of contributions from the non-perturbative region. An electronic computer is used to solve the nonlinear differential equation. We reach the conclusions that contributions from the non-perturbative region play an important role in explaining spontaneous chiral symmetry breaking quantitatively, and that effective coupling should be strong to some extent in the non-perturbative region.

Renormalization group and infrared behavior of quantum chromodynamics

A diagrammatic implementation of the generalized renormalization group is developed and used to study the infrared divergences of the photon-quark-quark amplitude in quantum chromodynamics. The leading-log result is simply obtained. We show that nonleading terms cause no qualitative change and that the leading-log result is accurate down to the nonperturbative region. The infrared behavior of QED is discussed as a pedagogical example.

Effect of Intensity on Multiphoton Ionization

For multiphoton processes, the higher-order terms of the perturbation series are treated by summing the class of irreducible diagrams. This allows the examination of the behavior of the cross section as a function of the incident photon flux at arbitrarily large intensities by means of analytic continuation to the nonperturbative region. The case of four-photon ionization of the ground state of hydrogen is discussed as an example.