What lattice calculations can tell us about the gluon gas

Higher order perturbative and nonperturbative corrections to the grand potential of hot QCD are considered qualitatively Comparing with lattice results, it is argued that the nonperturbative parts are small but that the O(g⁴) term in $\text{Ω}$ is large and positive.     

The Wigner Band Random Matrix Model: Studied from the View Point of a Generalization of Brillouin- Wigner Perturbation Theory

The Wigner band random matrix model is studied by making use of a generalization of Brillouin-Wigner perturbation theory. Energy eigenfunctions are shown to be divided into perturbative and nonperturbative parts. A relation between the average shape of eigenstates and that of the so-called local spectral density of states (LDOS) is derived by making use of some properties of energy eigenfunctions drawn from numerical results. Several perturbation strengths predicted by the perturbation theory are found to play important roles in the variation of the shape of the LDOS with perturbation strength.     

Variation on finite energy sum rules: Vacuum matrix elements

New finite energy sum rules for light quark systems are derived in QCD, which express nonperturbative vacuum matrix elements of a given dimension in terms of the spectral function and its derivatives. A phenomelogical definition of nonperturbative effects is proposed.     

Long-distance effects on the \mathrm{B}\to X_{\mathrm{s}}\gamma photon energy spectrum

We compute long-distance effects on the photon energy spectrum in inclusive radiative decays of B mesons using light-cone expansion and heavy-quark effective theory. We show that for sufficiently high photon energy, the leading nonperturbative QCD contribution is attributed to the distribution function. The distribution function is found to be universal in the sense that the same distribution function also encodes the leading nonperturbative contribution to inclusive semileptonic decays of B mesons at large momentum transfer. Some basic properties of the distribution function are deduced in QCD. Ways of extracting the distribution function directly from experiment and their implications are discussed. The theoretically clean methods for the determination of are described. Received: 7 June 1999 / Published online: 14 October 1999     

Perturbative and nonperturbative parts of eigenstates and local spectral density of states: the wigner-band random-matrix model

The Wigner-band random-matrix model is studied by making use of a generalization of Brillouin-Wigner perturbation theory. Energy eigenfunctions are shown to be divided into perturbative and nonperturbative parts. Several perturbation strengths predicted by the perturbation theory are found to play important roles in the variation of the shape of the local spectral density of states with perturbation strength.     

Determination of the mass spectrum of the bound state in the framework of the relativistic hamiltonian approach

We propose one a variant of calculation of the energy spectrum of bound state systems with relativistic corrections. In the framework of quantum field theory, an expression that takes into account relativistic corrections to the mass of the bound state with a known nonrelativistic pair interaction potential is proposed on the basis of calculating the asymptotic behavior of correlation functions of the corresponding field currents with the necessary quantum numbers. Excluding the time variables allows one to determine nonperturbative corrections to the interaction potential. The following results have been obtained in the framework of this approach. The nonperturbative corrections arising due to the relativistic nature of a system to the interaction Hamiltonian are determined. The dependence of the constituent mass of bound-state forming particles on the free state mass and on the orbital and radial quantum numbers is analytically derived. The energy level shift of muonic hydrogen taking into account relativistic corrections is calculated. The energy spectrum of a wide class of potentials that describe the Coulomb bound state is analytically derived with relativistic corrections. The mass spectrum of the glueballs and the constituent masses of the gluons are analytically calculated taking into account spin-orbit, spin—spin, and tensor interactions. Our numerical results have shown very good agreement with the lattice data. Taking into account nonperturbative and nonlocality characters of interactions, the mass spectrum of the mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only taking into account the nonperturbative and the nonlocal characters of interactions. The dependences of the constituent masses of constituent particles on the masses of a free state are certain. When quarks are light, then the difference between current and valent masses of quarks is greater than valent masses of quarks, and when quarks are heavy, then the difference between these masses is insignificant. One of the alternative variants of taking nonlocality into account has been suggested for the definition of properties of hadrons at large distances. The dependence of the constituent masses of constituent particles on the radius of confinement is determined.     

Mapping the proton unintegrated gluon distribution in dijets correlations in real and virtual photoproduction at HERA

We discuss how the dijet azimuthal correlations in DIS and real photoproduction at HERA probe the differential (unintegrated) gluon distribution in the proton. We find a strong dependence of the azimuthal correlation pattern on Bjorken-x, photon virtuality and the cut on the jet transverse momenta. A rise of the azimuthal decorrelations is observed with decreasing Bjorken-x due to the interplay of perturbative and nonperturbative effects. We predict a strong rise of the same-side jet rate with photon energy for real photoproduction. We discuss conditions for the correlation function to be dominated by hard perturbative gluons and ways of constraining the size of the nonperturbative soft component. We make some predictions for the THERA energy range. The analysis of the energy dependence of the isolated jet and two-jet cross sections in photoproduction would be a new way to study the not yet well constrained unintegrated gluon distributions and to explore the onset of the pQCD regime.     

On the Grand Canonical Gibbs Ensemble in Euclidean Field Theory

By generalizing the integration by parts formula on the function space, the isomorphism between the general class of selfinteracting Euclidean, Bose fields and classical gases is proven in a nonperturbative way. Rigorous, non-perturbative derivations of the Mayer equations and Bogoliubov-Born-Kirkwood-Grenn-Yvone hierarchical equations are given. Expansions of several physical quantities are discussed in terms of the linear graphs, for some general classes of Euclidean fields.     

SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond–Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.     

Instanton effects in quark form factor and quark-quark scattering at high energy

The nonperturbative effects in the high-energy processes involving strongly interacting particles are studied within the instanton liquid model of the QCD vacuum (ILM) by using the Wilson integral framework. The detailed analysis of nonperturbative contributions to the electromagnetic quark form factor is presented considering the structure of the instanton-induced effects in the evolution equation describing the high energy behavior of the form factor. It is shown that the instantons yield in high energy limit the logarithmic corrections to the amplitudes which are exponentiated in small instanton density parameter. By using the Gaussian interpolation of the constrained instanton solution, we show that the all-order multi-instanton contribution is well approximated by the weak field limit result. The role of the instantons in high energy diffractive quark-quark scattering, in particular, in formation of the soft Pomeron, is also considered. We show that within the ILM the C-odd diffractive amplitude is suppressed as 1/s compared to the C-even one. The further applications of the developed approach in studying the nonperturbative effects in high energy hadronic processes are briefly discussed.     

Nonperturbative model of hot <Emphasis Type="Italic">SU</Emphasis>(2) gluodynamics

A hot-gluodynamics model based on taking consistently into account nonperturbative fluctuations of the gluon field in the temperature-deconfining phase is proposed. In order to perform averaging over nonperturbative fields, the gluon system (partition function) is broken down into a fast and a slow subsystem. In one of these subsystems, nonperturbative fields play the role of rapidly changing (stochastic) degrees of freedom, whose effect on soft gluons is considered within the cluster-expansion method for Green’s functions in the nonperturbative background field. The effect of long-wavelength chromomagnetic fluctuations on hard gluons is studied within adiabatic perturbation theory in the strong-field approximation. The pressure and the energy density of SU(2) gluon matter are calculated for T > T _c .     

Magnetic moments of octet baryons in a chiral potential model

Incorporating the lowest-order pionic correction, the magnetic moments of the nucleon octet have been calculated in a chiral potential model. The potential, representing phenomenologically the nonperturbative gluon interactions including gluon self-couplings, is chosen with equally mixed scalar and vector parts in a power-law form. The results are in reasonable agreement with experiment.     

Breaking of scale invariance in the presence of instantons

The instanton tunnelling amplitude induces a nonperturbative violation of scale invariance which can be understood in terms of the anomaly in the trace of the stress energy tensor. The scaling violation determined by the trace anomaly is compared with the explicitly constructed instanton amplitude in the one-loop approximation.     

对单胶子交换势的非微扰修正研究

对单胶子交换势的非微扰修正进行了系统研究,结果表明,要获得规范不变的修正形式,QCD真空胶子场必须取为协变规范.在协变规范下,给出了单胶子交换势的非微扰修正的新形式.     

Cumulant t-Expansion for Strongly Correlated Electrons on a Lattice

Journal of Experimental and Theoretical Physics - A systematic nonperturbative scheme for calculating the ground state energy is adapted for studying systems of strongly correlated electrons on a...     

A variational approach to bound states in quantum field theory

We consider here in a toy model an approach to bound state problem in a nonperturbative manner using equal time algebra for the interacting field operators. The potential is replaced by offshell bosonic quanta inside the bound state of nonrelativistic particles. The bosonic dressing is determined through energy minimisation, and mass renormalisation is carried out in a nonperturbative manner. Since the interaction is through a scalar field, it does not include spin effects. The model however nicely incorporates an intuitive picture of hadronic bound states in which the gluon fields dress the quarks providing the binding between them and also simulate the gluonic content of hadrons in deep inelastic collisions.     

Nonperturbative shell correction to the Bethe-Bloch formula for the energy losses of fast charged particles

A simple method including nonperturbative shell corrections has been developed for calculating energy losses on complex atoms. The energy losses of fast highly charged ions on neon, argon, krypton, and xenon atoms have been calculated and compared with experimental data. It has been shown that the inclusion of the non-perturbative shell corrections noticeably improves agreement with experimental data as compared to calculations by the Bethe-Bloch formula with the standard corrections. This undoubtedly helps to reduce the number of fitting parameters in various modifications of the Bethe-Bloch formula, which are usually determined semiempirically.     

Decaying cosmological parameter in the early universe from NKK theory of gravity

Using a formalism recently introduced we study the decaying of the cosmological parameter during the early evolution of an universe, whose evolution is governed by a vacuum equation of state. We use a stochastic approach in a nonperturbative treatment of the inflaton field from a Noncompact Kaluza–Klein (NKK) theory, to study the evolution of energy density fluctuations in the early universe.     

Nonanalyticity of the perturbative expansion for super-renormalizable massless field theories

The complete infrared expansion of Feynman amplitudes is established at any dimension d. The so called infrared finite parts develop poles at rational d. We prove a conjecture by Parisi by constructing an infrared subtraction procedure which defines finite amplitudes in such dimensions. The corresponding counterterms are associated to nonlocal operators and are generated in a nonperturbative way for super-renormalizable theories. We determine at all orders the perturbative expansion which contains powers and logarithms of the coupling constant.     

Solution of the Balitzkij-Fadin-Kuraev-Lipatov Equation in the Low Q2 Region

The Balitzkij-Fadin-Kuraev-lipatov equation including the nonperturbative contribution is studied by using the characteristic method. The results show that the nonperturbative contribution is very important in the low Q₂ region.