Techniques of dimensional regularization and the two-point functions of QCD and QED

The necessary and useful tools of dimensional regularization (and renormalization), the so-called ?-scheme, are reviewed. A survey on a comparison of various renormalization schemes is done. The applications of the ?-scheme to the two-point funtions of quantum chromodynamics (QCD) and quantum electrodynamics (QED) are given. In these applications it is shown explicitly how to compute Feynman diagrams and how to use the renormalization group equation (RGE) for the prediction of some terms induced by higher order diagrams. Some phenomenological uses of the two-point functions are briefly discussed. These include the quark mass, the spectral function sum rules in QCD and the control of the asymptotic SU(n)×SU(n) flavour chiral symmetry, the proton-neutron electromagnetic mass difference in the light of QCD and the running electromagnetic charge of QED. We also confront the operator product expansion (OPE) results of the anomalous dimension of non-singlet operators to the result obtained from the method of factorization of mass singularities.     

Phase transition of the two-dimensional classicalXY-model

The two dimensional classicalXY-model, representative for two dimensional models with continuous symmetry, is shown to undergo a phase transition of continuous order in a low temperature region. In particular: 1. The correlation functions decay with a power law at large distance in a temperature range belowT′ with a characteristic singular exponentη which varies continuously between 0 and ∞; 2. For magnetic fieldB → 0 the free energy develops a singular part in the form of a power with a singular exponentκ which varies continuously between 1 and ∞ atT _∞ (<T′); 3. The singular exponentsκ, η, and a correlation length exponent are related to one another by scaling laws and are determined by a dispersion coefficient for low lying excitations.     

Direct photon production beyond leading order in QCD

The significance of the quark-quark scattering process (quark+quark→quark+quark+photon) for the production of large-q_T real photons is discussed in the framework of perturbative QCD. To extract the finite contribution of this process to the differential cross section dσ/dy d²q_T (hadron 1+hadron 2→photon+anything) we define the gluon distribution and the quark-to-photon fragmentation function beyond the leading approximation. The calculations are performed consistently in the dimensional regularization scheme. Our numerical estimates show the resulting finite qq→qqγ contribution to be a small (order α_s/2π) correction in comparison with the basic QCD subprocesses.     

Newtonian versus Langevin dynamics: Example of ϕ4-model with infinite range interactions

The functional integral representation for the generating functional (GF) of the canonically averaged ensemble with an underlying Newtonian dynamics is obtained. It is shown that for this representation the non-linear fluctuation-dissipation theorem (NFDT) has the same form as for the Langevin dynamics case. This GF-representation is used for the investigation of the dynamics of the ϕ⁴-model with infinite range interactions at T > T_c. It is shown that the kinetic equation for the complete correlation function has the same form as for the Langevin dynamics case, which was considered before. All peculiarities of Newtonian dynamics are absorbed by one-particle (2-point and 4-point) correlator and response functions. The analysis of this equation shows that the 1/N-fluctuations (where N is the number of particles) restore the ergodicity of the system with the characteristicsrate τ⁻¹ ∼ μ²/N, where μ is a coupling constant.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

Decays of intermediate vector bosons,radiative corrections and QCD jets

We investigate decay properties of the intermediate vector bosons W^± and Z⁰. QED and QCD radiative corrections to leptonic and hadronic decay modes are calculated. Implications of the results for decay widths, branching ratios, determination of the number of neutrino species, e-μ-τ universality and properties of hadronic jets produced in W^± and Z⁰ decays are examined.     

Fully quantum treatment of the Landau-Pomeranchik-Migdal effect in QED and QCD

A rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given for the first time. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e ⁺ e ^? pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.     

QCD and QED corrections to the longitudinal polarization asymmetry

The interplay between QED and QCD corrections to the longitudinal polarization asymmetry,A _LR, ine ⁺ e ^?, annihilation is studied. It is found that measurements with hadronic final states will be well suited for precision tests of the standard model. QCD corrections to the asymmetry are particularly small on top of theZ ⁰, with the leading terms induced by quark mass effects. The influence of initial state radiation inA _LR is essentially accounted for by a slight shift in beam energy. Initial/final state QED bremsstrahlung interference (QED boxes) is studied in detail and its influence onA _LR is found to be negligibly small, especially close to the top of theZ ⁰ peak. A comment on the importance of helicity nonconservation for polarized beams in the presence of photon emission is also included.     

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T _?? = 152.9 ± 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T _?? defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result but is quite familiar for ordinary liquids at the supercritical temperatures.     

Axion emission from a hot plasma

We give the technics for the calculation of production and energy loss rates for axion-like particles (scalar or pseudo-scalar coupling to the gauge boson) from a hot QED (or QCD) heat bath. We compute the contribution coming from, the decay mode of a transverse to a longitudinal photon (or gluon). The energy loss rate for this process behaves asT ⁷. Considering the supernova SN1987A event, this behaviour could improve the upper bound on the coupling constant between asions and photons.     

Duality symmetry group of two dimensional heterotic string theory

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8,24) symmetry algebra generating an O(8,24) loop group. In this paper we study how various known discrete S- and T- duality symmetries of the theory are embedded in this loop group. This allows us to identify the generators of the discrete duality symmetry group of the two dimensional string theory.     

Aspects of UA (1) breaking in the Nambu and Jona-Lasinio model

The six-quark instanton induced ’t Hooft interaction, which breaks the unwanted U_A (1) symmetry of QCD, is a source of perturbative corrections to the leading order result formed by the four-quark forces with the U_L (3) × U_R (3) chiral symmetry. A detailed quantitative calculation is carried out to bosonize the model by the functional integral method. We concentrate our efforts on finding ways to integrate out the auxiliary bosonic variables. The functional integral over these variables cannot be evaluated exactly. We show that the modified stationary phase approach leads to a resummation within the perturbative series and calculate the integral in the “two-loop” approximation. The result is a correction to the effective mesonic Lagrangian which may be important for the low-energy spectrum and dynamics of the scalar and pseudoscalar nonets.     

On the theory of interacting fields in the Foldy-Wouthuysen representation

The overview is devoted to quantum electrodynamics (QED) and the Standard Model in the Foldy-Wouthuysen representation. The Hamiltonian H _FW in the form of a power series in charge e is obtained as applied to the electromagnetic interaction in the FW representation. Quantum electrodynamics in lowest-order perturbation theory is examined. Calculations of specific QED processes are presented. For external fermion lines (p _f ² = m ²), a possibility to expand the scattering matrix, in powers of the coupling constant with matrix elements, not including fermion propagators, is shown. To take into account particle-antiparticle interaction, a modification of the Foldy-Wouthuysen representation is proposed. Fermions in the modified FW representation can be in two states that are characterized by the sign of a third component of the isotopic spin T _f ³ . The sign of T _f ³ is connected with the sign at mass terms in the modified Hamiltonian H _FW. Real fermions (p _f ² = m _f ² ), as well as antifermions, can interact with each other, while real fermions with a given sign of T _f ³ can only interact with real antifermions with the opposite sign of T _f ³ , and vice versa. The formulation of the Standard Model in the FW representation does not necessarily require an interaction of Higgs bosons with fermions. In this approach, the role of Higgs bosons narrows considerably as they are responsible only for gauge invariance of the theory and interact only with gauge bosons. Quantum electrodynamics in the FW representation is invariant under C, P, and T transformations. Weak interaction does not conserve C and P parity, but conserves combined CP parity. The theory allows a connection of CP violation and total or partial violation of isotopic symmetry in the modified Foldy-Wouthuysen representation.     

Large-pT production of single and double photons in proton-proton and pion-proton collisions

Quantum chromodynamic (QCD) predictions are made for the large transverse momentum production of single and double photons in proton-proton, proton-antiproton, and pion-proton collisions. In π^?p collisions at center-of-mass energy W = 27.4 GeV and p_T = 4.0 GeV, it is estimated that about 0.3% of the 90° single photon triggers will be balanced on the “away-side” by a single photon with roughly the same transverse momentum. In π⁺p collisions this fraction drops to about 0.09%. These fractions increase with p_T. In addition to the pure QED annihilation term $\text{q}\text{q}\text{→γγ}$, it is found that the QCD-induced subprocess gg→γγ provides an important source of double photons. Photon bremsstrahlung contributions are also examined. Experimental study of the systematics of single and double photon production in hadron-hadron collisions will provide information on the size of the strong interaction coupling constant, α_s(Q), and on the charges of the quarks. Knowledge of the gluon distributions within hadrons and of the effective transverse momentum of partons in hadrons can also be gained.     

Infrared instability of QCD at finite temperatures

The infrared behaviour of the transversal gluon propagator in QCD at T≠0 is investigated within the ghost-free axial gauge. The singularities found in this propagator for the momentum p ～ g²T remain for any choice of the gauge and indicate the infrared instability of QCD at finite temperatures.     

Temperature Dependence of the CPN-1 Model and the Analogy with Quantum Chromodynamics

The two-dimensional CP^N-1 model — a simple field-theoretic analogue of four-dimensional quantum chromodynamics (QCD) — is analysed and reviewed. The major themes are the temperature dependence of the CP^N-1 model, and the analogy between CP^N-1 and QCD. A detailed treatment of the 1/N approximation of the CP^N-1 model is given. The main results emerging from this approximation are discussed at length. These are: asymptotic freedom, dimensional transmutation, confinement and topological charge nonquantization at zero temperature T = O, screening and topological charge quantization at finite temperature T. The analogy with QCD is explained in detail. A new, qualitative, analysis of the CP^N-1 model at finite temperature is introduced. This approach exploits the conformal invariance of the model to “heat” an arbitrary CP^N-1 field from T = O to finite temperature. This is achieved by conformal-transforming the flat Euclidean space-time of the T = O theory to the cylindrical space-time of the finite temperature theory.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

A test for the gluon selfcoupling in the reactionse + e −→4 jets andZ 0→4 jets

We consider the reactionse ⁺ e ^?→γ^*→4 jets andZ ^o→4 jets with the 4 jets coming in two pairs of essentially back to back jets of high and low energy. We calculate the angular distribution of the low energy jet axis with respect to the high energy jet axis in QCD, in an abelian gluon model “QED” and a phase space model (PS). Using simple helicity arguments we show that our angular distribution is very sensitive to the triple gluon coupling in QCD. This is then confirmed by a complete calculation. Our correlation offers, therefore, a direct test for QCD as a non-abelian gauge theory.     

QCD potentials with dynamical quarks at finite temperatures

We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition T_c are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z₃ symmetry in the fermionic action for T<T_c and by an additional spontaneous Z₃ symmetry breaking for T<T_c.