Two-loop two-point functions with masses: asymptotic expansions and Taylor series,in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and smallq ², ind dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Padé approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for alld, and achieve highly accelerated convergence of its expansions in powers ofq ²/m ² orm ²/q ², ford=4.     

Baryon spectrum and the forces between quarks

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp _T ” in phenomenological applications of perturbative QCD.     

Quantum chromodynamics on the mass shell

I prove that in covariant gauges quark and gluon mass-shell renormalization constants obey Ward identities analogous to those of QED: Z₁ = Z₂ and Z₄ = Z₃. This implies that the mixing of ultraviolet and infrared singularities is not a peculiarity of dimensional regularization but a consequence of the Ward identities.     

Infrared singularities in the dimensional regularization scheme

Infrared singularities arising in some renormalized amplitudes of quantum electrodynamics are analyzed using the dimensional regularization method. We define infrared and ultraviolet convergent regions in the ν complex plane (ν is the number of dimensions of space time). It turns out that these regions do not overlap for quantum electrodynamics. Nevertheless, it is shown that there exists a unique analytic continuation from the infrared convergent region which allows us to interpret the infrared divergence in the renormalized electron self-energy amplitude as an isolated singularity at ν = 4. This statement seems to be true at all orders of perturbation theory. We also prove that the double limit μ → 0, ν → 4 (μ is the auxiliary photon mass) does not exist in quantum electrodynamics and we conjecture that this lack of uniformity provides theoretical support for the ansatz of Marciano and Sirlin.     

Order αs corrections to intermediate boson masses

We present the order α_s corrections to the masses of the Z and W bosons in the standard model. For the low mass quarks u, d, c and s the corrections are small and positive. Due to the Coulomb singularity which appears in the vector boson self-energy graph with one gluon exchange, we find a negative contribution from the t, b doublets.     

Next-to-leading corrections to the BFKL equation from gluon and quark production

The gluon and quark production in the quasi-multi-Regge kinematics for the final particles is considered. The differential cross section for different helicity states is calculated. Dimensional regularization is used to remove the infrared divergencies in the corresponding contributions to the BFKL equation. The other next-to-leading corrections are discussed.     

The light-cone expansion and the parton model in polarized muon-production

The relation between the light-cone expansion and the QCD improved parton model formalism for polarized deep inelastic muon-production is discussed in detail. The regulator dependence of the relevant quantities is explicity studied at the two-loop level for the first moment ofg ₁ ^P . It is shown that the anomalous gluon component is well defined if the quark term is specified as a conserved quantity that does not evolve inQ ². The behaviour of the first moment ofg ₁ ^P at the threshold for heavy quark production is also discussed.     

Gauge-invariant formalism and quark confinement in QCD2

New gauge-invariant vector and spinor fields are introduced. Gauge-invariant quark propagator is defined in terms of these new fields. The equation for such a propagator, taken in 1/N approximation, does not require the introduction of an infrared regularization. As the regularization parameter in our approach there stands such a parameter which limit value corresponds to the gauge-invariant fields and translationally invariant quark propagator. It is shown that in this limit the pole of the gauge-invariant quark propagator shifts towards infinity what is usually treated as the confinement of a single quark.     

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one should use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.     

Regularization scheme dependence of vacuum observables in the Nambu-Jona-Lasinio model

We consider a bosonized version of the Nambu-Jona-Lasinio model consisting of classical scalar and pseudoscalar fields. Various regularization schemes (sharp covariant and non-covariant, proper-time and Pauli-Villars) are used in order to determine ultraviolet divergent vacuum observables such as the quark condensate 〈¯qq〉 and the current quark mass. Both quantities turn out to be very sensitive to the special choice of the scheme applied. Without further modification the proper-time and Pauli-Villars scheme appear to be unable to reproduce simultaneously the commonly used values of the quark condensate and the current quark mass.     

Quantum Chromodynamics in 1+3 Dimensions at High Temperature: Dimensional Reduction Revisited

The gluon sector of QCD in 1+3 dimensions in analyzed at high temperature (much larger than the critical ones) thereby generalizing previous results by other authors. The imaginary time formalism is used. The analysis is carried out to all orders in an improved perturbation theory which includes all second-order internal quark loops in the “free” gluon propagators. General results are given for the leading high temperature contributions to all renormalized connected gluon Green's functions (for fixed external threemomenta, much smaller than the temperature). The latter are generated by a new (dimensionally reduced) high-temperature partition function Z_HT, which corresponds to: i) the Yang-Mills (“magnetic”) gluon field coupled to a massive scalar (“electric”) gluon field, all in 3 spatial dimensions and at zero imaginary time, ii) the quark field, which continues to depend on imaginary time, coupled to the above gluon fields Z_HT also depends on the renormalized quark masses and gauge coupling constant at zero temperature, the second order quark-loop contributions to the zero-temperature renormalization constants for the gluon field and the three and four gluon vertices and on new gluon mass terms. The latter correspond to a finite number of diagrams in the improved perturbation theory at high temperature. Z_HT could be useful as the starting point for further non-perturbative studies. For the pure Yang-Mills plus ghosts theory (no quarks), it is conjectured that contributions to Green's functions depending on external momenta due to internal electric gluons could be regarded, as subdominant. Arguments are given in order to justify that conjecture. Then, the above Z_HT can be simplified and another high-temperature generating functional depending only on magnetic gluon fields is given. For the full theory including quarks, the possibility of neglecting contributions due to internal quark loops is discussed: certain infrared divergences beyond the oneloop level appear to imply that such a simplification, although not discarded, is rather hard to establish.     

Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

Screening of instantons in the quark gas

The grand partition function of quark matter is developed about an arbitrary classical gauge field configuration in a systematic weak coupling expansion. In the presence of a finite density massless quark gas the instanton induced effective quark interaction is modified by a factor exp[?2N_F(ω?)²], i.e. the baryon number chemical potential μ acts as an intrinsic infrared cutoff on the instanton scale size ?. The equation of state of the quark matter is also briefly discussed.     

Plane-wave,coordinate-space,and moment techniques in the operator-product expansion: Equivalence,improved methods,and the heavy quark expansion

We compare plane-wave, coordinate-space and moment methods for evaluating operator-product expansion (OPE) coefficients of the light-quark and gluon condensates. Equivalence of these methods for quark condensate contributions is proven to all orders in the quark mass parameterm. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approach. An improved method for evaluating quarkcondensate OPE coefficients is presented for several (two-current) correlation functions. Gauge-dependent Green functions are also discussed. It is shown that contradictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approaches yield identical relations between the heavy-quark and gluon condensates, as anticipated from the gauge invariance of the heavy-quark expansion.     

The Nielsen identities for the two-point functions of QED and QCD

We consider the Nielsen identities for the twopoint functions of full QCD and QED in the class of Lorentz gauges. For pedagogical reasons the identities are first derived in QED to demonstrate the gauge independence of the photon self-energy, and of the electron mass shell. In QCD we derive the general identity and hence the identities for the quark, gluon and ghost propagators. The explicit contributions to the gluon and ghost identities are calculated to one-loop order, and then we show that the quark identity requires that in on-shell schemes the quark mass renormalisation must be gauge independent. Furthermore, we obtain formal solutions for the gluon selfenergy and ghost propagator in terms of the gauge dependence of other, independent Green functions.     

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.     

Aspects of the confinement mechanism in Coulomb-gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in the Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.