Dimensional regularization of infrared divergences

An analysis of the application of dimensional regularization to infrared divergences in lowest order radiative corrections is presented. The main emphasis of the paper is to show explicitly how dimensional regularization can lead in some cases of considerable interest to very simple and elegant evaluations of infrared divergent contributions and their associated finite parts, and to pinpoint the mathematical reason for the equivalence with the traditional method of regularization.     

Equivalence of massive and dimensional regularization in the infrared

We check the use of dimensional regularization for UV and IR divergences. We calculate Lee-Nauenberg cross sections in a gauge theory with scalars in which IR regularization can alternatively be done by masses generated by the Higgs-Kibble mechanism. The final results agree.     

The baryon spectrum in low order QCD with Migdal regularization

The 2-point functions of local gauge invariant baryonic operators in QCD are continued from the Euclidean to the hadronic region using the Migdal regularization procedure to orders α _s . The knowledge of the anomalous dimensions of baryonic operators allows to derive the mass spectrum of the leading δ- and of the first twoN-resonances.     

Leading non-cancelling infrared divergences in perturbative QCD

In perturbative QCD, for the inclusive cross section for the scattering of two coloured particles, we identify graphs which contribute to the general leading order α_s(α_s lnλ)ⁿ of uncancelled IR divergences, and we sum these contributions (λ is the IR cut-off). The work is done in the Coulomb gauge; an appendix discusses the Feynman gauge.     

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.     

Does QCD have infrared renormalons?

We give a naïve perturbative proof of the existence of infrared renormalons for large distance asymptotically free theories. We argue that the extension of the result for small distance asymptotically free theories is not obvious. Indeed we do not find infrared renormalons for QCD.     

Hadron spectrum in a Euclidean invariant regularization of QCD at strong coupling

A new random lattice regularization, which preserves exact euclidean invariance, is proposed for QCD. The corresponding action couples any two points on the random lattice with a gaussian damping of range b in the euclidean distance of the points. This property, which avoids the introduction of the concept of nearest neighbours on a random lattice, greatly simplifies computations of physical observables with respect to the situation of the standard random lattice models. The present calculation of the hadron spectrum of a SU(N = 3) gauge model is performed at strong coupling β = 0, at leading order in 1/N and in the inverse lattice point density ?. The results for mesons of definite spin-parity and flavor are quite good; the results for the baryons are, as usual, less satisfying (small N-Δ mass difference), but are also expected to be less reliable in our approximations. The problem of the regularization of chiral fermions is not settled in this paper where the used approximations yield a massless η-boson.     

An infrared renormalization group limit cycle in QCD

We use effective field theories to show that small increases in the up and down quark masses would move QCD very close to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. We conjecture that QCD can be tuned to the critical trajectory by adjusting the quark masses independently. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner would be tuned to zero and the triton would have infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states would approach a universal constant that is close to 515.     

How to regularize the infrared and mass singularities in QCD

The parton cross sections in perturbative QCD are mass (M) and infrared (IR) divergent. The singularities are prevented by on/off-shell parton masses or by dimensional regularization. All mass assignments must be chosen in agreement with Kinoshita's double-cut rule. The “off-shell” assignment, often used in the past, is incorrect. We demonstrate that Drell-Yan mass factorization in order α_S is independent of all regularizatiohns; the coffcient function is unique.     

More on the infrared renormalization group limit cycle in QCD

We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables. PACS 12.38.Aw, 21.45.+v, 11.10.Hi     

Exact calculation of the Fermion determinant in chiral QCD2 reflecting the full regularization dependence

The fermion determinant of non-abelian anomalous gauge theory in two space-time dimensions is computed using the path-integral approach. The regularization dependence of the fermion determinant is worked out. Apart from a regularization dependentA ² term, the fermion determinant contains a Wess-Zumino-Witten anomaly functional.     

A note on the dimensional regularization method in the presence of infrared divergences

We indicate a practical way of applying the dimensional regularization scheme in the presence of infrared divergences, consisting of a finite subtraction procedure.     

Gauge-invariant infrared regularization for non-abelian fields and the Lee-Nauenberg theorem

We test the gauge-invariant infrared regularization of non-abelian fields proposed by Slavnov by calculating the Lee-Nauenberg probability for scattering of gluons in an external potential.     

Following gluonic world lines to find the QCD coupling in the infrared

Using a parametrization of the Wilson loop with the minimal-area law, we calculate the polarization operator of a valence gluon, which propagates in the confining background. This enables us to obtain the infrared freezing (i.e. finiteness) of the running strong coupling in the confinement phase, as well as in the deconfinement phase up to the temperature of dimensional reduction. The momentum scale defining the onset of freezing is found both analytically and numerically. The nonperturbative contribution to the thrust variable, originating from the freezing, makes the value of this variable closer to the experimental one.     

Loop-space formalism and renormalization group for the infrared asymptotics of QCD

It is demonstrated that the IR asymptotics of an arbitrary hard process of perturbative QCD can be factorized out into the superposition of vacuum averages of path-ordered exponentials, the IR singularities of which are shown to be in a one-to-one correspondence with the UV ones, thus allowing one to apply renormalization group methods to study the IR asymptotics of perturbative QCD. The anomalous dimension Γ_cusp of the relevant RG equation is calculated up to two loops.     

An infrared singularity in the damping rate for longitudinal gluons in hot QCD

We calculate γ_l(0), the damping rate for longitudinal on-shell gluons with zero momentum in hot QCD using the hard-thermal-loop scheme, and find it to be divergent in the infrared. We argue that this result suggests that the scheme may be sensitive in this sector and thus may need to be improved upon. We discuss the validity of our result and emphasize the fact that it depends on the way we perform our calculation. In particular, we do not exclude the possibility that alternative approaches that we briefly comment on may in principle yield infrared-safe results.