Three-loop anomalous dimensions for squarks in supersymmetric QCD

In this Letter we evaluate the renormalization constants and anomalous dimensions for the squark wave function and mass within supersymmetric QCD. These results complement the ones obtained in Harlander et al. (2009) [1] and thus provide further confirmation on the applicability of dimensional reduction to supersymmetric QCD at three-loop order. The three-loop anomalous dimension constitute important input to precision predictions of the supersymmetric mass spectrum as obtained from the evolution from the GUT to the TeV energy scale.     

Cancellation of energy divergences in Coulomb gauge QCD

Electroweak unification is obtained in anSU(7) model at a mass scale 3×10¹⁰≦M≦3×10¹⁶ GeV's, with left-right symmetric subgroups and sin² θ _w (M)=3/8. BelowM, the model reduces toSU(3) _L ×SU(3) _R , the flavor sector of the “trinification theory” of Glashow et al., or of theE ₆ grand unified theory. This model predicts a natural massless neutrino, and fractionally charged leptons with masses in theM regime.     

A stagnant gauge for QCD

It is shown that the gauge-fixing parameter α of standard covariant gauges may legitimately be replaced by an operator α(□). In particular, α may be chosen so that the gluon propagator has a “stagnant” tensor structure proportional to g_ην for all momenta. This choice of gauge simplifies explicit calculations and leads to renormalization group equations with no $\text{?}\text{?α}$ term.     

The deconfining phase transition and the glueball channels in pure gauge QCD

We study the exponential decay of the smeared plaquettes, at large distance from a cold source, close to the deconfining phase transition of N_t=4 lattice QCD. We compare different lattice size results, and by using finite size scaling arguments we find a critical behavior that is in agreement with a continuous transition.     

Feynman rules for Coulomb gauge QCD

The Coulomb gauge in nonabelian gauge theories is attractive in principle, but beset with technical difficulties in perturbation theory. In addition to ordinary Feynman integrals, there are, at 2-loop order, Christ–Lee (CL) terms, derived either by correctly ordering the operators in the Hamiltonian, or by resolving ambiguous Feynman integrals. Renormalization theory depends on the sub-graph structure of ordinary Feynman graphs. The CL terms do not have a sub-graph structure. We show how to carry out renormalization in the presence of CL terms, by re-expressing these as ‘pseudo-Feynman’ integrals. We also explain how energy divergences cancel.     

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the beta function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.     

Three-loop anomalous dimension of the non-singlet transversity operator in QCD

We calculate the three-loop anomalous dimension of the non-singlet transverse operator from N=1$N=1$ to N=15$N=15$. Using some guess we have reconstructed a general form of three-loop anomalous dimension for arbitrary Mellin moment N. Obtained result is transformed into Bjorken-x space by an inverse Mellin transformation. The final expressions are presented in both Mellin-N and Bjorken-x space.     

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ–Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ–Lee term. We find that they cannot.     

Static quark anti-quark free and internal energy in two-flavor QCD

We study the change in free and internal energy due to the presence of a heavy quark anti-quark pair in a thermal heat bath in QCD with two flavors of staggered quarks at finite temperature. We discuss string breaking below as well as screening above the transition. Similarities and differences to the quenched case are discussed.Arrival of the final proofs: 24 March 2005PACS: 11.15.Ha, 11.10.Wx, 12.38.Mh, 25.75.Nq     

QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

QCD plasma parameters in axial gauge

Within the framework of imaginary time formalism we investigate the structure of the gluon polarization tensor and relate its structure functions to the dispersion relation of plasma eigenmodes. To one loop order, we calculate the transversal structure function to leading order in the high temperature expansion as well as the first subleading order contribution in the long wavelength limit. The result is used to express the dynamical mass and the damping constant for transversal plasma eigenmodes. The aim of our present paper is a systematic discussion of the gauge fixing vector dependence of the damping constant. In the limit of temporal axial gauge we encounter a negative damping constant contradicting previous results.     

Asymptotic constraint for chiral condensation of Coulomb gauge QCD

We study the³ P ₀ quark-antiquark pair condensation in QCD, representing the gluon-interaction approximately by instantaneous Coulomb plus Breit potential. Particular attention is paid to non-uniqueness of the solution of the gap equation. The genuine dynamical solution can be characterized by a rapidly convergent behavior at large momentum, as was recognized in covariant formulations of Landau gauge. We impose the required behavior and make a numerical study of the chiral condensation.     

BRST invariance in Coulomb gauge QCD

In the Coulomb gauge, the Hamiltonian of QCD contains terms of order ?²${?}^2$, identified by Christ and Lee, which are non-local but instantaneous. The question is addressed how do these terms fit in with BRST invariance. Our discussion is confined to the simplest, O(g⁴)$O\left(g^4\right)$, example.     

The free energy of lattice gauge theories at large β

An upper and a lower bound for the free energy density of a lattice gauge teory with compact gauge group are derived, valid for all values of β. For large β the first two terms of the asymptotic expansions of these bounds coincide, thus determining the corresponding terms of the free energy density. Moreover the gauge groups U(N) and SU(N) are treated explicitly.