Narrow Results

It is argued that while the scale dependence of the parton distributions in the fixed flavor factorization scheme is governed by three active flavors, the scale dependence of the running coupling should nevertheless be better governed by a variable number of active flavors.

We apply analytic perturbation theory (APT) to the QCD analysis of the xF₃(x, Q²) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Λ_QCD, the parameters of the form of the xF₃ structure function, and the x-shape of the higher twist (HT) contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the experimental errors and state that the greatest difference occurs for large x.

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. We found chiral symmetry breaking (χSB) for all flavors between N_f = 4 and N_f = 12 with most of the results discussed here for N_f = 4, 8, 12 as we approach the conformal window. To identify χSB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ϵ-regime. Chiral condensate enhancement is observed with increasing N_f when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(N_f) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at N_f = 16 inside the conformal window. Our work on the running coupling is presented separately.¹

In this paper, one uses a damped potential to present a description of the running coupling constant of QCD in the confinement phase. Based on a phenomenological perspective for the Debye screening length, one compares the running coupling obtained here with both the Brodsky–de Téramond–Deur and the Richardson approaches. The results seem to indicate the model introduced here corroborate the Richardson approach. Moreover, the Debye screening mass in the confinement phase depends on a small parameter, which tends to vanish in the nonconfinement phase of QCD.

Quantum Chromodynamics predicts that the strong coupling strength ${\alpha }_{\mathrm{\text{s}}}$ decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. The history and the status of experimental tests of asymptotic freedom are summarised in this review.

The gradient flow scheme has emerged as a prominent nonperturbative renormalization scheme on the lattice, where flow time is introduced to define the renormalization scale. In this study, we perturbatively compute the gradient flow coupling for the SU(N) Yang–Mills theory in the large-N limit in terms of the lattice bare coupling up to three-loop order. This is achieved by combining the twisted Eguchi–Kawai model with the numerical stochastic perturbation theory. We analyze the flow time dependence of the perturbative coefficients to determine the perturbative beta function coefficients, successfully computing the one-loop coefficient in the large-N limit using three matrix sizes $N=289,441,529$. However, the higher-order coefficients are affected by large statistical errors. We also explore the potential for reducing these statistical errors through variance reduction combined with the large-N factorization property of the SU(N) Yang–Mills theory, and estimate the required number of samples for the precise determination of the higher-order coefficients.

The conventional quark mass is not continuous at thresholds. In this paper, we derive matching-invariant quark masses which are continuous everywhere. They are generally expanded as an obvious function of the logarithmic $\mathrm{\Lambda }$ scaled energy. The expansion coefficients are related to the gamma and beta functions, with concretization to four-loop level. Due to the maximal elimination of their direct dependence on the coupling with large uncertainties, the new expressions for quark masses converge much fast and accurate.

Quantum Chromodynamics predicts that the strong coupling strength α_s decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. The history and the status of experimental tests of asymptotic freedom are summarised in this review.

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. We found chiral symmetry breaking (χ^SB) for all flavors between N_f = 4 and N_f = 12 with most of the results discussed here for N_f = 4, 8, 12 as we approach the conformal window. To identify χ^SB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ε-regime. Chiral condensate enhancement is observed with increasing N_f when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(N_f) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at N_f = 16 inside the conformal window. Our work on the running coupling is presented separately.

New strongly-interacting gauge theories are possible Beyond Standard Model candidates. It is essential to determine if a given non-abelian gauge theory is QCD-like or conformal. One way is to calculate the running of the renormalized gauge coupling. We describe a method to do this using Wilson loop ratios measured in lattice simulations. We demonstrate this in SU(3) pure gauge theory and show initial results for dynamical fermions in the fundamental representation.

In this paper we show how in the most natural extension of gravity with torsion, fermion fields are endowed with running coupling in spinorial interaction that are eventually shown to reproduce the strength and structure of the leptonic weak forces.