The QCD running coupling

We compute, for the first time, the order ${\ensuremath{\alpha}}_{s}^{4}$ contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop $\ensuremath{\beta}$ function in quenched QED. In particular, the appearance of an irrational contribution proportional to ${\ensuremath{\zeta}}_{3}$ in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order ${\ensuremath{\alpha}}_{s}^{4}$.

Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order α s 4 in a General Gauge Theory

Spin structure of the nucleon—status and recent results

We review the present knowledge for $\alpha_s$, the fundamental coupling underlying the interactions of quarks and gluons in QCD. The dependence of $\alpha_s(Q^2)$ on momentum transfer $Q$ encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on $\alpha_s(Q^2)$ at high $Q^2$, as predicted by perturbative QCD, and its analytic behavior at small $Q^2$, based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of $\alpha_s$, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain. In the second, more technical, part of the review, we discuss the behavior of $\alpha_s(Q^2)$ in the high $Q^2$ domain of QCD. We review how $\alpha_s$ is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as Commensurate Scale Relations which connect the various definitions of $\alpha_s$ without renormalization-scale ambiguity. We also report recent measurements and theoretical analyses which have led to precise QCD predictions at high energy. In the last part of the review, we discuss the challenge of understanding the analytic behavior $\alpha_s(Q^2)$ in the infrared domain. We also review important methods for computing $\alpha_s$, including lattice QCD, the Schwinger-Dyson equations, the Gribov-Zwanziger analysis and light-front holographic QCD. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of $\alpha_s$ in order to bring better unity to the subject.

/pdf/the-qcd-running-coupling-2ihr93xu3z.pdf

The QCD Running Coupling

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules -- such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons -- are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of...

/pdf/the-spin-structure-of-the-nucleon-2twylfcbgn.pdf

The Spin Structure of the Nucleon

http://www.rcnp.osaka-u.ac.jp/~panic02/paper/abs/abs_list/abs_data/1BAgpa/paper.pdf

Measurement of spin structure functions at moderate Q2 using CLAS

We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05l{Q}^{2}l2.92\text{ }\text{ }{\mathrm{GeV}}^{2}$. The integral is fit to extract the twist-4 element ${f}_{2}^{p\ensuremath{-}n}$ which appears to be relatively large and negative. Systematic studies of this higher twist analysis establish its legitimacy at ${Q}^{2}$ around $1\text{ }\text{ }{\mathrm{GeV}}^{2}$. We also performed an isospin decomposition of the generalized forward spin polarizability ${\ensuremath{\gamma}}_{0}$. Although its isovector part provides a reliable test of the calculation techniques of chiral perturbation theory, our data disagree with the calculations.

Experimental study of isovector spin sum rules

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Measurement of spin structure functions at moderate Q2 using CLAS

Experimental study of isovector spin sum rules