H. David Politzer

Asymptotic Freedom: An Approach to Strong Interactions

The discovery of asymptotic freedom has opened up the possibility of extracting new sorts of detailed, dynamical consequences from a strongly interacting quantum field theory. The necessary tools - perturbation theory, the renormalization group, gauge theories, and the operator product expansion - are not new. To anyone familiar with these field theoretic approaches to strong interactions, the novel feature is a simple fact: there is a unique class of theories in which “the origin is an ultraviolet fixed point”. But the consequences are so exciting that it seemed appropriate to review these ideas as they reflect on each other. Many important applications of the renormalization group and the operator product expansion to hadronic physics are omitted; the emphasis here is on recent work based on asymptotically free field theories. No doubt, there are some developments so recent that they are not treated in this article. The discussion of the basic results concerning short distance behavior is informal, but, hopefully, accurate and complete. The specific applications are treated in varying detail.

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ⩽ Q^2 ⩽ 16 GeV^2. Excellent agreement is obtained using g^2(2 GeV)4π^2 = 0.17 for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of M_0^2Q^2. We use data from the resonance region to show M_0 ⋍ 400 MeV, in agreement with theoretical expectations. Our fit to νW_2 in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of R = σLσT at large x and Q^2 are systematically higher than our predictions.

Effective Quark Masses in the Chiral Limit

The behavior of effective, scale dependent quark masses in the chiral limit is studied using the operator product expansion. Their relation to current and constituent quark masses is clarified. Current correlation functions are examined as an example of separating effects of spontaneous and explicit chiral symmetry breaking.

Perturbation theory and the parton model in QCD

We prove that for any process which admits a parton-model interpretation, the naive parton model can be modified to include the effects of QCD interactions to all orders in perturbation theory. This requires that the mass singularities in quark and gluon inclusive cross sections factor into universal functions which renormalize the naive parton model distribution and decay functions. We prove that this factorization takes place for all leading and non-leading logs and thus check consistency of the parton model to all orders in perturbation theory.

Leading logarithms of heavy quark masses in processes with light and heavy quarks

The matrix elements of operators containing both heavy quark (Q) and light quark (q) fields can contain large logarithms of the type ln(mQ2/μ2), where μ is a typical QCD mass scale and mQ is the heavy quark mass. We outline a method for summing leading logarithms of this type. We apply it to the decay constant fM of a low lying pseudoscalar meson M with Qq flavor quantum numbers and predict the ratios of decay constants for mesons with different heavy flavors. We also apply it to a matrix element of a four-quark operator which is relevant for B0−B0 mixing.

Power corrections at short distances

Hadronization, p_⊥ smearing, and higher twist are analyzed in terms of a factorization theorem that represents all hard scattering processes as a power series in 1/Q^2. the common large momentum scale. Process-independent functions are convoluted with perturbative amplitudes in an algorithm that rests on the equations of motion.

Gluon corrections to Drell-Yan processes

Assuming that the Drell-Yan picture is approximately valid, I compute the O(g^2) gluon radiative corrections in QCD. The corrections are self-consistent, i.e. they satisfy several non-trivial constraints necessary for the validity of the whole picture. There are logarithmic scaling violations in the quark distribution functions, precisely equal to those found in electroproduction. Large transverse momenta (of order of the c.m. energy) are produced, balanced by radiation in the opposite direction. I compute the transverse momentum differential cross section for μ pairs as an example

Factorization and the parton model in QCD

We argue that mass-singularities of inclusive cross sections in QCD factor to all orders in perturbation theory as required for a parton model interpretation.

Bounds on Particle Masses in the Weinberg-Salam Model

Various conditions necessary for the self-consistency of the Weinberg-Salam model are used to place constraints on fermion and Higgs Boson masses. We find that spontaneous symmetry breakdown cannot generate fermion masses in excess of about 300 GeV.

Kaon condensation in nuclear matter

Using the leading operators in the chiral lagrangian for meson-baryon interactions (at low momentum) and treating the meson fields classically, Kaplan and Nelson have observed, using numerical methods, that a charged kaon condensate forms at several times nuclear density. We derive an analytical expression for the critical density. The effects of virtual mesons and higher dimension operators are discussed. The possibility of a neutral kaon condensate is also considered.