lnQ2QCD2

lnQ2QCD2 is not a standard mathematical function but a compact notation that appears in some theoretical discussions of quantum chromodynamics in two spacetime dimensions (QCD2). It is used as a contextual shorthand for the natural logarithm of a squared momentum transfer, Q^2, within the framework of two-dimensional QCD. Because QCD in two dimensions behaves differently from its four-dimensional counterpart, authors sometimes emphasize the QCD2 context by attaching the notation to the logarithmic factor that arises in perturbative or semi-perturbative expressions.

Definition of the quantity typically associated with the notation: let Q^2 denote the squared momentum transfer or energy scale relevant to a given process, and let μ be a renormalization scale. The dimensionless logarithmic factor often encountered is ln(Q^2/μ^2). In discussions specific to QCD2, the condensed form lnQ2QCD2 may be used to indicate this logarithm in the QCD2 regime; however, the exact meaning and conventions can vary by source, so it is advisable to check the context of the citation.

Role in QCD2: In two-dimensional QCD, the gauge coupling g^2 has dimensions of mass, and perturbative corrections can involve logarithmic scale dependence. Logarithmic terms like ln(Q^2/μ^2) encode how observables change with energy scale and appear in calculations of propagators, correlation functions, or Wilson-loop evaluations within the QCD2 framework. The precise coefficients of these logarithms depend on the regularization scheme and the number of colors.

See also: Quantum chromodynamics in two dimensions, renormalization in lower dimensions, logarithmic divergences, renormalization group.