Physical Review D
American Physical Society
Brodsky-Lepage-Mackenzie method, BLM, QCD coupling, pion form factor, photon-to-pion transition form factor, heavy quark potential, electron-positron annihilation cross section, lattice gauge theory
We use the Brodsky-Lepage-Mackenzie (BLM) method to fix the renormalization scale of the QCD coupling in exclusive hadronic amplitudes such as the pion form factor and the photon-to-pion transition form factor at large momentum transfer. Renormalization-scheme-independent commensurate scale relations are established which connect the hard scattering subprocess amplitudes that control exclusive processes to other QCD observables such as the heavy quark potential and the electron-positron annihilation cross section. The commensurate scale relation connecting the heavy quark potential, as determined from lattice gauge theory, to the photon-to-pion transition form factor is in excellent agreement with γe⃗ π0e data assuming that the pion distribution amplitude is close to its asymptotic form 3√fπx(1−x). We also reproduce the scaling and normalization of the γγ⃗ π+π− data at large momentum transfer. Because the renormalization scale is small, we argue that the effective coupling is nearly constant, thus accounting for the nominal scaling behavior of the data. However, the normalization of the space-like pion form factor Fπ(Q2) obtained from electroproduction experiments is somewhat higher than that predicted by the corresponding commensurate scale relation. This discrepancy may be due to systematic errors introduced by the extrapolation of the γ*p⃗ π+nelectroproduction data to the pion pole.
Brodsky, Stanley J.; Ji, Chueng-Ryong; Pang, Alex; and Robertson, David G., "Optimal Renormalization Scale and Scheme for Exclusive Processes" (1998). Physics Faculty Scholarship. Paper 15.
Brodskey, S.J., Ji, C., Pang, A, & Robertson, D.G. (1998). Optimal renormalization scale and scheme for exclusive processes. Physical Review D, 57(1). DOI: 10.1103/PhysRevD.57.245
Copyright 1998 Physical Review D
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