Optimal renormalization scale and scheme for exclusive processes
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695 (United States)
- Nuclear Theory Center, Indiana University, Bloomington, Indiana 47404 (United States)
- Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)
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 {gamma}e{r_arrow}{pi}{sup 0}e data assuming that the pion distribution amplitude is close to its asymptotic form {radical} (3) f{sub {pi}}x(1{minus}x). We also reproduce the scaling and normalization of the {gamma}{gamma}{r_arrow}{pi}{sup +}{pi}{sup {minus}} 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 F{sub {pi}}(Q{sup 2}) 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 {gamma}{sup {asterisk}}p{r_arrow}{pi}{sup +}n electroproduction data to the pion pole. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 566101
- Journal Information:
- Physical Review, D, Journal Name: Physical Review, D Journal Issue: 1 Vol. 57; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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