Evaluation of the axial-vector commutator sum rule for pion-pion scattering

Journal Article · Fri Jun 01 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.116002· OSTI ID:20929583

Adler, Stephen L; Yndurain, F J ^[1]

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1. Institute for Advanced Study, Einstein Drive Princeton, New Jersey 08540 (United States)

We consider the sum rule proposed by one of us (S. L. A.), obtained by taking the expectation value of an axial-vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler-Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell. We find, with current data, that both the pion-pion and pion-nucleon sum rules are satisfied to better than 6%, and we give detailed estimates of the experimental and extrapolation errors in the closure discrepancies.

• OSTI ID: 20929583
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 11 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATORS
CROSS SECTIONS
ERRORS
EXPECTATION VALUE
EXTRAPOLATION
INTEGRALS
MASS
NUCLEONS
PARTICLE DECAY
PION-PION INTERACTIONS
PIONS
SUM RULES