Study of the anomalous process {gamma}{pi}{yields}{pi}{pi}

Technical Report · Tue Aug 01 04:00:00 EDT 1995

DOI:https://doi.org/10.2172/166446· OSTI ID:166446

Roberts, C. D.; Alkofer, R. ^[1]

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1. Univ. of Tuebingen (Germany)

The {gamma}{pi} {yields} {pi}{pi} form factor, F{sup 3{pi}}(s), is calculated in generalized impulse approximation within the Dyson-Schwinger Equation framework. This is an anomalous process and as such its form is a fundamentally important characteristic of the quantum field theoretical structure of QCD because it signals the breaking of the U{sub A} symmetry by quantization. There is only one experimental measurement of F{sup 3{pi}}(s) at s {approximately} 8m{sub {pi}}{sup 2}, which has large errors, however, there is an approved experiment at CEBAF to study F{sup 3{pi}}(s) in the reaction {gamma}{pi}{sup +} {yields} {pi}{sup +}{pi}{sup 0} near threshold. This is to be done by measuring {gamma}p {yields} {pi}{sup +}{pi}{sup 0}n cross sections near t {approx_equal} {sup -}m{sub {pi}}{sup 2}. Present calculations of F{sup 3{pi}}(s) are either unrelated to QCD or rely on {open_quotes}low-energy{close_quotes} expansions. The approach we employ, which manifestly incorporates the large space-like-q{sup 2} renormalization group properties of QCD and allows a realistic extrapolation to small space-like-q{sup 2}, allows us to go beyond such {open_quotes}low-energy{close_quotes} expansions and relate F{sup 3{pi}}(s) to the structure of the effective quark-quark interaction in the infrared. Our preliminary results are encouraging. The chiral limit value, F{sup 3{pi}}(s=0), obtained in our approach agrees with that which one expects from the connection between anomalous processes and the quantization of QCD. Our results also indicate that the form factor grows smoothly away from the chiral point. Our detailed calculation will allow us to address the question of the reliability of the extrapolation to the pion mass shell that is necessary in interpreting the data.

• Research Organization: Argonne National Lab., IL (United States)
• OSTI ID: 166446
• Report Number(s): ANL--95/14; ON: DE96000985
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DYSON REPRESENTATION
ELECTROMAGNETIC FORM FACTORS
ELECTRON-POSITRON INTERACTIONS
PHOTON-MESON INTERACTIONS
PION-PION INTERACTIONS
PIONS
PROGRESS REPORT
QUANTUM CHROMODYNAMICS
SCHWINGER FUNCTIONAL EQUATIONS