Determination of the pi0 gamma cross-section

Abstract

In this memo the authors address the following questions: how the {pi}{sup 0}{gamma} cross section, which is measured in E760, compares to the expected leakage from the {pi}{sup 0}{pi}{sup 0} final states; is it possible to affirm that a substantial fraction of the {pi}{sup 0}{gamma} events are due to continuum production? Naively, the expected continuum {pi}{sup 0}{gamma} cross section can be estimated using the Vector Meson Dominance Model (VDM). In that framework, a photon is coupled to a neutral vector meson V by G{sub {gamma}V}. Then {sigma}{sub {pi}{sup 0}{gamma}} = {sigma}{sub {pi}{sup 0}{rho}} x G{sub {gamma}{rho}}{sup 2} with G{sub {gamma}{rho}}{sup 2} = 1./160 {divided_by} 1./380 [1]. At E{sub CM} = 2.611 GeV, {sigma}{sub {pi}{sup 0}{rho}} = (70 {+-} 30){mu}b [2] which gives {sigma}{sub {pi}{sup 0}{gamma}} = 184 {divided_by} 438 nb. To predict the cross section within a limited acceptance they assume that the angular production of {pi}{sup 0}{gamma} is similar to the {pi}{sup 0}{pi}{sup 0} and {pi}{sup 0}{rho} ones. To estimate the fraction of events with |cos{theta}*| < 0.5, being {theta}* the center of mass production angle, they do use the total {pi}{sup +}{pi}{sup -} cross section {sigma}{sub {pi}{sup +}{pi}{sup -}} = (6.6 {+-} 3.5){mu}b at 2.975 GeV [3]. {sigma}{sub {pi}{sup 0}{pi}{sup 0}} = 0.5 x {sigma}{sub {pi}{sup +}{pi}{sup -}}, while for |cos{theta}*| < 0.5 E760 measures {sigma}{sub {pi}{sup 0}{pi}{sup 0}} {approx_equal} 180. nb at the above center of mass energy and |cos{theta}*| < 0.5. They obtain that the fraction of {pi}{sup 0}{pi}{sup 0} events with |cos{theta}*| < 0.5 is 5.4 x 10{sup -2}. Finally, multiplying the expected total cross section and the above fraction, they obtain {sigma}{sub {pi}{sup 0}{gamma}} = (10. {divided_by} 23.8) nb with |cos{theta}*| < 0.5. This prediction gives a value which is far from being negligible and certainly measurable in the experiment.