Annihilation range and final-state interaction inp¯pannihilation intoπ−

Abstract

The large set of accurate data on differential cross section and analyzing power from the CERN LEAR experiment onpp → π − π + in the range from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation approach. The initialpp scattering wave functions originate from a recentN N model. The transition operator is obtained from a combination of the 3 P0 and 3 S1 quarkantiquark annihilation mechanisms. A good fit to the data, in particular the reproduction of the double dip structure observed in the analyzing powers, requires quark wave functions for proton, antiproton, and pions with radii slightly larger than the respective measured charge radii. This corresponds to an increase in range of the annihilation mechanisms and consequently the amplitudes for total angular momentum J = 2 and higher are much larger than in previous approaches. The final state ππ wave functions, parameterized in terms of ππ phase shifts and inelasticities, are also a very important ingredient for the fine tuning of the fit to the observables.

Relativistic treatment of pion wave functions in the annihilationp¯p→π−π+

“…Another prominent feature of the A 0n data is a shift of the asymmetry from predominantly negative values at lower momenta toward positive values at higher momenta. As already mentioned in [2,3], this indicates the presence of several partial waves while most model calculations [4][5][6][7][8][9] lead to amplitudes dominated by total angular momentum J = 0 and J =1. The reason for this feature of all models is a rather short range annihilation mechanism, driven either by baryonic exchange in the t channel [4][5][6]9] or by overlap of quark and antiquark wave functions of the proton and antiproton as in [7,8].…”

“…This is done within the framework of a constituent quark model used previously [2,7,8] to describe d / d⍀ and A 0n data of this reaction. The Lorentz transformations are effected on both the spatial part as well as the quark spinor components in the intrinsic pion wave functions.…”

“…In Sec. I we recall that in a previous (nonrelativistic) attempt to explain the LEAR data on p p → − + [2], an increase of proton, antiproton, and pion radii effectively augments the range of the transition operators T R2 and T A2 . It is therefore surprising that one can obtain any improvement from the Lorentz contraction of pions.…”

“…(2). The distance between the peaks of the solid-line Gaussians represents the relative pion coordinate RЈ = R − − R + whereas the distance between the peaks of the dashed-line Gaussians is the relative p p coordinate R = R p − R p .…”

“…[2], there is another reason to believe that the geometry of the final pions is relevant to higher partial wave ͑J Ͼ 1͒ contributions to the total amplitude. At the center-of-mass (c.m.)…”