Quark-antiquark correlation in the pion

Abstract

The electromagnetic tensor for inclusive electron scattering off the pion, ($W^{\mu \nu }$), for momentum transfers such that $q^{+}=0$, ($q^{+}=q^0+q^3$) is shown to obey a sum-rule for the component $W^{++}$. From this sum-rule, one can define the quark-antiquark correlation function in the pion, which characterizes the transverse distance distribution between the quark and antiquark in the light-front pion wave-function. Within the realistic models of the relativistic pion wave function (including instanton vacuum inspired wave function) it is shown that the value of the two-quark correlation radius ($r_{q\bar{q}}$) is near twice the pion electromagnetic radius ($r_{\pi }$), where $r_{\pi }\approx 2/3$ fm. We also define the correlation length $l_{corr}$ where the two - particle correlation have an extremum. The estimation of $l_{corr}\approx 0.3-0.5$ fm is very close to estimations from instanton models of QCD vacuum. It is also shown that the above correlation is very sensitive to the pion light-front wave-function models.

Comments: 18 pages,include 3 Postscript figures (melo-2.ps,melo-3.ps and melo-4.ps), use latex,epsf,elsart, e-mail: pacheco@axpfep1.if.usp.br, tobias@fis.ita.cta.br, tomio@ift.unesp.br and dorokhov@thsun1.jinr.dubna.su, correction name authors. Accepted in Nucl.Phys. A (1997)