Quark-antiquark correlation in the pion

Abstract

The electromagnetic tensor for inclusive electron scattering off the pion, ($W^{μν}$), 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 ($r_π$), where $r_π \approx 2/3$ 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.