Hadron deformation from Lattice QCD

Hadronic matrix elements of twoand threecurrent correlators encode detailed information on hadron structure such as quark spatial distributions, charge radii and quadrupole moments. In the non-relativistic limit they reduce to the square of the wave function and therefore the shape of the hadron can be extracted. The issue of a deformation in the nucleon and ∆ was first examined in the context of the constituent quark model [1] with the one gluon exchange giving rise to a colour magnetic dipole-dipole interaction. The tensor component of this interaction causes a D-wave admixture in the nucleon and ∆ wave function and leads to a deformation. Other mechanisms have been invoked to explain hadron deformation: In cloudy bag models the deformation is caused by the asymmetric pion cloud [2]. In soliton models it is thought to be due to the non-linear pion field interaction. In the constituent quark model it was recently proposed to be due to two-body contributions to the electromagnetic current arising from the elimination of gluonic and quark-antiquark degrees of freedom [3]. Because of the strong experimental indications that the nucleon is deformed, it is interesting to address the general issue of hadron deformation within lattice QCD and try to understand its physical origin. In the first part of this talk we present results on the charge and matter density distributions evaluated on the lattice, both in the quenched and in the unquenched theory. A comparison between the charge and mat-