Signatures of chiral dynamics in the Nucleon to Delta transition

Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic $N\Delta$-transition current in the framework of the non-relativistic "small scale expansion" (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and coulomb quadrupole transition form factors up to a momentum transfer of $Q^2<0.3$ GeV$^2$. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form factors at small $Q^2<0.15$ GeV$^2$ arising from long distance pion physics, leading for example to negative radii in the (real part of the) quadrupole transition form factors. We compare our results with the EMR($Q^2$) and CMR($Q^2$) multipole-ratios from pion-electroproduction experiments and find a remarkable agreement up to four-momentum transfer of $Q^2\approx 0.3$ GeV$^2$. Finally, we discuss the chiral extrapolation of the three transition form factors at $Q^2=0$, identifying rapid changes in the (real part of the) quark-mass dependence of the quadrupole transition moments for pion masses below 200 MeV, which arise again from long distance pion dynamics. Our findings indicate that dipole extrapolation methods currently used in lattice QCD analyses of baryon form factors are not applicable for the chiral extrapolation of $N\Delta$ quadrupole transition form factors.