Quantum-mechanical picture of peripheral chiral dynamics

The nucleon's peripheral transverse charge and magnetization densities are computed in chiral effective field theory. The densities are represented in first-quantized form, as overlap integrals of chiral light-front wave functions describing the transition of the nucleon to soft pion-nucleon intermediate states. The orbital motion of the pion causes a large left-right asymmetry in a transversely polarized nucleon. The effect attests to the relativistic nature of chiral dynamics [pion momenta $k=O\left(M_{\pi }\right)$] and could be observed in form factor measurements at low momentum transfer.

Figure 1

Interpretation of the transverse densities in a nucleon state polarized in the $y$ direction, Eq. (2).

Figure 2

(a) Feynman diagrams of LO chiral EFT processes contributing to the peripheral transverse densities (two-pion cut of the form factors). Indicated below are the effective vertices obtained after isolating the nucleon pole term of the first diagram. (b) Chiral LF wave function of the nucleon.

Figure 3

Left and right peripheral transverse densities in LO chiral EFT, as given by Eq. (11) and the contact term. The plot shows the densities after extraction of the exponential factor $exp(-2M_{\pi }b)$. The transverse distance $b$ and the densities are given in units of the pion mass.

Figure 4

Quantum-mechanical picture of chiral dynamics in the peripheral transverse densities (explanation in text).