N. Dorey et Mp. Mattis, FROM EFFECTIVE LAGRANGIANS, TO CHIRAL BAGS, TO SKYRMIONS WITH THE LARGE-N-C RENORMALIZATION-GROUP, Physical review. D. Particles and fields, 52(5), 1995, pp. 2891-2914
We explicitly relate effective meson-baryon Lagrangian models, chiral
bags, and Skyrmions in the following way. First, effective Lagrangians
are constructed in a manner consistent with an underlying large-N-c Q
CD. An infinite set of graphs dress the bare Yukawa couplings at leadi
ng order in 1/N-c, and are summed using semiclassical techniques. What
emerges is a picture of the large-N, baryon reminiscent of the chiral
bag: hedgehog pious for r greater than or equal to Lambda(-1) patched
onto bare nucleon degrees of freedom for r less than or equal to Lamb
da(-1), where the ''bag radius'' Lambda(-1) is the UV cutoff on the gr
aphs. Next, a novel renormalization group (RG) is derived in which the
bare Yukawa couplings, baryon masses, and hyperfine baryon mass split
tings run with Lambda. Finally, this RG how is shown to act as a filte
r on the renormalized Lagrangian parameters: when they are fine-tuned
to obey Skyrme-model relations the continuum limit Lambda --> infinity
exists and is, in fact, a Skyrme model; otherwise there is no continu
um limit.