arXiv subjects

Michael Mattis

Publications and source records attributed to Michael Mattis.

4 recordsLinked to original sources

arXiv1995

The Large-N_c Renormalization Group

In this talk we review how effective theories of mesons and baryons become exactly soluble in the large-N_c limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N_c selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N_c. We show how all these leading-order diagrams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ^{-1} (Λbeing the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r < Λ^{-1}. The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δhyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N_c renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ--> \infty.

hep-ph↗

arXiv1995

The Rotationally Improved Skyrmion, or ``RISKY''

The perceived inability of the Skyrme model to reproduce pseudovector pion-baryon coupling has come to be known as the ``Yukawa problem.'' In this talk, we review the complete solution to this problem. The solution involves a new configuration known as the rotationally improved Skyrmion, or ``RISKY,'' in which the hedgehog structure is modified by a small quadrupole distortion. We illustrate our ideas both in the Skyrme model and in a simpler model with a global U(1) symmetry.

hep-ph↗

arXiv1995

From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group

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 QCD. An infinite set of graphs dress the bare Yukawa couplings at *leading* order in 1/N_c, and are summed using semiclassical techniques. What emerges is a picture of the large-N_c baryon reminiscent of the chiral bag: hedgehog pions for r > 1/Λpatched onto bare nucleon degrees of freedom for r < 1/Λ, where the ``bag radius'' 1/Λis the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived, in which the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings run with Λ. Finally, this RG flow is shown to act as a *filter* on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit Λ--> \infty exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.

hep-ph↗

arXiv1994

Skyrmion Quantization and the Decay of the Delta

We present the complete solution to the so-called ``Yukawa problem'' of the Skyrme model. This refers to the perceived difficulty of reproducing---purely from soliton physics---the usual pseudovector pion-nucleon coupling, echoed by pion coupling to the higher spin/isospin baryons $(I=J=3/2 , 5/2 , \cdots , N_c/2 )$ in a manner fixed by large-$N_c$ group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration, the ``new improved skyrmion''. This is the near-hedgehog obtained by minimizing the usual skyrmion mass functional augmented by an all-important isorotational kinetic term. The numerics are pleasing: a $Δ$ decay width within a few MeV of its measured value, and furthermore, the higher-spin baryons $(I=J \ge 5/2 )$ with widths so large ($Γ> 800 MeV$) that these undesirable large-$N_c$ artifacts effectively drop out of the spectrum, and pose no phenomenological problem. Beyond these specific results, we ground the Skyrme model in the Feynman Path Integral, and set up a transparent collective coordinate formalism that makes maximal use of the $1/N_c$ expansion. This approach elucidates the connection between skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.

hep-ph↗