Baryons with Many Colors and Flavors

Abstract

Using recently-developed diagrammatic techniques, I derive some general results concerning baryons in the $1/N$ expansion, where $N$ is the number of QCD colors. I show that the spin-flavor relations which hold for baryons in the large-$N$ limit, as well as the form of the corrections to these relations at higher orders in $1/N$, hold even if $N_F/N\sim 1$, where $N_F$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit $n$ mesons is $O(1/N^{n/2-1})$, and that meson loops attached to baryon lines are unsupressed in the large-$N$ limit, independent of $N_F$. For $N_F>2$, there are ambiguities in the extrapolation away from $N=3$ because the baryon flavor multiplets for a given spin grow with $N$. I argue that the $1/N$ expansion is valid for baryons with spin $O(1)$ and {\it arbitrary} flavor quantum numbers, including e.g. baryons with isospin and/or strangeness $O(N)$. This allows the formulation of a large-$N$ expansion in which it is not necessary to identify the physical baryons with particular large-$N$ states. $SU(N_F)$ symmetry can be made manifest to all orders in $1/N$, yet group theory factors must be evaluated explicitly only for $N_F=N=3$. To illustrate this expansion, I consider the non-singlet axial currents, baryon mass splittings, and matrix elements of $\mybar ss$ and $\mybar s \gam_μ\gam_5 s$ in the nucleon.

19 pages, plain TeX, 4 uuencoded postscrip figures, LBL-35539, NSF-ITP-94-42

References in corpus (7)

• The 1/N Expansion for Baryons
• Baryon-Pion Couplings from Large-N QCD
• 1/N Corrections to the Baryon Axial Currents in QCD
• Baryons from Quarks in the $1/N$ Expansion
• On Spin Independence in Large $N_c$ Baryons
• Strong and Electromagnetic Decays of the Baryon Decuplet
• Baryon Magnetic Moments in a Simultaneous Expansion in $1/N$ and $m_s$

Cited by in corpus (20)

• Small, Dense Quark Stars from Perturbative QCD
• Baryons and the phase diagram for a large number of colors and flavors
• Baryon Mass Splittings in the 1/N_c Expansion
• Baryon Magnetic Moments in a Simultaneous Expansion in $1/N$ and $m_s$
• Large-N_c Baryons
• Chiral Lagrangian for Baryons in the $1/N_c$ Expansion
• Minimally extended SILH
• Determination of SU(6) Clebsch-Gordan Coefficients and Baryon Mass and Electromagnetic Moment Relations
• Baryon masses in a chiral expansion with meson-baryon form factors
• Spin contribution to light baryons in different large-$N$ limits
• Possible Ferromagnetism in the Large N(c) and N(f) limit of quark matter
• Consistency of the Baryon-Multimeson Amplitudes for Large-N_c QCD
• Light baryon masses in different large-$N_c$ limits
• Weak coupling large-N transitions at finite baryon density
• Baryon masses at second order in large-$N$ chiral perturbation theory
• A Multiple Commutator Formula for the Sum of Feynman Diagrams
• Chiral perturbation theory analysis of baryon temperature mass shifts
• Pion-Nucleon Scattering in a Large-N Sigma Model
• From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group
• Large-N Baryons, Chiral Loops, and the Emergence of the Constituent Quark