nLab Cheshire cat principle

Idea

In nuclear physics (quantum chromodynamics) the Cheshire cat principle (NNZ 85) is the observation that in the quark bag model for confined quarks inside hadrons the radius of the “bag” is not actually observable. Hence the “bag” of the the bag model disappears, leaving only its confined content behind, whence the colorful term.

From Rho et al. 16:

One can make $[$chiral perturbation theory$]$ consistent with QCD by suitably matching the correlators of the effective theory to those of QCD at a scale near $\Lambda$. Clearly this procedure is not limited to only one set of vector mesons; in fact, one can readily generalize it to an infinite number of hidden gauge fields in an effective Lagrangian. In so doing, it turns out that a fifth dimension is “deconstructed” in a (4+1)-dimensional (or 5D) Yang–Mills type form. We will see in Part III that such a structure arises, top-down, in string theory.

$[...]$

$[$this holographic QCD$]$ model comes out to describe — unexpectedly well — low-energy properties of both mesons and baryons, in particular those properties reliably described in quenched lattice QCD simulations.

$[...]$

One of the most noticeable results of this holographic model is the first derivation of vector dominance (VD) that holds both for mesons and for baryons. It has been somewhat of an oddity and a puzzle that Sakurai’s vector dominance — with the lowest vector mesons ρ and ω — which held very well for pionic form factors at low momentum transfers famously failed for nucleon form factors. In this holographic model, the VD comes out automatically for both the pion and the nucleon provided that the infinite $[$KK-$]$tower is included. While the VD for the pion with the infinite tower is not surprising given the successful Sakurai VD, that the VD holds also for the nucleons is highly nontrivial. $[...]$ It turns out to be a consequence of a holographic Cheshire Cat phenomenon

From Nielsen-Zahed 09:

The Skyrmion is the ultimate topological bag model with zero size bag radius, lending further credence to the Cheshire cat principle.

Related concepts

• chiral perturbation theory

• quark bag model

• confinement

References

Original article:

• S. Nadkarni, Holger Bech Nielsen, Ismail Zahed, Bosonization Relations As Bag Boundary Conditions, Nucl. Phys. B 253 (1985) 308 (doi:10.1016/0550-3213(85)90533-4)

Further developments:

• Mannque Rho, Cheshire Cat Hadrons, Phys. Rept. 240 (1994) 1-142 (arXiv:hep-ph/9310300, doi:10.1016/0370-1573(94)90002-7)

  updated as: The Cheshire Cat Hadrons Revisited (arXiv:hep-ph/0206003)

Review:

• Mannque Rho, Lecture I in: Lectures on Effective Field Theories for Nuclei, Nuclear Matter and Dense Matter, 2002 (arXiv:nucl-th/0202078, cds:539674)

See also:

• Mannque Rho, Fractionalized Quasiparticles and the Hadron-Quark Duality in Dense Baryonic Matter (arXiv:2004.09082)

Derivation from the AdS/QCD correspondence:

• Holger Bech Nielsen, Ismail Zahed, The Cheshire Cat Principle from Holography (doi:10.1142/9789814280709_0017, arXiv:0904.0429), Chapter 17 in: The Multifaceted Skyrmion, World Scientific 2016 (doi:10.1142/9710)