Cheshire Cat Phenomenon Research Articles

The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so-called Proton Spin Problem. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated U A (1) anomaly. This anomaly is intimately associated with the η′ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the U A (1) anomaly is known to induce color anomaly leading to “leakage” of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This “color boundary term” inherits part or most of the dynamics of the volume (i.e., QCD). In this paper, we exploit this mapping of the volume to the surface via the color boundary condition to perform a complete analysis of the flavor singlet axial charge in the chiral bag model using the Cheshire Cat Principle. This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor singlet axial charge is small independent of the confinement (bag) size ranging from the skyrmion picture to the MIT bag picture, thereby confirming the (albeit approximate) Cheshire Cat phenomenon.

The Fields and Melatonin Mystery Changing Questions without Clear Answers

Questions concerning the possibility that exposure to power-frequency (50/60 Hz) electric fields might have adverse health effects have been of governmental, public and scientific interest in the United States since the late 1960s. Graves, Long, and Poznaniak (1) provided an apt summary of the in vivo laboratory experiments in 1979 when they suggested that the biological effects of 60–Hz electric fields were an Alice in Wonderland “Cheshire cat phenomenon” because “now you see it, and now you don't.” Interpreters of the data tended to fall into two groups. One said, “there are no effects; it is all noise.” The other said, “there are effects, but they are subtle and dependent upon specific exposure and biologic conditions.” The story might have ended then, but something new happened.

Color anomaly and flavor-singlet axial charge of the proton in the chiral bag: The Cheshire Cat revisited

Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the “proton spin problem” on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading order in the color gauge coupling and for a specific color electric monopole configuration in the bag, one can obtain a striking Cheshire-Cat phenomenon with a negligibly small singlet axial charge.

Phenomenological sizes of confinement regions in baryons

Standard order of magnitude estimates from QCD indicate that the radius of the quarkgluon core in the nucléon is Λ QCD −1 ≳1 fm. However, in work with the chiral bag model, we have found that the effective confinement size for low energy reactions can be as small as ∼ 1/2 fm or smaller. This shrinking of the effective confinement size has been attributed to the pressure of the pion cloud surrounding the quark core. The concept of confinement size is evidently subtle in light-quark systems, due to the chiral vacuum structure. This is indicated by the “Cheshire Cat” phenomenon, in which physical observables tend to be insensitive to the bag radiusR. In four dimensions, no exact Cheshire Cat principle has yet been established but it is likely to involve infinitely many mesons. We suggest that when strange quarks are present, a qualitative change occurs in the Cheshire Cat picture; in particular, we propose that strangeness provides an obstruction to this picture. We present a phenomenological indication that when strange quarks are present, the bag radiusR is frozen at a value substantially larger than 0.5 fm by as much as a factor of two. Roughly speaking, the Cheshire Cat picture emerges from a near cancellation between repulsive quark kinetic and attractive pion-cloud energies in the case of the nucleon. In theΛ andΣ particles, however, replacement of one up or down quark by a strange quark removes ∼ 1/Nc of the attraction from the coupling of the quarks to the pion cloud. This upsets the balance needed for the Cheshire Cat phenomenon and makes larger strange baryons more favorable energetically than the 0.5 fm ones appropriate for pureu- andd-systems. Since the above argument is crude, we appeal strongly to phenomenology. We find that magnetic moments of strange baryons favor a bag radius R≅1.1 fm. We find that the excited states of theΛ-hyperons favor similarly large bag radii. Somewhat less convincingly, we argue that — due to perturbative effects — the bag radius appropriate to the Δ(1232) lies intermediate between that of the nucleon and of the strange baryons.

The cheshire cat phenomenon in two-dimensional models

We study a simple two-dimensional model of fermions confined to a region of space, coupled to a background field, both in the abelian and non-abelian cases. After deriving the effective action for the bosonic field, we analyze its dependence on the position of the bag wall.