Axial anomaly

The fermionic determinant Detiow averaged over instanton anti-instanton positions, orientations and sizes leads to a partition function of light quarks Z. Then the properties of the hadrons and their interactions are concentrated in the QCD effective action written in terms of the quasiparticles. This approach leads to the Diakonov-Petrov(DP) effective action (D.I. Diakonov et.al., 1996). It was shown that DP effective action is a good tool in the chiral limit but fails beyond this limit, checked by the calculations of the axial-anomaly low energy theorems (M.M. Musakhanov et.al., 1997 E. Di Salvo et.al., 1998). 

Within this approach it was proposed so called improved effective action which is more properly takes into account current quark masses and satisfies axial-anomaly low energy theorems also beyond the chiral limit (M.M. Musakhanov, 1999) at least at 0(m). 

In order to check the gauging method, applied here, by axial-anomaly low-energy theorem, GG —> 2 photons correlator (M.M. Musakhanov et.al., 2003) was calculated. It was found that this gauged QCD low-energy effective action perfectly satisfies the theorem (M.M. Musakhanov et.al., 2003). 

Now, let us consider the divergence of axial currents in HDET, which is related to the axial anomaly and also to how the quark matter responds to external axial-current sources like electroweak probes. 

It is easy to show that the axial anomaly in dense matter is independent of density or the chemical potential p [11]. In general one may re-write the divergence of axial currents in dense QCD as follows ... 

Figure 7. Matching axial anomaly. + denotes ip+ and — denotes tp- ...

We see that the modes near the Fermi surface contributes only some parts of the axial anomaly. As in the vector current, the rest should come from modes in the deep Fermi sea and from anti-particles. To recover the full axial anomaly we add a counter term (See Fig. 7), which is two thirds of the axial anomaly plus a Chern-Simons term ... 

Quantum theory also opens a number of other options (see, e.g., [2]). One of them is a so-called anomaly. The violating term is a purely quantum effect proportional to h. It appears because of singularities in original theory. While in the classical case the theory is symmetrical under a number of transformations, it is not possible to regularize all singular operators to keep all classical symmetries. Some of them have to be violated in the quantum-field case. The most well-known example is a so-called axial anomaly, which violates chiral symmetry even for massless quarks. 

An interesting anomaly is a//-rra j-l,2,3,4,5,6-hexaisopropylcyclohexane, in which the six isopropyl groups prefer the axial position, although the six ethyl groups of the corresponding hexaethyl compound prefer the equatorial position. The alkyl groups of these compounds can of course only be all axial or all equatorial, and it is likely that the molecule prefers the all-axial conformation because of unavoidable strain in the other conformation. 

This dependence of p/fa on inductive effects was also found in nitrobenzene218 and aqueous methanol.219 Anomalies were found, however, particularly where the predominant con former had an axial OH group.215,217,218 These were explained in terms of interaction between inductive effects of geminal groups, or of steric effects,215,218,219 termed by the authors a stereopolar effect. These studies led to the conclusion that the inductive effect of substituents in such systems is registered at... 

Also, the heat capacity is affected by the axial ZFS parameter and, in excess of the lattice contribution, it shows a Schottky anomaly as modeled in Fig. 2. In the zero magnetic field the isofield heat capacity Ch collapses to the usual Cp and stays isotropic. 

Another remarkable anomeric effect has been observed which has beCn named the reverse anomeric effect .37 By protonation of the imidazole-substituted D-xylo derivative the equilibrium shifts from mainly axial form to mainly equatorial form (Scheme 1.3). There are no changes in the steric requirement between the two compounds and therefore only a stereoelectronic explanation can account for this anomaly. Lemieux has... 

Harrington et al. (1956) suspected that the anomaly was caused by approximations in the Simha equation for axial ratios less than 20. This however was refuted by Loeb and Scheraga (1956) on grounds that the viscosity increments, v, in the /8-function calculations are taken from the... 

LeDouaranS. and Francheteau J. (1981) Axial depth anomalies from 10 to 50 degrees north along the Mid-Atlantic Ridge correlation with other mantle properties. Earth Planet. Sci. Lett. 54, 29-47. 

Figure 1 Anterior view of an anencephalic human fetus. Notice the low-set ears, elevated nose and maxilla, the short neck (due to anomalies of the cervical vertebrae), and the prominent, protruding rudimentary brain. (Reproduced from Marin-Padilla M (1991) Cephalic axial skeletal-neural dysraphic disorders Embryology and pathology. Canadian Journal of Neurological Sciences 8 153-169, with permission.)...

The primary motivation for predicting the electrochemical properties of the coolant circuits of water-cooled nuclear power reactors has been that of explaining and predicting tenacious operating problems that include SCC and CF, mass transport of corrosion products and subsequent fouling of heat transfer surfaces, activity transport due to the movement of neutron-activated radionuclides from the core to out-of-core surfaces that are not shielded, and, in the case of PWRs, the axial offset anomaly (AOA). This latter phenomenon results from the deposition of boron... 

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