Narrow Results

We make a first crude direct estimate of the net gluon polarization in the proton, ΔG, combining data on the asymmetries in high-p_T hadron production from the HERMES, SMC and COMPASS collaborations. Although these data sample a restricted range of x, they provide no hint that ΔG is large. Fixing the normalizations of different theoretical parametrizations using the hadron asymmetry data, we find typical central values of ΔG ~ 0.5, with uncertainties of similar magnitude. Values of ΔG≥2 are disfavored by Δχ² ~ 9 to 20, depending on the parametrization used.

We study the axial anomaly problem in a non-Abelian topologically massive BF model with fermion coupling. The fermion is coupled to the vector and the tensor gauge fields in a non-minimal way.

In this note, we revise the problem of the axial anomaly in the framework of Very Special Relativity following Fujikawa’s path integral approach. We show nonperturbatively that no VSR contribution is present in the path integral measure in (3 + 1)-dimensional spacetime. Furthermore, we extend our results to (1 + 1) dimensions, as well as to the two-dimensional curved spacetime.

Following our previous work [C. Y. Liu, Mod. Phys. Lett. A 36, 2150080 (2021), doi:10.1142/S0217732321500802], we investigate the masses of some pseudoscalar mesons which have the anomalous decays from axial anomaly (the Adler–Bell–Jackiw anomaly). We apply a non-perturbative mass formula to study the neutral single flavor pseudoscalar meson $(f\bar{f})$. We find the mass of pseudoscalar meson $(c\bar{c})(m_{(c\bar{c})}\approx 7.6\mathrm{\text{GeV}})$ which can solve the problem of double $c\bar{c}$ production in $e^{+}{e}^{-}$ annihilation at $\sqrt{s}\approx 10.6\mathrm{\text{GeV}}$ and obtain the mass of pseudoscalar meson $(b\bar{b})(m_{(b\bar{b})}\approx 28.4\mathrm{\text{GeV}})$ which is the same as the invariant mass of ${\mu }^{+}{\mu }^{-}$ pairs produced in association with $b$ jet in $pp$-collisions at the LHC. We generalize this formula to three flavors pseudoscalar mesons, we obtain the mass of ${\eta }^{\prime }$ meson $(m_{{\eta }^{\prime }}\approx 961\mathrm{\text{MeV}})$ which is almost the same as the experimental value $(m_{{\eta }^{\prime }}^{\mathrm{\text{exp}}}\approx 958\mathrm{\text{MeV}})$.

The axial anomaly of the noncommutative U(1) gauge theory is calculated by a number of methods and compared with the commutative one. It is found to be given by the corresponding Chern class.

The noncommutative dipole QED is studied in detail for the matter fields in the adjoint representation. The axial anomaly of this theory is calculated in two and four dimensions using various regularization methods. The Ward–Takahashi identity is proved by making use of a nonperturbative path integral method. The one-loop β-function of the theory is calculated explicitly. It turns out that the value of the β-function depends on the direction of the dipole length L, which defines the noncommutativity. Finally using a semiclassical approximation a nonperturbative definition of the form factors is presented and the anomalous magnetic moment of this theory at one-loop order is computed.

Many meson processes are related to the U_A(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the Feynman graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: (1) by splitting of coordinates in the expression for the axial current and (2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the 't Hooft consistency condition is discussed. A few examples of the physical application of the axial anomaly are given.

We show that parity operator plays an interesting role in Dirac equation in (1+2) dimensions and can be used for defining chiral charges. Further the "anomalous" current induced by an external gauge field can be related to the anomalous divergence of an axial vector current which arises due to quantum radiative corrections provided by triangular loop Feynman diagrams in analogy with the corresponding axial anomaly in (1+3) dimensions. It is shown that the nonconservation of "chiral charge" due to anomaly is related with the topological Chern–Simons charge. As an application pair creation of massless fermions in electric field is discussed.

We calculate the $U$(1) axial-anomaly in two and four dimensions using a modified path integral method coupled to a Pauli–Villars regulator field in the noncommutative QED. Pauli–Villars regularization method provides us with unambiguous way to connect the modified path integral formalism with perturbative axial Ward identities at each step of calculations.

The conservation of the vector current and the axial anomaly responsible for the ${\pi }_0\to \gamma \gamma$ decay amplitude are obtained in leading order within the Taylor–Lagrange formulation of fields considered as operator-valued distributions. As for gauge theories, where this formulation eliminates all divergences and preserves gauge symmetry, it is shown that the different contributions can be evaluated directly in four-dimensional space–time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional nonphysical degrees of freedom like Pauli–Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.

We point out the problems affecting most quark–antiquark bound-state approaches when they are faced with the electromagnetic processes dominated by Abelian axial anomaly. However, these problems are resolved in the consistently coupled Schwinger–Dyson and Bethe–Salpeter approach. Using one of the most successful variants of this approach, we find the dynamically dressed propagators of the light u and d quarks, as well as the heavy c and b quarks, and find the Bethe–Salpeter amplitudes for their bound states π⁰, η_c and η_b. Thanks to incorporating the dynamical chiral symmetry breaking, the pion simultaneously appears as the (pseudo)Goldstone boson. We give the theoretical predictions for the γγ decay widths of π⁰, η_c and η_b, and for the π⁰γ^⋆→γ transition form factor, and compare them with experiment. In the chiral limit, the axial-anomaly result for π⁰→γγ is reproduced analytically in the consistently coupled Schwinger–Dyson and Bethe–Salpeter approach, provided that the quark–photon vertex is dressed consistently with the quark propagator, so that the vector Ward–Takahashi identity of QED is obeyed. On the other hand, the present approach is also capable of quantitatively describing systems of heavy quarks, concretely η_c and possibly η_b, and their γγ-decays. We discuss the reasons for the broad phenomenological success of the bound-state approach of Jain and Munczek.

We formulate natural regularization (NR) as a variant of dimensional regularization (DR). We replace the conventional dimensional reduction by a dimensionless regulator, allowing a transparent regularization of standard D-dimensional Feynman integrals. For arbitrary dimensions, we motivate and demonstrate explicitly the transition from the dimensionally reduced integration space to natural regularization. We establish the relation to cut-off regularization and point out the basic differences from dimensional regularization. Possible applications, such as to the axial anomaly or to gauge theories are briefly touched upon.

Particles are spontaneously created from the vacuum by time-varying gravitational or electromagnetic backgrounds. It has been proven that the particle number operator in an isotropically expanding universe is an adiabatic invariant. In this work we show that, in some special cases the expected adiabatic invariance of the particle number breaks down in presence of electromagnetic backgrounds. We also show a close relation between this breaking of the adiabatic invariance and the emergence of the axial anomaly.

Gribov viewed the axial anomaly as a manifestation of the collective motion of Dirac fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current – this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss the experimental status and recent developments.