Axial Anomalies Research Articles

Characteristics of heat transfer in corrosion products deposited on the surface of pressurized water reactor fuel elements

The occurrence of porous deposits on the core surface during the operation of a pressurized water reactor can seriously affect its heat transfer characteristics and increase the surface temperature of the cladding. Continued heat transfer deterioration causes subcooled boiling and boron enrichment within porous deposits, leading to axial power anomalies in the core, and the study of porous deposits is beneficial to improving the economics and safety of reactor operation. In this paper, a two-dimensional boiling unit model of a porous deposits was established using COMSOL software to couple heat conduction, darcy flow, solute transport and chemical reactions in a multiphysics field to reasonably predict the temperature field, velocity field, boric acid concentration distribution, and PH distribution within the porous deposits. On this basis, the influence of different parameters (porosity, boiling unit radius of porous deposits, heat flow density) on the maximum effective thermal conductivity, the pattern of thermal parameters (temperature, superheat, percentage of subcooled boiling, and saturation temperature) on the chimney boundary are analyzed. The results show that localized superheating, maximum boric acid concentration and subcooled boiling occur at the bottom of the porous deposits. There is a negative correlation between the porosity and the percentage of subcooled boiling area, and a positive correlation between the radius of the porous deposits and the heat flow density and the percentage of subcooled boiling area.

Axion effective potentials induced by heavy sterile fermions

A model of (3 + 1)-dimensional leptogenesis, proposed previously by the authors, requires a CPT Violating (CPTV) background of the Kalb–Ramond (KR) axion field. The KR axion is a pseudoscalar, which is dual to the field strength of the spin-one field present in the massless gravitational multiplet in the theory of closed bosonic strings (compactified to four dimensions). Microscopic models for the emergence of such backgrounds are provided both by low-energy string-inspired gravitational theories with torsion (including (primordial) gravitational and axial gauge anomalies) and by Einstein–Cartan gravity, a closely related simpler model. In this work we examine the pseudoscalar quanta of the KR axion in this background using the methods of effective field theory. In our model for leptogenesis there is a single sterile right-handed neutrino (RHN) with mass m_N. At energies lower than m_N, an axion potential is derived by integrating out at one loop the sterile neutrino in the spirit of effective field theory. The stability of this axion potential is important for the viability of our model. The vacuum of this potential is generally metastable. The stability of the vacuum is determined by the ratio of the torsion-induced-axion coupling (which depends on the string mass scale) to m_N, which should be larger or equal to one, for the validity of our effective field theory. The vacuum is metastable only for axion couplings much larger than the sterile neutrino mass (large string mass scales, e.g. comparable to the four-dimensional Planck mass), with a lifetime much larger than the age of the observable Universe. By contrast, if axion couplings are comparable to the RHN mass the false vacuum is highly unstable, with a lifetime much smaller than the age of the observable Universe; in this case the CPTV leptogenesis scenario is not viable.

Quantum Field Theory Anomalies in Condensed Matter Physics

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.

The diverse pleiotropic effects of spliceosomal protein PUF60: A case series of Verheij syndrome.

Verheij syndrome (VRJS) is a rare craniofacial spliceosomopathy presenting with craniofacial dysmorphism, multiple congenital anomalies and variable neurodevelopmental delay. It is caused by single nucleotide variants (SNVs) in PUF60 or interstitial deletions of the 8q24.3 region. PUF60 encodes a splicing factor which forms part of the spliceosome. To date, 36 patients with a sole diagnosis of VRJS due to disease-causing PUF60 SNVs have been reported in peer-reviewed publications. Although the depth of their phenotyping has varied greatly, they exhibit marked phenotypic heterogeneity. We report 10 additional unrelated patients, including the first described patients of Khmer, Indian, and Vietnamese ethnicities, and the eldest patient to date, with 10 heterozygous PUF60 variants identified through exome sequencing, 8 previously unreported. All patients underwent deep phenotyping identifying variable dysmorphism, growth delay, neurodevelopmental delay, and multiple congenital anomalies, including several unique features. The eldest patient is the only reported individual with a germline variant and neither neurodevelopmental delay nor intellectual disability. In combining these detailed phenotypic data with that of previously reported patients (n= 46), we further refine the known frequencies of features associated with VRJS. These include neurodevelopmental delay/intellectual disability (98%), axial skeletal anomalies (74%), appendicular skeletal anomalies (73%), oral anomalies (68%), short stature (66%), cardiac anomalies (63%), brain malformations (48%), hearing loss (46%), microcephaly (41%), colobomata (38%), and other ocular anomalies (65%). This case series, incorporating three patients from previously unreported ethnic backgrounds, further delineates the broad pleiotropy and mutational spectrum of PUF60 pathogenic variants.

Torsional anomaly in Kerr black hole and quantization in Einstein–Cartan gravity

Recently, presence of gravitational and axial anomalies in Riemann–Cartan (RC) spacetime [Garcia de Andrade, Class. Quantum Gravity 38 (2021)] indicates that topological densities expressed in terms of torsion may be very useful in understanding the physics involved. Pontryagin and Euler density may be presented in terms of torsion in teleparallelism. In this paper, computation of these topological torsional densities in Kerr black holes is given. The geometric quantisation of torsion is also discussed in terms of the teleparallel metric. Actually, the recent work of Del Grosso and Poplawski [arXiv: 2107.06112] showed that the torsion quantization appears when torsion is the generator of momentum quantum mechanical commutator. Moreover, Poplawski et al. showed that use of quantum torsion in quantum electrodynamic (QED) may avoid the divergences in Feynmann integrals, process called, a torsion regularization. Here, we compute the momenta components in terms of teleparallel Kerr black hole torsion generator, like a Casimir tensor. The quantum generator, while not yet related by torsion, is seen to be naturally associated to axial torsion skew-symmetric in the teleparallel geometry. An important fact is that from torsion quantization, torsion chirality appears naturally in the Einstein–Cartan spin-torsion analogy, where now spin-angular momentum of the black hole is connected to torsion. Torsional chiral anomalies are shown to diverge at black hole singularity, and then they cannot be canceled at singularity.

Confined chiral dynamo action in torsional dilatonic DWs from CME discontinuities

In this paper, spin polarized domain walls in Einstein–Cartan (EC) gravity have been recently investigated [L. C. Garcia de Andrade, Einstein–Cartan non-supersymmetric dynamo walls, Ann. Phys. 432 (2021).], where the spin polarizes along the direction orthogonal to planar domain wall. In this case, dynamo effects may appear on the wall. Moreover, dilatonic domain walls (DDWs) have shown to be responsible for inflating DWs in EC gravity, where DWs were non-magnetized [L. Garcia de Andrade, Axial and chiral anomalies in Riemann–Cartan spacetime black holes and electrodynamics, Class. Quantum Grav. 16 (1999) 2097–2103.]. In this paper, our goal is to show that when we consider a magnetized DW in the EC–Maxwell cosmology, the dilaton potential in the form of a DDW potential expressed in terms of torsion and the magnetic energy density may drive dynamo effects. Analytical solution of the dynamo equation shows that depending on the handness of DDW metric, the magnetic fields are amplified by dynamo action. From the coupled system of ECM and dilaton field equations, we find a relation between the magnetic energy density of [Formula: see text] and the DDW torsion of [Formula: see text] which leads to a thin DDW thickness of [Formula: see text]. For a galactic magnetic field, energy density of [Formula: see text] leads to a thickness of [Formula: see text], a much thinner DDW. For galactic dynamo amplification, the ratio r between the magnetic energy density and photon energy density is around [Formula: see text]. From this ratio, a relation between photon mass density and torsion is obtained. Chiral Magnetic effect (CME), torsion and magnetic discontinuities along the wall are investigated. Magnetic field discontinuity across the wall allows us to understand why the magnetic fields at DDW must be located along the wall since the orthogonal magnetic field may vanish.

Dynamo seeds from gravitational torsional anomalies and de Sitter magnetized metrics

Recently gravitational and Nieh–Yan (NY) chiral anomalies have been obtained in Riemann–Cartan space–time (L.C. Garcia de Andrade. Class Quantum Grav. 38(6), 065005 (2021). doi: 10.1088/1361-6382/abd25f ), where electrodynamics is encoded in the metric geometry. In this paper we follow the same pathway by obtaining a class of deformed de Sitter metrics in teleparallelism. The existence of the unmagnetized de Sitter metric (DSMM) without axial anomalies is proved. Unified theories à la Einstein, Eddington, and Schroedinger, called modified de Sitter metrics, present some novel features. First, we show that a pure DSMM in T4 does not induce gravitational anomalies. This is a motivation to study modifications of DSMM. NY torsional anomaly in DSMM teleparallel T4 geometry is shown to vanish in all cases. Gravitational non-trivial anomalies are obtained from these metrics. Torsional anomaly, much used in condensed matter physics, does not vanish. From these deformed DSMM, we show that a dynamo equation with torsional gradient sources is valid from class III of the metrics but is torsionless sourced in class II. We show that in the gravitational anomaly of new deformed de Sitter metric one may cancel the gravitational anomaly, by a proper choice of the metric function. The axial anomaly is obtained for some metric deformation as well. A simple deformation leads to the existence of the NY density in the case of DSMM. This would be class IV of DSMM.

Cosmological constant, axial anomalies and photon mass dynamos from chiral fermionic torsion

Motivated by Palle’s investigation on the handness of chirality of vorticity in Einstein–Cartan cosmology [Entropy 5 (2014)], several aspects of chiral torsional handness in magnetogenesis and cosmology are presented. In the first one, we obtain torsion bounds from massive photons and axial anomalies. In the second, we deal with magnetogenesis from photon mass and in the third, we discuss chiral torsion degrees of freedom to obtain a torsion cosmological constant dependent solution. The torsion solution decays fast and implies a strong suppression of torsion at present universe. Our result contains the Poplawski [Phys. Lett. B (2010)] results in the case axial torsion vector associated to Einstein–Cartan fermionic sector matter and conformal anomalies of quarks. In the third example, a magnetic field bound from chiral torsionic dynamos is obtained as [Formula: see text]. In the non-minimal cosmological models, chiral dynamos are sourced by massive photons, London currents and chiral magnetic effect (CME). Chiral chemical potential is found to be mimic by torsion. Cosmological constant bound [Formula: see text] is found. At the early universe, the cosmological constant [Formula: see text] is obtained. Torsion used in the present universe is [Formula: see text]. In the last and fourth example, chiral anisotropic currents are obtained and magnetic helicity is shown to depend upon torsion when the chiral chemical potential is non-constant.

A Study of Axial Skeletal Anomalies in Common Roach Rutilus rutilus (Cyprinidae) from the Angara River System

A Study of Axial Skeletal Anomalies in Common Roach Rutilus rutilus (Cyprinidae) from the Angara River System

Spinless mesons and glueballs mixing patterns in SU(3) flavor limit

We present a detailed study of the interactions among scalar and pseudoscalar mesons and glueballs within the framework of the generalized linear sigma model in the SU(3) flavor limit. The basis of our approach is to develop a global understanding of light scalar and pseudoscalar mesons (up to around 2 GeV) and thereby explore the underlying mixings among composite quark matter fields and glueballs. The chiral sector of the Lagrangian is formulated in terms of two chiral nonets representing quark-antiquarks and tetraquarks (in the leading order, this sector contains terms with eight or fewer number of quark or antiquark lines). The Lagrangian also contains a sector that represents scalar and pseudoscalar glueballs and their interactions with the matter chiral fields, in a manner that the axial and trace anomalies of QCD are exactly realized. In this construct, the model has two scalar octets and two pseudoscalar octets (each a linear combination of two- and four-quark components), as well as three scalar SU(3) singlets and three pseudoscalar SU(3) singlets (each a linear combination of two- and four-quark components as well as a glueball component). With the inputs of the experimental masses of a0(980), a0(1450), and the masses of π(137), π(1300) and their decay constants, we perform an extensive numerical simulation to determine the boundaries of the parameter space of the model. We further incorporate experimental data on the mass spectrum of eta states as well as on several decay widths and decay ratios of f0 states to zoom in on the parameter space and make predictions for the substructure of pseudoscalar and scalar SU(3) octets and singlets as well as for the pseudoscalar and scalar glueball masses. We find the scalar and pseudoscalar glueball masses around 1.6 and 2.0 GeV, respectively.

Conformal anomaly and helicity effects in kinetic theory via scale-dependent coupling

We modify a kinetic theory of massless fermions to incorporate the effects of the conformal anomaly. Working in a collisionless regime, we emulate the conformal anomaly via a momentum-dependent electric coupling. In this prescription, the conformal anomaly leads to a hedgehog-like structure in the momentum space similar to the Berry phase associated with the axial anomaly. The interplay between the axial and conformal anomalies generates the axial current, proportional to the helicity flow of the electromagnetic background. The corresponding conductivity is determined by the running of the electric coupling between the tip of the Dirac cone and the Fermi surface.

Riemann–Cartan gravitational and axial anomalies in electrodynamics and black holes

In this paper two examples are given of a chiral torsional anomaly Nieh–Yan (NY) topological invariant in Riemann–Cartan (RC) spacetime: in the first it is shown that a certain class of RC spacetime metrics yields a chiral torsional axial anomaly possessing a term proportional to E ⋅ B. Here E and B are respectively the electric and magnetic fields. Besides, since Cartan connection does not vanish, this example is a mixed gravitational axial anomaly. In this case the axial torsional anomaly in RC manifold is computed. Second example is that of a Kerr metric of non-stationary black hole (BH) which possesses gravitational anomaly. The metric which produces the axial anomaly keeps some similarity with Eddington–Schroedinger–Einstein–Strauss metric of unified field theories of gravity and electromagnetism. These ideas, show us the possibility of having analogous BHs models in Weyl semimetals. Moreover, electrodynamics in Cartan spacetime is discussed in this context. This is based on teleparallel metrics used by Letelier (1995 Class Quantum Grav. 12 2221) and Tod (1994 Class Quantum Grav. 11 5). NY RC gravitational anomalies are obtained for BHs Kerr metric using an orthogonal tetrad system.

Torsional Landau levels and geometric anomalies in condensed matter Weyl systems

We consider the role of coordinate-dependent Fermi velocities, equivalent to effective tetrad (or vierbein) frame fields characterizing momentum space geometry, and torsional Landau levels (LLs) in condensed matter systems with low-energy Weyl quasiparticles. In contrast to their relativistic counterparts, they arise at finite momenta and with an explicit cutoff to the linear spectrum. Via the universal coupling of tetrads to momentum, they experience geometric chiral and axial anomalies with gravitational character. More precisely, at low energy, the fermions experience background fields corresponding to emergent anisotropic Riemann-Cartan and Newton-Cartan space-times, depending on the form of the low-energy dispersion. On these backgrounds, we show how torsion and the Nieh-Yan (NY) anomaly appear in condensed matter Weyl systems with an ultraviolet (UV) parameter with dimensions of momentum. The torsional NY anomaly arises from the spectral flow of torsional LLs and the linear Weyl description with a cutoff. We carefully review the torsional anomaly and spectral flow for relativistic fermions at zero momentum and contrast this with the spectral flow, nonzero torsional anomaly, and the appearance of the dimensionful UV-cutoff parameter in condensed matter systems at finite momentum. We apply this to chiral transport anomalies sensitive to the emergent tetrads in nonhomogeneous chiral superconductors, superfluids, and Weyl semimetals under elastic strain. This leads to previously overlooked suppression of anomalous density at nodes from momentum space geometry, as compared to (pseudo)gauge fields. We also briefly discuss torsion in anomalous thermal transport for nonrelativistic Weyl fermions, which arises via Luttinger's fictitious gravitational field corresponding to thermal gradients.

Functional evidence that Activin/Nodal signaling is required for establishing the dorsal-ventral axis in the annelid Capitella teleta.

ABSTRACTThe TGF-β superfamily comprises two distinct branches: the Activin/Nodal and BMP pathways. During development, signaling by this superfamily regulates a variety of embryological processes, and it has a conserved role in patterning the dorsal-ventral body axis. Recent studies show that BMP signaling establishes the dorsal-ventral axis in some mollusks. However, previous pharmacological inhibition studies in the annelid Capitella teleta, a sister clade to the mollusks, suggests that the dorsal-ventral axis is patterned via Activin/Nodal signaling. Here, we determine the role of both the Activin/Nodal and BMP pathways as they function in Capitella axis patterning. Antisense morpholino oligonucleotides were targeted to Ct-Smad2/3 and Ct-Smad1/5/8, transcription factors specific to the Activin/Nodal and BMP pathways, respectively. Following microinjection of zygotes, resulting morphant larvae were scored for axial anomalies. We demonstrate that the Activin/Nodal pathway of the TGF-β superfamily, but not the BMP pathway, is the primary dorsal-ventral patterning signal in Capitella. These results demonstrate variation in the molecular control of axis patterning across spiralians, despite sharing a conserved cleavage program. We suggest that these findings represent an example of developmental system drift.

Photon mass limits driven by axions, Lorentz violation, chiral and gravitational anomalies in non-Riemannian spaces, and helical dynamo seeds

In this paper two types of applications of Cartan torsion to cosmology and quantum field theory are given. The first is given by massive photon axial torsion mixing through non-minimal coupling. It is shown that chiral anomalies induce upper limits on the photon mass and galactic dynamo seeds. In this example we obtain magnetic field seeds of the order of 10−16 G from a strong chiral battery magnetic field of the order of 1030 G. This cosmic magnetic field is in accordance with previous magnetic dynamo seed limits as 10−22 G ≤ Bseed ≤ 10−12 G given by Barrow et al. (Phys. Rev. D, 86, 023533 (2012). doi: 10.1103/PhysRevD.86.023533 ). In this example, as in the Prokopec et al. (Phys. Rev. Lett. 89, 101301 (2002). doi: 10.1103/PhysRevLett.89.101301 ) torsionless case, which associates Dolgov anomalies to photon mass limits, we show that at early universe scales, 10−32 eV is a very stringent limit. Here we can show that the parameter [Formula: see text], which is well within the lower bound of r needed for the magnetic field to seed galactic dynamos. Helical magnetic fields are obtained. One can also derive massive photon limits from axial chiral anomalies with torsion degrees of freedom (Duncan et al. Nucl. Phys. B, 387, 215 (1992). doi: 10.1016/0550-3213(92)90052-D ) leading to photon mass of the order of 10−11 eV. Dynamo equations are obtained from anomalous Maxwell equations as well as magnetic wave equations with photon mass, which are analytically solved. In the second example one shows that Chern–Simons (CS) current is affected by the presence of minimal coupled torsion. In this case as well one obtains a photon mass limit of the order 10−18 eV. Gravitational anomalies in Riemann–Cartan spacetime with axial torsion are also obtained. Recently, Terrano et al. (Phys. Rev. Lett. 122, 231301 (2019). doi: 10.1103/PhysRevLett.122.231301 ) computed dark matter mass constraints of the order of 10−23 eV from spin-polarised torsion balances, which has given some support for torsion theories of Einstein–Cartan type. Here, however, we deal with torsion with dynamical degrees of freedom. Lorentz violation in non-Riemannian CS currents are investigated.

Klippel Feil Syndrome: Clinical Phenotypes Associated With Surgical Treatment.

Retrospective study. To define distinct Klippel-Feil syndrome (KFS) patient phenotypes that are associated with the need for surgical intervention. KFS is characterized by the congenital fusion of cervical vertebrae; however, patients often present with a variety of other spinal and extraspinal anomalies suggesting this syndrome encompasses a heterogeneous patient population. Moreover, it remains unclear how the abnormalities seen in KFS correlate to neurological outcomes and the need for surgical intervention. Principal component (PC) analysis was performed on 132 KFS patients treated at a large pediatric hospital between 1981 and 2018. Thirty-five variables pertaining to patient/disease-related factors were examined. Significant PCs were included as independent variables in multivariable logistic regression models designed to test associations with three primary outcomes: cervical spine surgery, thoracolumbar/sacral spine surgery, and cranial surgery. Fourteen significant PCs accounting for 70% of the variance were identified. Five components, representing four distinct phenotypes, were significantly associated with surgical intervention. The first group consisted of predominantly subaxial cervical spine fusions, thoracic spine abnormalities and was associated with thoracolumbar/sacral spine surgery. The second group was largely represented by axial cervical spine anomalies and had high association with cervical subluxation and cervical spine surgery. A third group, heavily represented by Chiari malformation, was associated with cranial surgery. Lastly, a fourth group was defined by thoracic vertebral anomalies and associations with sacral agenesis and scoliosis. This phenotype was associated with thoracolumbar/sacral spine surgery. This is the first data-driven analysis designed to relate KFS patient phenotypes to surgical intervention and provides important insight that may inform targeted follow-up regimens and surgical decision-making. 3.

Trace and Axial Anomalies on Equal Footing

We discussed that for some particular nonsupersymmetric theories, a generalized symmetry that includes both the scale and axial transformations and leads to a single current may contain also a pseudoscalar term. The method, inspired by the superconformal anomalies, has important application for low-energy effective models where it allows the introduction of a single complex glueball field with a scalar and a pseudoscalar component on the same footing with the complex meson nonet fields made of quarks. Both axial and trace anomalies are satisfied in accordance to the meson structure and the QCD requirements.

Developmental anomalies and South American paleopathology: A comparison of block vertebrae and co-occurring axial anomalies among three skeletal samples from the El Brujo archaeological complex of northern coastal Peru

Though developmental anomalies have been noted for over a century in South American paleopathology, they have received less attention than other pathological conditions. When anomalies are reported, they tend to be unusual case studies or incidental findings. Paleopathological research should also consider anomalies from a population perspective, to broaden our understanding about the frequency of specific anomalies, and potentially offer insight into genetic relationships, cultural behavior, or environmental factors. This investigation compared block vertebrae and co-occurring postcranial axial anomalies among three skeletal samples reflecting an occupational sequence at the El Brujo Archaeological Complex of Peru. Block vertebrae demonstrate both considerable antiquity and persistence through time, though frequencies, vertebral level, and co-occurring anomalies varied by sex and cultural period. Among the Late Preceramic sample, the frequency of C2-C3 block vertebrae was highest and only seen among females, which may suggest familial influence, genetic isolation, and potentially matrilocality. The Moche sample demonstrated a moderate frequency of blocks, which in combination with the frequencies of other developmental anomalies, may suggest population continuity paired with an influx of new genes, demographic expansion, and possible cultural change with regard to postmarital residence. The Lambayeque sample demonstrated the lowest frequency of blocks and the highest frequency and greatest diversity of anomalies, which may suggest genetic continuity from the Moche, an expanded gene pool, broader opportunities for mate choice, and cultural change. It is hoped that this investigation will provide data for future comparisons and call attention to the need for the broader study of developmental anomalies in South America.

Discordant malformations in monochorionic twins: a retrospective cohort study in La Reunion Island

Background: Discordant malformation between monochorionic twins is a rare and unknown phenomenon.Objectives: To estimate the incidence of discordant monochorionic twins and to describe their characteristics.Study design: A retrospective multicenter cohort of pregnancies between 2002 and 2015 in La Reunion Island was analyzed, thanks to a population-based register. Only monochorionic pregnancies were included in order to analyze specifically monozygotic twins. We defined as discordant twin pairs those in which different malformations were identified for each twin and those with only one fetus showing a malformation.Results: During the study period, 203,807 births occurred, including 410 monochorionic twin pairs. Congenital anomalies rate for monochorionic twin pairs was 10.7%. We included 38 monochorionic twin pairs with discordant phenotypes, which represent 9.3% of monochorionic twin pairs and 86.4% of monochorionic twin pairs affected by congenital anomalies. Among them, both twins were affected by different congenital anomalies in 7 pairs (18.4%), and only one twin was affected in 31 pairs (81.6%). We identified 20 congenital heart anomalies (44.4%), 5 brain anomalies (11.1%), 5 genital anomalies (11.1%), 4 axial bones and skull anomalies (8.9%), 4 limb anomalies (8.9%), 4 facial anomalies (8.9%), 3 urological anomalies (6.6%), 2 thoracic anomalies (4.4%), 1 bile duct anomaly (2,2%), 1 abdominal parietal defect (2.2%), and 1 aneuploidy (2.2%). Among them, 3 (6.6%) fetuses had an association of malformations. Among the 45 fetuses with malformations, 37 fetuses (82.2%) were born alive and 21 (46.6%) had postnatal surgery.Conclusions: Despite a supposed identical genome, discordant congenital anomalies in monochorionic twin pregnancies are not exceptional and related to genetic and epigenetic mechanisms. Sonographers and pediatricians should know that in monochorionic twin a pair, the occurrence of discordant phenotypes is high (9.3%).

Dispersive approach to non-Abelian axial anomaly

Manifestations of strong and electromagnetic axial anomalies in two-photon decays of $\eta$ and $\eta'$ mesons are studied. Applying dispersive approach to axial anomaly in the singlet current, we obtain an anomaly sum rule containing strong and electromagnetic anomaly contributions. The relevant low energy theorem was generalized to the case of mixed states and used to evaluate the subtraction constant of the strong anomaly-related form factor $\langle 0 |G\tilde{G} |\gamma\gamma \rangle$. We made a numerical estimation of the contributions of gluon and electromagnetic anomalies to the two-photon decays of $\eta$ and $\eta'$ mesons and found significant suppression of the gluon anomaly contribution.