Axial Anomaly and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and two vector currents triangle diagram of Bardeen, which yields the contribution of the axial anomaly. The octonion possesses the triality symmetry, and there are 5 symmetry operations G _ij and G _ijk (ijk = 123), in which mixing of spinors and vectors occur. G ₂₃ does not mix vectors and spinors, but mismatch of the spinor and vector fields occurs. Hence, electro magnetic (EM) wave emitted from galaxies transformed by the five transformations would not be detected by EM detectors in our galaxy, and the source would be regarded as dark matter. The axial anomaly appears as a reflection of the symmetry of the matter field and not as a reflection of the symmetry of the pure vacuum, which is consistent with recent arguments on condensates and confinement.     

Geometrical Aspects of Skyrmions, Reflection Group, and the Internal Symmetry of Hadrons

The topological aspects of skyrmions are studied and it is shown that hadronscan be viewed as composite states of baby skyrmions when the internal symmetrySU(3) is generated from reflection. It is shown that in an anisotropic space aparticle can move with l = 1/2 with a specific l _x value, and a bosonic constituentmoving with l = 1/2 will appear as a baby skyrmion and a fermionic constituentwill appear as if a spin carrier is attached to a baby skyrmion. The associatedmagnetic field causes a strong statistical attraction which helps to form the boundstate of such constituents. The doublet of such particles having opposite l _x valuesform a conformal spinor when each member behaves as a Cartan semispinor.The conformal reflection then helps us to generate the internal SU(3) symmetry,which splits as SU(3) SU(2) × U(1), giving rise to the hadronic spectra. Thestrong interaction involves a composite cluster in such a bound system whenrearrangement of the constituents takes place preserving the direction vectors,and an elementary constituent can take part in a weak interaction, causing parityviolation. These features help us to consider elementary constituents as knownparticles like leptons.     

The Magnetic Mass of Transverse Gluon, the B-Meson Weak Decay Vertex and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass m _mag becomes approximately equal to T _c at ${T=T_c\sim 1.14\Lambda_{\overline{MS}} \sim 260}$ MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.     

EFV Method with the Constraints of Time Reversal Invariance and Axial Symmetry

Based on the general EFV method,with the constraints of time reversal invariance and axial symmetry,simplified formulas are deduced from the HFB transformation.These results make EFV a practical method in microscopic nuclear structure physics for describing arbitrary spin and parity states in both even-even and odd-odd nuclei,including states with various correlations.     

Breaking of the Axial Symmetry of Terahertz Radiation from Single-Color Filament Plasma

JETP Letters - Two-dimensional distribution patterns of terahertz radiation generated in a laser single-color filament plasma are measured at several frequencies. In the low-frequency region...     

Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for the two spin structures k₀ and k₁ for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure k₀, and no axial anomaly exists in this case.     

Hadrons with charm and beauty

Zeitschrift für Physik C Particles and Fields - By combining potential models and QCD spectral sum rules (QSSR), we discuss the spectroscopy of the $$(b\bar c)$$ mesons and of the (bcq), (ccq)...     

Triality and Quantization of Singularities in Massive Fermion

It is proved that fermions can acquire the mass through the additional non-integrable exponential factor. For this propose the special vector potential associated with the spinor field was introduced. Such a vector potential has closk relation with the. triality property in Dirac spinors and plays crucial role in the construction of massive term. It is shown that the change in phase of a wavefunction round any closed curve with the possibility of there being singularities in our vector potential will lead to the law of quantization of physical constants including the mass. The triality properties of Dirac's spinors are studied and it leads to a double covering vector representation of Dirac spinor field. It is proved that massive Dirac equation in the bosonic representation is self-dual.     

Masses of Ground- and Excited-State Hadrons

We present the first Dyson–Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector–vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Δ masses and those of the dressed-quark and diquark correlations they contain.     

Triality,exotics and the dynamical basis of the quark model

A non-relativistic three-triplet model with a simple two-body interaction is shown to bind only q$\text{q}$ and qqq states. Three triplets and unobserved charmed states are crucial in preventing binding of 4q$\text{q}$ and 2 q$\text{q}$ systems. They provide repulsive channels to make the q$\text{q}$ and 3q systems behave like “neutral atoms” with canceling attractive and repulsive forces between them and additional quarks. The ratio of q$\text{q}$ and qq interactions is just right to bind the q$\text{q}$ and 3q systems properly while leaving the qq system with the mass of a quark.     

CP Properties of Leptons within the Mirror Mechanism

The formation of the quark and lepton mass matrices through intermediate states of heavy mirror fermions is able to reproduce basic observable qualitative properties of weak-mixing matrices—specifically, the Cabibbo—Kobayashi—Maskawa (CKM) matrix and the Pontecorvo—Maki—Nakagawa-Sakata (PMNS) matrix. The reproduction in question includes the hierarchy of the CKM matrix elements and a general form of the PMNS matrix, including the smallness of the neutrino mixing angle θ₁₃ and leads to extremely small neutrino masses. For leptons, these properties arise only if Standard Model neutrinos are Dirac particles and if the spectrum of their generations has an inverse character. In such a lepton system, the mechanism of spontaneous mirror-symmetry violation and the observed mass hierarchy of charged leptons (e, μ, and τ) specify the structure of the PMNS matrix and make it possible to estimate the complex-valuedness of its elements—that is, to assess the CP properties of leptons. In this case, the PMNS matrix does not involve Majorana phases, whereas its Dirac phase δ_CP corresponds to ∣ sin δ_CP ∣ that is substantially smaller than unity.

     

Leptons with high weak isospin and compositeness

Heavy leptons with high weak isospin, predicted in a subcomponent model of quarks and leptons with SU(2)_L × U(1) symmetry, are examined phenomenologically in connection with recently reported anomalous events and super high energy physics. In constructing the effective lagrangian based on the subcomponent structure, I_W = 1 heavy leptons play a special role in the effective interaction.     

Looking into the Matter of Light-Quark Hadrons

In tackling QCD, a constructive feedback between theory and extant and forthcoming experiments is necessary in order to place constraints on the infrared behaviour of QCD’s β-function, a key nonperturbative quantity in hadron physics. The Dyson–Schwinger equations provide a tool with which to work toward this goal. They connect confinement with dynamical chiral symmetry breaking, both with the observable properties of hadrons, and hence can plausibly provide a means of elucidating the material content of real-world QCD. This contribution illustrates these points via comments on: in-hadron condensates; dressed-quark anomalous chromo- and electro-magnetic moments; the spectra of mesons and baryons, and the critical role played by hadron-hadron interactions in producing these spectra.     

Critical Current of the Ionization Waves and Anomaly of the Positive Column in an Axial Magnetic Field

Influences of an axial magnetic field on the ionization wave and the positive column in rare gas discharges are studied experimentally. The upper critical current I_c for the appearance of ionization waves in the magnetic field B is newly found. As B is gradually increased, the value of I_e slightly increases from the Pupp's value and after passing a prominent maximum, finally become very small. In addition an anomaly takes place in the axial electric field E of the positive column stable for helical instabilities. With increasing the magnetic field the value of E goes through a weak maximum before decreasing. It is concluded that this anomaly, apparently incompatible with classical diffusion theory, is closely related to the appearance of ionization waves in the positive column.     

Hadrons and broken symmetries with WASA-at-COSY

The WASA Detector Facility is an internal experiment at the cooler synchrotron (COSY) in Jülich, Germany. The COSY accelerator provides proton and deuteron beams with momenta up to 3.7 GeV/c giving access to hadron physics including the strange quark sector. The physics program with the WASA detector involves hadron dynamics and hadron structure. Key experiments address fundamental symmetries and symmetry violations via the study of rare and not-so-rare meson decays. From the very first production run, results on the Dalitz plot slope parameter in the isospin violating η → 3π ⁰ decay have been obtained. The 3π ⁰ final state is also used to study meson production mechanisms. Investigations of other decay modes of the η-meson address C, P, and T symmetries and combinations. Higher orders in chiral perturbation theory are probed with the η → π ⁰ decay. The status and plans for studying hadron structure with Dalitz decays of mesons are presented.     

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σ_π = m_π/2. This truncation also provides a decent estimate of σ_ρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σ_ρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σ_ω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σ_N and σ_Δ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σ_N ≃ 60 MeV and σ_Δ ≃ 50 MeV.