Hadronic Symmetry Research Articles

Symmetries and Their Breaking in the Fundamental Laws of Physics

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) × U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark–Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter–antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout–Englert–Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Pseudospin Symmetry as a Bridge between Hadrons and Nuclei

Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativistic origins . We show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei. Since QCD sum rules predict that the sum of the scalar and vector potentials is small, we discuss the quark origins of pseudospin symmetry in nuclei and spin symmetry in hadrons.

Hadron masses in strong magnetic fields

Hadron masses under strong magnetic fields are studied. In the presence of strong magnetic fields exceeding the QCD energy scale $ eB \gg \Lambda^2_{\rm QCD} $, ${\rm SU(3)}_{\rm flavor} \otimes {\rm SU(2)}_{\rm spin}$ symmetry of hadrons is explicitly broken so that the quark components of hadrons differ from those with zero or weak magnetic fields $ eB \lesssim \Lambda^2_{\rm QCD} $. Also, squeezing of hadrons by strong magnetic fields affects the hadron mass spectrum. We develop a quark model which appropriately incorporates these features and analytically calculate various hadron masses including mesons, baryons and those with strangeness.

Axial Anomaly and the Triality Symmetry of Leptons and Hadrons

We apply the supersymmetric model of \'E. Cartan to the pseudoscalar meson decay into two photons, $\pi_0\to\gamma\gamma$, $\eta\to\gamma\gamma$ and $\eta'\to\gamma\gamma$. In the book of \'E. Cartan published in 1966, Dirac spinors ${^t(}A,B)$ and ${^t(}C,D)$ and vector fields $E$ and $E'$ were introduced and five supersymmetric transformations $G_{23}, G_{12}, G_{13}, G_{123}$ and $G_{132}$ were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group ($EE$ or $E'E'$), we call the diagram rescattering diagram. When they belong to different groups ($EE'$), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.

Symmetries of hadrons after unbreaking the chiral symmetry

We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the \Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.

Half-Skyrmions, tensor forces, and symmetry energy in cold dense matter

In a previous article, the 4D half-skyrmion (or 5D dyonic salt) structure of dense baryonic matter described in crystalline configuration in the large $N_c$ limit was shown to impact nontrivially on how anti-kaons behave in compressed nuclear matter with a possible implication on an "ice-9" phenomenon of deeply bound kaonic matter and condensed kaons in compact stars. We extend the analysis to make a further prediction on the scaling properties of hadrons that have a surprising effect on the nuclear tensor forces, the symmetry energy and hence on the phase structure at high density. We treat this problem relying on certain topological structure of chiral solitons. Combined with what can be deduced from hidden local symmetry for hadrons in dense medium and the "soft" dilatonic degree of freedom associated with the trace anomaly of QCD, we uncover a novel structure of chiral symmetry in the "supersoft" symmetry energy that can influence the structure of neutron stars.

MURRAY AND THE OMEGA MINUS

The exciting findings and activities in particle physics in the 50's and 60's will be discussed from an experimentalist's viewpoint. Particular emphasis will be placed on the description of several crucial discoveries (including the omega minus) and on the remarkable insight, guidance, and major contributions of Murray Gell-Mann to the understanding of the symmetry of hadrons which led to the development of the standard model of the strong interactions.

Dilatons in hidden local symmetry for hadrons in dense matter

With the explicit breaking of scale invariance by the trace anomaly of QCD rephrased in terms of spontaneous breaking, low-energy strong interaction dynamics of dense and/or hot matter can be effectively captured by – in addition to the Nambu–Goldstone bosons and the vector mesons – two dilaton fields, the “soft” field that is locked to chiral symmetry and the “hard” field which remains unaffected by chiral symmetry. The scale anomaly in which the soft component intervenes can be shown to vanish at the chiral transition, while that of the hard component remains broken throughout the QCD sector. We argue for a remarkable role of the “homogeneous Wess–Zumino term” of the form ω μ B μ on the structure of a single baryon as well as dense baryonic matter. The emerging structure of the dense hadronic matter so obtained suggests a chiral symmetry restored but (quark-)confined phase at high density and a possible remedy to the defect found in the structure of holographic dense matter described in string theory.

πB8B8andσB8B8couplings from a chiral quark potential model

From an SU(2)$\ensuremath{\bigotimes}$SU(2) chiral quark potential model incorporating spontaneous chiral symmetry breaking the asymptotic $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ exchange pieces of the $\mathit{NN}$ potential are generated. From them the $\ensuremath{\pi}\mathit{NN}$ and $\ensuremath{\sigma}\mathit{NN}$ coupling constants can be extracted. The generalization to SU(3)$\ensuremath{\bigotimes}$SU(3) allows for a determination of $\ensuremath{\pi}{B}_{8}{B}_{8}$ and $\ensuremath{\sigma}{B}_{8}{B}_{8}$ coupling constants according to exact SU(3) hadron symmetry. The implementation of the values of the couplings at ${Q}^{2}=0$ provided by QCD sum rules and/or phenomenology makes also feasible the extraction of the meson-baryon-baryon form factors. In this manner a quite complete knowledge of the couplings may be attained.

On the Lorentz nature of confinement in heavy—light quarkonia

The Lorentz nature of the effective interquark interaction in a heavy—light quarkonium is studied using the vacuum correlators method and the generalized Nambu—Jona-Lasinio potential quark model. An effective scalar interaction is demonstrated to appear self-consistently owing to chiral-symmetry breaking and to dominate for low-lying states in the bound-state spectrum. The relation between such an effective interquark interaction and the QCD string approach is discussed. On the contrary, the upper part of this spectrum is found to be governed by the spatial Lorentz vector interaction which leads to a degeneracy for the states with opposite parity—the so-called restoration of chiral symmetry for excited hadrons.

Isotopic Liftings of Clifford Algebras and Applications in Elementary Particle Mass Matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra \(\mathfrak {su}(6)\) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.

A SIMPLE TOY MODEL FOR EFFECTIVE RESTORATION OF CHIRAL SYMMETRY IN EXCITED HADRONS

A simple solvable toy model exhibiting effective restoration of chiral symmetry in excited hadrons is constructed. A salient feature is that while physics of the low-lying states is crucially determined by the spontaneous breaking of chiral symmetry, in the high-lying states the effects of chiral symmetry breaking represent only a small correction. Asymptotically the states approach the regime where their properties are determined by the underlying unbroken chiral symmetry.

Goldstone bosons decoupling from high-lying hadrons

In this paper, we discuss a decoupling of the Goldstone bosons from highly excited hadrons in relation to the restoration of chiral symmetry in such hadrons. We use a generalized Nambu-Jona-Lasinio model with the interaction between quarks in the form of an instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard self-energy loops for valence quarks. For highly excited hadrons, where the typical momentum of valence quarks is large, the loop contributions represent only a small correction to the chiral-invariant classical contributions and asymptotically vanish. Consequently, the chiral symmetry violating Lorentz-scalar dynamical mass of quarks vanishes. Then the conservation of the axial-vector current in the chiral limit requires, via the Goldberger-Treiman relation, that the valence quarks decouple from the Goldstone boson. As a consequence, the whole hadron decouples from the Goldstone boson as well, which implies that its axial constant also vanishes.

Chiral symmetry for hadrons at finite density(Hadrons at finite density)

Chiral symmetry for hadrons at finite density(Hadrons at finite density)

The priority of internal symmetries in particle physics

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of “Platonic realism.” The notion of physical “structure” is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: (1) According to the so-called “gauge argument,” gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. (2) In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter.

Quantum algebras in phenomenological description of particle properties

Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U q ( su n ) corresponding to Lie algebras of the groups SU n , taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-oscillator algebras along with q-Bose gas picture in modelling the properties of the intercept λ of two-pion (two-kaon) correlations in heavy-ion collisions, as λ shows sizable observed deviation from the expected Bose-Einstein type behavior. The deformation parameter q is in case (i) argued and in case (ii) conjectured to be connected with the Cabibbo angle θ c.

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 lx 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 lx 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.

On a deviation of the precise three flavor symmetry of hadrons from SU(3) F

The celebrated SU(3) F symmetry is shown to be inconsistent with the Noether structure of the fundamental electromagnetic current of the udcs-quark quadrupled when considered in the limit of frozen charm degree of freedom. Thus, the SU(3) F is found to be replaced by the heavy c-quark limit of SU(2) ud⊗SU(2) cs⊗U(1). The resulting three-flavor symmetry has the merit of being consistent from the very beginning with the OZI rule, and thereby respects the underlying QCD gluon dynamics. The difference between the two symmetries is revealed by the properties of the non-isotriplet part of the neutral axial current. The latter is probed by the ηN coupling.

Interior symmetries of hadrons:SO(3,2) as a spectrum-generating group

In this work, we study some applications of the spectrum-generating group (SGG) formalism to obtain the mass-spin spectra of hadrons. The possibility of classifying (medium-energy) hadrons in terms of a symmetry group defining the center-of-mass motion and an SGG defining the interior motion is discussed. After considering the defining commutation relations and equations of motion of the generators of the SGG, it is shown how the hadronic spectral information is obtained through a Hamiltonian that is a constraint relation between the generators of the symmetry group and those of the SGG.

Internal symmetry of hadrons: Finsler geometrical origin

The microlocal space of hadronic matter extension has recently been characterized as a Finsler space. This consideration of hadrons extended as composites of constituents can give rise to a dynamical theory of hadrons. The macrospaces, the space-time of common experience (the Minkowski flat space-time) and the Robertson-Walker background space-time of the universe, are found to appear as the “averaged” space-times of the Finsler space that describes the anisotropic nature of the microdomain of hadrons. From the assumed property of the fields of the constituents in the microspace it is possible to find the field (or wave) equations of the particles (or constituents) through the quantization of space-time at small distances (to an order of or less than a fundamental length). If the field (or wave) function is separable in the functions of the coordinates of the underlying manifold and the directional arguments of the Finsler space, then the former part of the field function is found to satisfy the Dirac equation in the Minkowski space-time or in the Robertson-Walker space-time according to the nature of the underlying manifold. In the course of finding a solution for the other part of the field function a relation between the mass of the particle and a parameter in the metric of the space-time has been obtained as a byproduct. This mass relation has cosmological implications and is relevant in the very early stage of the evolution of the universe. In fact, it has been shown elsewhere that the universe might have originated from a nonsingular origin with entropy and matter creations that can account for the observed photon-to-baryon ratio and total particle number of the present universe. The equations in the directional arguments for the constituents in the hadron configuration are found here and give rise to an additional quantum number in the form of an “internal” helicity that can generate the internal symmetry of hadron if one incorporates the arguments of Budini in generating the internal isospin algebra from the conformal reflection group. This consideration can also account for the meson-baryon mass differences.