Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Chirality index and dimensional reduction of fermions

The number of four-dimensional chiral fermions obtained from dimensional reduction of models with spinor matter fields coupled to pure gravity in d > 4 dimensions is linked to topological properties of the internal d ? 4 dimensional space. This gives important restrictions on possible ground states of such models consistent with a realistic four-dimensional unified theory. Connections with spontaneous symmetry breaking and Yukawa couplings of fermions in unified theories are discussed.     

Confront holographic QCD with Regge trajectories of vectors and axial-vectors

By matching the predictions of the Dp–Dq soft-wall model in type II superstring theory with the spectra of vector and axial-vector mesons, we show the dependence of the Regge trajectories parameters on the metric parameters of the model. From the experimental results of Regge parameters for vector mesons, it is found that the D3 background brane with both q=5 and q=7 probe brane and D4 background brane with q=4 probe brane are close to the realistic holographic QCD. We also discuss how to realize chiral symmetry breaking in the vacuum and asymptotic chiral symmetry restoration in high excitation states. We find that the constant component of the 5-dimension mass square of axial-vector mesons plays an efficient role to realize the chiral symmetry breaking, and a small negative z ⁴ correction in the 5-dimension mass square is helpful to realize the chiral symmetry restoration in high excitation states.     

Role of square root threshold singularity in current algebra and chiral symmetry breaking calculations of Kℓ3, Kℓ4 and τ →πKν decays

It is shown that discrepancies between soft pion current algebra (or chiral symmetry) calculations in K?₄ and experiments are mostly due to the square root threshold singularity of the pion-pion interaction. For the same reason, chiral symmetry breaking calculations of the scalar K?₃ form factor cannot be extended to the threshold of τ → Kπν decay.     

Model building on asymmetric Z3 orbifolds: Non-supersymmetric models

Four-dimensional string models arising in the asymmetric Z₃ orbifold compactifications of the heterotic string are studied. A mechanism for supersymmetry breaking that gives rise to chiral models in four dimensions is presented, and some typical models are discussed. A formalism for calculating one-loop partition functions in Z₃ models is developed. One partition function is constructed that may correspond to a non-supersymmetric, tachyon-free theory, with a vanishing cosmological constant as a consequence of Atkin-Lehner symmetry. The negative result of a search for the model corresponding to this partition function is reported.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

Hierarchical chiral symmetry breaking and quark mass matrices revisited

We demonstrate how the assumption of hierarchical chiral symmetry breaking can be systematically used to create phenomenologically satisfactory mass matrices. In place of postulating a particular set of mass matrices at the outset, we emphasize that once a particular basis for the first stage of chiral symmetry breaking is selected, the following steps are determined by the known information on quark masses and mixings. We illustrate this procedure for the basis originally chosen by Fritzsch and find a modified set of quark mass matrices, corresponding to equal final-stage nondiagonal radiative contributions, which fits the data much better in the minimal Higgs framework, providedm _t ?88 GeV and the mixing ratio |V _ub |/|V _cb |?0.15.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

Spontaneous breakdown of the gauge chiral symmetry and the cabibbo angle

From the general treatment of the spontaneous breakdown of the chiral SU(3)xSU(3) group down to the electromagnetic U(l) gauge group it is conjectured that the bare Cabibbo angle isπ/4. Imposing the self-consistency condition of Cabibbo and Maiani on the weak and electromagnetic corrections to the chiral symmetry breaking Hamiltonianh=ε₀ u ₀+ +ε₃ u ₃+ε₈ u ₈ leads to the determination of the physical Cabibbo angle. The agreement with the experimental value is reached when the parametrization ofh of Brandt and Preparata is used.     

Structure and experimental consequences of chiral SU3 × SU3 breaking

Chiral SU₂ × SU₂ breaking, Cabibbo angle, non-electromagnetic isospin breaking, η → 3π decay rate, and pion and kaon mass differences are related to one another in a nonlinear Lagrangian model of broken chiral SU₃ × SU₃ symmetry. The agreement with experiment is very good.     

Chiral U(1) symmetry and weak neutral currents at high energy

If chiral U(1) symmetry is a gauge symmetry, CP is automatically conserved despite the instanton effects, and the weak neutral currents have a definite structure. A realistic SU(2) _L ?U(1)?U(1) _R model contains an axion which is consistent with present data. Furthermore the neutrino interactions to lowest order are identical to the Weinberg-Salam model. Implications for the chiral U(1) currents are discussed.     

Departures from chiral symmetry

We review the physical concepts supporting the notion of an approximate hadron symmetry with special emphasis on the Nambu-Goldstone realizations of chiral SU (2) × SU (2) and SU (3) × SU (3). We stress the role of perturbation theory in the symmetry breaking as the technical instrument to connect broken symmetries with experiment. This is an alternate to the treatments that stress PCAC and current algebra. We find that chiral SU (2) × SU (2) is a good hadron symmetry to within 7% making it the best hadron symmetry after isotopic symmetry. The nonrenormalization theorem, Σ-terms, K_l3 decay, η→3π decay, the Goldberger-Treiman relation and many other specific processes and their relation to approximate chiral symmetry are discussed.     

Renormalisation group improved leptogenesis in family symmetry models

We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli–Feruglio A₄$A_4$ model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of right-handed neutrino masses. More generally, the results of this paper show that RG corrections to leptogenesis cannot be ignored for any family symmetry model involving sizeable neutrino and τ Yukawa couplings.     

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

Chiral quarks,chiral limit,nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactions, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (μ/Λ_χ)² and higher.     

Light hadron spectra in the constituent quark model with the Kobayashi-Kondo-Maskawa-’t Hooft effective UA (1) symmetry breaking interaction

We make a critical comparison of several versions of instanton-induced interactions present in the literature, all based on ITEP group’s extension to three colours and flavours of ’t Hooft’s effective lagrangian, with the predictions of the phenomenological Kobayashi-Kondo-Maskawa (KKM) chiral quark lagrangian. We analyze the effects of all versions of the effective U_A (1) symmetry breaking interactions on light hadron spectra in the non-relativistic constituent quark model. We show that the KKMT force, when used as a residual hyperfine interaction reproduces the correct ordering of pseudoscalar and vector mesons even without explicitly taking chiral symmetry into account. Moreover, the nucleon spectra are also correctly reproduced, only the Roper resonance remains too high, albeit lower than usual, at 1660 MeV. The latter’s lower than expected mass is not due to a small excitation energy, as in the Glozman-Riska (GR) model, but to a combination of colour, flavour, and spatial wave function properties that enhance the relevant matrix elements. The KKMT interaction explicitly depends on flavour and spin of the quarks, but unlike the GR flavour-spin one it has a firm footing in QCD. In the process we provide several technical advances, in particular we show the first explicit derivation of the three-body Fierz transformation and apply it to the KKM interaction. We also discuss the ambiguities associated with the colour degree of freedom.     

On the breaking of chiral symmetry in the Schwinger model

The Schwinger model is reinvestigated in the A₁ = 0 gauge. Based on the explicit operator solution, it is suggested that the breaking of chiral symmetry is dynamical and the vacuum is unique contrary to the arguments by Kogut and Susskind.