The spontaneous breakdown of chiral symmetry in the semiclassical method: (I). Boundary condition on the path integral

It is suggested that the usual path integral representation of the euclidean vacuum amplitude in QCD must be supplemented by the explicit boundary condition corresponding to the spontaneous breaking of chiral SU(N) × SU(N). The analogy with the quantum mechanical example naturally leads to the trial wave function of Nambu and Jona-Lasinio and this in turn gives the starting point for self-consistent calculation.     

A study of 75Se by neutron capture and the SU(3)-SU(5) transition in the quadrupole-phonon representation

The γ and e^? spectra following thermal neutron capture in ⁷⁴Se were studied with curved-crystal, β, and pair spectrometers. Precise energies have been obtained for the transitions and levels at low energies. Two primary E2 transitions were found. The neutron separation energy for ⁷⁵Se was determined as 8027.6 keV. Precise γ-energies following the electron capture decay of ⁷⁵Se were also measured, resulting in precise level energies in ⁷⁵As. The calculation of the energy levels in ⁷⁵Se has been performed in the SU(6) particle-vibrational model (PTQM) and 27 theoretical states have been tentatively assigned to the experimental levels. The spectrum of the core nucleus ⁷⁴Se has been calculated in the SU(6) quadrupolephonon model (TQM). The structure of theoretical states, the relation to SU(3) and SU(5) limits, and potential energy surface are discussed. The E2, M1 and E1 transitions have been calculated in PTQM and compared to the experiment. Also, an overview is presented of theoretical explanations of the I = j, j?1, j?2 anomalous triplet emphasizing the rule with shell-model classification corrected for quadrupole phonons.     

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.     

Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU(N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.     

Grand unified theories in the framework of the SU(N) group

Due to the problem of flavour, the general SU(N) gauge group is considered as a candidate for grand unification. Starting from a set of general requirements, we find restrictions and conditions for the construction of grand unified theories within the framework of such a group. The allowed groups get restricted to SU(6), SU(7) and SU(8).     

The complete N = 3 matter coupled supergravity

The complete N = 3 matter coupling to supergravity is obtained in a geometrical framework. This coupling always exists if the 3n complex scalars of the n vector multiplets are co-ordinates of the Kähler-grassmannian manifold SU(3, n)/SU(3) × SU(n) × U(1). Subgroups of SO(3, n) ⊂ SU(3, n) of dimension 3 + n can be gauged and give rise to a non-trivial scalar potential. The techniques used in this paper allow for the calculation of scalar potentials of extended supergravities in any dimension without explicit construction of the lagrangian. This opens the possibility of discussing patterns of partial supersymmetry and gauge symmetry breaking on a purely group-theoretical ground.     

Fermionic composite models from confining SU(2)L

A class of fermionic composite models with SU(2)_L as confining group is discussed utilizing the notion of complementarity. The models are, in some sense, fermionic realizations of the bosonic Abbott-Farhi model, avoiding fundamental scalars. Model A has SU(2)_L as confining group; model B has an additional chiral SU(M) and coincides with a model by Abbott, Fahri and Schwimmer; model C has an additional vector SU(M) and provides for a closer realization of the original basonic model.     

On the structure of the QCD vacuum in the large-N limit

We present an approximate QCD vacuum for SU(N → ∞). It is a generalization of the ferromagnetic vacuum first obtained by Savvidy for SU(2) and generalized by one of us to SU(3) and SU(4). Problems occuring for N ? 5 are handled in the large-Nlimit by a contnious formalism, and the vacuum obtained is characterized by N ? 1 constant, commuting, color magnetic fields with an isotropic distribution of spatial directions. The energy density of this vacuum is lower than of the perturbative vacuum by a number proportional to N², as expected from general large-N arguments. Like the Savvidy vacuum the large-N vacuum may decay into a variant of the domained Copenhagen vacuum. We give a lower limit on the domain size.     

Loop average for a baryon in the largeN limit

The Schwinger Dyson equation for the Wilson loop is derived for a baryon in theSU(N) gauge group. The obtained equation is linearized in the largeN limit and is shown to yield the planar diagrams to the first and second order in the coupling constant square. The connection with the string model is discussed.     

Amplitude analysis of Kaon-nucleon scattering data

The KN scattering amplitudes have been extracted from experimental data in the energy range 3 ? k ? 14 GeV/c and for transfer values between ?0.05 and ?0.6 GeV².The ω and P+f helicity-flip amplitudes and the A₂ helicity non-flip amplitude have been neglected; it is shown, that these simplifications are compatible with the data and have no significant influence on our results. One needs to assume the approximate validity of SU(3) symmetry for the ? and A₂ couplings. A very important constraint for this analysis comes from recent experimental data for the reaction K_L⁰p → K_S⁰p. The results for A₂ and ω exchanges are analysed as functions of momentum transfer and energy and we test several current theoretical ideas. Information about f-exchange is also obtained when some further assumptions are made concerning SU(3) symmetry and duality at t = 0. Extrapolating the amplitudes to t = 0 a comparison is made with dispersion relation calculations; at other t-values we compare with results obtained from finite energy sum rules and other analyses based on fixed f analyticity. The predictions for KN data which have not been considered in this analysis are shown to be in good agreement. One of our results is that the ?-ω universality rule is approximately satisfied; we also find a strong indication for a peripheral behaviour of the imaginary part of the non-flip f-exchange amplitude.     

Chiral dynamics andK l4 form factors

The axial vector form factors for the decayK _l4 are studied in the context of effective Lagrangian invariant under chiralSU(3)?SU(3) symmetry. The hadronic part of the process is converted into a scattering process by using a field-current identity and the amplitude in turn is calculated by assuming pole dominance. The relations for the form factors thus obtained are (in some soft limit) consistent with those of current algebra and Veneziano model.     

Asymptotic freedom in extended conformal supergravities

We present the calculation of the one-loop β-function in extended conformal supergravities. N = 1, 2, 3, theories (free or coupled to the Einstein supergravities) are found to the asymptotically free (like the N = 0 Weyl theory) while the N = 4 theory becomes finite under some plausible hypothesis. The results support the possibility to solve the problem of ghosts in these theories. The obtained sequence of SU(N) β-functions appears to be in remarkable correspondence with that for gauged O(N) supergravity theories.     

A grand unification preon model with E6 metacolor

We have constructed a version of the chiral three-preon model E₆ × SO(10) that satisfies the condition of asymptotic freedom in the metacolor and composite color-flavor sectors. The construction is based on the global color-flavor symmetry group SU(18). By applying the 't Hooft anomaly matching condition to the subgroup SU(16) × SU(2) of SU(18), together with a few physical constraints, we obtain a unique solution that gives rise to precisely three generations of the spinorial representation 16 of SO(10) without exotics. Except for N = 18, no solution exists for the global color-flavor group satisfying metacolor asymptotic freedom (N < 22) when SU(N) breaks to SU(16) × SU(N − 16).     

Representation mixing and the ideal description of mesons

Representation mixing of meson states is considered with particular reference to the 1 ←→ 15 mixing in SU(4). The 16 meson states are assigned to the representation (4*, 4) of a non-chiral group SU(4) ? SU(4), whose factors are related by charge-conjugation. Mass formula, mixing angles and electromagnetic mass shifts are rigorously derived. Connection of the present formalism with conventional quark model is pointed out and generalisations to higher groups SU(n) ? SU(n) as well as to higher representations, are indicated.     

On the sign of the n-p mass difference in gauge models

We examine the sign of the n-p mass difference in some gauge models based on the SU(2) × U(1) × U(1) or SU(2)_L × SU(2)_R × U(1) group, and show that a few specific elements of the neutral-vector-meson mass matrix can determine the sign of Δm|_n?p. We also present an SU(2) × U(1) × U(1) model which can give the correct Δm|_n?p.     

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3)^c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν_e). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν_e). It turns out that the result is sensitive to the ratios x_(i) = M_{H (i)}/M_X where M_H(i) are the masses of the twelve superheavy Higgs scalars in the $\text{24}$ multiplet which breaks SU(5) → SU(3)×SU(2)×U(1).     

Mixing of leptonic number in a general SU(2)L ⊗ U(1) ⊗ SU(2)R model

We discuss a general leptonic model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group and we present general results for the ? → ?′ γ and ν? → ν?′γ processes, which can be used for any model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group or on any of its subgroups. The predictions of the μ → eγ branching ratio and of the neutrino lifetime for various models discussed in the literature are reviewed. The main results are summarized in tables.     

Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

     

Correlations and static energies in the standard Higgs model

Correlations in the W-boson and Higgs boson channels and the static energy of an external SU(2) doublet charge pair are investigated by Monte Carlo calculations in the SU(2) lattice gauge theory with a scalar Higgs doublet field. The mass ratio m_W/m_H and the shape of the static potential are used to obtain information on the renormalization group trajectories in the three-dimensional coupling constant space. As a function of an appropriately chosen varibale, the measured quantities are, within errors, independent from the scalar self-coupling (λ) in a wide range 0.1 ⩽ λ ⩽ ∝. In the Higgs phase, a lower bound m_W/m_H ⩾ (1.0 ± 0.3) is obtained for the ratio of the Higgs boson mass to the W-boson mass.     

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.