Spontaneous symmetry breaking in O(10)

We consider the most general renormalizable O(10) invariant potential for a $\text{45 + 16 +}\text{16}$ representation of Higgs fields. We show that O(10) can be spontaneously broken down to SU(5), SU(4) × U(1) or SU(3) × SU(2) × U(1), this last case being, of course, the most appealing.     

Effects of heavy colored Higgs scalars on SU(5) predictions

We show that the inclusion in the renormalization group equations of heavy colored Higgs scalars present in the grand unified model of SU(5) can affect the predictions of the model. If only the $\text{24}$ and $\text{5}$ of Higgs are present, the effects on the predictions are small. However, if a $\text{45}$ of Higgs were present, it will lead to large uncertainties in the values of sin²θ_W and the lifetime of the proton due to unknown parameters in the Higgs potential; the uncertaity in the latter due to colored Higgs is a factor of 60. The effect on the b-quark mass prediction is also discussed.     

A low right-handed scale in a supersymmetric context

We investigate the prospects for a low right-handed scale M_R in the context of locally supersymmetric O(10), limiting ourselves to the most interesting case of a single breaking scale between the grand unified scale M_X and the W-mass. It is found that supersymmetry seems to imply a unique solution as regards the Higgs content and the intermediate symmetry group if a low right-handed scale (less than 10⁴ GeV) exist at all. Apart from a minimal set of representations providing the symmetry battern, the Higgs sector consist of a pair of 16 and $\text{16}$ spinor representations ying at scale M_R and the residual symmetry is SU(3)_c × U(1)_B?L × SU(2)_L × U(1)_R.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

“Virtual effects of excited quarks as probes of a possible new hardonic mass scale”

The effects of $\text{spin}\text{-}\text{3}\text{2}$ excited quarks are considered as probes of a possible new hadronic mass-scale Λ. A specific model is developed which describes virtual $\text{spin}\text{-}\text{3}\text{2}$ quarks of mass of O(Λ). Induced effects, which are corrections to the standard SU(2) × U(1) electroweak model, include right-handed charged currents and flavor changing neutral currents. A model-independent classification of all SU(3) × SU(2) × U(1) invariant quark operators of dimension six or less is also presented. Ambiguities in converting this analysis and existing experiments to a definitive lower-bound for Λ are discussed. It is found, depending on the strength of certain Higgs couplings and the underlying global flavor symmetries in the absence of Higgs couplings, that a lower bound as small as Λ > 500 GeV or as large as Λ > 100 TeV is possible.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

Higgs bosons and matter-antimatter oscillations in GUTS

The presence of Higgs bosons of diquark and dilepton types at intermediate mass scales in GUTs is analysed in connection with the possible generation of neutron-antineutron and hydrogen-antihydrogen oscillations. Their renormalization effects on the calculation of the parameters sin²θ_w and m_b/m_τ are investigated in SU(5) and in an SO(10) version with a left-right symmetric breaking chain. In correspondence with suitable combination of higgses, we find solutions in SU(5) for n_G=3 and reasonable values of sin²θ_w, m_b/m_τ and proton lifetime τ_p, which allow detectable $\text{n}\text{-}\text{n}$, but undetectable $\text{H}\text{-}\text{H}$ transitions. Solutions of this type, but with higher τ_p, are also found in a particular scheme of SO(10), where the intermediate mass is at the scale M_R at which the left-right symmetry is broken and is of order 10²×m_w. This modifies then conclusions of analyses of SO(10) models, where either no diquarks and dileptons or only a specific set of them are taken into account.An extension of our analysis to supersymmetric versions of SU(5) and SO(10) does not produce acceptable solutions.     

The price of natural flavour conservation in neutral weak interactions

The natural conservation of flavours to O(G_F²) in neutral weak interactions severely constrains choices of gauge groups as well as their fermion representations. In the absence of exactly conserved quantum numbers other than charge, and of |ΔQ| ? 2 charged currents, essentially the only weak and electromagnetic gauge groups whose neutral interactions naturally conserve all flavours are SU(2)_L ? U(1) and SU(2)_L ? [U(1)]². The plausible extensions of these gauge groups to grand unified models including the strong interactions are based on SU(5) and SO(10) respectively. Making the SU(5) model completely natural, including in the Higgs sector, gives the prediction $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{/m}{}_{\mathrm{<mtext>e</mtext>}}\text{? m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{\mu }}\text{? m}{}_{\mathrm{<mtext>b</mtext>}}\text{/m}{}_{\mathrm{\tau }}\text{? 2605}$ where τ is the probable new heavy lepton and b is the conjectured third flavour of charge $\text{?1}\text{3}\text{quark}$. The SO(10) model contains a potential SU(2)_L ? SU(2)_R ? U(1) weak and electromagnetic gauge group, and has a complicated Higgs structure which does not naturally conserve quark flavours.     

Spontaneous CP violation in a Z4 horizontal symmetry model for flavor mixing

The implications of a Z₄ horizontal symmetry model of flavor mixing for CP violation are studied in the framework of minimal SU(2)_L × SU(2)_R × U(1)_{B – L} gauge theory. We show that CP violation in this model arises purely from right-handed currents. We also note that spontaneous breaking of CP symmetry requires a fine tuning of coupling parameters to the level of , which can be avoided by the inclusion of one additional singlet Higgs field, of the kind recently introduced for other purposes.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Possibility of a doubly-charged structure at theS-meson mass

The various symmetry breaking patterns that are possible with a 24-plet and a 5-plet of Higgs fields in SU(5) are classified. Spontaneous breakdown of SU(5) to SU(3)_colour×U(1) _em can be achieved (excluding the gauge hierarchy problem) without imposing unnatural constraints on the parameters of the Higgs potential.     

Spectroscopic amplitudes for complex cluster systems

By expanding the Bargmann-Segal integral transform of nomi and overlap kernels in appropriately SU(3) coupled Bargmann space functions, the calculation of norm and overlap matrix elements in a cluster model basis is reduced to purely algebraic techniques involving the algebra of SU(3) recoupling transformations. This technique has been further developed to make calculations possible for systems of two heavy fragments other than closed-shell nuclei. In one application of the method, analytic expressions are given for the norms of binary fragment systems in which a light fragment of mass number ?, ? ? 4, is combined with a heavy fragment of mass number $\text{A-?,}\text{with}\text{A-? ? 24}$. The $\text{A-?}$ fragment nuclei with different p- and sd-shell structure illustrate somewhat different problems in the recoupling technique. In a second application, spectroscopic amplitudes are calculated for the most important open channels of the ¹²C+ ¹²C resonances. Eigenvalues and eigenvectors of the antisymmetrizer are evaluated in a “molecular basis” of the ¹²C + ¹²C system, in which each ¹²C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations of 0⁺,2⁺ and 4⁺. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: α+²⁰Ne with ²⁰Ne internal functions of (80) SU(3) symmetry, (K = 0⁺ band, and (82) SU(3) symmetry, (K = 2^? band); ¹⁶O+⁸Be; and ²³Na+p or ²³Mg+n fragments with ²³Na or ²³Mg excitations in $\text{K =}\text{3}\text{2}\text{and}\text{1}\text{2}$ rotational bands of SU(3) symmetry (83).     

Yang-Baxter algebras of monodromy matrices in integrable quantum field theories

We consider a large class of two-dimensional integrable quantum field theories with non-abelian internal symmetry and classical scale invariance. We present a general procedure to determine explicitly the conserved quantum monodromy operator generating infinitely many non-local charges. The main features of our method are a factorization principle and the use of $\text{P}$, $\text{T}$, and internal symmetries. The monodromy operator is shown to satisfy a Yang-Baxter algebra, the structure constants (i.e. the quantum R-matrix) of which are determined by two-particle S-matrix of the theory. We apply the method to the chiral SU(N) and the O(2N) Gross-Neveu models.     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

Effective lagrangian of mesons and baryons in the strong-coupling expansion of lattice QCD

U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g²N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈$\text{ψ}\text{ψ}$t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈$\text{ψ}\text{ψ}$〉 coincides very well with that calculated by MC simulations.     

On chiral realizations of confining theories

It is argued that chirality is not necessarily broken in SU(N) colour theories with a chiral flavour symmetry. In this case, massless fermion bound states contributr to anomaly equations, and loop expansions in a 1/N approach are invalid. As a hint to understanding which option is realized by the theory, we investigate it in two dimensions for very small quark masses. The light spectrum shows a rich structure not obtained in a $\text{1}\text{N}$ expansion. Light flavoured baryons and mesons indicate a partial realization of the chiral symmetry.     

Effect of the renormalization group on the symmetry breaking patterns of SU(n) Higgs potentials

As a first step toward the study of the effects of radiative corrections on spontaneously broken potentials we consider the renormalization group equations for those parameters which determine the shape of the potential and the symmetry breaking patterns. As examples we consider the Higgs potential for a single scalar field and for the adjoint represention of SU(n). In the latter case we also obtain some results at the classical level - a new proof of the Michel conjecture, the Higgs mass spectrum and an explicit expression for the parameter that determines the symmetry breaking pattern.     

Gravitational effects on the SU(5) breaking phase transition for a Coleman-Weinberg potential

The gravitational coupling Rφ² plays a crucial role in determining the fate of the symmetric, high temperature state in a graud unified model with Coleman-Weinberg type symmetry breaking. If this term enters in the lagrangian with a negative sign, it drives the SU(5) breaking phase transition at a temperature of about 10¹⁰ GeV. If it enters with a positive sign, and in particular with the coefficient $\text{1}\text{12}$ which is required for a conformally invariant classical theory, this term prevents the phase transition from being completed, at least until temperatures are reached for which the SU(5) coupling becomes large.     

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.     

Kaon in flight excitation of strangeness analog states

Strangeness-exchange reactions induced by kaons in flight on nuclei have been investigated. A two-channel optical potential is derived by folding a suitable chosen $\text{K}\text{N}$ potential that reproduces the $\text{K}\text{N}$ reaction data into the nucleon density. The deduced potential, invariant with respect to the SU(3) Sakata symmetry, describes elastic scattering and the reaction in which the kaon is transformed into a pion, and the target into a strangeness analog state that belongs to the same SU(3) supermultiplet. The calculated cross sections for the excitation of strangeness analog states are for light elements of the order of a few milibarns and show broad giant resonance-like maxima.