Configuration-mixed effective SU(3) symmetries

The procedure of Jarrio et al. (Nucl. Phys. A 528, 409 (1991)) for the determination of the effective SU(3) symmetry of nuclear states is extended to small deformations and to oblate nuclei. Self-consistency checks are carried out both for light and for heavy nuclei. Received: 23 April 2002 / Accepted: 25 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: hess@nuclear.unam.mx Communicated by A. Molinari     

Abelian decomposition method for G<Subscript>2</Subscript> gauge theory

The method of Abelian decomposition proposed by Faddeev and Niemi is used to derive the low-energy effective lagrangian of G₂ gauge theory. The G₂ algebra is studied. The commutation relations among the generators of the G₂ algebra are established, based on the framework of its regular maximal subalgebra, an SU(3) algebra. Received: 19 December 2002 / Revised version: 10 January 2003 / Published online: 14 March 2003 RID="a" ID="a" e-mail: suw@phy.ccu.edu.tw     

On the Prasad-Sommerfield dyon (monopole) solution

We prove that the Prasad-Sommerfield dyon (monopole) solution for an SU(2) Yang-Mills field coupled with an SU(2) Higgs multiplet can be associated to a certain minimal immersion in S ³ (SU(2)) i.e. it has a differential-geometric content similar to that of self-dual solutions for the pure SU(2) Yang-Mills field. Implications of this result as well as possibilities to extend it to higher gauge groups are discussed.     

Symmetry in exotic nuclei

Symmetries have played an important role in the elucidation of the structure of nuclei and will continue to do so for exotic nuclei. As an example, an application of pseudo-SU(4) symmetry is discussed. It can be used as a starting point for a boson model that includes T = 0 as well as T = 1 bosons (IBM-4); applications are presented for N = Z nuclei from ⁵⁸Cu to ⁷⁰Br. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: isacker@ganil.fr     

SU(3) classification of p-wave ηπ and π systems

An exotic meson, the π₁(1400) with J ^PC = 1^{- +}, has been seen to decay into a p-wave ηπ system. If this decay conserves flavor SU(3), then it can be shown that this exotic meson must be a four-quark state ( qˉq + qˉq) belonging to a flavor ˉ10 representation of SU(3). In contrast, the π₁(1600) with a substantial decay mode into π is likely to be a member of a flavor octet. Received: 27 March 2002 / Accepted: 8 August 2002 / Published online: 10 December 2002 RID="b" ID="b"e-mail: klempt@iskp.uni-bonn.de Communicated by V. Vento     

Gauge theories with non-unitary parallel transporters: a soluble Higgs model<Superscript>*</Superscript>

It has been proposed to abandon the requirement that parallel transporters in gauge theories are unitary (or pseudo-orthogonal). This leads to a geometric interpretation of Vierbein fields as parts of gauge fields, and non-unitary parallel transport in extra directions yields Higgs fields. In such theories, the holonomy group H is larger than the gauge group G. Here we study a one-dimensional model with fermions which retains only the extra dimension, and which is soluble in the sense that its renormalization group flow may be exactly computed, with G = SU(2) and non-compact , or G = U(2), H = GL(2,C). In all cases the asymptotic behavior of the Higgs potential is computed, and with one possible exception for G = SU(2), H = GL(2,C), there is a flow of the action from a UV fixed point which describes a SU(2)-gauge theory with unitary parallel transporters, to a IR fixed point. We explain how exponential mass ratios of fermions of different flavor can arise through spontaneous symmetry breaking, within the general framework.Received: 2 June 2003, Revised: 14 September 2004, Published online: 21 January 2005PACS: 11.10.Hi, 11.10.Kk, 11.15.Ex, 11.15.Tk, 12.15.Ff, 12.15.HhWork supported by Deutsche Forschungsgemeinschaft.     

Spontaneous symmetry breaking with quaternionic scalar fields and electron-muon mass ratio

We investigate the problem of using quaternionic scalar fields as Higg's mesons in theories of spontaneously broken symmetries. We are led to the symplecticSp(1,Q) U(1) as a possible gauge group for a unified theory of electromagnetic and weak interactions. The features of this model are worked out and compared with those of Weinberg'sSU(2) U(1) model.     

Single <Emphasis Type="Italic">Z</Emphasis>′ production at compact linear collider based on <Emphasis Type="Italic">e</Emphasis>-γ collisions

We analyze the potential of the compact linear collider (CLIC) based on e-γ collisions to search for the new Z′ gauge boson. Single Z′ production on e-γ colliders in two SU(3)_C?SU(3)_L ? U(1)_N models, the minimal model and the model with right-handed neutrinos is studied in detail. The results show that new Z′ gauge bosons can be observed on the CLIC and that the cross sections in the model with right-handed neutrinos are bigger than those in the minimal one.     

Top–bottom mass hierarchy, s-\mu puzzle and gauge coupling unification with split multiplets

Supersymmetric 5D SU(5) grand unification is considered. SU(5) is broken down to by the assignment of the bulk field(s). The matter fields are located at the fixed point(s). In the bulk, a Higgs multiplet (containing the bottom doublet ) and the SU(5) gauge multiplet are located. At one fixed point, (the top doublet) and the standard model matter multiplets are presented. Because of the difference of the locations of and , one can obtain a hierarchy between top and bottom Yukawa couplings. We also present a possible way to understand the s– mass puzzle in this framework of the split multiplet. Received: 10 December 2001 / Revised version: 22 January 2002 / Published online: 5 April 2002     

Non-commutative standard model: model building

A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by _U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just . We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions. Received: 23 January 2003, Published online: 18 June 2003     

Minkowski space Yang-Mills fields from Euclidean self-dual fields

It is examined, if it is possible, to obtain solutions of the SU(2) Yang-Mills field equations in Minkowski space from Euclidean self-dual Yang-Mills fields by method proposed by Bernreuther. It is shown that the conditions, which are imposed on the Euclidean self-dual fields by this method, make every Euclidean self-dual field and the corresponding Minkowski space field obtained from it, equivalent to a pure gauge field, F _ab 0.     

Maximal atmospheric neutrino mixing in an <Emphasis Type="Italic">SU</Emphasis>(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the U(1) _F symmetry associated with a suitably defined family number F, together with a Z₂ symmetry which does not commute with F. U(1) _F is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in additio n, U(1) _F is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale 10¹⁶ GeV < m _U < 10¹⁹ GeV; indeed, we have found a particula r solution to this problem which yields results almost identical to the ones of the minimal supersymmetric standard model. Received: 29 November 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: walter.grimus@univie.ac.at RID="b" ID="b" e-mail: balio@cfif.ist.utl.pt     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

High scale perturbative gauge coupling in R-parity conserving SUSY <Emphasis Type="Italic">SO</Emphasis>(10) with longer proton lifetime

It is well known that in single step breaking of R-parity conserving SUSY SO(10) that needs the Higgs representations , the GUT gauge coupling violates the perturbative constraint at mass scales a few times larger than the GUT scale. Therefore, if the SO(10) gauge coupling is to remain perturbative up to the Planck scale ( GeV), the scale M_U of the GUT symmetry breaking is to be bounded from below. The bound depends upon specific Higgs representations used for SO(10) symmetry breaking but, as we find, cannot be lower than $1.5 \times 10$¹⁷ GeV. In order to obtain such a high unification scale we propose a two-step SO(10) breaking through SU(2)_L $\times$ SU(2)_R $\times$ U(1)_B-L $\times$SU(3)_C ( ) intermediate gauge symmetry. We estimate the potential threshold and gravitational corrections to the gauge coupling running and show that they can make the picture of perturbative gauge coupling running consistent at least up to the Planck scale. We also show that when by the Higgs representations , gravitational corrections alone with negligible threshold effects may guarantee such perturbative gauge coupling. The lifetime of the proton is found to increase by nearly 6 orders over the present experimental limit for . For the proton decay mediated by a dim = 5 operator a wide range of lifetimes is possible, extending from the current experimental limit up to values 2-3 orders longer. Received: 1 July 2005, Revised: 21 August 2005, Published online: 11 October 2005     

Discrete anomalies of binary groups

We derive the discrete anomaly conditions for the binary tetrahedral group as well as the binary dihedral groups . The ambiguities of embedding these finite groups into SU(2) and SU(3) lead to various possible definitions of the discrete indices which enter the anomaly equations. We scrutinize the different choices and show that it is sufficient to consider one particular assignment for the discrete indices. Thus it is straightforward to determine whether or not a given model of flavor is discrete anomaly free.     

Hierarchy of symmetry breakings and neutral currents in anSU(6) grand unification model

In anSU(6) grand unification model with eight quarks and eight leptons belonging to 15-plet and singlet representations, the symmetry is spontaneously broken by the sequenceSU(6)SU(3) ^c ×SU(2)×U(1)×U(1)SU(3) ^c ×U(1). Fror two cases of symmetry breakings the effective weak neutral current coupling constants are compared with experiment. For theSU(3) ^c ×SU(2)×U(1)×U(1)×SU(3) ^c ×U(1) symmetry breaking, the coupling constants reproduce the Weinberg-Salam model with a small correction term. Agreement with the experimental mean values is improved with the correction term. Parity violation in atomic physics is also discussed.     

Strange and singlet form factors of the nucleon: Predictions for G0, A4, and HAPPEX II experiments

We investigate the strange and flavor-singlet electric and magnetic form factors of the nucleon within the framework of the SU(3) chiral quark-soliton model. Isospin symmetry is assumed and the symmetry-conserving SU(3) quantization is employed, rotational and strange-quark mass corrections being included. For the experiments G0, A4, and HAPPEX II we predict the quantities G⁰_E + G⁰_M and G^s_E + G^s_M. The dependence of the results on the parameters of the model and the treatment of the Yukawa asymptotic behavior of the soliton are investigated.     

The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.