Symmetry Group SU Research Articles

Odd-parity light baryon resonances

We use a consistent SU(6) extension of the meson-baryon chiral Lagrangian within a coupled channel unitary approach in order to calculate the T-matrix for meson-baryon scattering in s-wave. The building blocks of the scheme are the pion and nucleon octets, the rho nonet and the Delta decuplet. We identify poles in this unitary T-matrix and interpret them as resonances. We study here the non exotic sectors with strangeness S=0,-1,-2,-3 and spin J=1/2, 3/2 and 5/2. Many of the poles generated can be associated with known N, Delta, Sigma, Lambda and Xi resonances with negative parity. We show that most of the low-lying three and four star odd parity baryon resonances with spin 1/2 and 3/2 can be related to multiplets of the spin-flavor symmetry group SU(6). This study allows us to predict the spin-parity of the Xi(1620), Xi(1690), Xi(1950), Xi(2250), Omega(2250) and Omega(2380) resonances, which have not been determined experimentally yet.

GRAVITY-ASSISTED SOLUTION OF THE MASS GAP PROBLEM FOR PURE YANG–MILLS FIELDS

In 1979, Louis Witten demonstrated that stationary axially symmetric Einstein field equations and those for static axially symmetric self-dual SU (2) gauge fields can both be reduced to the same (Ernst) equation. In this paper, we use this result as point of departure to prove the existence of the mass gap for quantum source-free Yang–Mills (Y–M) fields. The proof is facilitated by results of our recently published paper, J. Geom. Phys.59 (2009) 600–619. Since both pure gravity, the Einstein–Maxwell and pure Y–M fields are described for axially symmetric configurations by the Ernst equation classically, their quantum descriptions are likely to be interrelated. Correctness of this conjecture is successfully checked by reproducing (by different methods) results of Korotkin and Nicolai, Nucl. Phys. B475 (1996) 397–439, on dimensionally reduced quantum gravity. Consequently, numerous new results supporting the Faddeev–Skyrme (F–S)-type models are obtained. We found that the F–S-like model is best suited for description of electroweak interactions while strong interactions require extension of Witten's results to the SU(3) gauge group. Such an extension is nontrivial. It is linked with the symmetry group SU (3) × SU (2) × U (1) of the standard model. This result is quite rigid and should be taken into account in development of all grand unified theories. Also, the alternative (to the F–S-like) model emerges as by-product of such an extension. Both models are related to each other via known symmetry transformation. Both models possess gap in their excitation spectrum and are capable of producing knotted/linked configurations of gauge/gravity fields. In addition, the paper discusses relevance of the obtained results to heterotic strings and to scattering processes involving topology change. It ends with discussion about usefulness of this information for searches of Higgs boson.

Low-lying even-parity meson resonances and spin-flavor symmetry

A study is presented of the $s-$wave meson-meson interactions involving members of the $\rho-$nonet and of the $\pi-$octet. The starting point is an SU(6) spin-flavor extension of the SU(3) flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry breaking terms are then included to account for the physical meson masses and decay constants, while preserving partial conservation of the axial current in the light pseudoscalar sector. Next, the $T-$matrix amplitudes are obtained by solving the Bethe Salpeter equation in coupled-channel with the kernel built from the above interactions. The poles found on the first and second Riemann sheets of the amplitudes are identified with their possible Particle Data Group (PDG) counterparts. It is shown that most of the low-lying even parity PDG meson resonances, specially in the $J^P=0^+$ and $1^+$ sectors, can be classified according to multiplets of the spin-flavor symmetry group SU(6). The $f_0(1500)$, $f_1(1420)$ and some $0^+(2^{++})$ resonances cannot be accommodated within this SU(6) scheme and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances ($I \ge 3/2$ and/or $|Y|=2$) with masses in the range 1.4--1.6 GeV, which would complete the $27_1$, $10_3$, and $10_3^*$ multiplets of SU(3)$\otimes$SU(2).

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

AbstractWe examine the hypothesis that space‐time is a product of a continuous four‐dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this notation is used to determine the spectral data of the standard model. The particle spectrum with all of its symmetries is derived, almost uniquely, under the assumption of irreducibility and of dimension 6 modulo 8 for the finite space. The reduction from the natural symmetry group SU(2) × SU(2) × SU(4) to U(1) × SU(2) × SU(3) is a consequence of the hypothesis that the two layers of space‐time are finite distance apart but is non‐dynamical. The square of the Dirac operator, and all geometrical invariants that appear in the calculation of the heat kernel expansion are evaluated. We re‐derive the leading order terms in the spectral action. The geometrical action yields unification of all fundamental interactions including gravity at very high energies. We make the following predictions: (i) The number of fermions per family is 16. (ii) The symmetry group is U(1) × SU(2) × SU(3). (iii) There are quarks and leptons in the correct representations. (iv) There is a doublet Higgs that breaks the electroweak symmetry to U(1). (v) Top quark mass of 170–175 GeV. (v) There is a right‐handed neutrino with a see‐saw mechanism. Moreover, the zeroth order spectral action obtained with a cut‐off function is consistent with experimental data up to few percent. We discuss a number of open issues. We prepare the ground for computing higher order corrections since the predicted mass of the Higgs field is quite sensitive to the higher order corrections. We speculate on the nature of the noncommutative space at Planckian energies and the possible role of the fundamental group for the problem of generations.

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E 6→SU(3)3 in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E 6 unification, inspired by superstring theory, restores the broken mirror parity at the scale ∼1018 GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E 6→SO(10)×U(1) Z in the O-world, and E′6→SU(6)′×SU(2)′ θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ C ×SU(2)′ L ×SU(2)′ θ ×U(1)′ Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ θ . The assumption that Λ′ θ ≈2.3⋅10−3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E 6, from cosmology.

Phenomenology of a three-family model with gauge symmetry SU(3)c ⊗ SU(4)L ⊗ U(1)X

We study an extension of the gauge group SU(3)c ⊗ SU(2)L ⊗ U(1)Y of the standard model to the symmetry group SU(3)c ⊗ SU(4)L ⊗ U(1)X (3-4-1 for short). This extension provides an interesting attempt to answer the question of family replication in the sense that models for the electroweak interaction can be constructed so that anomaly cancellation is achieved by an interplay between generations, all of them under the condition that the number of families must be divisible by the number of colours of SU(3)c. This method of anomaly cancellation requires a family of quarks transforming differently from the other two, thus leading to tree-level flavour changing neutral currents (FCNC) transmitted by the two extra neutral gauge bosons Z′ and Z′′ predicted by the model. In a version of the 3-4-1 extension, which does not contain particles with exotic electric charges, we study the fermion mass spectrum and some aspects of the phenomenology of the neutral gauge boson sector. In particular, we impose limits on the Z − Z′ mixing angle and on the mass scale of the corresponding physical new neutral gauge boson Z2, and establish a lower bound on the mass of the additional new neutral gauge boson Z′′ ≡ Z3. For the analysis we use updated precision electroweak data at the Z-pole from the CERN LEP and SLAC Linear Collider, and atomic parity violation data. The mass scale of the additional new neutral gauge boson Z3 is constrained by using updated experimental inputs from neutral meson mixing in the analysis of the sources of FCNC in the model. The data constrain the Z − Z′ mixing angle to a very small value of , and the lower bounds on and are found to be of and , respectively.

Superintegrability of the caged anisotropic oscillator

We study the caged anisotropic harmonic oscillator, which is a new example of a superintegrable or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n) but additionally with barrier terms describing repulsive forces from the principal planes. This confines the classical motion to a sector bounded by the principal planes, or a cage. In three degrees of freedom, there are five isolating integrals of motion, ensuring that all bound trajectories are closed and strictly periodic. Three of the integrals are quadratic in the momenta, the remaining two are polynomials of order 2(l+m−1) and 2(l+n−1). In the quantum problem, the eigenstates are multiply degenerate, exhibiting l2m2n2 copies of the fundamental pattern of the symmetry group SU(3).

SU(4)L⊗U(1)Xthree-family model for the electroweak interaction

An extension of the gauge group SU(2){sub L} x U(1){sub Y} of the standard model to the symmetry group SU(4){sub L} x U(1){sub X} (3-4-1 for short) is presented. The model does not contain exotic electric charges and anomaly cancellation is achieved with a family of quarks transforming differently from the other two, thus leading to FCNC. By introducing a discrete Z{sub 2} symmetry we obtain a consistent fermion mass spectrum, and avoid unitarity violation of the Cabibbo-Kobayashi-Maskawa mixing matrix arising from the mixing of ordinary and exotic quarks. The neutral currents coupled to all neutral vector bosons are studied, and by using CERN LEP and SLAC Linear Collider data at Z-pole and atomic parity violation data, we bound parameters of the model related to tree-level Z-Z{sup '} mixing. These parameters are further constrained by using experimental input from neutral meson mixing in the analysis of sources of FCNC present in the model. Constraints coming from the contribution of exotic particles to the one-loop oblique electroweak parameters S, T and U are also briefly discussed. Finally, a comparison is done of the predictions of different classes of 3-4-1 models without exotic electric charges.

FLIPPED SU(5), SEESAW SCALE PHYSICS AND DEGENERATE VACUA

We investigate the requirement of the existence of two degenerate vacua of the effective potential as a function of the Weinberg–Salam Higgs scalar field norm, as suggested by the multiple point principle, in an extension of the Standard Model including seesaw scale physics. Results are presented from an investigation of an extension of the Standard Model to the gauge symmetry group SU (3)C× SU (2)L× U (1)′×Ũ(1), where U (1)′ and Ũ(1) originate at the seesaw scale M SS , when heavy (right-handed) neutrinos appear. The consequent unification of the group SU (3)C× SU (2)L× U (1)′ into the flipped SU (5) at the GUT scale leads to the group SU (5)×Ũ(1). We assume the position of the second minimum of the effective potential coincides with the fundamental scale, here taken to be the GUT scale. We solve the renormalization group equations in the one-loop approximation and obtain a top-quark mass of 171±3 GeV and a Higgs mass of 129±4 GeV , in the case when the Yukawa couplings of the neutrinos are less than half that of the top quark at the GUT scale.

Bi-large neutrino mixing and CP violation in an SO(10) SUSY GUT for fermion masses

We construct a simple SO(10) SUSY GUT with D3 family symmetry and low energy R-parity. The model describes fermion mass matrices with 14 parameters and gives excellent fits to 20 observable masses and mixing angles in both quark and lepton sectors, giving 6 predictions. Bi-large neutrino mixing is obtained with hierarchical quark and lepton Yukawa matrices; thus avoiding the possibility of large lepton flavor violation. The model naturally predicts small 1–3 neutrino mixing, sinθ13≃0.05, and a CP violating phase δ close to π/2. Among other interesting predictions is a tiny effective Majorana mass for neutrinoless double-beta decay. Leptogenesis is also possible with the decay of the lightest right-handed neutrino giving an acceptable CP violating asymmetry ε1 of order 10−6, and with the correct sign for the resultant baryon asymmetry. Note, similar models with the non-Abelian symmetry groups SU(2) or D4, instead of D3, can be constructed.

LOCAL SYMMETRIES BEYOND THE STANDARD MODEL INDICATED BY NEUTRINO RESULTS

The present atmospheric neutrino oscillation data viewed within the context of see-saw mechanism for small neutrino masses, requires right handed neutrino masses (MR) around the conventional GUT scale i.e. 1015 to 1016 GeV. This raises a new hierarchy puzzle i.e. why MR≪Mpℓ? This can be interpreted as an indication in favor of new local symmetries around MR. In this paper, we argue that depending on the nature of neutrino mass patterns, this symmetry could either be: (i) the local B-L symmetry arising from a larger symmetry group such as in the left-right symmetric model of weak interactions, grand unified SO(10) models etc. or (ii) a local horizontal symmetry group SU(2)H operating on the fermions of the first two generations which is often invoked to understand the generation puzzles. We discuss some simple consequences of these symmetries and propose experimental for these ideas.

Higher-dimensional analogue of the Blau–Thompson model and NT=8, D=2 Hodge-type cohomological gauge theories

The higher-dimensional analogue of the Blau–Thompson model in D=5 is constructed by a N T =1 topological twist of N=2, D=5 super-Yang–Mills theory. Its dimensional reduction to D=4 and D=3 gives rise to the B-model and the N T =4 equivariant extension of the Blau–Thompson model, respectively. A further dimensional reduction to D=2 provides another example of a N T =8 Hodge-type cohomological theory with global symmetry group SU(2)⊗ SU(2) . Moreover, it is shown that this theory possesses actually a larger global symmetry group SU(4) and that it agrees with the N T =8 topological twisting of N=16, D=2 super-Yang–Mills theory.

Mysterious zero inAdS5×S5supergravity

It is shown that all the states in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ supergravity have zero eigenvalue for all Casimir eigenvalues of its symmetry group SU(2,2|4). To compute this zero in supergravity we refine the oscillator methods for studying the lowest weight unitary representations of $\mathrm{SU}(N,M|R+S).$ We solve the reduction problem when one multiplies an arbitrary number of super-doubletons. This enters in the computation of the Casimir eigenvalues of the lowest weight representations. We apply the results to SU(2,2|4) that classifies the Kaluza-Klein towers of ten-dimensional type IIB supergravity compactified on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}.$ We show that the vanishing of the SU(2,2|4) Casimir eigenvalues for all the states is indeed a group-theoretical fact in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ supergravity. By the AdS-CFT correspondence, it is also a fact for gauge invariant states of super-Yang-Mills theory with four supersymmetries in four dimensions. This nontrivial and mysterious zero is very interesting because it is predicted as a straightforward consequence of the fundamental local Sp(2) symmetry in 2T-physics. Via the 2T-physics explanation of this zero we find a global indication that these special supergravity and super-Yang-Mills theories hide a twelve-dimensional structure with (10,2) signature.

NEUTRINO MASSES AND THE BARYON ASYMMETRY

Due to sphaleron processes in the high-temperature symmetric phase of the standard model the cosmological baryon asymmetry is related to neutrino properties. For hierarchical neutrino masses, with B-L broken at the unification scale ΛGUT~1016 GeV, the observed baryon asymmetry nB/s~10-10 can be naturally explained by the decay of heavy Majorana neutrinos. We illustrate this mechanism with two models of neutrino masses, consistent with the solar and atmospheric neutrino anomalies, which are based on the two symmetry groups SU(5)×U(1)F and SU(3)c×SU(3)L×SU(3)R×U(1)F. We also review related cosmological bounds on Majorana neutrino masses and the use of Boltzmann equations.

On colour non-singlet representations of the quark–gluon system at finite temperature

We use a group theoretical technique to project out the partition function for a system of quarks, antiquarks and gluons onto a particular representation of the internal symmetry group SU(3): the colour singlet, colour octet and colour 27-plet, at finite temperature. We do this to calculate the thermodynamic quantities for those representations. We also calculate the change in free energy of the plasma droplet formed from the hot hadronic gas. We find that the size of the droplet in the colour-octet representation is smaller than that in the colour-singlet representations at different temperatures in the vicinity of the critical temperatures of the phase transitions.

Chiral symmetry breaking in the AdS/CFT correspondence

We study the SU(3)-invariant relevant deformation of D=4 N=4 SU(N) gauge theory at large N using the AdS/CFT correspondence. At low energies, we obtain a nonsupersymmetric gauge theory with three left-handed quarks in the adjoint of SU(N). In terms of the five dimensional gauged supergravity, there is an unstable critical point in the scalar potential for fluctuations of some fields in a nontrivial representation of the symmetry group SU(3). On the field theory side, this corresponds to dynamical breaking of the SU(3) chiral symmetry down to SO(3). We compute the condensate of the quark bilinear and the two-point correlation function of the spontaneously broken currents from supergravity and find a nonzero `pion' decay constant, f_pi.

Masses of the Higgs and the Z′-gauge boson in broken SU(2)⊗ U(1)⊗ U(1)

A new method is proposed to break the electroweak symmetry group SU(2)⊗ U(1)⊗ U(1) to U em(1) at the electroweak symmetry breaking scale. Generalising the known quadratic and quartic sum rules to include the Z ′ boson, we calculate the value of the masses to be M H ≃203.6±9.7 GeV and M Z ′ ≃221.0±7.1 GeV.

Z′-GAUGE BOSON AND INFLATION IN THE ELECTROWEAK SCALE

An enlarged electroweak symmetry group SU L(2)⊗ U Y(1)⊗ U ′(1) is broken to U em(1) at σ=246 GeV due to radiative corrections. The resulting Coleman–Weinberg potential explains the inflation at 246 GeV scale successfully and the mass of the additional weakly coupled gauge boson Z′ has a value close to 252 GeV accessible to present-day high energy accelerators.

Spontaneous CP Violation from High-Dimensional Operators

We investigate spontaneous CP violation that arises from high-dimensional operators in an effective Lagrangian with the symmetry group SU(3)×SU(2)×U(1)×Z7. We show that such a model does not necessarily require a very large scale Λ by simultaneously satisfying the constraints from the parameter in the neutral kaon system and the electric dipole moment (EDM) of the neutron. We find that the EDM of the electron in this model could be at the level of 10−27 ecm. However, the CP violating muon polarizations in η ,KL → μ+μ− decays are small.

The large- N expansion of unitary-matrix models

The general features of the 1/ N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the large- N properties of spin and gauge models possessing the symmetry group SU( N)×SU( N). An extensive discussion of the known properties of the single-link integral (equivalent to YM 2 and one-dimensional chiral models) includes finite- N results, the external field solution, properties of the determinant, and the double scaling limit. Two major classes of solvable generalizations are introduced: one-dimensional closed chiral chains and models defined on a d−1 dimensional simplex. In both cases, large- N solutions are presented with emphasis on their double scaling properties. The available techniques and results concerning unitary-matrix models that correspond to asymptotically free quantum field theories (two-dimensional chiral models and four-dimensional QCD) are discussed, including strong-coupling methods, reduced formulations, and the Monte Carlo approach.