Symmetries Of Standard Model Research Articles

The algebra of grand unified theories

The Standard Model is the best tested and most widely accepted theory of elementary particles we have today. It may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three ‘grand unied theories’: theories that unify forces and particles by extending the Standard Model symmetry group U(1) SU(2) SU(3) to a larger group. These three are Georgi and Glashow’s SU(5) theory, Georgi’s theory based on the group Spin(10), and the Pati{Salam model based on the group SU(2) SU(2) SU(4). In this expository account for mathematicians, we explain only the portion of these theories that involves nite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.

Strongly coupled semidirect mediation of supersymmetry breaking

Strongly coupled semidirect gauge mediation models of supersymmetry breaking through massive mediators with standard-model charges are investigated by means of composite degrees of freedom. Sizable mediation is realized to generate the standard-model gaugino masses for a small mediator mass without breaking the standard-model symmetries.

Searching for Nambu-Goldstone bosons at the LHC

Phenomenological implications of a minimal extension to the Standard Model are considered, in which a Nambu-Goldstone boson emerges from the spontaneous breaking of a global U(1) symmetry. This is felt only by a scalar field which is a singlet under all Standard Model symmetries, and possibly by neutrinos. Mixing between the Standard Model Higgs boson field and the new singlet field may lead to predominantly invisible Higgs boson decays. The ``natural'' region in the Higgs boson mass spectrum is determined, where this minimally extended Standard Model is a valid theory up to a high scale related with the smallness of neutrino masses. Surprisingly, this region may coincide with low visibility of all Higgs bosons at the LHC. Monte-Carlo simulation studies of this ``nightmare'' situation are performed and strategies to search for such Higgs boson to invisible (Nambu-Goldstone boson) decays are discussed. It is possible to improve the signal-to-background ratio by looking at the distribution of either the total transverse momentum of the leptons and the missing transverse momentum, or by looking at the distribution of the azimuthal angle between the missing transverse momentum and the momentum of the lepton pair for the Z- and Higgs-boson associated production. We also study variations of the model with non-Abelian symmetries and present approximate formulae for Higgs boson decay rates. Searching for Higgs bosons in such a scenario at the LHC would most likely be solely based on Higgs to ``invisible'' decays.

Physics program at the DAΦNE collider upgraded in luminosity

We review the physics program at the Frascati e + e − collider, whose upgrade in luminosity is currently underway, giving a summary of the proposals for experiments at the upgraded collider, and an outlook on the improvement of the measurements of interest for precision tests of the Standard Model, CP and CPT symmetries, and low-energy QCD interactions.

The Surabale of Space-Time and Its Algebra Signature Split

A “surable” is a category given by a special manifold of geometric algebra frames. It is a bale brought on by a surjective map the equivalence classes of which can constitute base elements of the associative algebra. It is also a stranded braid of idempotents based on a sheaf of base unipotents. The stranded braid of idempotents which are thought to represent particles or fields consists of fibers strictly separated by mutual annihilation throughout the bundle. The surabale can be defined on the Clifford algebra of space-time. Then it constitutes a bundle of frames which – though covering all dimensions of the geometric algebra – turn out as isomorphic to the ground space generating the algebra. Because of this, the mass shell and the Dirac-Hestenes equation can be defined on the whole surabale. As a result the equation is preserved when acted on by the symmetries of the transformation group of the standard model. The Kahler-equation simply turns into a Dirac-Hestenes equation on the inhomogenous surabale, yet with the same simple differential 1-forms of the linear equation. This shows very beautifully that the equation of motion as well as the invariance of the surabale under the standard model symmetry can be formulated base free. The Clifford bases – instead of Grasmann – just brings in the riches of representation, that is, the emergence of the standard model. But its grading, in a way, is an illusion. Studying the dimension of the space-time-split in quadratic Clifford algebras, it turns out that the dimension of the positive space-like component reproduces their period-8 properties. Considering as an example the Minkowski space-time in the Lorentz metric rather than in (+ − − − ) we can see that physicists found the electroweak symmetries in the negative part of the geometry, here denoted as $$ {\user1{\mathcal{N}}}^{ - } $$ , but did not realize the strong force symmetries in the positive part since those depend on the graded motion in the graded subspace $$ {\user1{\mathcal{P}}}^{ + } $$ . It is comparatively difficult to find the generators of the group capable to represent the classic SU(3) with its root space A2. Though the approach put forward gives satisfying answers to some classical problems of relativistic quantum mechanics, it does not solve the most important riddle which has been variously pointed out by Professor Oziewicz, namely, mechanics is not governed by the Lorentz- or Poincare-group. The simplest argument to be held against it, is that the Lorentz/Poincare group by definition is the symmetry group of the metric tensor in the empty space-time without bodies and radiation. How can such a Bewegungsgruppe of the empty space-time be related to the physics and mechanics of material bodies? [1], [2] May be this first argument is not convincing enough. But Oziewicz has listed a considerable number of arguments concerning the whole observation process against the present day unquestioned but incorrect application of the full Lorentz group. To clarify this will still need some more fundamental efforts which do not concern the main subject of this paper.

GRAND UNIFICATION AS A BRIDGE BETWEEN STRING THEORY AND PHENOMENOLOGY

In the first part of this paper, we explain what empirical evidence points to the need for having an effective grand unification-like symmetry possessing the symmetry SU(4)-color in 4D. If one assumes the premises of a future predictive theory including gravity — be it string/M-theory or a reincarnation — this evidence then suggests that such a theory should lead to an effective grand unification-like symmetry as above in 4D, near the string-GUT-scale, rather than the standard model symmetry. Advantages of an effective supersymmetric G (224) = SU (2) L × SU (2) R × SU (4)c or SO(10) symmetry in 4D in explaining (i) observed neutrino oscillations, (ii) baryogenesis via leptogenesis, and (iii) certain fermion mass-relations are noted. And certain distinguishing tests of a SUSY G(224) or SO(10)-framework involving CP and flavor violations (as in μ → eγ, τ → μγ, edm's of the neutron and the electron) as well as proton decay are briefly mentioned. Recalling some of the successes we have had in our understanding of nature so far, and the current difficulties of string/M-theory as regards the large multiplicity of string vacua, some comments are made on the traditional goal of understanding vis a vis the recently evolved view of landscape and anthropism.

Symmetric Spaces of Matter and Real Fermion Manifolds

The geometric algebra Cl3,1 generated by the Minkowski spacetime with signature {+++− } possesses a natural ternary partition which provides the Lie algebra of the standard model symmetry in an improved form. The symmetric spaces of matter embed a differentiable manifold of primitive idempotents which represents a real valued fermion space as an 8-dimensional real unitsphere in a 10-dimensional subspace with positive definite signature. The algebraic properties of the present theory of spacetime-matter are developed, beginning with the definiteness of the stabilizer algebra of neutrinos, investigating the orthogonality between fermions and neutrinos and ending with the curvature of the symmetric spaces of the strong force. The model brings together the quantum theory and relativity, as we conceive it at present, such that the standard model turns out to be a definite property of the spacetime algebra.

Split fermions baryogenesis from the Kobayashi-Maskawa phase

A new scenario of baryogenesis is presented, within the split fermions framework. Our model employs a first order phase transition of the localizer field. The standard model (SM), Kobayashi-Maskawa phase induces a sizable CP asymmetry. The usual suppression of CP violation which arises in the SM baryogenesis is absent due to the existence of order one Yukawa couplings before the fermions are localized in the extra dimension. Models of the above type naturally contain B-L violating operators, allowed by the SM symmetries, which induce the baryon asymmetry. Our mechanism demonstrates the following concept: the flavor puzzle and the SM failure to create the baryon asymmetry are linked and may have a common resolution which does not rely on introduction of new CP violating sources.

A NEUTRINO MASS MODEL WITH REFLECTION SYMMETRY

We demonstrate that an SU (2)L× U (1)Y model with the same particle content as Standard Model (SM) and discrete reflection symmetry between second and third generations of leptons gives rise to charged lepton and neutrino mass matrices which can accommodate the present solar, atmospheric, WMAP neutrino experimental results. The model predicts the value of |U13| which could be tested in neutrino factories and the effective Majorana neutrino mass <mee> which is at the lower end of the present experimental value. Neutrino masses are generated through dim=5 operators and the scale of which are constrained by the value of <mee>. If, in future neutrinoless double beta decay experiments namely, MOON, EXO, GENIUS shift the lower bound on <mee> by one order, the present model will fail to accommodate the solar neutrino mixing angle due to LMA solution.

Model building with gauge-Yukawa unification

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling unification, g_i=y_f, in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactification. We consider gauge-Yukawa unified models based on a variety of four dimensional symmetries, including SO(10), SU(5), Pati-Salam symmetry, trinification, and the Standard Model. Only in the case of Pati-Salam and the Standard Model symmetry, we do obtain gauge-Yukawa unification. Partial gauge-Yukawa unification is also briefly discussed.

Classification and Dynamics of Equivalence Classes in SU(N) Gauge Theory on the Orbifold S1/Z2

The dynamical determination of the boundary conditions in SU(N) gauge theory on the orbifold $S^1/Z_2$ is investigated. We classify the equivalence classes of the boundary conditions, and then the vacuum energy density of the theory in each equivalence class is evaluated at one loop order. Unambiguous comparison of the vacuum energy densities in the two theories in different equivalence classes becomes possible in supersymmetric theories. It is found that in the supersymmetric SU(5) models with the Scherk-Schwarz supersymmetry breaking, the theory with the boundary conditions yielding the standard model symmetry is in the equivalence class with the lowest energy density, though the low energy theory is not identically the minimal supersymmetric standard model. We also study how particular boundary conditions are chosen in the cosmological evolution of the universe.

LQGENEP: a leptoquark generator for ep scattering

LQGENEP is a Leptoquark (LQ) generator for electron/positron–proton scattering which simulates processes involving LQ production and exchange using the Büchmuller–Rückl–Wyler effective model. The model is based on the most general Lagrangian compatible with the Standard Model symmetries and conserving lepton and baryon numbers. The generated LQs can have coupling with quarks and leptons belonging to any generation, allowing also the simulation of lepton flavor violating processes with a μ or a τ in the final state. The generator is fully interfaced with the simulation program Pythia which is widely used in the high energy physics community. The interest in the study of such processes, which are clear signs of physics beyond the Standard Model, recently received new boost by the results of the experiments which operates at the ep collider HERA.

Gauge interactions in the dual standard model

We present a geometric argument for the transformation properties of SU(5) --> S(U(3) x U(2)) monopoles under the residual gauge symmetry. This strongly supports the proposal that monopoles of the dual standard model interact via a gauge theory of the standard model symmetry group, with the monopoles having the same spectrum as the standard model fermions.

Supersymmetry and electroweak breaking from extra dimensions at the TeV scale

We analyze some features of the role that extra dimensions, of radius $R$ in the TeV$^{-1}$ range, can play in the soft breaking of supersymmetry and the spontaneous breaking of electroweak symmetry. We use a minimal model where the gauge and Higgs sector of the MSSM are living in the bulk of five dimensions and the chiral multiplets in a four-dimensional boundary. Supersymmetry is broken in the bulk by the Scherk-Schwarz mechanism and transmitted to the boundary by radiative corrections. The particle spectrum is completely predicted as a function of a unique $R$-charge. The massless sector corresponds to the pure Standard Model and electroweak symmetry is radiatively broken with a light Higgs weighing $\simlt$ 110 GeV. The $\mu$-problem is solved and Higgsinos, gauginos and heavy Higgses acquire masses $\sim 1/R$. Chiral sfermions acquire radiative squared-masses $\sim \alpha_i/R^2$. The effective potential is explicitly computed in the bulk of extra dimensions and some cosmological consequences can be immediately drawn from it. Gauge coupling running and unification is studied in the presence of Scherk-Schwarz supersymmetry breaking. The unification is similar to that in the supersymmetric theory.

Possible Candidates for SUSY E6 GUT with an Intermediate Scale

We study the possibility of an intermediate scale existing in supersymmetric E$_6$ grand unified theories. The intermediate scale is demanded to be around $10^{12}$ GeV so that neutrinos can obtain masses suitable for explaining the experimental data on the deficit of solar neutrinos with the Mikheev-Smirnov-Wolfenstein solution and the existence of hot dark matter. We require that at the intermediate scale, a certain symmetry breakdown to the Standard Model symmetry. We show that only a few E$_6$ subgroups are likely to be realized as the intermediate symmetry, though there are many candidates for the intermediate symmetry in E$_6$ GUT.

Dynamics of the Standard Model

Preface Inputs to the standard model Interactions of the standard model Symmetries and anomalies Introduction to effective Lagrangians Leptons Very low energy QCD - Pions and photons Introducing kaons and etas Kaons and the S=1 interaction Kaon mixing and CP violation The large N expansion Phenomenological models Baryon properties Hadron spectroscopy Weak interactions of heavy quarks The Higgs boson The electroweak gauge bosons Appendices References Index.

Gauge invariance and CP-odd (un) observables at LEP

We reexamine some CP-odd observables for the processes e +e −→ ff and e +e −→ ffγ for f = e, μ, τ, q in light of an effective CP-odd lagrangian which respects the standard model symmetry. We find a relationship between some terms of this lagrangian and the well-known dipole moments. Both using this relation and by explicit computation we find that the gauge symmetry systematically induces cancelations which render the observables either difficult or impossible to observe.

Flavor selection rules and two-body decays of charmed mesons into pseudoscalar plus vector mesons

We analyse the measured branching ratios for the Cabibbo-allowed decays of charmed mesons into pseudoscalar plus vector mesons in terms of the flavor SU (3) selection rules of the standard model plus nonet symmetry. Our fit to the invariant amplitudes for the 6 ∗ and 15 interactions indicates that the effective hamiltonian involves comparable admixtures of the two SU (3) representations. The branching ratio for D s→ φπ + is foound to be 2.5% and that for D 0→ K 0∗η is close to its upper limit of 2.9%; the branching ratios for the K ∗+ K 0 and ϱ + η decay modes of the D s are predicted to be 4.3% and 5.8% respectively.

Vector meson dominance and the KSRF relation as consequences of the interplay between the standard electroweak model and hidden local symmetry

The old concept of vector meson dominance and the KSRF relation are shown to be natural consequences (i.e. without the choice of any arbitrary parameter) of the assumption that ϱ mesons are dynamical gauge bosons of a hidden local symmetry in the non-linear chiral lagrangian and of SU(2) L × U(1) Y gauge invariance. This result intrinsically links the standard electroweak model to the strong isospin group.

Primordial magnetic fields and symmetry restoration

In the standard cosmological model symmetry breaking in grand unified theories will occur at times ∼10−39 s after the initial singularity when the Universe has cooled to a temperature ∼1016 GeV. We investigate here whether it is possible for a uniform, large-scale, magnetic field present in the early universe to delay significantly the time at which symmetry breaking occurs. Given the present magnitude of the intergalactic B-field (≲10−11–10−9 G) it is found that no significant effects are introduced.