SU Color Research Articles

Magnetic monopoles as a new solution to strong CP problem

A non-perturbative solution to strong CP problem is proposed. It is shown that the gauge orbit space with gauge potentials and well-defined gauge transformations topologically restricted on the space boundary in non-abelian gauge theories with a θ term has a monopole structure if there is a magnetic monopole in the ordinary space. The Dirac's quantization condition in the corresponding quantum theories ensures that the vacuum angle θ in the gauge theories must be quantized. The quantization rule for θ is derived as θ = 0,2 π/ n ( n ≠ 0) with n being the topological charge we obtain for the magnetic monopole. Therefore, the strong CP problem is automatically solved non-perturbatively in the presence of magnetic monopoles, with charge ±1 so that θ = ±2 π, or with a very large (| n| ⩾ 10 9 × 2 π) total topological charge for the same generator, or with non-abelian monopoles of more than one non-zero n i corresponding to color SU(3) so that the relevant effective θ = 0. The fact that the strong CP violation can be only so small or vanishing may be a signal for the existence of magnetic monopoles and the universe is open. If there exists an axion field a( x), the value of the physical axion field a phy( x) will not be quantized. However, the expectation value of the CP violating density ϵ μνγσ F μσ a F γσ a will be quantized. For the special values of the topological number n, it can be vanishing or very small even without using the Peccei-Quinn dynamical adjusting. In the usual gauge theories without magnetic monopoles, there may be at most a Z 2 monopole structure in the gauge orbit space in SP(2 N) gauge theories.

Cornering color SU(5).

Planned collider experiments will decisively test the color SU(5) model of Foot and Hernandez, in which an extended QCD group is broken at the TeV scale. Constraints from cosmology and from neutral-kaon mixing imply that exotic charge-1/2 fermions of this model cannot all be given masses above about 1 TeV. These quirks'' carry a new strong confining force, from the surviving unbroken gauge symmetry. Searches for the leptonic decay products of quirkonium at CERN LEP II will probe quirk masses up to near the beam energy, while searches at planned hadron colliders will be sensitive to quirk masses all the way up to the TeV upper bound.

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursNf≧2, whereas forNf=1 it is nonzero for the arbitrary high temperature.

Dynamical Electroweak Symmetry Breaking with Color-Sextet Quarks

Massive quarks belonging to a sextet representation of the color SU(3) of quantum chromodynamics are assumed to exist and to trigger the dynamical breaking of the electroweak SU(2) x U(l) symmetry. Quantum numbers are assigned to the color-sextet quarks and their masses are estimated together with the mass of the top quark by using the mass formulae for the weak-boson masses. Phenomenological implication of the model is discussed.

Global color SU(3) is not a spontaneously broken symmetry in quantum chromodynamics

We find that the global color SU(3) is not a spontaneously broken symmetry in quantum chromodynamics from analysis of the Dyson–Schwinger equation. From this we conclude that the global color symmetry remains exact.

A new electroweak and strong interaction unification scheme

I explore the consequences of requiring the electroweak gauge group to contain an SU(2) subgroup rotating the charged fermions to their antiparticles. This is implemented by coupling the leptons l L, l L c, ν L of each family as a 3 L representation of an electroweak SU(3) gauge group, and coupling the corresponding quarks as a second 3 L and two 3 R's or 3 L ∗'s. In the absence of strong interactions, the model predicts sin 2θ w = 1 4 at the electroweak unification energy. Since the electroweak SU(3) does not commute with the color SU(3) group, the minimal consistent electroweak-strong gauge group is obtained from the closure of their commutator algebra. This has been determined to be the 151-generator semi-simple Lie algebra SU(3) × SU(12), and gives a corrected formula sin 2θ w = 1 4 + 1 3 α/α s at the SU(3) × SU(12) unification energy, which is computed to be 10 10.8±0.8 GeV. Unification in the simple group SU(15) is attained at an energy approximately a factor of 10 higher. To cancel anomalies in the closure group, it is necessary to double the fermion content by adding “mirror” families with the roles of left- and right-handed electroweak couplings reversed with respect to the original families. Extension of the model and embeddings in SO(32) are discussed; in particular, the group SU(15) with two families of fermions and mirror fermions can be embedded in SO(32) with all fermions in the adjoint 496 representation.

The order parameter problem in lattice QCD thermodynamics

The symmetry properties of the effective action of lattice QCD at finite temperature are studied. The findings of our analytical investigations in the approximation based on the “spherical model of a ferromagnet” are employed in argueing that the imaginary part of the Polyakov line could be the order parameter of the phase transition which does not imply spontaneous breaking of Z 3− symmetry, the center of the colour SU(3)-group.

On massless fermions in composite models with exceptional confining groups

A systematic study of the massless fermion problem in composite models with exceptional confining groups has been carried out. It has been shown that for the exceptional groups G 2, F 4, E 6 and E 8 a natural fulfilment of the axial anomaly matching and decoupling (or n-independence) conditions is possible. An exclusive role in the framework of the three-particle composite models of the exceptional E 6 group as well as its difference from the colour SU(3) one are discussed.

Meson-meson interaction with a flip-flop model for quark confinement

The meson-meson interaction with a new type of confinement potential (a flip-flop model) is investigated in the framework of the nonrelativistic quark model. For a particular choice of the parameters describing the confinement of the hidden-color configuration, the meson-meson scattering amplitude is of order 1 N for large N in the case of color SU( N ). This fact agrees with the result of the 1 N expansion phenomenology for the SU( N ) gauge theory. Approximate methods of solution for large tN are presented and effective meson-meson potentials are constructed. The relation between the scattering amplitudes and the bound states of the totally confined system is briefly discussed. The flip-flop model is compared with the conventional models based on two-body confining forces using the resonating group method.

Nucleon-nucleon interaction with a new model for quark confinement

The nucleon-nucleon interaction is studied in the framework of the constituent quark model using a new confinement potential which avoids the difficulties of Van der Waals forces and which is believed to cover the main features of color SU(3) gauge invariance. The calculated phase shifts are in general not much affected and the experimental values are reproduced quite well in case of S- and P-wave scattering. It is shown that the short range repulsion is due to one-gluon exchange, whereas the medium and long range part of the interaction is provided by pion and phenomenological σ-meson exchange.

Numerical simulation of two-dimensional QCD

A Monte Carlo simulation with dynamical fermions and flavour and colour SU(2) on a 16×16 euclidean space-time lattice is presented, using the Wilson lattice fermion action. The screening and spectrum of the theory is studied which is compared to those of the real four-dimensional world.

Higgs couplings in the integer-charge quark model

Colour SU(3) symmetry is broken spontaneously by the introduction of coloured Higgs scalars in the standard SU(3)×SU(2)×U(1) model, so as to make the quarks integrally charged. The resulting couplings of the Higgs bosons with the gauge bosons are worked out.

Baryon-baryon interaction with a flip-flop model for quark confinement: The case of color SU(2)

The baryon-baryon interaction with a new type of confinement potential (a flip-flop model) free from the pathology of the color van der Waals force is studied in the framework of the quark-cluster model in the case of color SU(2). For moderate values of the parameter describing the confinement of the “hidden-color” part, the confinement potential turns out not to contribute to the scattering so much. The Galilei-invariant part of the spin-orbit interaction arising as a relativistic effect from the confinement potential is also studied in comparison with the one from the OGEP. The former does not contribute significantly between baryons even if its strength is determined so as to cancel the latter in the excited state of a single baryon, which suggests the possibility that the latter is an important source of the baryon-baryon spin-orbit interaction. Similar results are expected for the more realistic case of color SU(3).

Color Confinement in Quantum Chromodynamics. II

has been imposed on physical states Iphys) on the assumption of the absence of the spontaneous symmetry breaking with respect to the color charge Qa. **) Since the condition (1·2) puts only a constraint on the total color charge of the state Iphys) integrated over the whole three-dimensional space, this condition may not seem to be sufficient for preventing the colored objects from being observed locally. This objection applies to the cases of the charges constituting a symmetry group which is not semisimpleor which allows the existence of local observables behaving nontrivially under it. For instance, in QED having a non-semisimple gauge group U(1), the observation of electrically charged objects is certainly possible in the chargeless state composed of an electron on the earth and a positron behind the moon. In the case of the rotation group SU(2), it is a (semi)simple group, but rotation-group~variant local observables such as angular-momentum density allow us to measure the spin of a particle in the decay products of a spinless particle. Contrary to these cases, the semisimplicity of the color SU(3) and the absence of colored local observables in QCD have been shown in Ref. 1) to protect the colored particles from being observed in the colorless total state satisfying (1' 2). Let Q 1 and Q 2 be spacetime regions spacelikely separated, the former of which is in our side and the

Algebraic unification

A symplectic geometric algebra is proffered as a setting for a strong-weak-electromagnetic unification theory. Four families of leptons and quarks arise and the neutrinos acquire completely chargeless right-handed components and Dirac masses. A single mathematical origin is found for an exact, nonchiral color SU(3), and a broken, chiral isospin SU(2).

New Scheme for Spontaneous Symmetry Breaking of Color SU(3)

A new spontaneous-symmetry-breaking mechanism is formulated for SU(3), which is used to describe the formation of bags around quarks. The Higgs field is replaced by the scalar product of two colored fermion fields. This model gives mass only to one gluon (equivalent to ${{A}_{\ensuremath{\mu}}}^{8}$) when spontaneously broken. The consequences of this scheme are discussed, and it is argued that it can explain several puzzling high-energy heavy-ion experiments.

More about baryon number violation catalyzed by grand unified monopoles

We investigate the large rates for ΔB ≠ 0 processes catalyzed by grand unified monopoles (GUMs). We demonstrate that a Dirac monopole in the exact low energy colour SU(3) × U(1) electromagnetism group can have large ΔB ≠ 0 cross sections. Therefore there are no factors of exp {−8 π 2/ g 2}, 1/ m x 2 or 1/ m w 2 in the rates for such reactions. Regularizing the Dirac monopole in a specific grand unified theory (GUT) enables one to discuss flavour mixing. We find there is none in simple SU(5) and SO(10) GUTs, and give the low-energy effective ΔB ≠ 0 interaction for more than one fermion generation. We estimate the ΔB ≠ 0 GUM-baryon cross section to be O(10 −3 to 10 −5)/β GeV −2 where β is the GUM velocity. We discuss how proton decay experiments could look for GUMs, including the expected hierarchy of “decay” modes: B → e + π ⪢ B → μ + K ⪢ e + πμ +μ −, μ + Ke + e − ; B↛ e + K, μ +π, ν X and the possibility of seeing a chain of baryon “decays” in a large detector. Astrophysical restrictions on the GUM flux and ΔB ≠ 0 cross sections are studied, and it is found that neutron stars can provide significant but not fatal constraints for β between 10 −3 and 10 −4. In the unlikely event that GUMs were trapped in the sun there could be an observable flux of O(100) MeV neutrinos at the earth's surface. We speculate on the possibility of trapping GUMs and utilizing the energy released if they catalyze baryon “decays” in large quantities.

Monopole Topology and the Problem of Color

Topological obstructions to the definition of unbroken-symmetry transformations in the presence of monopoles with non-Abelian flux are exposed. Consequences for color and electroweak SU(2) in the context of the SU(5) model are discussed.

Raising the axion mass

We present a mechanism which raises the axion mass while maintaining the standard axion-fermion coupling and the removal of strong CP violation. The source of this new contribution to the axion mass is small color SU(3) instantins; these may be important if new physics above the weak interaction scale causes the color coupling constant to grow strong and produces anomalous dimensions for certain many-fermion operators. Strongly interacting hyperquarks may be responsible for both effects. We discuss the working of this mechanism in an explicit hypercolor-sideways interaction model in which a Peccei-Quinn symmetry appears naturally. In this particular model, heavy axion exchange could produce significant DODO mixing.

The heavy quarks static potential in the leading log and the leading log log models

We give numerical and analytical results for the static potential of quasi-abelian quark and antiquark source charges, in the models in which radiative corrections to leading log order, and to leading log plus leading log log order, are retained in the gauge gluon effective dielectric functional. When the scale length of the latter model is fixed to give a second order fit to Martin's phenomenological heavy quark potential, the point of tangency with Martin's curve lies at 0.51 fermi (in the center of the cc̄ and bb̄ quarkonium region), and the long- and short-distance limits yield, respectively, a string tension of 320 MeV, and an asymptotic freedom scale mass of Λ MS =220 MeV [all for color SU(3) with 3 light quark flavors]. Thus, effective action methods, using only renormalization group-improved perturbation theory as input, give a reasonable account of the behavior of the heavy quark-antiquark static potential at all length scales.