SU Color Research Articles

Dynamics of superconformal axion: Quality and scalegenesis

We explore a dynamical mechanism to realize the emergence of a global U(1)PQ symmetry and its spontaneous breaking at an intermediate scale for an axion solution to the strong CP problem. Such a dynamics is provided by a new supersymmetric QCD near the middle of conformal window that couples to fields spontaneously breaking the U(1)PQ symmetry. A large anomalous dimension of the U(1)PQ breaking fields leads to the suppression of explicit U(1)PQ-violating higher dimensional operators. The U(1)PQ breaking vacuum is generated at a scale hierarchically smaller than the Planck scale by a non-perturbative effect. The U(1)PQ breaking drives the conformal breaking, and all the new quarks become massive. The axion potential is generated by the ordinary color SU(3)C effect as the U(1)PQ symmetry is only anomalous under the SU(3)C. The saxion direction is stabilized by supersymmetry breaking and cosmologically harmless.

The ℤ2 anomaly in some chiral gauge theories

We revisit the simplest Bars-Yankielowicz (BY) model (the ψη model), starting from a model with an additional Dirac pair of fermions in the fundamental representation, together with a complex color-singlet scalar ϕ coupled to them through a Yukawa interaction. This model possesses a color-flavor-locked 1-form ℤN symmetry, due to the intersection of the color SU(N) and two nonanomalous U(1) groups. In the bulk, the model reduces to the ψη model studied earlier when ϕ acquires a nonzero vacuum expectation value and the extra fermions pair up, get massive and decouple (thus we will call our extended theory as the “X-ray model”), while it provides a regularization of the ℤ2 fluxes needed to study the ℤ2 anomaly. The anomalies involving the 1-form ℤN symmetry reduce, for N even, exactly to the mixed ℤ2 anomaly found earlier in the ψη model. The present work is a first significant step to clarify the meaning of the mixed ℤ2 − [ {mathbb{Z}}_N^{(1)} ]2 anomaly found in the ψη and in other BY and Georgi-Glashow type SU(N) models with even N.

Long-lived electroweak-singlet colored scalars

There has been much recent interest in long-lived massive particles at the LHC, understood as those with lifetimes between tens of micrometers and several meters. In this context, we consider the possibility of long-lived electroweak singlet scalars charged under the color SU(3) with masses near a TeV. The shortest lifetime of interest is already longer than typical hadronization scales. These exotic new particles would therefore appear as color-singlet bound states of the new scalars with quarks and gluons, and it is their color charge that prevents them from decaying. In particular, we consider color representations consistent with maintaining asymptotic freedom, those with dimensionality ${d}_{R}\ensuremath{\le}15$. We find that only the octets can decay, and they do so into multijet final states through the two-gluon channel. The other representations are stable and form fractionally charged color singlets, with the decuplet being the only one that can form electrically neutral color singlets.

Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra

In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the SU(3) colour, the SU(2) flavour, and broken SU(3) providing the family triplets. In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the SU(3) colour algebra is endowed with natural Z3-graded discrete automorphisms, in order to introduce entanglement the Z3-graded version of Lorentz algebra with its vectorial and spinorial realizations are considered. The colour multiplets of quarks are described by 12-component colour Dirac equations, with a Z3-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We show that all quarks in the Standard Model can be described by the 72-component master quark sextet of 12-component coloured Dirac fields, which is required in order to implement the faithful spinorial representation of the Z3-graded Lorentz transformations.

Axion quality from superconformal dynamics

We discuss a possibility that a superconformal dynamics induces the emergence of a global U(1)PQ symmetry to solve the strong CP problem through the axion. Fields spontaneously breaking the U(1)PQ symmetry couple to new quarks charged under the ordinary color SU(3)C and a new SU(N) gauge group. The theory flows into an IR fixed point where the U(1)PQ breaking fields hold a large anomalous dimension leading to the suppression of U(1)PQ-violating higher dimensional operators. The spontaneous breaking of the U(1)PQ makes the new quarks massive. The U(1)PQ symmetry is anomalous under the SU(3)C but not under the SU(N) so that the axion couples to only the color SU(3)C and the usual axion potential is generated. We also comment on a model that the U(1)PQ breaking fields are realized as meson superfields in a new supersymmetric QCD.

Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

Symmetries and Their Breaking in the Fundamental Laws of Physics

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) × U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark–Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter–antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout–Englert–Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Towards a Z3-graded approach to quarks’ symmetries

Colour SU(3) group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, SU(2) and U(1), it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour SU(3) symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values 1/3 and 2/3 suggest that the cyclic group Z3 may play a crucial role in quark field dynamics.In this paper we consequently apply the Z3 symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured 12-component spinors is introduced and its properties are discussed. Imposing Z3-graded Lorentz and Poincaré covariance leads to enlargement of quark fields multiplets and incorporates additional Z2 × Z3 symmetry which leads to the appearance of three generations (families) of distinct quark doublets.

Calculating pull for non-singlet jets

The pull vector is a jet observable sensitive to the distribution of soft radiation controlled by the color flow in a collider event. We present calculations to leading order in the soft and collinear limits for the pull vector measured between pairs of jets that do not form a color-singlet dipole. Our calculations are presented within the context of e+e−→ three jets events, on which pull is measured between the two subleading jets. A subset of these calculations can be re-interpreted as a bottom-anti-bottom quark jet pair in a color octet configuration, which can be a background to Higgs production at large boost. We also present a universal expression for the pull distribution in the high-boost and small jet radius limit. This distribution is controlled by color SU(3) quadratic Casimirs that arise from product representations of pairs of QCD jets.

Ultraviolet to infrared evolution and nonperturbative behavior of SU(N)⊗SU(N−4)⊗U(1) chiral gauge theories

We analyze the ultraviolet to infrared evolution and nonperturbative properties of asymptotically free ${\rm SU}(N) \otimes {\rm SU}(N-4) \otimes {\rm U}(1)$ chiral gauge theories with $N_f$ copies of chiral fermions transforming according to $([2]_N,1)_{N-4} + ([\bar 1]_N,[\bar 1]_{N-4})_{-(N-2)} + (1,(2)_{N-4})_N$, where $[k]_N$ and $(k)_N$ denote the antisymmetric and symmetric rank-$k$ tensor representations of SU($N$) and the rightmost subscript is the U(1) charge. We give a detailed discussion for the lowest nondegenerate case, $N=6$. These theories can exhibit both self-breaking of a strongly coupled gauge symmetry and induced dynamical breaking of a weakly coupled gauge interaction symmetry due to fermion condensates produced by a strongly coupled gauge interaction. A connection with the dynamical breaking of ${\rm SU}(2)_L \otimes {\rm U}(1)_Y$ electroweak gauge symmetry by the quark condensates $\langle \bar q q\rangle$ due to color SU(3)$_c$ interactions is discussed. We also remark on direct-product chiral gauge theories with fermions in higher-rank tensor representations.

Novel families of SU(N) AKLT states with arbitrary self-conjugate edge states

Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color SU(N) symmetry, finite correlation lengths, and edge states that can belong to any self-conjugate irreducible representation (irrep) of SU(N). In particular, SU(2) spin-1 AKLT states with edge states of arbitrary spin s=1/2,1,3/2,⋯ are constructed, and a general formula for their correlation length is given. Furthermore, we show how to construct local parent Hamiltonians for which these AKLT states are unique ground states. This enables us to study the stability of the edge states by interpolating between exact AKLT Hamiltonians. As an example, in the case of spin-1 physical degrees of freedom, it is shown that a quantum phase transition of central charge c=1 separates the Symmetry Protected Topological (SPT) phase with spin-1/2 edge states from a topologically trivial phase with spin-1 edge states. We also address some specificities of the generalization to SU(N) with N>2, in particular regarding the construction of parent Hamiltonians. For the AKLT state of the SU(3) model with the 3-box symmetric representation, we prove that the edge states are in the 8-dimensional adjoint irrep, and for the SU(3) model with adjoint irrep at each site, we are able to construct two different reflection-symmetric AKLT Hamiltonians, each with a unique ground state which is either even or odd under reflection symmetry and with edge states in the adjoint irrep. Finally, examples of two-column and adjoint physical irreps for SU(N) with N even and with edge states living in the antisymmetric irrep with N/2 boxes are given, with a conjecture about the general formula for their correlation lengths.

Anomalous discrete flavor symmetry and domain wall problem

Discrete flavor symmetry is often introduced for explaining quark/lepton masses and mixings. However, its spontaneous breaking leads to the appearance of domain walls, which is problematic for cosmology. We consider a possibility that the discrete flavor symmetry is anomalous under the color SU(3) so that it splits the energy levels of degenerate discrete vacua as a solution to the domain wall problem. We find that in most known models of flavor symmetry, the QCD anomaly effect can only partially remove the degeneracy and there still remain degenerate vacua.

Ternary Z2 × Z3 Graded Algebras and Ternary Dirac Equation

The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the "u" and "d" quarks, but also the three colors, and is therefore invariant under the product group Z2 x Z2 x Z3. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) x U(1) that arise automatically in this model, leading to the full bosonic gauge sector of the Standard Model.

An oscillator-representation of elementary particles

Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituent of the hadrons, (a) have an approximate flavor SU(3)f symmetry, (b) have an exact color SU(3)c symmetry, and (c) as spin particles, have a Lorentz SO(3, 1) symmetry. So does a 3D harmonic oscillator. (a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 oscillators are not identical. (b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each oscillator, and mimic the color of the elementary particles. (c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we propose a one-to-one correspondence (a) between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, and (b) between the permuted modes of the oscillator and the color and anticolor multiplets of the particles. The bi-colored gluons are represented by the generators of the color SU(3)c symmetry of the oscillator. Harmonic oscillators are common place objects and, wherever encountered, are analytically solvable. Elementary particles, on the other hand, are abstract entities far from one’s reach. Understanding of one may help a better appreciation of the other.

Phenomenology with F-theory SU(5)

We explore the low energy phenomenology of an F-theory based SU(5) model which, in addition to the known quarks and leptons, contains Standard Model singlets, and vector-like color triplets and SU(2) doublets. Depending on their masses and couplings, some of these new particles may be observed at the LHC and future colliders. We discuss the restrictions by CKM constraints on their mixing with the ordinary down quarks of the three chiral familes. The model is consistent with gauge coupling unification at the usual supersymmetric GUT scale, dimension five proton decay is adequately suppressed, while dimension-six decay mediated by the superheavy gauge bosons is enhanced by a factor of 5-7. The third generation charged fermion Yukawa couplings yield the corresponding low-energy masses in reasonable agreement with observations. The hierarchical nature of the masses of lighter generations is accounted for via non-renormalisable interactions, with the perturbative vacuum expectation values of the SM singlet fields playing an essential role.

Ternary generalization of Pauli’s principle and the Z 6-graded algebras

We show how the discrete symmetries $Z_2$ and $Z_3$ combined with the superposition principle result in the $SL(2, {\bf C})$-symmetry of quantum states. The role of Pauli's exclusion principle in the derivation of the SL(2, C) symmetry is put forward as the source of the macroscopically observed Lorentz symmetry, then it is generalized for the case of the Z3 grading replacing the usual Z2 grading, leading to ternary commutation relations. We discuss the cubic and ternary generalizations of Grassmann algebra. Invariant cubic forms are introduced, and their symmetry group is shown to be the $SL(2,C)$ group The wave equation generalizing the Dirac operator to the Z3-graded case is constructed. Its diagonalization leads to a sixth-order equation. The solutions cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.

Quartified leptonic color, bound states, and future electron–positron collider

The [SU(3)]4 quartification model of Babu, Ma, and Willenbrock (BMW), proposed in 2003, predicts a confining leptonic color SU(2) gauge symmetry, which becomes strong at the keV scale. It also predicts the existence of three families of half-charged leptons (hemions) below the TeV scale. These hemions are confined to form bound states which are not so easy to discover at the Large Hadron Collider (LHC). However, just as J/ψ and ϒ appeared as sharp resonances in e−e+ colliders of the 20th century, the corresponding ‘hemionium’ states are expected at a future e−e+ collider of the 21st century.

Colored-hadron distribution in hadron scattering in SU(2) lattice QCD

In color SU(2) lattice QCD, we investigate colored-diquark distributions in two-hadron scatterings by means of Bethe-Salpeter amplitudes on the lattice. With colored-diquark operators in the Coulomb gauge, we measure components of two colored diquarks realized as intermediate states via one gluon exchange (OGE) processes in hadron scattering. From the colored-diquark distributions, we estimate the dominant range of gluon (color) exchanges between closely located two hadrons. We find that the colored-diquark components are enhanced at the short range ($\leq$0.2 fm) and their tails show the single-exponential damping. In order to distinguish the genuine colored-diquark components originating in the color exchange processes from trivial colored two-quark components contained in two color-singlet hadrons as a result of simple transformation of hadronic basis, we repeat the analyses on the artificially constructed gauge fields, where low- and high-momentum gluon components are decoupled and only restricted pair of quarks can share and exchange low-momentum gluons. We observe qualitatively the same behaviors and confirm that the short-range enhancement of the colored-diquark distributions is the genuine OGE-origin color excitation in hadron scattering.

Moo-Young Han

Moo-Young Han

Electromagnetic currents induced by color fields

The quark production in classical color fields is investigated with a focus on the induction of an electromagnetic current by produced quarks. We show that the color SU(2) and the SU(3) theories lead significantly different results for the electromagnetic current. In uniform SU(2) color fields, the net electromagnetic current is not generated, while in SU(3) color fields the net current is induced depending on the color direction of background fields. Also the numerical study of the quark production in inhomogeneous color fields is done. Motivated by gauge field configurations provided by the color glass condensate framework, we introduce an ensemble of randomly distributed color electric fluxtubes. The spectrum of photons emitted from the quarks by a classical process is shown.