SU Color Research Articles

Probing the gauge content of heavy resonances with soft radiation

The use of energy flow is investigated as a diagnostic tool for determining the color SU(3) representation of new resonances. It is found that the pattern of soft gluon radiation into a rapidity gap depends on color flow in the hard scattering, and reflects the gauge content of new physics. The massive soft anomalous dimension matrix for rapidity gap events is introduced for describing soft gluon emission analytically in heavy quark pair production. A gap fraction is used for quantifying the amount of soft radiation into the gap region. In general, the results illustrate that radiation is greater for a singlet resonance than for an octet. Especially, it is found that the quantitative difference is quite distinguishable for spin-1 resonances, depending on the gauge content in the new sector.

Quarkyonic Matter in Lattice QCD at Strong Coupling

We study the phase diagram of quark matter at finite temperature and density in the strong coupling lattice QCD with one species of unrooted staggered fermions including finite coupling ($1/g^2$) effects for color SU($N_c$). We find that we may have partially chiral restored medium density matter at $N_c=3$, which would correspond to the quarkyonic matter suggested at large $N_c$.

Fermion particle production in semiclassical Boltzmann-Vlasov transport theory

We present numerical solutions of the semiclassical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in ($1+1$) and ($3+1$) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and antiquarks on a second Casimir invariant of color SU(3).

Time-Dependent Variational Approach to the Non-Abelian Pure Gauge Theory: Its Application to Evaluation of the Shear Viscosity of Quantum Gluonic Matter

The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schroedinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the transport coefficients, such as the shear viscosity, for the pure gluonic matter by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.

Gauge-invariant quantities characterizing gauge fields in chromodynamics

We calculate Lorentz-invariant and gauge-invariant quantities characterizing the product $\ensuremath{\sum}_{a}{D}_{R}({T}^{a}){F}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}$, where ${D}_{R}({T}^{a})$ denotes the matrix for the generator ${T}^{a}$ in the representation $R=\mathrm{\text{fundamental}}$ and adjoint, for color SU(3). We also present analogous results for an SU(2) gauge theory.

Baryon mass at finite chemical potential in the strong coupling limit of lattice QCD for color SU(3)(Thermal Quantum Field Theories and Their Applications)

Baryon mass at finite chemical potential in the strong coupling limit of lattice QCD for color SU(3)(Thermal Quantum Field Theories and Their Applications)

Phase diagram at finite temperature and quark density in the strong coupling region of lattice QCD for colour SU(3)

We study the phase diagram of quark matter at finite temperature (T) and chemical potential (μ) in the strong coupling region of lattice QCD for colour SU(3). Baryon has effects to extend the hadron phase to a larger μ direction relative to Tc at low temperatures in the strong coupling limit. With the 1/g2 corrections, Tc is found to decrease rapidly as g decreases, and the shape of the phase diagram becomes closer to that expected in the real world.

Model study of the sign problem in the mean-field approximation

We consider the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from quantum chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle point of which we can estimate the expectation value of the Polyakov loop.

Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)

We study the phase diagram of quark matter at finite temperature ($T$) and chemical potential ($\ensuremath{\mu}$) in the strong coupling limit of lattice QCD for color SU(3). We derive an analytical expression of the effective free energy as a function of $T$ and $\ensuremath{\mu}$, including baryon effects. The finite temperature effects are evaluated by integrating over the temporal link variable exactly in the Polyakov gauge with an antiperiodic boundary condition for fermions. The obtained phase diagram shows the first and the second order phase transition at low and high temperatures, respectively, and those are separated by the tricritical point in the chiral limit. Baryon has effects to reduce the effective free energy and to extend the hadron phase to a larger $\ensuremath{\mu}$ direction at low temperatures.

Dimensional reduction of Dirac operator

We construct an explicit example of dimensional reduction of the free massless Dirac operator with an internal SU(3) symmetry, defined on a 12-dimensional manifold that is the total space of a principal SU(3)-bundle over a four-dimensional (nonflat) pseudo-Riemannian manifold. Upon dimensional reduction the free 12-dimensional Dirac equation is transformed into a rather nontrivial four-dimensional one: a pair of massive Lorentz spinor SU(3)-octets interacting with an SU(3)-gauge field with a source term depending on the curvature tensor of the gauge field. The SU(3) group is complicated enough to illustrate features of the general case. It should not be confused with the color SU(3) of quantum chromodynamics where the fundamental spinors, the quark fields, are SU(3) triplets rather than octets.

Color SU(3) symmetry, confinement, stability, clustering and quark mass dependence in theq4q¯system

We examine the color SU(3) dynamics of q{sup 4}q system, i.e. of the pentaquark. First we study this system in the model with two-body interaction proportional to the color charges. We construct the potential matrix and show, (1) Confinement: the color singlet qq potential energy rises infinitely with the separation distance, (2) Stability: All colorless states' energies are bounded from below (3) Color singlet clustering: the pentaquark color-singlet state Hamiltonian turns into a sum of a three-quark (baryon) and a quark-antiquark (meson) cluster Hamiltonian, in the limit of asymptotically large separations. We evaluate the four excitation eigenfrequencies of pentaquarks in the harmonic oscillator two-body confining potential and the ground states' dependence on the quark-antiquark mass ratio. We show that the pentaquark is unlikely to bind even with a top antiquark, in contrast to tetraquarks.

Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)(Thermal Quantum Field Theories and Their Applications)

Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)(Thermal Quantum Field Theories and Their Applications)

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric dense color superconducting phase of a Nambu–Jona-Lasinio–type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.

Phase structures of strong coupling lattice QCD with finite baryon and isospin density

Quantum chromodynamics (QCD) at finite temperature $(T),$ baryon chemical potential $({\ensuremath{\mu}}_{\mathrm{B}}),$ and isospin chemical potential $({\ensuremath{\mu}}_{\mathrm{I}})$ is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, ${\ensuremath{\mu}}_{\mathrm{B}},$ and ${\ensuremath{\mu}}_{\mathrm{I}}.$ The phase structure in the space of T and ${\ensuremath{\mu}}_{\mathrm{B}}$ is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite ${\ensuremath{\mu}}_{\mathrm{I}}$ on the phase diagram are discussed. We also investigate the phase structure in the space of T, ${\ensuremath{\mu}}_{\mathrm{I}},$ and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.

Color SU(3) symmetry, confinement, stability, and clustering in theq2q2system

We examine the assumptions underlying the (model-dependent) predictions of ${q}^{2}{q}^{2}$ or tetraquark spectra. The models implemented so far have used only two-body interactions proportional to the color charges; that assumption is the source of many serious shortcomings. We extend the analysis to three- and four-body interactions based on color SU(3) algebra, while including all relevant information one has about three-quark forces from lattice QCD. Thus we find that (quasi)stable tetraquarks are not necessarily a consequence of color SU(3) dynamics, let alone of QCD. We make this statement and the conditions under which it holds more precise in the text. In the process we are led to a set of sufficient conditions for a mathematical description of the hadronic world as we know it, i.e., of baryons and $q\overline{q}$ mesons, without going into the question of tetraquark existence. These conditions are as follows. (1) Stability: All the (colorless and colored) states' energies must be bounded from below. (2) Confinement: A color singlet $q\overline{q}$ potential energy must (infinitely) rise with the separation distance. (3) Color ordering: Colored states must be heavier than color-neutral ones. (4) Clustering: Any multiquark color-singlet state Hamiltonian must turn into a sum of three-quark (baryons) and quark-antiquark (mesons) cluster Hamiltonians, in the limit of asymptotically large separations. We discuss the consistency of these four requirements with color SU(3) symmetry and with each other.

YANG–MILLS DUALITY AS THE ORIGIN OF FERMION GENERATIONS

A non-Abelian extension of electric-magnetic duality implies that dual to confined colour SU(3), there also ought to be a broken threefold symmetry which can play the role of fermion generations. A model constructed on these premises not only gives a raison d'être for 3 and only 3 generations as observed but also offers a natural explanation for the distinctive fermion mass and mixing patterns seen in experiment. A calculation to one-loop order in this model with only 3 fitted parameters already gives correct values, all within present experimental errors, for the following quantities: the mass ratios mc/mt, ms/mb, mμ/mτ, all 9 matrix elements of the CKM mixing matrix |Vrs| for quarks, plus the lepton MNS mixing matrix elements |Uμ3| and |Ue3| studied in neutrino oscillation experiments with respectively atmospheric and reactor neutrinos.

Dynamical rearrangement of gauge symmetry on the orbifold S1/ Z2

Gauge theory defined on the orbifold M 4×( S 1/ Z 2) is investigated from the viewpoint of the Hosotani mechanism. Rearrangement of gauge symmetry takes place due to the dynamics of Wilson line phases. The physical symmetry of the theory, in general, differs from the symmetry of the boundary conditions. Several sets of boundary conditions having distinct symmetry can be related by gauge transformations, belonging to the same equivalence class. The Hosotani mechanism guarantees the same physics in all theories in one equivalent class. Examples are presented in the SU(5) theory. Zero modes of the extra-dimensional components, A y , of gauge fields acquire masses by radiative corrections. In the nonsupersymmetric SU(5) model the presence of bulk fermions leads to the spontaneous breaking of color SU(3). In the supersymmetric model with Scherk–Schwarz SUSY breaking color SU(3) is spontaneously broken, and zero modes of A y 's acquire masses of order of the SUSY breaking.

Colour-SU(3)-Ginzburg–Landau effective potential for order parameter with 3 × 3 symmetry

Ginzburg–Landau effective potential is studied for the order parameter that transforms in the (3, 3) representation under the colour SU(3) group. All the SU(3)-invariant terms to the fourth order of the order parameter are classified and the effective potential is constructed in its most general form. The conditions which stabilize the condensed phases are also obtained. As applications, the classification of the condensed phase is discussed in some special cases and the Higgs phenomenon associated with symmetry breaking is studied by introducing a coupling to the gauge boson.

Behavior of hadrons at finite density.: Lattice study of color SU(2) QCD

Using two-color lattice QCD with Wilson fermions, we report a study of the finite baryon number density system with two-flavors. First we investigate the Polyakov line and thermodynamical quantities in the (κ,μ) plane, where κ and μ are the hopping parameter and chemical potential in the fermion action, respectively. Then we calculate propagators of meson (q̄Γq) and baryon (qΓq) states. We find that the vector meson propagators are strongly modified in large μ regions, indicating the reduction of the mass. This anomalous behavior of the vector meson is observed for the first time in lattice QCD.

Screening of hot gluon.: Lattice study of gluon screening masses

We calculate electric and magnetic masses of gluons between T=Tc and 6Tc using lattice QCD (quantum chromodynamics) in the quench approximation for color SU(3). We find that magnetic mass has finite values in this region, and the temperature dependence of the electric mass is consistent with that determined using the hard-thermal-loop perturbation. The hard-thermal-loop resummation improves the magnitude of the electric mass comparing to the leading order perturbation. Both screening masses have little gauge parameter dependence.