QCD Color Research Articles

Gluon-photon mixing in dense QCD

At high baryonic density with the formation of a diquark condensate $\ensuremath{\Delta}\ensuremath{\ne}0,$ the QCD color symmetry is spontaneously broken. Being massive by the Anderson-Higgs mechanism, a gluon and photon should mix together within two linear combinations due to the color nonconservation. Consequently a gluon $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}$ could decay into an ${e}^{\ensuremath{-}}{e}^{+}$ pair via its photon component. With a low invariant mass (about a few ten MeV) and an extremely narrow width peaking above the continuum background, the purely leptonic decay of a strongly interacting gluon $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{+e}^{+}$ constitutes a very distinctive signature of the color superconductivity phase. By a similar scenario of gluon-Z mixing, another ``missing-energy'' decay into invisible neutrinos $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}\ensuremath{\rightarrow}\ensuremath{\nu}+\overline{\ensuremath{\nu}}$ could arise; its amplitude is, however, $(\ensuremath{\Delta}{/M}_{Z}{)}^{2}$ power suppressed.

A measurement of the QCD colour factors using event shape distributions at $\sqrt{s}=14$ to 189 GeV

Measurements of the QCD colour factors C_A and C_F and of the number of active quark flavours n_f in the process e+e- -> hadrons at high energy are presented. They are based on fits of O(alpha_S**2)+NLLA QCD calculations to distributions of the event shape observables 1-T, C, B_T and B_W measured at centre-of-mass energies from 14 GeV to 189 GeV. Hadronisation effects are approximated with power correction calculations which also depend on the QCD gauge structure. In this approach potential biases from hadronisation models are reduced. Our results for individually measured quantities are n_f = 5.64 +- 1.35, C_A = 2.88 +- 0.27 and C_F = 1.45 +- 0.27 in good agreement with QCD based on the SU(3) symmetry group where n_f=5 for the energies considered here, C_A=3 and C_F=4/3. From simultaneous fits of C_A and C_F we find C_A = 2.84 +- 0.24 and C_F = 1.29 +- 0.18, which is also in good agreement with the QCD expectation.

A simultaneous measurement of the strong coupling and the QCD colour charges

Using data from e + e − annihilation into hadrons, taken with the OPAL detector at LEP at the Z 0 pole between 1991 and 1995, we performed a simultaneous measurement of the strong coupling α s and the colour factors of the underlying gauge group of the strong interaction, C F and C A . The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with either a multi-jet rate or an event-shape variable. Our combined results provide a test of perturbative QCD with the assumptions only of non-abelian gauge symmetry and standard hadronization models. Our results are in agreement with SU(3) expectations for C F and C A and the world average of α s ( M Z 0 ).

Power correction analysis in e +e − annihilation

The current status of theoretical work and experimental analyses on power corrections in QCD for e +e − annihilation will be reviewed. Measurements of the number of active quark flavours n f and the QCD colour factors C A and C F derived from QCD fits to event shape distributions at lower energies and LEP energies will be presented. The fits are based on O(α 2 s )+NLLA QCD predictions with power corrections to model hadronisation.

Dirac and Gor'kov spectra in two color QCD with chemical potential

We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement transition are examined. The bulk of the spectrum and its relation to quantum chaos is considered. A comparison with predictions from random matrix theory is presented. An analogous analysis is performed for the spectrum of the Gor'kov representation of the fermionic action.

A simultaneous measurement of the QCD colour factors and the strong coupling

Using data from $e^+e^-$ annihilation into hadrons, taken with the OPAL detector at LEP at the Z pole between 1991 and 1995, we performed a simultaneous measurement of the colour factors of the underlying gauge group of the strong interaction, $C_F$ and $C_A$ , and the strong coupling, $\alpha_s$ . The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with multi-jet related variables. Our results, \[ C_A=3.02\pm 0.25\mathrm{(stat.)} \pm 0.49\mathrm{(syst.)}\:,\quad C_F=1.34\pm 0.13\mathrm{(stat.)} \pm 0.22\mathrm{(syst.)}\:, \] \[ \alpha_s (M_Z)=0.120\pm 0.011\mathrm{(stat.)} \pm 0.020\mathrm{(syst.)}\:, \] provide a test of perturbative QCD in which the only assumptions are non-abelian gauge symmetry and standard hadronization models. The measurements are in agreement with SU(3) expectations for $C_F$ and $C_A$ and the world average of $\alpha_s(M_{Z})$ .

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential mu, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N=1 adjoint flavor on a 4^3x8 lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N>=2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N=1.

MINIMAL EXTENDED FLAVOR GROUPS, MATTER FIELDS CHIRAL REPRESENTATIONS, AND THE FLAVOR QUESTION

We show the specific unusual features on chiral gauge anomalies cancellation in the minimal, necessarily 3-3-1, and the largest 3-4-1 weak isospin chiral gauge semisimple group leptoquark–bilepton extensions of the 3-2-1 conventional standard model of nuclear and electromagnetic interactions. In such models a natural answer for the fundamental question of fermion generation replication arises directly from the self-consistency of a local gauge quantum field theory, which constrains the number of the QFD fermion families to the QCD color charges.

Determination of the QCD color factor ratioCA/CFfrom the scale dependence of multiplicity in three jet events

I examine the determination of the QCD color factor ratio CA/CF from the scale evolution of particle multiplicity in e+e- three jet events. I fit an analytic expression for the multiplicity in three jet events to event samples generated with QCD multihadronic event generators. I demonstrate that a one parameter fit of CA/CF yields the expected result CA/CF=2.25 in the limit of asymptotically large energies if energy conservation is included in the calculation. In contrast, a two parameter fit of CA/CF and a constant offset to the gluon jet multiplicity, proposed in a recent study, does not yield CA/CF=2.25 in this limit. I apply the one parameter fit method to recently published data of the DELPHI experiment at LEP and determine the effective value of CA/CF from this technique, at the finite energy of the Z0 boson, to be 1.74+-0.03+-0.10, where the first uncertainty is statistical and the second is systematic.

Lattice gauge theories and the Heisenberg antiferromagnetic chain

We study the strongly coupled2-flavor lattice Schwinger model and the SU (2)-color QCD 2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin 1 2 chain.

On two-color QCD with baryon chemical potential

We study SU(2) color QCD with even number of quark flavors. First, using QCD inequalities we show that at finite baryon chemical potential μ, condensation must occur in the channel with scalar diquark quantum numbers. This breaks the U(1) symmetry generated by baryon charge (baryon superconductivity). Then we derive the effective Lagrangian describing low lying meson and baryon excitations using extended local chiral symmetry of the theory. This enables us to determine the leading term in the dependence of the masses on μ exactly.

Nonperturbative QCD vacuum and colour superconductivity

We discuss the possibility of existence of colour superconducting state in real QCD vacuum with nonzero 〈 α s GG〉. We argue, that nonperturbative gluonic fields might play a crucial role in colour superconductivity scenario.

String breaking in quenched QCD

We present results on a new operator for the investigation of string-breaking effects in quenched SU(2)-colour QCD. The ground state of a spatially-separated static-light meson-antimeson pair is a combination of a state with two distinct mesons, expected to dominate for large separations, and a state where the light quarks have annihilated, which contributes at short distances. The cross-over between these two regimes provides the string-breaking scale.

Experimental properties of gluon and quark jets from a point source

Gluon jets are identified in hadronic Z\(^0\) decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large \(p_{\rm T}\), we observe the charged particle multiplicity ratio of gluon to quark jets to be \(2.29\pm0.09\,{\mathrm{(stat.)}} \pm0.15\,{\mathrm{(syst.)}}\), in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, \({\rm C_A/C_F}= 2.25\). The intervals used to define soft particles and large \(p_{\rm T}\) for this result, \(p < 4\) GeV/\(c\) and \(0.8 < p_{\rm T}< 3.0\) GeV/\(c\), are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data.

String breaking in quenched QCD

We present preliminary quenched results on a new operator for the investigation of string-breaking within SU(2)-colour QCD. The ground-state of a spatially-separated static-light meson-antimeson pair is a combination of a state with two distinct mesons, expected to dominate for large separations, and a state where the light-quarks have annihilated, which contributes for short distances. The crossover between these two regimes provides a measure of the string-breaking scale length.

Multijet rates in e +e − annihilation: perturbation theory versus LEP data

We show that the next-to-leading order perturbative prediction, matched with the next-to-leading logarithmic approximation for predicting both two-, three- and four-jet rates using the Durham jet-clustering algorithm, in the 0.001 < y cut < 0.1 range gives a very accurate description of the data obtained at the Large Electron Positron Collider. This information can be utilized either for simultaneous measurement of the strong coupling and the QCD colour charges, or for improving the QCD background prediction in new particle searches at LEP2.

Experimental properties of gluon and quark jets from a point source

Gluon jets are identified in hadronic Z $^0$ decays as all the particles in a hemisphere opposite to a hemisphere containing two tagged quark jets. Gluon jets defined in this manner are equivalent to gluon jets produced from a color singlet point source and thus correspond to the definition employed for most theoretical calculations. In a separate stage of the analysis, we select quark jets in a manner to correspond to calculations, as the particles in hemispheres of flavor tagged light quark (uds) events. We present the distributions of rapidity, scaled energy, the logarithm of the momentum, and transverse momentum with respect to the jet axes, for charged particles in these gluon and quark jets. We also examine the charged particle multiplicity distributions of the jets in restricted intervals of rapidity. For soft particles at large $p_{\rm T}$ , we observe the charged particle multiplicity ratio of gluon to quark jets to be $2.29\pm0.09\,{\mathrm{(stat.)}} \pm0.15\,{\mathrm{(syst.)}}$ , in agreement with the prediction that this ratio should approximately equal the ratio of QCD color factors, ${\rm C_A/C_F}= 2.25$ . The intervals used to define soft particles and large $p_{\rm T}$ for this result, $p < 4$ GeV/ $c$ and $0.8 < p_{\rm T}< 3.0$ GeV/ $c$ , are motivated by the predictions of the Herwig Monte Carlo multihadronic event generator. Additionally, our gluon jet data allow a sensitive test of the phenomenon of non-leading QCD terms known as color reconnection. We test the model of color reconnection implemented in the Ariadne Monte Carlo multihadronic event generator and find it to be disfavored by our data.

Measurements of the QCD colour factors at LEP

A summary of the measurements of the QCD colour factors at LEP is presented. Such measurements provide a test of the gauge group structure underlying the theory of strong interactions. A variety of methods have been applied by the various experiements, and perfect consistency with the expectation of QCD with SU(3) as gauge group is found.

Four-jet angular distributions and color charge measurements: Leading order versus next-to-leading order

We present the next-to-leading order perturbative QCD prediction to the four-jet angular distributions used by experimental collaborations at LEP for measuring the QCD color charge factors. We compare our results to ALEPH data corrected to parton level. We perform a leading order ``measurement'' of the QCD color factor ratios by fitting the leading order perturbative predictions to the next-to-leading order result. Our result shows that in an experimental analysis for measuring the color charge factors the use of the O($\alpha_s^3$) QCD predictions instead of the O($\alpha_s^2$) results may shift the center of the fit by a relative factor of $1+2\as$ in the $T_R/C_F$ direction.

Measurements of the QCD colour factors at LEP and a limit on the light glunio

A summary of the measurements of the QCD colour factors at LEP is presented. Such measurements provide a test of the gauge group structure underlying the theory of strong interactions. A variety of methods have been applied by the various experiments, and perfect consistency with the expectation of QCD with SU(3) as gauge group is found. By translating a colour factor measurement into a determination of the number of active flavours, ALEPH exludes a light gluino for masses below 6.3 GeV/ c 2.