Julius Kuti

The quark bag model

Abstract The quark bag model is reviewed here with particular emphasis on spectroscopic applications and the discussion of exotic objects as baryonium, gluonium, and the quark phase of matter. The physical vacuum is pictured in the model as a two-phase medium. In normal phase of the vacuum, outside hadrons, the propagation of quark and gluon fields is forbidden. When small bubbles in a second phase are created in the medium of the normal phase with a characteristic size of one fermi, the hadron constituent fields may propagate inside the bubbles in normal manner. The bubble (bag) is stabilized against the pressure of the confined hadron constituent fields by vacuum pressure and surface tension. Inside the bag the colored quarks and gluons are governed by the equations of quantum chromodynamics.

Fine structure of the QCD string spectrum.

Using advanced lattice methods in quantum chromodynamics, three distinct scales are established in the excitation spectrum of the gluon field around a static quark-antiquark pair as the color source separation R is varied. On the shortest length scale, the excitations are consistent with states created by local gluon field operators arising from a multipole operator product expansion. An intermediate crossover region below 2 fm is identified with a dramatic rearrangement of the level orderings. On the largest length scale of 2-3 fm, the spectrum agrees with that expected for stringlike excitations. The energies nearly reproduce asymptotic pi/R string gaps, but exhibit a fine structure, providing important clues for developing an effective bosonic string description.

The equivalence of the top quark condensate and the elementary Higgs field

Abstract Several recent works suggested to replace the fundamental Higgs boson by a top quark condensate in analogy with the Nambu-Jona-Lasinio (NJL) mechanism. We show that the field theoretically correct replacement is a generalized NJL model with the minimal choice of three independent interaction terms in the lagrangian. We demonstrate in the large- N color limit that the physics of this model is fully equivalent to the corresponding simplified Standard Model where the Higgs boson is represented by an elementary scalar field with the usual Yukawa- and self-interactions. The generalized NJL mechanism does not lead to new physical predictions or constraints and the complete parameter range of the simplified Standard Model is recovered. Since there exists a simple mapping between the couplings of these two models, it is difficult to give physical significance to notions like composite versus fundamental, or dynamical symmetry breaking in this scheme. We also present some new numerical results on the relevant phase diagrams.

The Yang-Mills gradient flow in finite volume

A bstractThe Yang-Mills gradient flow is considered on the four dimensional torus T4 for SU(N) gauge theory coupled to Nf flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared TrFμνFμν (t) is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to Nf = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative prediction for small renormalized coupling as expected.

Nearly conformal gauge theories in finite volume

Abstract We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU ( 3 ) color gauge group as the number of fermion flavors is varied in the N f = 4 – 16 range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.

Twelve massless flavors and three colors below the conformal window

We report new results for a frequently discussed gauge theory with twelve fermion flavors in the fundamental representation of the SU(3) color gauge group. The model, controversial with respect to its conformality, is important in non-perturbative studies searching for a viable composite Higgs mechanism Beyond the Standard Model (BSM). To resolve the controversy, we subject the model to opposite hypotheses inside and outside of the conformal window. In the first hypothesis we test chiral symmetry breaking ( SB) with its Goldstone spectrum, F , the SB condensate, and several composite hadron states as the fermion mass is varied in a limited range with our best e ort to control finite volume e ects and extrapolation to the massless chiral limit. Supporting results for SB from the running coupling based on the force between static sources and some preliminary evidence for the finite temperature transition are also presented. In the second test for the alternate hypothesis we probe conformal behavior driven by a single anomalous mass dimension under the assumption of unbroken chiral symmetry. Our results show a very low level of confidence in the conformal scenario. Staggered lattice fermions with stout-suppressed taste breaking are used throughout the simulations.

Ab Initio Study of Hybrid bgb Mesons

Hybrid {ovr b}gb molecules in which the heavy {ovr b}b pair is bound together by the excited gluon field g are studied using the Born-Oppenheimer expansion and quenched numerical simulations. The consistency of results from the two approaches reveals a simple and compelling physical picture for heavy hybrid states. {copyright} {ital 1999} {ital The American Physical Society}

Can the nearly conformal sextet gauge model hide the Higgs impostor

Abstract New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β -function (DeGrand et al. [3] ). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β -function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.

{ital Ab Initio} Study of Hybrid {ovr b}gb Mesons

Hybrid {ovr b}gb molecules in which the heavy {ovr b}b pair is bound together by the excited gluon field g are studied using the Born-Oppenheimer expansion and quenched numerical simulations. The consistency of results from the two approaches reveals a simple and compelling physical picture for heavy hybrid states. {copyright} {ital 1999} {ital The American Physical Society}

LATTICE QCD AND STRING THEORY

Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding around a compact dimension is also discussed.