arXiv subjects

John B. Kogut

Publications and source records attributed to John B. Kogut.

At least 19 recordsLinked to original sources

arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

hep-ph↗

arXiv2011

Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter

We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED3) with N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on the divergence of the monopole susceptibility (polarizability) with the lattice size at weak gauge couplings. A weak four-Fermi term added to the cQED3 action enabled simulations with massless fermions. The exact chiral symmetry of the interaction terms forbids symmetry breaking lattice discretization counterterms to appear in the theory's effective action. It is also shown that the scenario of a monopole plasma does not depend on the strength of the four-Fermi coupling. Other observables such as the densities of "isolated" dipoles and monopoles and the so-called specific heat show that a crossover from a dense monopole plasma to a dilute monopole gas occurs at strong couplings. The implications of our results on the stability of U(1) spin liquids in two spatial dimensions are also discussed.

hep-lat↗

arXiv2010

Chiral symmetry breaking and monopole dynamics in non-compact QED3 coupled to a four-fermi interaction

We present results from the first lattice simulations of three dimensional non-compact quantum electrodynamics (QED3) with N_f four-component fermion flavors coupled to a weak Z(2) chirally invariant four-fermi interaction. Results with $N_f \ge 4$ show that the scaling near the strong coupling chiral transition or sharp crossover is determined by the 3d Gross Neveu ultraviolet-stable renormalization group fixed point. Small deviations of the N_f=4 critical exponents from the respective Gross Neveu ones, hint at evidence for non-zero fermion mass generated by the gauge fields dynamics that might have been enhanced by the four-fermi coupling. It is also shown that the scaling region is suppressed at weak four-fermi couplings and large N_f values. Measurements of i) a monopole susceptibility which is the polarizability of the monopole configurations, and ii) the density of isolated monopoles, imply that for $N_f \ge 1$ and weak gauge couplings the monopoles do not affect the theory's confining properties, because they are shielded.

hep-lat↗

arXiv2008

Chiral Symmetry breaking in Three Dimensional QED

Over the past few years three dimensional Quantum Electrodynamics (QED$_3$) has attracted a lot of attention, because it may be an effective theory for the underdoped and non-superconducting region of the phase diagram of high $T_c$ cuprate compounds. We present results from lattice simulations of the non-compact version of the theory in order to address the issue of whether chiral symmetry is spontaneously broken when the number of fermion flavours $N_f$ is less than a critical value $N_{fc}$. Our results provide strong evidence that QED$_3$ is chirally symmetric for $N_f \geq 1.5$, implying that a pseudogap phase separates the superconducting phase from the antiferromagnetic phase.

cond-mat.supr-con↗

arXiv2008

The Phases of Non-Compact QED(3)

Non-compact three-dimensional QED is studied by computer simulations to understand its chiral symmetry breaking features for different values of the number of fermion flavors N_f. We consider the four-component formulation for the fermion fields, which arises naturally as the continuum limit of the staggered fermion construction in (2+1) dimensions. We present preliminary results for the equation of state of the theory in an effort to understand the properties of the chiral phase transition of the theory at a critical number of fermion flavors N_{fc}. Our preliminary results indicate that N_{fc}~1.5.

hep-lat↗

arXiv2005

On the Interplay of Fermions and Monopoles in Compact QED_3

The infra-red properties of three-dimensional abelian lattice gauge theory are known to be governed by a neutral plasma of magnetic monopole excitations. We address the fate of these monopoles in the presence of light dynamical fermions, using a lattice formulation of compact QED_3 with N_f=4 fermion flavors supplemented by a four-fermi contact term permitting numerical Monte Carlo simulations in the chiral limit. Our data hint at a restoration of chiral symmetry above a critical value of the (inverse) coupling beta. By performing simulations in a sector of non-vanishing magnetic charge, we are able to study the response of the theory to an external magnetic test charge. Our results suggest that the monopole plasma persists even once chiral symmetry is restored, and hence survives the continuum limit.

hep-lat↗

arXiv2005

The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction

This is the completion of an exploratory study of Compact lattice Quantum Electrodynamics with a weak four-fermi interaction and four species of massless fermions. In this formulation of Quantum Electrodynamics massless fermions can be simulated directly and Finite Size Scaling analyses can be performed at the theory's chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau's zero charge problem.

hep-lat↗

arXiv2004

The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model

We use a hadron resonance gas model to study the QCD phase diagram at nonzero temperature, baryon, isospin and strangeness chemical potentials. We determine the temperature of the transition from the hadronic phase to the quark gluon plasma phase using two different methods. We find that the critical temperatures derived in both methods are in very good agreement. We find that the critical surface has a small curvature. We also find that the critical temperature's dependence on the baryon chemical potential at zero isospin chemical potential is almost identical to its dependence on the isospin chemical potential at vanishing baryon chemical potential. This result, which holds when the chemical potentials are small, supports recent lattice simulation studies. Finally, we find that at a given baryon chemical potential, the critical temperature is lowered as either the isospin or the strangeness chemical potential are increased. Therefore, in order to lower the critical temperature, it might be useful to use different isotopes in heavy ion collision experiments.

hep-ph↗

arXiv2003

Fermi Surface Phenomena in the (2+1)d Four-Fermi Model

We study the Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu using both analytical and numerical methods. For mu greater than a critical value the model is chirally symmetric and has a Fermi surface with Fermi momentum ~mu. We have calculated the particle interaction in medium due to scalar meson exchange to leading order in 1/N, where N is the number of flavors, in the hard dense loop approach. The result has been used to calculate the relation between mu and the Fermi momentum and velocity in the resulting Fermi liquid to O(1/N). Simulation results from a 32^2x48 lattice for fermion and meson dispersion relations and meson wavefunctions are then presented, showing qualitative and in some cases quantitative agreement with analytic predictions. In particular, the simulations show clear evidence for the in-medium modification of the scalar propagator, oscillatory behaviour in the wavefunction consistent with a sharp Fermi surface, and tentative evidence for a massless pole in the vector meson channel resembling zero sound.

hep-lat↗

arXiv2002

The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction

Compact lattice Quantum Electrodynamics (QED) with four species of fermions is simulated with massless quarks by using the $χ$QED scheme of adding a four-fermi interaction to the action. Simulations directly in the chiral limit of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices, and the phase diagram, parameterized by the gauge and the four-fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the Universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the $16^4$ simulations predict critical indices far from mean field values. We discuss a speculative scenario in which anti-screening provided by double-helix strands of monopole and anti-monopole loops are the agent that balances the screening of fermion anti-fermion pairs to produce an ultra-violet fixed point in the electric coupling.

hep-lat↗

arXiv2002

QCD in Extreme Environments

I review present challenges that QCD in extreme environments presents to lattice gauge theory. Recent data and impressions from RHIC are emphasized. Physical pictures of heavy ion wavefunctions, collisions and the generation of the Quark Gluon Plasma are discussed, with an eye toward engaging the lattice and its numerical methods in more interaction with the experimental and phenomenological developments. Controversial, but stimulating scenarios which can be confirmed or dismissed by lattice methods are covered. In the second half of the talk, several promising developments presented at the conference Lattice 2002 are reviewed.

hep-lat↗

arXiv2002

SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential mu and temperature T and the results are compared to the predictions of Effective Lagrangians. Simulations on 16^4 lattices indicate that at zero T the theory experiences a second order phase transition to a diquark condensate state which is well described by mean field theory. Nonzero T and mu are studied on 12^3 times 6 lattices. For low T, increasing mu takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing T at high mu, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase.

hep-lat↗

arXiv2002

The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $μ$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $μ$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $μ$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $μ$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.

hep-lat↗

arXiv2001

Gauged Nambu-Jona Lasinio Studies of the Triviality of Quantum Electrodynamics

By adding a small, irrelevant four fermi interaction to the action of noncompact lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial, with the same systematics as the Nambu-Jona Lasinio model. The irrelevance of the four fermi coupling is established numerically. The widths of the scaling windows are examined in both the coupling constant and bare fermion mass directions in parameter space. For vanishing fermion mass we find a broad scaling window in coupling. By adding a small bare fermion mass to the action we find that the width of the scaling window in the fermion mass direction is very narrow. Only when a subdominant scaling term is added to the leading term of the equation of state are adequate fits to the data possible. The failure of past studies of lattice QED to produce equation of state fits with adequate confidence levels to seriously address the question of triviality is explained. The vacuum state of the lattice model is probed for topological excitations, such as lattice Monopoles and Dirac strings, and these objects are shown to be non-critical along the chiral transition line as long as the four fermi coupling is nonzero.

hep-lat↗

arXiv2001

Diquark Condensation at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is studied at nonzero chemical potential $μ$ and temperature $T$ by computer simulation and Effective Lagrangian techniques. Simulations are done on $8^4$, $8^3 \times 4$ and $12^3 \times 6$ lattices and the diquark condensate, chiral order parameter, Wilson line, fermion energy and number densities are measured. Simulations at a fixed, nonzero quark mass provide evidence for a tricritical point in the $μ$-$T$ plane associated with diquark condensation. For low $T$, increasing $μ$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $μ$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Using Effective Lagrangians we estimate the position of the tricritical point and ascribe its existence to trilinear couplings that increase with $μ$ and $T$.

hep-lat↗

arXiv2000

Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential

We study the symmetry behavior of the Gross-Neveu model in three and two dimensions with random chemical potential. This is equivalent to a four-fermion model with charge conjugation symmetry as well as Z_2 chiral symmetry. At high temperature the Z_2 chiral symmetry is always restored. In three dimensions the initially broken charge conjugation symmetry is not restored at high temperature, irrespective of the value of the disorder strength. In two dimensions and at zero temperature the charge conjugation symmetry undergoes a quantum phase transition from a symmetric state (for weak disorder) to a broken state (for strong disorder) as the disorder strength is varied. For any given value of disorder strength, the high-temperature behavior of the charge conjugation symmetry is the same as its zero-temperature behavior. Therefore, in two dimensions and for strong disorder strength the charge conjugation symmetry is not restored at high temperature.

hep-th↗

arXiv1999

Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical potential

We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero chemical potential $μ$. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and condensates at non-zero chemical potential are considered. Using the molecular dynamics algorithm on small lattices we find qualitative changes in the theory's spectroscopy at small and large values of $μ$. This preliminary study should lay the groundwork for future large scale simulations.

hep-lat↗

arXiv1999

Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential

We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density (chemical potential mu =/= 0). It is possible to formulate this model with a real action and therefore to perform standard hybrid Monte Carlo simulations with mu =/= 0 in the functional measure. We compare the physical observables from these simulations with simulations using the Glasgow method where the value of mu in the functional measure is fixed at a value mu_upd. We find that the observables are sensitive to the choice of mu_upd. We consider the implications of our findings for Glasgow method QCD simulations at mu =/= 0. We demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu model is fundamentally different from that in QCD. We find that this difference explains why there is an unphysical transition in QCD simulations at mu =/= 0 associated with the pion mass scale whereas the transition in the Gross-Neveu model occurs at a larger mass scale and is therefore consistent with theoretical predictions. We note classes of theories which are exceptions to the Vafa-Witten theorem which permit the possibility of formation of baryon number violating diquark condensates.

hep-lat↗