Linear Sigma EFT for Nearly Conformal Gauge Theories

We construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum ($\sigma$) can be much lighter than the vector state ($\rho$) and nearly degenerate with the PNGBs ($\pi$) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality $M_{\sigma}^2 \ge 3 M_{\pi}^2$, allowing for consistency with current lattice data.Comment: 9 pages, 1 figure, published versio

Analysis of a dilaton EFT for lattice data

In a recent paper, we developed and applied a dilaton-based effective field theory (EFT) to the analysis of lattice-simulation data for a class of confining gauge theories with near-conformal infrared behavior. It was employed there at the classical level to the SU(3) gauge theory with eight Dirac fermions in the fundamental representation. Here, we explore the structure of the EFT further. We examine its application to lattice data (newly updated) for the SU(3) theory with eight Dirac fermions in the fundamental representation, and the SU(3) theory with two Dirac fermions in the sextet representation. In each case, we determine additional fit parameters and discuss uncertainties associated with extrapolation to zero fermion mass. We highlight universal features, study the EFT at the quantum loop level and discuss the importance of future lattice simulations

Computations of Viking Lander Capsule Hypersonic Aerodynamics with Comparisons to Ground and Flight Data

Comparisons are made between the LAURA Navier-Stokes code and Viking Lander Capsule hypersonic aerodynamics data from ground and flight measurements. Wind tunnel data are available for a 3.48 percent scale model at Mach 6 and a 2.75 percent scale model at Mach 10.35, both under perfect gas air conditions. Viking Lander 1 aerodynamics flight data also exist from on-board instrumentation for velocities between 2900 and 4400 m/sec (Mach 14 to 23.3). LAURA flowfield solutions are obtained for the geometry as tested or flown, including sting effects at tunnel conditions and finite-rate chemistry effects in flight. Using the flight vehicle center-of-gravity location (trim angle approx. equals -11.1 deg), the computed trim angle at tunnel conditions is within 0.31 degrees of the angle derived from Mach 6 data and 0.13 degrees from the Mach 10.35 trim angle. LAURA Mach 6 trim lift and drag force coefficients are within 2 percent of measured data, and computed trim lift-to-drag ratio is within 4 percent of the data. Computed trim lift and drag force coefficients at Mach 10.35 are within 5 percent and 3 percent, respectively, of wind tunnel data. Computed trim lift-to-drag ratio is within 2 percent of the Mach 10.35 data. Using the nominal density profile and center-of-gravity location, LAURA trim angle at flight conditions is within 0.5 degrees of the total angle measured from on-board instrumentation. LAURA trim lift and drag force coefficients at flight conditions are within 7 and 5 percent, respectively, of the flight data. Computed trim lift-to-drag ratio is within 4 percent of the data. Computed aerodynamics sensitivities to center-of-gravity location, atmospheric density, and grid refinement are generally small. The results will enable a better estimate of aerodynamics uncertainties for future Mars entry vehicles where non-zero angle-of-attack is required

Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors

The SU(3) gauge theory with $N_f=8$ nearly massless Dirac fermions has long been of theoretical and phenomenological interest due to the near-conformality arising from its proximity to the conformal window. One particularly interesting feature is the emergence of a relatively light, stable flavor-singlet scalar meson $\sigma$ $(J^{PC}=0^{++})$ in contrast to the $N_f=2$ theory QCD. In this work, we study the finite-volume dependence of the $\sigma$ meson correlation function computed in lattice gauge theory and determine the $\sigma$ meson mass and decay constant extrapolated to the infinite-volume limit. We also determine the infinite volume mass and decay constant of the flavor-nonsinglet scalar meson $a_0$.Comment: 36 pages, 11 figures, supplementary data in zenodo https://dx.doi.org/10.5281/zenodo.800795

Dilaton EFT framework for lattice data

We develop an effective-field-theory (EFT) framework to analyze the spectra emerging from lattice simulations of a large class of confining gauge theories. Simulations of these theories, for which the light-fermion count is not far below the critical value for transition to infrared conformal behavior, have indicated the presence of a remarkably light singlet scalar particle. We incorporate this particle by including a scalar field in the EFT along with the Nambu-Goldstone bosons (NGB's), and discuss the application of this EFT to lattice data. We highlight the feature that data on the NGB's alone can tightly restrict the form of the scalar interactions. As an example, we apply the framework to lattice data for an SU(3) gauge theory with eight fermion flavors, concluding that the EFT can describe the data well

Viking Afterbody Heating Computations and Comparisons to Flight Data

Computational fluid dynamics predictions of Viking Lander 1 entry vehicle afterbody heating are compared to flight data. The analysis includes a derivation of heat flux from temperature data at two base cover locations, as well as a discussion of available reconstructed entry trajectories. Based on the raw temperature-time history data, convective heat flux is derived to be 0.63-1.10 W/sq cm for the aluminum base cover at the time of thermocouple failure. Peak heat flux at the fiberglass base cover thermocouple is estimated to be 0.54-0.76 W/sq cm, occurring 16 seconds after peak stagnation point heat flux. Navier-Stokes computational solutions are obtained with two separate codes using an 8-species Mars gas model in chemical and thermal non-equilibrium. Flowfield solutions using local time-stepping did not result in converged heating at either thermocouple location. A global time-stepping approach improved the computational stability, but steady state heat flux was not reached for either base cover location. Both thermocouple locations lie within a separated flow region of the base cover that is likely unsteady. Heat flux computations averaged over the solution history are generally below the flight data and do not vary smoothly over time for both base cover locations. Possible reasons for the mismatch between flight data and flowfield solutions include underestimated conduction effects and limitations of the computational methods

Linear sigma EFT for nearly conformal gauge theories

We construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum (σ) can be much lighter than the vector state (ρ) and nearly degenerate with the PNGBs (π) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality M2σ ≥ 3M2π, allowing for consistency with current lattice data

Goldstone Boson Scattering with a Light Composite Scalar

The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT

Goldstone Boson Scattering with a Light Composite Scalar

The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT

Light Scalar Meson and Decay Constant in SU(3) Gauge Theory with Eight Dynamical Flavors

The SU(3) gauge theory with $N_f=8$ nearly massless Dirac fermions has long been of theoretical and phenomenological interest due to the near-conformality arising from its proximity to the conformal window. One particularly interesting feature is the emergence of a relatively light, stable flavor-singlet scalar meson $\sigma$ $(J^{PC}=0^{++})$ in contrast to the $N_f=2$ theory QCD. In this work, we study the finite-volume dependence of the $\sigma$ meson correlation function computed in lattice gauge theory and determine the $\sigma$ meson mass and decay constant extrapolated to the infinite-volume limit. We also determine the infinite volume mass and decay constant of the flavor-nonsinglet scalar meson $a_0$