A novel approach for the study of near conformal theories for electroweak symmetry breaking

The discovery of a light scalar at the Large Hadron Collider is in basic agreement with the predictions of an elementary Higgs in the Standard Model (SM). Nonetheless, a light, fundamental scalar is difficult to accommodate in the SM because quantum corrections suggest its mass should be much higher than the scale of electroweak symmetry breaking (EWSB). A natural possibility is to replace the Higgs by a strongly coupled composite. Composite dynamics also gives a natural explanation to the origin of EWSB. Phenomenologically viable composite models of EWSB are constrained by experiment to feature approximate scale invariance. This behavior may follow from near conformal dynamics. At present, lattice gauge theory (LGT) provides the only quantitative method to study near conformal composite Higgs dynamics in a fully consistent strongly coupled relativistic quantum field theory. As a novel approach to the question of finding and studying near conformal theories, I will apply LGT to the study of a generalization of Quantum ChromoDynamics (QCD) with four chiral fermion flavors plus eight flavors of finite, tunable mass. By continuously varying the mass of the eight heavy flavors, I can tune between the four flavor chirally broken theory, which exhibits features similar to QCD, and the twelve flavor theory, which is known to have a conformal fixed point. This is the "4+8 Model" for directly studying near-conformal behavior. In this dissertation, I will review modern composite phenomenology, followed by outlining a study of the 4+8 Model over a range of heavy flavor masses. As a check of near-conformal behavior, I will measure the scale dependent coupling with the method of the Wilson Flow. After verifying the existence of controllable, approximate scale invariance, I will measure the low energy particle spectrum of the 4+8 Model. This includes a Higgs-like light composite scalar. Throughout this dissertation I will make reference to LGT measurement code I wrote and contributed to the software package FUEL

Thermonuclear .Ia Supernovae from Helium Shell Detonations: Explosion Models and Observables

During the early evolution of an AM CVn system, helium is accreted onto the surface of a white dwarf under conditions suitable for unstable thermonuclear ignition. The turbulent motions induced by the convective burning phase in the He envelope become strong enough to influence the propagation of burning fronts and may result in the onset of a detonation. Such an outcome would yield radioactive isotopes and a faint rapidly rising thermonuclear ".Ia" supernova. In this paper, we present hydrodynamic explosion models and observable outcomes of these He shell detonations for a range of initial core and envelope masses. The peak UVOIR bolometric luminosities range by a factor of 10 (from 5e41 - 5e42 erg/s), and the R-band peak varies from M_R,peak = -15 to -18. The rise times in all bands are very rapid (<10 d), but the decline rate is slower in the red than the blue due to a secondary near-IR brightening. The nucleosynthesis primarily yields heavy alpha-chain elements (40Ca through 56Ni) and unburnt He. Thus, the spectra around peak light lack signs of intermediate mass elements and are dominated by CaII and TiII features, with the caveat that our radiative transfer code does not include the non-thermal effects necessary to produce He features.Comment: Accepted for publication in The Astrophysical Journal; 9 pages, 9 figures; v2: Minor changes to correct typos and clarify conten

Backward running or absence of running from Creutz ratios

We extract the running coupling based on Creutz ratios in SU(2) lattice gauge theory with two Dirac fermions in the adjoint representation. Depending on how the extrapolation to zero fermion mass is performed, either backward running or an absence of running is observed at strong bare coupling. This behavior is consistent with other findings which indicate that this theory has an infrared fixed point.Comment: 12 pages, 3 figures; v2 fifth mass point added, three extrapolations now performed, conclusions softene

Multigrid for Chiral Lattice Fermions: Domain Wall

Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the M\"obius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the K\"ahler-Dirac spectral map used in a recent staggered MG algorithm [1].Comment: 39 pages, 13 figure