Partially Natural Two Higgs Doublet Models

It is possible that the electroweak scale is low due to the fine-tuning of microscopic parameters, which can result from selection effects. The experimental discovery of new light fundamental scalars other than the Standard Model Higgs boson would seem to disfavor this possibility, since generically such states imply parametrically worse fine-tuning with no compelling connection to selection effects. We discuss counterexamples where the Higgs boson is light because of fine-tuning, and a second scalar doublet is light because a discrete symmetry relates its mass to the mass of the Standard Model Higgs boson. Our examples require new vectorlike fermions at the electroweak scale, and the models possess a rich electroweak vacuum structure. The mechanism that we discuss does not protect a small CP-odd Higgs mass in split or high-scale supersymmetry-breaking scenarios of the MSSM due to an incompatibility between the discrete symmetries and holomorphy.Comment: 31 pages, 4 figures. v2: refs updated, accepted for publication in JHE

The construction of saturated 2Rk-p designs

Combinatorial and sequential analyses for optimization of saturated design

Decuplet Baryon Structure from Lattice QCD

The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented giving the first model independent insight to the shape of the quark distribution in the baryon ground state. As in our octet baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent experimental measurements are available. The lattice prediction of the $\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good agreement with the experimental ratio.Comment: RevTeX manuscript, 34 pages plus 21 figures (available upon request

Chiral Properties of Pseudoscalar Mesons on a Quenched 20420^4 Lattice with Overlap Fermions

The chiral properties of the pseudoscalar mesons are studied numerically on a quenched $20^4$ lattice with the overlap fermion. We elucidate the role of the zero modes in the meson propagators, particularly that of the pseudoscalar meson. The non-perturbative renormalization constant $Z_A$ is determined from the axial Ward identity and is found to be almost independent of the quark mass for the range of quark masses we study; this implies that the $O(a^2)$ error is small. The pion decay constant, $f_{\pi}$, is calculated from which we determine the lattice spacing to be 0.148 fm. We look for quenched chiral log in the pseudoscalar decay constants and the pseudoscalar masses and we find clear evidence for its presence. The chiral log parameter $\delta$ is determined to be in the range 0.15 -- 0.4 which is consistent with that predicted from quenched chiral perturbation theory.Comment: Version accepted for publication by PRD. A few minor typographical errors have been corrected. 24 pages, 11 figure

Topological Charge Fluctuations and Low-Lying Dirac Eigenmodes

We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized.Comment: 3 pages, 4 figures, Lattice2001(confinement

Pion Decay Constant, ZAZ_A and Chiral Log from Overlap Fermions

We report our calculation of the pion decay constant $f_\pi$, the axial renormalization constant $Z_A$, and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched $20^4$ lattice at $a=0.148$ fm using tree level tadpole improved gauge action. The smallest pion mass we reach is about 280 MeV. The lattice size is about 4 times the Compton wavelength of the lowest mass pion.Comment: Lattice2001(Hadronic Matrix Elements), 3pages, 5figure