The Littlest Higgs

We present an economical theory of natural electroweak symmetry breaking, generalizing an approach based on deconstruction. This theory is the smallest extension of the Standard Model to date that stabilizes the electroweak scale with a naturally light Higgs and weakly coupled new physics at TeV energies. The Higgs is one of a set of pseudo Goldstone bosons in an $SU(5)/SO(5)$ nonlinear sigma model. The symmetry breaking scale $f$ is around a TeV, with the cutoff \Lambda \lsim 4\pi f \sim 10 TeV. A single electroweak doublet, the ``little Higgs'', is automatically much lighter than the other pseudo Goldstone bosons. The quartic self-coupling for the little Higgs is generated by the gauge and Yukawa interactions with a natural size $O(g^2,\lambda_t^2)$, while the top Yukawa coupling generates a negative mass squared triggering electroweak symmetry breaking. Beneath the TeV scale the effective theory is simply the minimal Standard Model. The new particle content at TeV energies consists of one set of spin one bosons with the same quantum numbers as the electroweak gauge bosons, an electroweak singlet quark with charge 2/3, and an electroweak triplet scalar. One loop quadratically divergent corrections to the Higgs mass are cancelled by interactions with these additional particles.Comment: 15 pages. References added. Corrected typos in the discussion of the top Yukawa couplin

Minimal Composite Higgs Model with Light Bosons

We analyze a composite Higgs model with the minimal content that allows a light Standard-Model-like Higgs boson, potentially just above the current LEP limit. The Higgs boson is a bound state made up of the top quark and a heavy vector-like quark. The model predicts that only one other bound state may be lighter than the electroweak scale, namely a CP-odd neutral scalar. Several other composite scalars are expected to have masses in the TeV range. If the Higgs decay into a pair of CP-odd scalars is kinematically open, then this decay mode is dominant, with important implications for Higgs searches. The lower bound on the CP-odd scalar mass is loose, in some cases as low as $\sim$ 100 MeV, being set only by astrophysical constraints.Comment: 33 pages, latex. Corrections in eqs. 3.21, 3.23, 4.1, 4.5-10. One figure adde

Non--decoupling, triviality and the ρ\rho parameter

The dependence of the $\rho$ parameter on the mass of the Higgs scalar and the top quark is computed non--perturbatively using the $1/N_F$ expansion in the standard model. We find an explicit expression for the $\rho$ parameter that requires the presence of a physical cutoff. This should come as no surprise since the theory is presumably trivial. By taking this cutoff into account, we find that the $\rho$ parameter can take values only within a limited range and has finite ambiguities that are suppressed by inverse powers of the cutoff scale, the so called ``scaling--violations". We find that large deviations from the perturbative results are possible, but only when the cutoff effects are also large.Comment: 16pp, Figures NOT included, harvmac, minor modifications incl. wording, refs., UCLA/92/TEP/23,OHSTPY-HEP-T-92-00

Little Higgses from an Antisymmetric Condensate

We construct an SU(6)/Sp(6) non-linear sigma model in which the Higgses arise as pseudo-Goldstone bosons. There are two Higgs doublets whose masses have no one-loop quadratic sensitivity to the cutoff of the effective theory, which can be at around 10 TeV. The Higgs potential is generated by gauge and Yukawa interactions, and is distinctly different from that of the minimal supersymmetric standard model. At the TeV scale, the new bosonic degrees of freedom are a single neutral complex scalar and a second copy of SU(2)xU(1) gauge bosons. Additional vector-like pairs of colored fermions are also present.Comment: 13 page

Flavor Physics and the Triviality Bound on the Higgs Mass

The triviality of the scalar sector of the standard one-doublet Higgs model implies that this model is only an effective low-energy theory valid below some cut-off scale $\Lambda$. The underlying high-energy theory must include flavor dynamics at a scale of order $\Lambda$ or greater in order to give rise to the different Yukawa couplings of the Higgs to ordinary fermions. This flavor dynamics will generically produce flavor-changing neutral currents and non-universal corrections to Z -> b b-bar. We show that the experimental constraints on the neutral D-meson mass difference imply that $\Lambda$ must be greater than of order 21 TeV. We also discuss bounds on $\Lambda$ from the constraints on extra contributions to the K_L - K_S mass difference and to the coupling of the Z boson to b-quarks. For theories defined about the infrared-stable Gaussian fixed-point, we estimate that this lower bound on $\Lambda$ yields an upper bound of approximately 460 GeV on the Higgs boson's mass, independent of the regulator chosen to define the theory.Comment: 11 pages, 2 embedded figures, LaTeX; references and discussion of CP violation adde

Phenomenology of the Little Higgs Model

We study the low energy phenomenology of the little Higgs model. We first discuss the linearized effective theory of the "littlest Higgs model" and study the low energy constraints on the model parameters. We identify sources of the corrections to low energy observables, discuss model-dependent arbitrariness, and outline some possible directions of extensions of the model in order to evade the precision electroweak constraints. We then explore the characteristic signatures to test the model in the current and future collider experiments. We find that the LHC has great potential to discover the new SU(2) gauge bosons and the possible new U(1) gauge boson to the multi-TeV mass scale. Other states such as the colored vector-like quark T and doubly-charged Higgs boson Phi^{++} may also provide interesting signals. At a linear collider, precision measurements on the triple gauge boson couplings could be sensitive to the new physics scale of a few TeV. We provide a comprehensive list of the linearized interactions and vertices for the littlest Higgs model in the appendices.Comment: 43 pages, 6 figures; v2: discussion clarified, typos corrected; v3: version to appear in PRD; v4: typos fixed in Feynman rule

Big Corrections from a Little Higgs

We calculate the tree-level expressions for the electroweak precision observables in the SU(5)/SO(5) littlest Higgs model. The source for these corrections are the exchange of heavy gauge bosons, explicit corrections due to non-linear sigma-model dynamics and a triplet Higgs VEV. Weak isospin violating contributions are present because there is no custodial SU(2) global symmetry. The bulk of these weak isospin violating corrections arise from heavy gauge boson exchange while a smaller contribution comes from the triplet Higgs VEV. A global fit is performed to the experimental data and we find that throughout the parameter space the symmetry breaking scale is bounded by f > 4 TeV at 95% C.L. Stronger bounds on f are found for generic choices of the high energy gauge couplings. We find that even in the best case scenario one would need fine tuning of less than a percent to get a Higgs mass as light as 200 GeV.Comment: 20 pages, 5 figures included, typos fixed, comments on the effects of extra vector-like heavy fermions adde

Polygenic transcriptome risk scores for COPD and lung function improve cross-ethnic portability of prediction in the NHLBI TOPMed program

While polygenic risk scores (PRSs) enable early identification of genetic risk for chronic obstructive pulmonary disease (COPD), predictive performance is limited when the discovery and target populations are not well matched. Hypothesizing that the biological mechanisms of disease are shared across ancestry groups, we introduce a PrediXcan-derived polygenic transcriptome risk score (PTRS) to improve cross-ethnic portability of risk prediction. We constructed the PTRS using summary statistics from application of PrediXcan on large-scale GWASs of lung function (forced expiratory volume in 1 s [FEV1] and its ratio to forced vital capacity [FEV1/FVC]) in the UK Biobank. We examined prediction performance and cross-ethnic portability of PTRS through smoking-stratified analyses both on 29,381 multi-ethnic participants from TOPMed population/family-based cohorts and on 11,771 multi-ethnic participants from TOPMed COPD-enriched studies. Analyses were carried out for two dichotomous COPD traits (moderate-to-severe and severe COPD) and two quantitative lung function traits (FEV1 and FEV1/FVC). While the proposed PTRS showed weaker associations with disease than PRS for European ancestry, the PTRS showed stronger association with COPD than PRS for African Americans (e.g., odds ratio [OR] = 1.24 [95% confidence interval [CI]: 1.08–1.43] for PTRS versus 1.10 [0.96–1.26] for PRS among heavy smokers with ≥ 40 pack-years of smoking) for moderate-to-severe COPD. Cross-ethnic portability of the PTRS was significantly higher than the PRS (paired t test p < 2.2 × 10−16 with portability gains ranging from 5% to 28%) for both dichotomous COPD traits and across all smoking strata. Our study demonstrates the value of PTRS for improved cross-ethnic portability compared to PRS in predicting COPD risk

Whole genome sequence analysis of pulmonary function and COPD in 19,996 multi-ethnic participants

Chronic obstructive pulmonary disease (COPD), diagnosed by reduced lung function, is a leading cause of morbidity and mortality. We performed whole genome sequence (WGS) analysis of lung function and COPD in a multi-ethnic sample of 11,497 participants from population- and family-based studies, and 8499 individuals from COPD-enriched studies in the NHLBI Trans-Omics for Precision Medicine (TOPMed) Program. We identify at genome-wide significance 10 known GWAS loci and 22 distinct, previously unreported loci, including two common variant signals from stratified analysis of African Americans. Four novel common variants within the regions of PIAS1, RGN (two variants) and FTO show evidence of replication in the UK Biobank (European ancestry n ~ 320,000), while colocalization analyses leveraging multi-omic data from GTEx and TOPMed identify potential molecular mechanisms underlying four of the 22 novel loci. Our study demonstrates the value of performing WGS analyses and multi-omic follow-up in cohorts of diverse ancestry