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Christopher T. Hill

Publications and source records attributed to Christopher T. Hill.

At least 73 records · Page 4Linked to original sources
arXiv2002

Fractal Theory Space: Spacetime of Noninteger Dimensionality

We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant ``compactification scale,'' M. The energy distribution of KK modes above M is controlled by an exponent in a scaling relation of the vacuum energy (Coleman-Weinberg potential), and corresponds to the dimensionality. For truncated-s-simplex lattices with coordination number s the spacetime dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space involve subtleties, owing to the 1+3 kinetic terms, yet the resulting dimensionalites are equivalent to thermal spin systems. Physical implications are discussed.

hep-th↗
arXiv2002

Deconstructing 5-D QED

We discuss periodic compactification and latticization of a 5-D U(1) theory with a Dirac fermion, yielding a 1+3 effective theory. We address subtleties in the lattice fermionic action,such as fermion doubling and the Wilson term. We compute the Coleman-Weinberg potential for the Wilson line which is finite for N-branes >= 3, due to the Z_N symmetry, which replaces translations in the 5th dimension. This mode becomes a PNGB in the low energy 1+3 theory. We derive its anomalous coupling to the "photon" and its KK-modes.

hep-ph↗
arXiv2002

Natural Theories of Ultra-Low Mass PNGB's: Axions and Quintessence

We consider the Wilson Line PNGB which arises in a U(1)^N gauge theory, abstracted from a latticized, periodically compactified extra dimension U(1). Planck scale breaking of the PNGB's global symmetry is suppressed, providing natural candidates for the axion and quintessence. We construct an explicit model in which the axion may be viewed as the 5th component of the U(1)_Y gauge field in a 1+4 latticized periodically compactified extra dimension. We also construct a quintessence PNGB model where the ultra-low mass arises from Planck-scale suppressed physics itself.

hep-ph↗
arXiv2001

Topological Solitons from DeConstructed Extra Dimensions

A topological monopole-like field configuration exists for Yang-Mills gauge fields in a 4+1 dimensions. When the extra dimension is compactified to 3+1 dimensions with periodic lattice boundary conditions, these objects reappear in the low energy effective theory as a novel solution, a gauged-bosonic Skyrmion. When the low energy theory spontaneously breaks, the Nambu-Goldstone mode develops a VEV, and the gauged-bosonic Skyrmion morphs into a `t Hooft--Polyakov monopole.

hep-th↗
arXiv2001

Top Quark Seesaw, Vacuum Structure and Electroweak Precision Constraints

We present a complete study of the vacuum structure of Top Quark Seesaw models of the Electroweak Symmetry Breaking, including bottom quark mass generation. Such models emerge naturally from extra dimensions. We perform a systematic gap equation analysis and develop an improved broken phase formulation for including exact seesaw mixings. The composite Higgs boson spectrum is studied in the large-N_c fermion-bubble approximation and an improved renormalization group approach. The theoretically allowed parameter space is restrictive, leading to well-defined predictions. We further analyze the electroweak precision constraints. Generically, a heavy composite Higgs boson with a mass of ~1TeV is predicted, yet fully compatible with the precision data.

hep-ph↗
arXiv2001

Dynamical Electroweak Breaking and Latticized Extra Dimensions

Using gauge invariant effective Lagrangians in 1+3 dimensions describing the Standard Model in 1+4 dimensions, we explore dynamical electroweak symmetry breaking. The Top Quark Seesaw model arises naturally, as well as the full CKM structure. We include a discussion of effects of warping, and indicate how other dynamical schemes may also be realized.

hep-ph↗
arXiv2001

The Standard Model in the Latticized Bulk

We construct the manifestly gauge invariant effective Lagrangian in 3+1 dimensions describing the Standard Model in 4+1 dimensions, following the transverse lattice technique. We incorporate split generation fermions and we explore naturalness for two Higgs configurations: a universal Higgs VEV, common to each transverse brane, and a local Higgs VEV centered on a single brane with discrete exponential attenuation to other branes, emulating the split-generation model. Extra dimensions, with explicit Higgs, do not ameliorate the naturalness problem.

hep-th↗
arXiv2001

Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes

We construct a manifestly gauge invariant Lagrangian in 3+1 dimensions for N Kaluza-Klein modes of an SU(m) gauge theory in the bulk. For example, if the bulk is 4+1, the effective theory is Π_{i=1}^{N+1} SU(m)_i with N chiral (\bar{m},m) fields connecting the groups sequentially. This can be viewed as a Wilson action for a transverse lattice in x^5, and is shown explicitly to match the continuum 4+1 compactifed Lagrangian truncated in momentum space. Scale dependence of the gauge couplings is described by the standard renormalization group technique with threshold matching, leading to effective power law running. We also discuss the unitarity constraints, and chiral fermions.

hep-th↗
arXiv2000

Electroweak Symmetry Breaking and Extra Dimensions

Electroweak symmetry can be naturally broken by observed quark and gauge fields in various extra-dimensional configurations. No new {\it fundamental} fields are required below the quantum gravitational scale ($\sim$ 10 - 100 TeV). We examine schemes in which the QCD gauge group alone, in compact extra dimensions, forms a composite Higgs doublet out of (t,b)_L and a linear combination of the Kaluza-Klein modes of t_R. The effective theory at low energies is the Standard Model. The top-quark mass is controlled by the number of active t_R Kaluza-Klein modes below the string scale, and is in agreement with experiment.

hep-ph↗
arXiv2000

Topology in the Bulk: Gauge Field Solitons in Extra Dimensions

Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of images to construct solutions satisfying D-brane boundary conditions. The $θ$-term on the brane becomes a topological current source, yielding an emission amplitude for monopoles into the bulk. Instantons have a novel reinterpretation in terms of monopole exchange between branes.

hep-th↗
arXiv2000

Electroweak symmetry breaking by extra dimensions

Electroweak symmetry breaking may be naturally induced by the observed quark and gauge fields in extra dimensions without a fundamental Higgs field. We show that a composite Higgs doublet can arise as a bound state of $(t, b)_L$ and a linear combination of the Kaluza-Klein states of $t_R$, due to QCD in extra dimensions. The top quark mass depends on the number of active $t_R$ Kaluza-Klein modes, and is consistent with the experimental value.

hep-ph↗
arXiv2000

The Diffractive Quantum Limits of Particle Colliders

Quantum Mechanics places limits on achievable transverse beam spot sizes of particle accelerators. We estimate this limit for a linear collider to be Δx > \hbar c f/Eδ_0 where f is the final focal length, E the beam energy, and δ_0 the intrinsic transverse Gaussian width of the electron wave-function. δ_0 is determined in the phase space damping rings, and we find δ_0 \approx \sqrt{\hbar c /eB} where B is the typical wiggler magnetic field strength in this system. For the NLC δ_0 = 25 nm, and Δx = 0.06 nm, about two orders of magnitude smaller than the design goal. We can recover a crude estimate of the classical result when we include radiative relaxation effects. We also consider a synchrotron and obtain Δx > \sqrt{\hbar c f/E} = O(1.0) nm. We discuss formulation of quantum beam optics relevant to these issues.

hep-ph↗
arXiv2000

Teaching "Symmetry" in the Introductory Physics Curriculum

Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.

physics.ed-ph↗
arXiv1999

Cross Section for Topcolor Z' decaying to top-antitop

We present a calculation of the cross section for the process p pbar -> Zt' -> t tbar, the production of a Topcolor Z' with subsequent decay to top quark pairs in proton anti-proton collisions at 1.8 TeV. Variations of the cross section with varying assumptions about the model, the resonance width, the parton distributions and the renormalization scale are presented.

hep-ph↗
arXiv1999

Gauge Coupling Unification with Extra Dimensions and Gravitational Scale Effects

We study gauge coupling unification in the presence of extra dimensions compactified at a few TeV. Achieving unification requires a large number of gauge boson Kaluza-Klein excitations lighter than the string scale, such that the higher-dimensional gauge couplings are O(1) in string scale units. Corrections to the gauge couplings from two or more loops are about 10% or larger, hence string (or M) theory is generally expected to be strongly coupled in TeV-scale extra-dimensional scenarios. Higher-dimensional operators induced by quantum gravitational effects can shift the gauge couplings by a few percent. These effects are sufficiently large that even the minimal Standard Model, or the MSSM, allow unification at a scale in the TeV range. The strongly coupled unified theory may induce dynamical electroweak symmetry breaking.

hep-ph↗
arXiv1998

Top Quark Seesaw Theory of Electroweak Symmetry Breaking

We study electroweak symmetry breaking involving the seesaw mechanism of quark condensation. These models produce a composite Higgs boson involving the left-handed top quark, yet the top mass arises naturally at the observed scale. We describe a schematic model which illustrates the general dynamical ideas. We also consider a generic low-energy effective theory which includes several composite scalars, and we use the effective potential formalism to compute their spectrum. We develop a more detailed model in which certain features of the schematic model are replaced by additional dynamics.

hep-ph↗
arXiv1998

Electroweak Symmetry Breaking via Top Condensation Seesaw

We propose a new mechanism in which all of the electroweak symmetry breaking is driven by a natural top quark condensate, produced by topcolor interactions at a multi-TeV scale. The scheme allows the observed top quark mass, and acceptable T and S parameters, by invoking a seesaw mechanism involving mixing of the top with an additional isosinglet quark.

hep-ph↗