Search

I show that if a dimensionless parameter is tuned to be close to the boundary of the positivity domain and symmetry breaking is driven by a cubic term in the Lagrangian, the scale of the physics of symmetry breaking in a quantum field theory as measured by the Higgs mass can be much greater than the dimensional scales in the classical Lagrangian. Radiative corrections produce large and physically important corrections, helping to stabilize the large VEV. The resulting picture contrasts sharply with the "modern" view of QFT as an effective field theory. I describe how this mechanism might produce the GUT scale in an SU(5) model in which the dimensional parameters in the Lagrangian are at the low scale., Comment: 4 pages, 2 figures

I bosonize the position-space correlators of flavor-diagonal scalar fermion bilinears in arbitrary generalizations of the Schwinger model with $n_F$ massless fermions coupled to $n_A$ gauge bosons for $n_F\geq n_A$. For $n_A=n_F$, the fermion bilinears can be bosonized in terms of $n_F$ scalars with masses proportional to the gauge couplings. As in the Schwinger model, bosonization can be used to find all correlators, including those that are forbidden in perturbation theory by anomalous chiral symmetries, but there are subtleties when there is more than one gauge boson. The new result here is the general treatment of the dependence on gauge boson masses in models with more than one gauge symmetry. For $n_A

I discuss the 2-flavor Schwinger model with $\theta=0$ and small equal and opposite fermion masses (or $\theta=\pi$ with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special mass term modifies the conformal sector without breaking the conformal symmetry. I show in detail how mass-perturbation-theory works for correlators of flavor-diagonal fermion scalar bilinears. The result provides quantitative evidence that the theory has no mass gap for small non-zero fermion masses. The massive fermions are bound into conformally invariant unparticle stuff. I show how the long-distance conformal symmetry is maintained when small fermion masses are turned on and calculate the relevant scaling dimensions for small mass. I calculate the corrections to the 2- and 4-point functions of the fermion-bilinear scalars to leading order in perturbation theory in the fermion mass and describe a straightforward procedure to extend the calculation to all higher scalar correlators. I hope that this model as a useful and non-trivial example of unparticle physics, a sector with unbroken conformal symmetry coupled to interacting massive particles, in which we can analyze the particle physics in a consistent approximation., Comment: 20 pages, 0 figures - extensively revised with a new section on higher correlators (confusing statement after eq (21) clarified in the last revision - no other changes)-typos corrected in eqs (44) and (66) - reference [12] added in revision before publication - extensive revision of sections 1-3 to make the paper easier to read

Talk at the KITP Conference: Snowmass Theory Frontier - Feb. 23, 2022, Comment: 6 pages

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors; v3 references added, some updates, additional authors

I discuss the 2-flavor Schwinger model both without and with fermion masses. I argue that the concept of "conformal coalescence," in unparticle physics in which linear combinations of short distance operators can disappear from the long-distance theory, makes it easy to understand some puzzling features of the model with small fermion masses. In particular, I argue that for an average fermion mass $m_f$ and a mass difference $\delta m$, so long as both are small compared to the dynamical gauge boson mass $m=e\sqrt{2/\pi}$, isospin breaking effects in the low energy theory are exponentially suppressed by powers of $\exp\Bigl(-(m/m_f)^{2/3}\Bigr)$ even if $\delta m\approx m_f$! In the low energy theory, this looks like exponential fine-tuning, but it is done automatically by conformal coalescence., Comment: 8 pages (suggestions of referees incorporated)

We analyze generalizations of the Schwinger model with more massless fermions and more vector fields. We focus on models with the gauge structure of ``diagonal color $SU(n)$'' but unlike previous investigators, we do not assume that all the gauge boson masses are the same. Unlike the Schwinger model, these are Banks-Zaks models with conformal sectors that survive at long distances. In addition to local operators that go to ``unparticle operators'' with non-zero anomalous dimensions at long distances, they contain local operators like the $\bar\psi_L\psi_R$ operator in the Schwinger model which go to constants at long distances. These operators have calculable vacuum expectation values (up to phases). Cluster decomposition applied to correlation functions involving these operators yields nontrivial and calculable non-perturbative constraints on correlation functions. One consequence is ``conformal coalescence'' in which linear combinations of short distance operators disappear from the long-distance theory, leaving only one kind of unparticle stuff in the low-energy theory. We believe that our detailed analysis of diagonal color $SU(n)$ paints an appealing picture of unparticle operators as the result of an incomplete binding of the massless fermions. We complete the picture (and the binding) by analyzing the diagonal color $U(n)$ model with a very small $U(1)$ coupling and thus a gauge boson with a dynamical mass much smaller than the other masses in the model. This model has a mass gap and we can see explicitly the transition from free-fermion behavior at short distances to unparticle physics at intermediate distances to the physics of massive particles at long distances., Comment: 24 pages, 7 figures - greatly expanded (note that the one author has changed her name)

The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The "physics" of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). We analyze generalizations of the Sommerfield model, and the corresponding generalizations of the Schwinger model, with more massless fermions and more vector fields., Comment: 14 pages, 1 figure - new references and an expanded discussion added in revised version

The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The `physics' of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). I discuss the `Schwinger point' of the Sommerfield model in which the vector boson mass goes to zero. The limit is singular but gauge invariant quantities should be well-defined. I give a number of examples, both (trivially) with local operators and with nonlocal products connected by Wilson lines (the primary technical accomplishment in this note is the explicit and very pedestrian calculation of correlators involving straight Wilson lines). I hope that this may give some insight into the nature of bosonization in the Schwinger model and its connection with unparticle physics which in this simple case may be thought of as `incomplete bosonization.', Comment: 19 pages, 2 figures, new discussion of n-flavor Schwinger model - version 3 minor changes to prepare for submission

We discuss the issue of complementarity between the confining phase and the Higgs phase for gauge theories in which there are no light particles below the scale of confinement or spontaneous symmetry breaking. We show with a number of examples that even though the low energy effective theories are the same (and trivial), discontinuous changes in the structure of heavy stable particles can signal a phase transition and thus we can sometimes argue that two phases which have different structures of heavy particles cannot be continuously connected and thus the phases cannot be complementary. We discuss what this means and suggest that such "stability conditions" can be a useful physical check for complementarity., Comment: 12 pages

We explore a "partial unification" model that could explain the diphoton event excess around $750 \, \rm GeV$ recently reported by the LHC experiments. A new strong gauge group is combined with the ordinary color and hypercharge gauge groups. The VEV responsible for the combination is of the order of the $SU(2)\times U(1)$ breaking scale, but the coupling of the new physics to standard model particles is suppressed by the strong interaction of the new gauge group. This simple extension of the standard model has a rich phenomenology, including composite particles of the new confining gauge interaction, a coloron and a $Z'$ which are rather weakly coupled to standard model particles, and massive vector bosons charged under both the ordinary color and hypercharge gauge groups and the new strong gauge group. The new scalar glueball could have mass of around $750 \, \rm GeV$, be produced by gluon fusion and decay into two photons, both through loops of the new massive vector bosons. The simplest version of the model has some issues: the massive vector bosons are stable and the coloron and the $Z'$ are strongly constrained by search data. An extension of the model to include additional fermions with the new gauge coupling, though not as simple and elegant, can address both issues and more. It allows the massive vector boson to decay into a colorless, neutral state that could be a candidate of the dark matter. And the coloron and $Z'$ can decay dominantly into the new fermions, completely changing the search bounds. In addition, $SU(N)$ fermions below the symmetry breaking scale make it more plausible that the lightest glueball is at $750$~GeV. Whatever becomes of the $750$~GeV diphoton excess, the model is an unusual example of how new physics at small scales could be hidden by strong interactions., Comment: 33 pages, 4 figures, 7 tables

A talk presented at the April 2016 APS meeting in Salt Lake City: The speaker had the great good fortune to take an undergraduate course in group theory from Sidney Coleman, and (after graduate school away) was hired by Coleman to a postdoctoral position and eventually became a faculty colleague. He will share some still vivid memories of this remarkable character., Comment: 21 pages

I construct a quantum field theory model with discrete scale invariance at tree level. The model has some unusual mathematical properties (such as the appearance of $q$-hypergeometric series) and may possibly have some interesting physical properties as well. In this note, I explore some possible physics that could be regarded as a violation of standard effective field theory ideas., Comment: 18 pages, 24 figures

I describe a class of iterative jet algorithms that are based on maximizing a fixed function of the total 4-momentum rather than clustering of pairs of jets. I describe some of the properties of the simplest examples of this class, appropriate for jets at an $e^+e^-$ machine. These examples are sufficiently simple that many features of the jets that they define can be determined analytically with ease. The jets constructed in this way have some potentially useful properties, including a strong form of infrared safety., Comment: 7 pages, 0 figures

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0-flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET., Comment: 14 pages

We derive the photon propagator in light-shell gauge, which was first introduced in the context of light-shell effective theory.

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at $c$ and are associated with a non-linear $\sigma$-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider., Comment: 11 pages, no figures

We develop techniques for studying the effects of self-interactions in the conformal sector of an unparticle model. Their physics is encoded in the higher n-point functions of the conformal theory. We study inclusive processes and argue that the inclusive production of unparticle stuff in standard model processes due to the unparticle self-interactions can be decomposed using the conformal partial wave expansion and its generalizations into a sum over contributions from the production of various kinds of unparticle stuff, corresponding to different primary conformal operators. Such processes typically involve the production of unparticle stuff associated with operators other than those to which the standard model couples directly. Thus just as interactions between particles allow scattering processes to produce new particles in the final state, so unparticle self-interactions cause the production of various kinds of unparticle stuff. We discuss both inclusive and exclusive methods for computing these processes. The resulting picture, we believe, is a step towards understanding what unparticle stuff "looks like" because it is quite analogous to way we describe the production and scattering of ordinary particles in quantum field theory, with the primary conformal operators playing the role of particles and the coefficients in the conformal partial wave expansion (and its generalization to include more fields) playing the role of amplitudes. We exemplify our methods in the 2D toy model that we discussed previously in which the Banks-Zaks theory is exactly solvable., Comment: 65 pages, 27 figures; v2: added section 8 on massive bosons, minor improvements, references; v3: references

We discuss what can be learned about unparticle physics by studying simple quantum field theories in one space and one time dimension. We argue that the exactly soluble 2D theory of a massless fermion coupled to a massive vector boson, the Sommerfield model, is an interesting analog of a Banks-Zaks model, approaching a free theory at high energies and a scale invariant theory with nontrivial anomalous dimensions at low energies. We construct a toy standard model coupling to the fermions in the Sommerfield model and study how the transition from unparticle behavior at low energies to free particle behavior at high energies manifests itself in interactions with the toy standard model particles., Comment: 8 pages, 2 figures

The peculiar propagator of scale invariant unparticles has phases that produce unusual patterns of interference with standard model processes. We illustrate some of these effects in $e^+e^-\to\mu^+\mu^-$., Comment: 9 pages, 8 figures - minor wording changes and additional reference in v2

I discuss some simple aspects of the low-energy physics of a nontrivial scale invariant sector of an effective field theory -- physics that cannot be described in terms of particles. I argue that it is important to take seriously the possibility that the unparticle stuff described by such a theory might actually exist in our world. I suggest a scenario in which some details of the production of unparticle stuff can be calculated. I find that in the appropriate low energy limit, unparticle stuff with scale dimension $d_{\mathcal{U}}$ looks like a non-integral number $d_{\mathcal{U}}$ of invisible particles. Thus dramatic evidence for a nontrivial scale invariant sector could show up experimentally in missing energy distributions., Comment: 9 pages, 1 figure - more references and minor wording changes in v3

{I construct a renormalizable $SU(2)^{89}\times U(1)$ gauge theory with standard-model-like phenomenology for the gauge bosons masses and the weak interactions of the light fermions (including the $b$) but in which all vacuum expectation values are about 2 TeV. This is a deconstructed version of a Higgsless model with a flat extra dimension. The fermions are delocalized on the theory space in an unusual way, with LH and RD fermions on alternate nodes., Comment: 12 pages, latex with pictex figure embedded

Motivated by recent works on ``Higgsless theories,'' I discuss an $SU(2)_0\times SU(2)^{N}\times U(1)$ gauge theory with arbitrary bifundamental (or custodial SU(2) preserving) symmetry breaking between the gauge subgroups and with ordinary matter transforming only under the U(1) and $SU(2)_0$. When the couplings, $g_j$, of the other SU(2)s are very large, this reproduces the standard model at the tree level. I calculate the $W$ and $Z$ masses and other electroweak parameters in a perturbative expansion in $1/g_j^2$, and give physical interpretations of the results in a mechanical analog built out of masses and springs. In the mechanical analog, it is clear that even for arbitrary patterns of symmetry breaking, it is not possible (in the perturbative regime) to raise the Higgs mass by a large factor while keeping the $S$ parameter small., Comment: 20 pages, 5 figures, LaTeX - another reference

We discuss exact results for the full nonperturbative effective superpotentials of four dimensional $\mathcal{N}=1$ supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large $N$ limit., Comment: 14 pages; v2: typos corrected; v3: the scheme for computing exact superpotentials including both the Veneziano-Yankielowicz term and all instanton corrections directly using matrix models is emphasized and references added, to appear in JHEP

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale Mpl and a mass mg, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Lambda parametrically above mg. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Lambda ~ (mg^4 Mpl)^(1/5) for the Fierz-Pauli theory, but can be raised to Lambda ~ (mg^2 Mpl)^(1/3) in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions., Comment: 22 pages, 7 diagrams; references and some clarifying comments added, typos corrected

We summarize our findings on the quantum moduli constraints and superpotentials of an infinite family of moose extensions of $n_f = n_c$ SUSY QCD. For $n_c=2$, we perform concrete calculations using traditional integrating out techniques as well as Intriligator's ``integrating in'' technique. Checking the constraints and superpotentials in the limits of setting $\Lambda$'s to zero or integrating out mass terms, we find that the quantum moduli constraints are local in theory space and are equivalent to a consistent structure of ``splitting relations'' amongst the different theories. Extending the results to arbitrary $n_c$, we show that the splitting relations, along with a set of rules for flowing from a high energy theory to a low energy theory, incorporate much of the physics of the moose chain. The relations can be used both to simplify perturbative calculations of symmetry breaking and to incorporate nonperturbative effects., Comment: 25 pages, Latex; changed analysis on power-law running section now with weaker results, added references and acknowledgements

We present examples of four dimensional, non-supersymmetric field theories in which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings and the vacuum energy, are suppressed by $(\alpha/4 \pi)^{N}$, where $\alpha$ is a weak coupling factor and $N$ can be made arbitrarily large. The particle content and interactions of these models are conveniently represented by a graph with sites and links, describing the gauge theory space structure. While the theories are supersymmetric ``locally'' in theory space, supersymmetry can be explicitly broken by topological obstructions., Comment: 9 pages, revtex4

We construct four dimensional gauge theories in which the successful supersymmetric unification of gauge couplings is preserved but accelerated by N-fold replication of the MSSM gauge and Higgs structure. This results in a low unification scale of $10^{13/N}$ TeV., Comment: 4 pages, revtex4

We propose a new class of four-dimensional theories for natural electroweak symmetry breaking, relying neither on supersymmetry nor on strong dynamics at the TeV scale. The new TeV physics is perturbative, and radiative corrections to the Higgs mass are finite. The softening of this mass occurs because the Higgs is an extended object in theory space, resulting in an accidental symmetry. A novel Higgs potential emerges naturally, requiring a second light SU(2) doublet scalar., Comment: 11 pages. Additional references and further clarifying remarks to agree with version to appear in PLB

We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension., Comment: 10 pages, latex

We discuss the form of the chiral anomaly on an S1/Z2 orbifold with chiral boundary conditions. We find that the 4-divergence of the higher-dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the chiral zero mode there. Nevertheless the anomaly, appropriately defined as the five dimensional divergence of the current, lives entirely on the orbifold fixed planes and is independent of the shape of the zero mode. Therefore long distance four dimensional anomaly cancellation ensures the consistency of the higher dimensional orbifold theory., Comment: 11 pages, latex, no figures

We compute loop corrections to the effective action of a field theory on a five-dimensional $S_1/Z_2$ orbifold. We find that the quantum loop effects of interactions in the bulk produce infinite contributions that require renormalization by four-dimensional couplings on the orbifold fixed planes. Thus bulk couplings give rise to renormalization group running of brane couplings., Comment: 10 pages, Latex with pictex figures

We note that orbifold boundary conditions that produce chiral fermion zero modes in compactified higher dimensional theories may distort scalar field vacuum expectation values, giving rise to nontrivial dependence on the extra dimensions. We illustrate this in a simple five dimensional model which has chiral fermion zero-modes stuck to fat branes. The model could provide a simple and explicit realization of the separation of quarks and leptons in the fifth dimension. We discuss the KK expansion in some detail. We find that there are in general non-zero-mode states stuck to the brane, like the chiral zero modes. We see explicitly the transition from states dominated by the internal structure of the fat brane to those dominated by the compactification., Comment: 16 pages, Latex, revised reference, acknowledgements and a short section on zero-modes near the orbifold fixed-points

We discuss an alternative to the topcolor seesaw mechanism. In our scheme, all the light quarks carry topcolor, and there are many composite SU(2) doublets. This makes it possible to get the observed top quark mass and observed $SU(2) \times U(1)$ breaking in a way that is quite different from the classic seesaw mechanism. We discuss a model of this kind that arises naturally in the context of dynamically broken topcolor. There are many composite scalars in a theory of this kind. This has important effects on the Pagels-Stokar relation and the Higgs mass. We find $m_{\rm Higgs} < 330$ GeV, lighter than in typical topcolor models. We also show that the electroweak singlet quarks in such a model can be lighter than the corresponding quarks in a seesaw model., Comment: 23 pages, LaTeX, uses epsf and psfig

The top quark seesaw mechanism offers a method for constructing a composite Higgs field without the usual difficulties that accompany traditional technicolor or topcolor theories. The focus of this article is to study the phenomenology of the new physics required by this mechanism. After establishing a set of criteria for a plausible top quark seesaw theory, we develop two models, the first of which has a heavy weak singlet fermion with hypercharge 4/3 while the second has, in addition, a heavy weak singlet hypercharge -2/3 fermion. At low energies, these theories contain one or two Higgs doublets respectively. We then derive the low energy effective Higgs potential in detail for the two-doublet theory as well as study the likely experimental signatures for both theories. A strong constraint on the one-doublet model is the measured value of the rho parameter which permits the new heavy fermion to have a mass of about 5-7 TeV, when the Higgs has a mass greater than 300 GeV. In the two-doublet model, mixing of the new heavy Y=-2/3 fermion and the b quark affects the prediction for R_b. In order to agree with the current limits on R_b, the mass of this fermion should be at least 12 TeV. The mass of the heavy Y=4/3 fermion in the two-doublet model is not as sharply constrained by experiments and can be as light as 2.5 TeV., Comment: 33 pages, 12 figures, uses harvmac and pictex

We analyze a model of dynamically broken topcolor in the limit in which the number of colors is large. We show that the second order nature of the phase transition, necessary for the success of topcolor models, passes the nontrivial check of consistency with the large N limit. We also identify and discuss a class of theories that generalizes the topcolor phenomenon to a theory with a richer structure of fermions and global symmetries., Comment: 25 pages, 16 figures

Observations of atmospheric neutrinos offer compelling evidence that neutrinos have mass and do oscillate. Preliminary data are compatible with maximal $\nu_\mu$--$\nu_\tau$ mixing, but not with pure $\nu_\mu$--$\nu_e$ mixing. In a general three-family scenario with just one relevant squared-mass difference, atmospheric neutrino oscillations involve two mixing angles. The special cases mentioned above are not favored by convincing theoretical arguments. As more precise data are accumulated, both at Superkamiokande and at proposed or ongoing long-baseline experiments, it will become feasible and desirable to measure both angles. To this end, we offer a brief portfolio of illustrations from which the qualitative effects of the two mixing angles on various observable quantities can be discerned., Comment: 9 pages, 6 figures included as EPS files

The S_3 symmetry corresponding to permuting the positions of the quarks within a baryon allows us to study the 70-plet of L=1 baryons without an explicit choice for the spatial part of the quark wave functions: given a set of operators with definite transformation properties under the spin-flavor group SU(3) x SU(2) and under this S_3, the masses of the baryons can be expressed in terms of a small number of unknown parameters which are fit to the observed L=1 baryon mass spectrum. This approach is applied to study both the quark model and chiral constituent quark model. The latter theory leads to a set of mass perturbations which more satisfactorily fits the observed L=1 baryon mass spectrum (though we can say nothing, within our approach, about the physical reasonableness of the parameters in the fit). Predictions for the mixing angles and the unobserved baryon masses are given for both models as well as a discussion of specific baryons., Comment: 24 pages, requires pictex

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., Comment: 30 pages, latex (two figures require PicTex). Minor corrections in eqs. 2.17, 2.18, 2.22 and 2.24

Recent data lead us to a simple and intriguing form of the neutrino mass matrix. In particular, we find solar neutrino oscillations to be nearly maximal (and rule out the small-angle MSW explanation of solar neutrino observations) if relic neutrinos comprise at least one~percent of the critical mass density of the universe., Comment: 7 pages, harvmac, minor changes and new references in revised version

We discuss a class of models in which CP is violated softly in a heavy sector adjoined to the standard model. Heavy-sector loops produce the observed CP violation in kaon physics, yielding a tiny and probably undetectable value for $\epsilon^\prime$. All other CP-violating parameters in the effective low-energy standard model, including the area of the unitarity triangle and $\bar\theta$, are finite, calculable and can be made very small. The leading contribution to $\bar\theta$ comes from a four-loop graph. These models offer a natural realization of superweak CP violation and can resolve the strong CP puzzle. In one realization of this idea, CP is violated in the mass matrix of heavy majorana neutrinos., Comment: 12 pages, embedded figures - this version was further revised after acceptance for publication

Simple models of topcolor and topcolor-assisted technicolor rely on a relatively strong U(1) gauge interaction to ``tilt'' the vacuum. This tilting is necessary to produce a top-condensate, thereby naturally obtaining a heavy top-quark, and to avoid producing a bottom-condensate. We identify some peculiarities of the Nambu-Jona-Lasinio approximation often used to analyze the topcolor dynamics. We resolve these puzzles by constructing the low-energy effective field theory appropriate to a mass-independent renormalization scheme. We construct the power-counting rules for such an effective theory. By requiring that the Landau pole associated with the U(1) gauge theory be sufficiently above the topcolor gauge boson scale, we derive an upper bound on the strength of the U(1) gauge-coupling evaluated at the topcolor scale. The upper bound on the U(1) coupling implies that these interactions can shift the composite Higgs boson mass-squared by only a few per cent and, therefore, that the topcolor coupling must be adjusted to equal the critical value for chiral symmetry breaking to within a few per cent., Comment: 15 pages, LaTeX and Pictex. Minor comments and references added to clarify relation of current work to previous work on composite Higgs models

In the effective field theory framework, we consider the effect of supersymmetry breaking via gaugino condensation and supergravity in the hidden sector gauge group on the hidden sector vacuum angle $\theta_h$. The $\theta_h$ parameter dependence of the potential yields phenomenologically acceptable invisible axion solutions if the $U(1)_R$ symmetry is broken down to a discrete subgroup $Z_N$ with $N\ge 3$ (N=4 is marginal). Anomalous U(1) superstring models are good candidates for this invisible axion resolution of the strong CP puzzle., Comment: 7 pages, no figures

Topcolor and topcolor-assisted technicolor provide examples of dynamical electroweak symmetry breaking which include top-condensation, thereby naturally incorporating a heavy top quark. In this note we discuss the roles of the Nambu-Jona-Lasinio (NJL) and large-N approximations often used in phenomenological analyses of these models. We show that, in order to provide for top-condensation but not bottom-condensation, the top-color coupling must be adjusted to equal the critical value for chiral symmetry breaking up to O(1/N) in any theory in which the isospin-violating ``tilting'' interaction is a U(1) gauge interaction. A consequence of these considerations is that the potentially dangerous ``bottom-pions'' are naturally light. We also show that the contributions to rho-1 previously estimated are of leading-order in N, are not included in the usual NJL analysis, and are the result of ``vacuum-alignment''., Comment: 12 pages, 5 epsf figures

We introduce a new sum-rule for large-$N_c$ QCD which relates the density of heavy quarkonium states, the state-averaged square of the wavefunction at the origin, and the heavy quark current-current correlator. Focusing on the region of energy just above perturbative threshold, we calculate the correlator by incorporating arbitrarily high orders in the QCD coupling $\alpha_s$. We use the sum-rule to determine the bottomonium potential using experimentally measured s-wave leptonic widths and compare the result with the potential obtained by direct calculation from the measured s-wave spectrum. We discuss the utility of the sum-rule method for accurate determination of the confining potential., Comment: 14 pages, Latex, Pictex --- revised version corrects minor typos in formulas and includes minor changes in exposition