Searcharxiv⌕ Search

arXiv subjects

Howard Georgi

Publications and source records attributed to Howard Georgi.

At least 55 records · Page 3Linked to original sources
arXiv1999

Soft Superweak CP Violation and the Strong CP Puzzle

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 $ε^\prime$. All other CP-violating parameters in the effective low-energy standard model, including the area of the unitarity triangle and $\barθ$, are finite, calculable and can be made very small. The leading contribution to $\barθ$ 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.

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

S_3 and the L=1 Baryons in the Quark Model and the Chiral Quark Model

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.

hep-ph↗
arXiv1998

Neutrinos on Earth and in the Heavens

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.

hep-ph↗
arXiv1998

Effective Field Theory of Vacuum Tilting

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.

hep-ph↗
arXiv1998

Hidden Sector Gaugino Condensation and the Model-independent Axion

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 $θ_h$. The $θ_h$ 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.

hep-ph↗
arXiv1998

Large-N and Vacuum Alignment in Topcolor Models

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''.

hep-ph↗
arXiv1997

Sum-rule for large-$N_c$ QCD and application to heavy quarkonia

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 $α_s$. 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.

hep-ph↗
arXiv1997

Reparameterization Invariance Revisited

Reparameterization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparameterization transformation are shown to induce the same constraints on operators that do not vanish under the equation of motion to order $1/m^2$, and to be related by a redefinition of the heavy quark field. We give a new, very straightforward proof that that the reparameterization invariance constraints apply to all orders in $α_s$ under matching to full QCD and renormalization-group running, at least up to and including $O(1/m^2)$.

hep-ph↗
arXiv1996

A Little Large N Group Theory

We discuss the group theory relevant to the ground-state baryons in large N_c QCD. For very large representation, the group generators become classical variables. We find the form of the classical generators for the completely symmetric N index representation of $SU(m)$ as $N\rightarrow\infty$ and derive an integral formula for the matrix elements of an arbitrary polynomial in the group generators between low-spin baryon states in the large N limit.

hep-ph↗
arXiv1996

Decays of a Leptophobic Gauge Boson

We discuss the theory and phenomenology of decays of a leptophobic $U(1)_\X$ gauge boson $X$, such as has been proposed to explain the alleged deviations of $R_b$ and $R_c$ from standard model predictions. If the scalars involved in the breaking of the $SU(2)\times U(1)$ symmetry are sufficiently light, $X$ will sometimes decay into a charged (or neutral) scalar along with an oppositely-charged $W$ (or $Z$). These decay modes could yield clean signals for the leptophobic gauge bosons at hadron colliders and provide an interesting window into the Higgs sector of the theory.

hep-ph↗
arXiv1995

Effects of Top Compositeness

We investigate the effects of top quark compositeness on various physical parameters, and obtain lower limits on the compositeness scale from electroweak precision data. We consider corrections to top quark decay rates and other physical processes. Our results depend sensitively on whether the left-handed top is composite. A considerable enhancement of $t \bar t$ production is possible if only the right-handed top is composite.

hep-ph↗
arXiv1994

Decays of $\ell=1$ Baryons --- Quark Model versus Large-$N_c$

We study nonleptonic decays of the orbitally excited, \su6 \rep{70}-plet baryons in order to test the hypothesis that the successes of the nonrelativistic quark model have a natural explanation in the large-$N_c$ limit of QCD. By working in a Hartree approximation, we isolate a specific set of operators that contribute to the observed s- and d-wave decays in leading order in $1/N_c$. We fit our results to the current experimental decay data, and make predictions for a number of allowed but unobserved modes. Our tentative conclusion is that there is more to the nonrelativistic quark model of baryons than large-$N_c$.

hep-ph↗
arXiv1993

On Spin Independence in Large $N_c$ Baryons

We argue directly from Witten's analysis of large $N_c$ baryons that the structure of the $s$-wave low-spin baryon states in QCD becomes spin-independent as $N_c\rightarrow\infty$. This property leads to $SU(6)$-like behavior of static matrix elements, such as the axial-vector current matrix elements recently studied by Dashen, Manohar and Jenkins. Our analysis suggests a method for applying large $N_c$ results for $N_c=3$, even though the baryon states for large $N_c$ are very different.

hep-ph↗
arXiv1993

Effective Field Theories with Instantons

We explain how nonperturbative effects can be systematically included when constructing an effective field theory. We concentrate in particular on the matching calculation, by which a low energy theory without a heavy particle degree of freedom is matched onto the full theory. The matching calculation requires some new formalism, because for a large class of theories, instantons occur in a continuous range of scales from far below the mass of the heavy particle to far above. We show how the complete IR finiteness of the usual matching formalism arises in this new context. As an example, we formally integrate out a heavy quark in QCD. %%%% Includes 14 PiCTeX figures. %%%%

hep-ph↗
arXiv1993

Technicolor with a Massless Scalar Doublet

We consider a minimal technicolor model in which the ordinary and technicolor sectors are coupled by a {\it massless} scalar doublet. When technicolor interactions become strong, the resulting technicolor condensate not only breaks the electroweak symmetry, but also causes the scalar to develop a vacuum expectation value. With the appropriate choice of the scalar's Yukawa couplings, fermion masses are generated, giving us the conventional pattern of flavor symmetry breaking. Although no explicit scalar mass term appears in the full lagrangian of the model, the pseudoscalar states that remain in the low-energy effective theory gain sufficient mass through technicolor interactions to evade detection. We show that this model does not generate unacceptably large flavor changing neutral currents, and is consistent with the experimental constraints on oblique electroweak radiative corrections. We determine the experimentally allowed region of the model's parameter space, and discuss the significance of a phenomenologically viable model that has no arbitrary dimensionful parameters. In terms of parameter counting, our model is the simplest possible extension of the standard model.

hep-ph↗