Howard Georgi

• PhD
• Harvard University

A bstract 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 ≥ 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...

A bstract I discuss the 2-flavor Schwinger model with θ = 0 and small equal and opposite fermion masses (or θ = π 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-pertu...

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 pa...

A bstract 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 Somm...

A bstract 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...

We explore a “partial unification” model that 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)×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 gr...

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), we can sometimes argue that...

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 c...

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 rema...

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 sta...

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 tha...

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 origi...

We derive the photon propagator in light-shell gauge (LSG) vμAμ=0, where vμ=(1,r^)μ. This gauge is an important ingredient of the light-shell effective theory—an effective theory for describing high energy jet processes on a 2-dimensional spherical shell expanding at the speed of light around the point of the initial collision producing the jets. S...

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...

Misha Shifman knows much more about conformal symmetry than I do, but I have been thinking hard about it, and I thought it would be fun to present some of my ideas as a little birthday present.

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-interact...

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...

The old idea of the Higgs as a pseudo-Goldstone boson has been revived and re-energized as a possible solution to the little hierarchy puzzle in the Standard Model. Its most natural implementation may be in the context of models with supersymmetry not far above the electroweak breaking scale. To cite this article: H. Georgi, C. R. Physique 8 (2007)...

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−→μ+μ−.

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 scenari...

I will talk first about the status of grand unified theories today. I will then tell the story of the discovery of the SU(5) and SO(10) GUTs back in 1973.

{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 fe...

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 ver...

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 Di...

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 ma...

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 ma...

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 limi...

This brief note is abstracted from a talk to the SLAC Summer Institure Topical Conference. I discuss little higgs models.

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.

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 (α/4π)N, where α is a weak coupling factor and N can be made arbitrarily large. The particle content and interactions of these models are conveniently...

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 spac...

We construct renormalizable, asymptotically free, four-dimensional gauge theories that dynamically generate a fifth dimension.

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 dimens...

We compute loop corrections to the effective action of a field theory on a five-dimensional S1/Z2 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 r...

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 gro...

We discuss an alternative to the top-color seesaw mechanism. In our scheme, all the light quarks carry top-color, and there are many composite SU(2) doublets. This makes it possible to get the observed t quark mass and observed SU(2)×U(1) breaking in a way that is quite different from the classic seesaw mechanism. We discuss a model of this kind th...

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....

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 thi...

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 to...

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 involv...

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 sees...

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 o...

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 θh. The θh parameter dependence of the potential yields phenomenologically acceptable invisible axion solutions if the U(1)R symmetry is broken down to...

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 eff...

Top-color and top-color-assisted technicolor provide examples of dynamical electroweak symmetry breaking which include top-quark condensation, thereby naturally incorporating a heavy top quark. In this paper we discuss the roles of the Nambu–Jona-Lasinio (NJL) and large-N approximations often used in phenomenological analyses of these models. We sh...

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, harvma...

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...

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...

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 approximatio...

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 $U(1)_R$ symmetr...

We introduce a sum-rule for large-Nc 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 QC...

We derive the relations between the nonleptonic decay amplitudes of B-mesons in the vector symmetry limit. The transverse components of vector mesons are neglected. Numerical estimations for decay rates for some final states are made taking symmetry breaking in the forms of fv/fS ≠ 1 into account.

We introduce a sum-rule for large-Nc 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 QC...

Reparametrization invariance, a symmetry of heavy quark effective theory, appears in different forms in the literature. The most commonly cited forms of the reparametrization transformation are shown to induce the same constraints on operators that do not vanish under the equation of motion to order 1/m2, and to be related by a redefinition of the...

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...

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 Rb and Rc from standard model predictions. If the scalars involved in the breaking of the SU(2) × U(1) symmetry are sufficiently light, X will sometimes decay into a charged (or neutral) scalar along...

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 n...

I would like to begin by thanking Nino Zichichi, Harvey Newman, Tom Ypsilantis, and all the staff for the opportunity to be in this beautiful place and to reminisce about a fun decade of physics. Because time is so short, I am going to focus very narrowly on the decade of the 70′s, and to concentrate particularly on a 24 hour period which, for me,...

We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension.

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 quark is composite. A considerable enha...

Theoretical discussions of hadrons remind me of the parable of the blind men and the elephant. You may remember that the blind men give dramatically different descriptions of the elephant depending on what part of the elephant they are feeling, the trunk, the leg, the ear, the body, etc. The problem for hadrons is far worse.

We study hadronic two-body decays of the orbitally excited, SU(6) 70-plet baryons in order to test the hypothesis that the successes of the nonrelativistic quark model have a natural explanation in the large-Nc 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 d...

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 enhancemen...

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 larg...

We examine a paradox, suggested by Banks and Dabholkar, concerning nonperturbative effects in an effective field theory which is obtained by integrating out a generation of heavy fermions, where the heavy fermion masses arise from Yukawa couplings. They argue that light fermions in the effective theory appear to decay via instanton processes, where...

I describe a technicolor model (without walking) of all interactions up to energies of the order of 1000 TeV. The low-energy extended technicolor model has the CTSM form. But at intermediate energy scales, additional interactions are required to give the KM mixing. I discuss the characteristic flavor changing neutral current interactions arising fr...

We argue directly from Witten's analysis of large Nc baryons that the structure of the s-wave low-spin baryon states in QCD becomes spin-independent as Nc --> ∞. This property leads to an 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 sugg...

If the number of colors is large the ratio mη/mη′ is bounded from above. The bound is not satisfied by the observed η and η′ masses.

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 larg...

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 choic...

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 choic...

I give a simple qualitative derivation and interpretation of a generalization of so-called naive dimensional analysis, a rule for estimating the sizes of terms in an effective theory below the scale of chiral symmetry breaking induced by a strong gauge interaction. The generalization includes the well known Nc dependence of as a special case but I...

Electromagnetic interactions are incorporated into heavy hadron chiral perturbation theory. Short- and long-distance magnetic moment contributions to the chiral lagrangian are identified, and M1 radiative decays of heavy vector mesons and sextet baryons are studied. Using recent branching fraction ratio data, we fit the meson coupling to the axial...

I analyze mixing using the techniques of heavy quark effective theory. The analysis suggests that the there may be important cancellations among the dispersive effects of different kinds of final states, so that the total mixing may be considerably smaller than previous estimates.

I will begin by giving a formal description of the process of matching in effective field theories. I argue that the picture suggests that it should be possible to compute nonperturbative corrections to matching reliably. I then go on to speculate about a scheme for extending chiral fermions to extra dimensions.

We analyze hadronic D-decays involving two mesons in the final states based on vector symmetry. We perform multiparameter chi2-fits to the data and find that while vector symmetry breaking is not overwhelming for the best fit, higher-order corrections are required to reproduce data.

We investigate the renormalization of ``nonlocal'' interactions in an effective field theory using dimensional regularization with minimal subtraction. In a scalar field theory, we write an integro-differential renormalization group equation for every possible class of graph at one loop order.

We discuss the chiral lagrangian for octet and decuplet baryons in the language of the heavy particle effective theory. We show that the effective theory qualitatively reproduces the Pauli amplitudes for the nonleptonic hyperon decays, calculated recently by Trofimenkoff. We discuss the relation of our results to nonrelativistic SU(6). We argue tha...

I discuss the S- and T-parameters introduced by Peskin and Takeuchi to characterize the “oblique” radiative corrections to the electroweak interactions. Following Golden and Randall, and Holdom and Terning, I re-interpret these parameters in an effective field theory language. I hope to draw attention to the fact that the effective field theory fra...

I show how to organize the coefficients in an effective field theory so that the accuracy of the effective field theory calculation is less seriously degraded when there are ratios of mass scales in the problem that are not large. I show how this new effective field theory can be obtained automatically, by doing the matching calculation on the pert...

I write in a compact form the results of Isgur and Wise on heavy baryon form factors.

The six form factors which characterize the matrix elements of the axial vector and vector currents that occur in semileptonic decay are expressible, to leading order, in terms of a single function of v′v, normalized at zero recoil. We show that including terms proportional to , the form factors are still expressible in terms of a single function (...

We identify and exemplify a new mechanism which leads to a nonzero magnetic moment for a neutrino, while suppressing the neutrino's mass. The mechanism requires that the contribution to the neutrino mass of the new particles that are responsible for its magnetic moment is approximately canceled by a contribution from neutral particles, related by a...

We calculate the leading QCD radiative corrections to the relations which follow from the decoupling of the heavy quark spin as the quark mass goes to infinity and from the symmetry between systems with different heavy quarks. One of the effects we calculate gives the leading q2-dependence of the form factor of a heavey quark, which in turn dominat...

We use the techniques of an effective field theory for heavy quark systems to calculate inclusive lepton energy distributions in heavy meson decays. Our approach is patterned after the operator product expansion analysis of R in e+ −e− annihilation and deep inelastic electroproduction. We extend the idea of an operator product expansion to a situat...

We discuss the effects of the breaking of vector symmetry for the two-body hadronic decays of charmed mesons, D+ and D0. Supported in part by the Mary Ingraham Bunting Institute of Radcliffe College.

We discuss a variant of the Voloshin mechanism in which the transition magnetic moment neutrino, Omegaetau, is nonzero in one loop, while the neutrino mass is a three loop effect. For a neutrino mass of less than 1 eV, the transition moment can easily be as large as ~ 10-11 Bohr magnetons. Research supported in part by the Director, Office of Energ...

We extend the heavy quark spin and flavor symmetry discussed by Voloshin and Shifman and by Isgur and Wise to systems in which the heavy colored particles have different spins. We discuss in detail the superflavor symmetry between a heavy quark and a heavy color triplet scalar.

I construct a Lorentz invariant effective field theory description of QCD in the presence of heavy quarks at energies large compared to the QCD scale and small compared to the heavy quark mass, formalizing the ideas of Isgur and Wise and of Eichten and Hill. The theory is built by “integrating in” degrees of freedom to implement a superselection ru...

We discuss the consequences of the vector symmetry recently suggested by one of us for the decays of heavy quarks, b and c.