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Howard Georgi

Publications and source records attributed to Howard Georgi.

At least 19 recordsLinked to original sources
arXiv2024

Tuning to the Edge of the Abyss in SU(5)

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.

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arXiv2023

Gauge Boson Mass Dependence and Chiral Anomalies in Generalized Massless Schwinger models

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 $n_A<n_F$, there are fermion bilinears with nontrivial anomalous dimensions and there are unbroken chiral symmetries so some correlators vanish while others are non-zero due to chiral anomlies. Taking careful account of the dependence on the masses, I show how the $n_A<n_F$ models emerge from $n_A=n_F$ as gauge couplings (and thus gauge boson masses) go to zero. When this is done properly, the limit of zero gauge coupling is smooth. Our consistent treatment of gauge boson masses guarantees that anomalous symmetries are broken while unbroken chiral symmetries are preserved because correlators that break the non-anomalous symmetries go to zero in the limit of zero gauge coupling.

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arXiv2022

Mass Perturbation Theory in the 2-Flavor Schwinger Model with Opposite Masses

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.

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arXiv2020

Automatic Fine-Tuning in the 2-Flavor Schwinger Model

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.

hep-th↗
arXiv2019

Non-perturbative Effects and Unparticle Physics in Generalized Schwinger Models

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.

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arXiv2019

Generalizations of the Sommerfield and Schwinger models

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.

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arXiv2019

The Schwinger Point

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.'

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arXiv2017

Complementarity and Stability Conditions

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.

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arXiv2016

Diboson Excess from a New Strong Force

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.

hep-ph↗
arXiv2016

Sidney Coleman's Harvard

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.

physics.hist-ph↗
arXiv2016

Physics Fun with Discrete Scale Invariance

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.

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arXiv2016

Towards an Effective Field Theory on the Light-Shell

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.

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arXiv2015

Color Fields on the Light-Shell

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 $σ$-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.

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arXiv2014

A Simple Alternative to Jet-Clustering Algorithms

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.

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arXiv2010

Unparticle self-interactions

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.

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arXiv2008

An Unparticle Example in 2D

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.

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