Steven C. Frautschi

Asymptotic Freedom and Color Superconductivity in Dense Quark Matter

In the present talk I shall deal with densities much higher than nuclear - densities which, as far as we know, were achieved only in the very early stages of the big bang. I shall review two issues: i) The current view that QCD predicts an approximately free quark-gluon gas phase at high densities and temperatures, which is incompatible with the kind of non-perturbative confinement effects that would be needed to yield a limiting Hagedorn temperature at high densities. ii) The recent suggestion of my student, Bertrand Barroisl1, that QCD leads to a different kind of non-perturbative phase, analogous to superconductivity, at high densities and low temperatures.

Lepton non-conservation and solar neutrinos

The consequences for experiments involving solar neutrinos of a small amount of lepton non-conservation are examined following the discussion of Gribov and Pontecorvo.

SU(5) Higgs problem with adjoint + vector representations☆

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with 5 and 24 higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.

Statistical Treatment of the Average Resonance Width

Abstract Saturation of hadron scattering amplitudes by direct channel resonances implies that the average level width Γ ( m ), level density ϱ ( m ), and number of open channels N ( m ) are related by Γ ( m ) ϱ ( m ) = N ( m )/2 π . From this relation and the dependence of N on ϱ there results, for any given ϱ ( m ), a definite Γ ( m ). We find that: 1. (i) A power law growth ϱ ( m ) ∼ m a results in an experimentally disfavored exponential growth of Γ ( m ). 2. (ii) The exponentially growing ϱ ( m ) of the statistical bootstrap model results in Γ ( m ) → constant. 3. (iii) The forms of ϱ ( m ) suggested by various versions of the dual resonance model result in Γ ( m ) → constant, or decreasing to zero, or at most a power law increase. Arguments are given why Γ ( m ) → constant is the most physically reasonable choice. Studies of Ericson fluctuations in reactions such as elastic πN scattering at a few GeV offer the best hope of experimentally determining the behavior of Γ ( m ).

Remarks concerning φ production in the thermodynamics picture

Abstract We examine the options that central production of φ(1.019) in hadron-hadron collisions is dominated (i) completely by Hagedorn-Frautschi thermodynamics and (ii) by thermodynamics modified by a mild form of Zweig suppression at sufficiently high energy. Predictions on σ( AB → φ + anything ), σ( AB → φ K + K − + anything ), ( φ π ), ( φ ϱ 0 ), ( φ ω 0 ) ratios at P ⊥ ≈ 1 GeV c , are made where A = π, p , p and B = p . These can be readily checked for E lab ≳ 300 GeV at Fermilab and ISR.

Statistical Studies of Hadrons

In recent years my activities have shifted towards interesting beginning students in physics, helping to produce a 26-hour video called “The Mechanical Universe” on freshman physics, and the like. I am not currently active in studies of Hot Hadronic Matter. Therefore, this talk will be historical and reminiscent in nature. In brief, I’ll describe how I started with few-body issues, how the physics then led me to many-body and statistical studies, and how finally I learned that it could all be viewed as a manifestation of string theory.

Zweig suppression and statistical factors in pison and φ production

Abstract Central production of J/ψ, ψ,′, … is suppresed by Zweigs rule. One can also argue that statistical factors suppress these reactions. We search for a prescription which incorporates both types of suppression, and is consistent with the data on psion production as well as the analogous data on φ production. A consistent prescription is possible only if we adopt the mild form of Zweig suppression implied by the Einhorn-Ellis proposal that psions and φs are produced by the gluon constituents of the incoming hadrons. The prescription leads to simple predictions for production of both Zweig-forbidden and Zweig-allowed combinations such as ψ, D D , ψ D D , … .

PHYSICS AT THE ORIGIN OF TIME

In the conventional big-bang model of cosmology,’ the energy density is so high during the period before t Nsecond that pairs of pions and other hadrons are copiously produced. To describe this “hadron era” in detail, a model of hadrons is needed. The traditional procedure has been to consider a small number of species of fundamental hadrons in thermal equilibrium. The temperature then goes as T N t l l 2 , and matter is dominated by ultrarelativistic particles during the hadron era. The subsequent periods then behave according to the description of Gamow and collaborators :2-4

Ericson Fluctuations and the New Argonne Data on πN Scattering

Most people nowadays think of hadrons as made of quark constituents trapped in a potential well. The well may or may not be infinitely high; it must rise at least above the present energy range to make free quarks so rare. As in any potential well, we expect to find excited states right up to the top of the well. We also expect the density of levels to rise rapidly with mass since there are so many ways to form a highly excited level: any one of the valence quarks can be raised to an excited level, or more than one can be raised at the same time, or quark pairs or gluons can be added.