Paul M. Fishbane

Expansion formulas and addition theorems for Gegenbauer functions

We give a systematic summary of the properties of the Gegenbauer functions Cαλ(x) and Dαλ(x) for general complex degree and order, with emphasis on the functions of the second kind, Dαλ(x), and on results useful in scattering theory. The results presented include Sommerfeld–Watson type expansion formulas and two reciprocal addition formulas for the functions of the second kind.

Anomalous phi production in N-barN annihilation: Four-quark exotics or ss-bar components in the nucleon?

We argue that four-quark (/ital Q//sup 2//bar Q//sup 2/) intermediate-stateresonances containing a sizable /ital ss/bar // admixture produce selectiveenhancements in particular /ital NN/bar // annihilation channels with /phi/mesons. The pattern of enhanced /phi/ production induced by /ital NN/bar //coupling to /ital Q//sup 2//bar Q//sup 2/ resonances is compared to that due to/ital ss/bar // admixtures in the /ital N/ and /ital N/bar //.

Nucleon-antinucleon annihilation into two pseudoscalar mesons: quark rearrangement versus quark annihilation

Abstract We investigate the interference between planar and rearrangement mechanisms in the quark model for two pseudoscalar annihilation modes of the N N system. Both mechanisms seem to be necessary even to partially understand the data.

Glueballs: Their Spectra, Production and Decay

What is a glueball? It is a colorless and flavorless composite of two or more gluons whose existence is implied in quantum chromodynamics (QCD) [1–3]. That we are even considering such an object today is a true tribute to serendipity. Let us see why I say that.

Two-phase model of hadronic matter and high energy nuclear production

Abstract We present a simple descriptive model of the dynamics of hadronic processes which fits experimental data on nuclear multiparticle production.

Glueballs: Their experimental signature

Abstract We study hadrons with a 2-gluon valence component, emphasizing states not found in the quark model. We predict that 0 ++ , 0 −+ , 1 ++ , and the particularly interesting 1 −+ glueballs will be narrow, with widths ranging from a few MeV to less than one MeV, and that spin 0 glueballs will mimic ss quarkonium states in their decay. We also comment on photonic couplings.

E (1440): GLUEBALL OR QUARKONIUM?

Abstract The most likely assignment of the E(1440) is that of an ordinary ss, L = 1, J PC = 1 ++ meson, rather than a flavor singlet meson or a J PC = 0 −+ or 1 ++ glueball.

Standard model constraints on fermions

We present a catalog of fermions allowed by the standard model. These new fermious are restricted to sets which are anomaly free, vector-like with respect to electric charge and color, and have either ΔIW = 0 (totally vector-like) or ΔIW = 12 (chiral) (masses). We list some simple examples where the anomaliesof the leptons (quarks) cancel among themselves as well as against each other.

ON NEUTRINO MASSES AND LEPTONIC MIXING

Using recent data on neutrino oscillations, we argue that a hierarchical solution for neutrino masses in a three-family context is possible, and that the masses of the and ? neutrinos are very nearly determined within that possibility. We also examine the predictions of a model that determines neutrino and charged lepton mass matrices as well as its consistency with data.

Neutrino propagation in matter and a CP-violating phase

Abstract We point out that the dependence on the order of the matter through which neutrinos pass can provide a window into the presence of a CP-violating phase in the mixing matrix of the neutrino sector. This allows for study of CP in the neutrino sector without the necessity of making a comparison between the behavior of neutrinos and that of antineutrinos.