C.S. Lam

Gauge invariant geometric variables for Yang-Mills theory☆

Abstract In a previous publication, local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero-modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.

A multiple commutator formula for the sum of Feynman diagrams

Abstract In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get canceled in the sum. This is known to happen in large-Nc QCD in the presence of a baryon, and also in the case of high-energy electron-electron as well as quark-quark scatterings. We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancelations. It is a non-abelian generalization of the eikonal formula, and will be applied in subsequent publications to study the consistency of large-Nc QCD involving baryons, as well as high-energy quark-quark scattering in ordinary QCD.

Photoproduction of charged pions in the veneziano model

SummaryPhotoproduction of charged pions on nucleons is studied in the framework of the Veneziano representation. General conditions for the elimination of parity doublets are derived. A model with a small number of beta-function terms provides a very satisfactory (and essentially parameter-free) description of differential cross-sections and asymmetry ratios of forward γp→π+n and γn→π−p in a wide energy range; it also correctly predicts a significant number of residues of higher baryon resonances. However, it leads to backward cross-sections for γp→π+n significantly larger than the data. Introduction of satellite terms provides a relatively simple parametrization which correctly accounts for all the differential backward cross-sections and for all the known baryon residues.RiassuntoSi studia, nel quadro della rappresentazione di Veneziano, la fotoproduzione di pioni carichi su nucleoni. Si deducono le condizioni generali per l’eliminazione dei doppietti di parità. Un modello con un piccolo numero di termini di funzioni beta fornisce una descrizione molto soddisfacente (ed essenzialmente libera da parametri) delle sezioni d’urto differenziali e dei rapporti di asimmetria delle reazioni in avanti γp → π+n e γn → π−p in un ampio intervallo di energie; esso anche predice correttamente un significativo numero di residui di risonanze barioniche superiori. Però esso porta a sezioni d’urto all’indietro per γp → π+n significativamente maggiori dei dati. L’introduzione dei termini satellite fornisce una parametrizzazione relativamente semplice che tiene conto correttamente di tutte le sezioni d’urto differenziali all’indietro e di tutti i residui barionici noti.РеэюмеВ рамках представления Венециано исследуется фоторождение эаряженных пионов на нуклонах. Выводятся обшие условия для исключения дублетов по четности. Модель с небольщим числом бета-функциональных членов обеспечивает очень удовлетворительное (и, по сушеству, свободное от параметров) описание дифференциальных поперечных сечений и асиммеричные отнощения рассеяния вперед γр → π+n и γn → π−р в щирокой области знергий. Эта модель также правильно предскаэывает эначительное число вычетов для более высоких барионных реэо-нансов. Однако, зто приводит к эначительно больщим поперечным сечениям рассеяния наэад для γр → π+n, чем зкспериментальные данные. Введение сопутствуюших членов обеспечивает относительно простую параметриэацию, которая правильно общясняет все дифференциальные поперечные сечения рассеяния наэад и все иэвестные барионные вычеты.

PERTURBATION THEORY OF HARD PROCESSES IN AN ASYMPTOTICALLY FREE FIELD THEORY

We study the interplay of lepton pair production and deep inelastic scattering in a version of six-dimensional φ3 with quarks and gluons. We carefully distinguish the various mass scales of the theory. Our purpose is to clarify the physical mechanisms involved. We establish the validity of the Drell-Yan relation as well as factorization and the Altarelli-Parisi differential equations.

Decay angular correlations for J/ϕ produced in hadronic collisions via intermediate χ states

Abstract The most general forms of the double and single angular distributions for the sequential production process of J/ ϕ , h 1 + h 2 → χ + X, χ → J/ ϕ + γ , J/ ϕ → μ + + μ − are given, as well as simplifications resulting from specific kinematical approximations and/or dynamical assumptions.

The dual-resonance model with unequal intercepts

SummaryThe dual-resonance operator formalism is extended to the case of unequal intercepts in all channels. By imposing factorization we get a parametrization of the Regge trajectories and are forced into a quark picture of the dual model. Whereas some of the operators of the theory remain unchanged in the unequal-intercept case, others such as the gauge operator are modified. These modifications have effects that reinforce our quark interpretation of the dual-resonance amplitude. Ghost compensation on the first daughter trajectory is still valid providing certain conditions on the quark « masses » are satisfied. Finally, anSU1,1 analysis of theN-point amplitude is displayed by couplingN «vertex fields», each with differentSU1,1 spin, to anSU1,1 scalar.RiassuntoSi estende il formalismo dell’operatore della risonanza duale al caso di intercette disuguali in tutti i canali. Imponendo la fattorizzazione si ottiene una parametrizzazione delle traiettorie di Regge e si è spinti verso una rappresentazione a quark del modello duale. Mentre alcuni degli operatori della teoria rimangono invariati nel caso delle intercette disuquali, altri, come l’operatore di gauge, si modificano. Queste modifiche producono effetti che rinforzano la nostra interpretazione a quark dell’ampiezza della risonanza duale. La compensazione dei fantasmi sulla prima traiettoria figlia è ancora valida purché siano soddisfatte alcune condizioni sulle « masse » dei quark. Infine si presenta un analisi inSU1,1 dell’ampiezza diN punti accoppiandoN « campi di vertice », ciascuno con differente spin diSU1,1, ad uno scalare diSU1,1.РеэюмеОператорный формалиэм дуальных реэонансов обобшается на случай неравных пересечений во всех каналах. Предполагая факториэацию, мы получаем параметриэацию траекторий Редже и кварковую картину для дуальной модели. Тогда как некоторые операторы теории остаются неиэменными в случае неравных пересечений, то другие, такие, как калибровочный оператор, видоиэменяются. Эти видоиэменения приводят к следствиям, которые укрепляют нащу кварковую интерпретацию амплитуды дуальных реэонансов. Компенсация духа на первой дочерней траектории является справедливой, предполагая, что выполняются некоторые условия на ?массы? кварков. В эаключение, проводится аналиэN-точечной амплитуды, посредством свяэиN « верщинных полей », каждого с раэличнымSU1,1 спином, сSU1,1 скаляром.

Veneziano models for ππ → η+ boson of any spin

Abstract The process ππ → η X, where X has any spin and parity is considered in the Veneziano representation. By means of simple, satellitefree models and the Adler condition a number of particle masses and trajectory intercepts are determined. The special case X = D o (1270), studied in more detail, leads to mass and width estimates of certain newly discovered bosons and to a calculation of the Dalitz plot for the decay D o → π + π − η in accord with the data.

Boundary conditions of Feynman path integrals

Abstract Feynman path integral expressions for transition matrix elements between bare vacua are derived for scalar and spinor fields. Proper boundary conditions are used to avoid the usual somewhat artificial iϵ prescriptions of previous authors.