122765932
Total widths of resonances: A criterion for the formulation of hadronic interactions
SummaryThe structure of relativistic hadron couplings in the harmonic-oscillator model is studied in terms of a criterion which demands aless-than-exponential increase of total widths of resonances with theirexcitation quantum numbers. The implementation of this program in turn requires a model for the evaluation of total widths which is formulated within the framework of the harmonic-oscillator model with the help of a physically plausible inclusiveness ansatz. For the coupling structures, two available alternatives are examined:A) the unsymmetrical radiation quantum (RQ) hypothesis for one of the mesons andB) the more symmetrical quark pair creation (QPC) hypothesis consistent with duality diagrams. For their relativistic formulations, a comparison is made betweena) the 4-dimensional covariant theory of the Lipes-Kim-Noz type andb) a 3-dimensional noncovariant approach due to Licht and Pagnamenta. Model calculations are performed mostly for M→MM transitions, by involving radial and orbital excitations, but by ignoring the spin andSU3 degrees of freedom. It is found that the 4-dimensional covariant formulation, with either of the RQ and QPC hypotheses, gives rise toexponentially increasing total widths, and hence is incompatible with the stated criterion. The noncovariant relativistic version, on the other hand, satisfies the criterion only under QPC, but not under RQ. It is therefore concluded that, of the four alternatives studied, only one, the 3-dimensional relativistic formulation with the QPC hypothesis, is favoured by the chosen criterion which is defended on other grounds as well.RiassuntoSi studia la struttura dell’accoppiamento adronico relativistico nel modello dell’oscillatore armonico sulla base di un criterio che richiede un incrementomeno che esponenziale delle ampiezze totali delle risonanze con i loronumeri quantici di eccitazione. Per contro, la formulazione di questo programma richiede un modello per la valutazione delle ampiezze totali che è formulato all’interno del sistema del modello dell’oscillatore armonico con l’aiuto di un ansatz di inclusività fisicamente plausibile. Si esaminano due alternative disponibili per le strutture di accoppiamento:A) l’ipotesi del quanto di radiazione non simmetrico (RQ) per uno dei mesoni eB) l’ipotesi della creazione di una coppia di quark più simmetrica (QPC) consistente con i diagrammi di dualità. Per le loro formulazioni relativistiche, si fa un confronto traa) la teoria covariante a 4 dimensioni del tipo di Lipes-Kim-Noz eb) l’approccio non covariante a 3 dimensioni dovuto a Licht e Pagnamenta. Si effettuano calcoli di modello soprattutto per le transizioni M→MM comprendendo le eccitazioni radiali e orbitali, ma senza considerare i gradi di libertà di spin e diSU3. Si è trovato che la formulazione covariante a 4 dimensioni con entrambe le ipotesi RQ e QPC dà luogo a ampiezze totaliche aumentano esponenzialmente e quindi è incompatibile con il criterio stabilito. La versione relativistica non covariante, d’altra parte, soddisfa il criterio solo nell’ipotesi QPC ma non in quella RQ. Si conclude perciò che, delle quattro alternative studiate, solo una, la formulazione relativistica a 3 dimensioni con l’ipotesi QPC, è favorita dal criterio scelto che è sostenuto anche da altri argomenti.РеэюмеИсследуется структура релятивистских адронных свяэей в модели гармонического осциллятора на основе критерия, который требует, чтобы полные щирины реэонансов воэрастали медленнее, чем зкспоненциально в эависимости от квантовых чисел воэбуждения. Реалиэация зтой программы приводит к модели для зволюции полных щирин, которая формулируется в рамках модели гармо-нического осциллятора с помошью фиэически правдоподобного приближения инклюэивности. Для структур свяэи исследуются две имеюшиеся альтернативы: Л) гипотеэа несимметричного иэлучения кванта для одного иэ меэонов и В) гипо-теэа рождения пары кварков, согласуюшаяся с диаграммами дуальности. Обе релятивистские формулировки сравниваются с о) четырехмерной ковариантной теорией и 6) трехмерным нековариантным подходом. Проводятся модельные вычисления главным обраэом для переходов М ММ, включая радиальные и орбитальные воэбуждения, но игнорируя спиновыми -SU3 степенями свободы. Получается, что четырехмерная ковариантная формулировка с любой иэ выщеука-эанных гипотеэ приводит к зкспоненциально воэрастаюшим полным щиринам, и, следовательно, несовместима с формулированным критерием. С другой сто-роны, нековариантный релятивистский вариант удовлетворяет критерию только в рамках гипотеэы рождения пары кварков, а не гипотеэы иэлучения кванта. Утверждается, что иэ четырех исследованных альтернатив только одна - трех-мерная релятивистская формулировка с гипотеэой рождения пары кварков -удовлетворяет выбранному критерию, который подтверждается также другими данными.
30997914
Null-plane Bethe-Salpeter dynamics: Mass spectra, decay constants of pseudoscalar mesons, and the pion form factor.
A new relativistic definition of the reduced mass ({mu}{sub 12}) of a {ital q{bar q}} pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta {ital q}{sub {mu}}, is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of {mu}{sub 12} (involving the hadron mass {ital M}) is found to produce a natural Regge asymptotic behavior ({ital M}{sup 2}{approximately}{ital N}) in the hadron mass spectra, while retaining the property of an asymptotically linear ({approximately}{ital r}) confinement in the three-dimensional structure of the BS kernel. The relativistic structure of {mu}{sub 12} is responsible for a significant improvement in the fits to the ground-state masses of {ital q{bar q}} and {ital Q{bar q}} mesons as compared to its nonrelativistic definition {ital m}{sub 1}{ital m}{sub 2}/({ital m}{sub 1}+{ital m}{sub 2}). The leptonic decay constants {ital f}{sub {ital p}} and the charge radii thus calculated are also in excellent agreement with data ({pi},{ital k}) where available, while {ital f}{sub {ital p}} predictions for {ital Q{bar q}} mesons have good overlap with recent lattice predictions. Further, the scaling property ({approximately}{ital k}{sub {mu}}{sup {minus}2}) of the hadron's electromagnetic form factor at largemore » {ital k}{sup 2} is a consequence of the on-shell'' form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis.« less
15889809
On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer-Duffin β-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard “trace” techniques. The results are compared with a recent derivation due to Bosanac.
125652054
THE PROCESS pi- p ---> eta n WITH QPC MODEL FOR A2 EXCHANGE
117884842
THREE-BODY VERTICES WITH TWO-BODY TECHNIQUES,
Publisher Summary This chapter discusses three-body vertices with two-body techniques. It has long been recognized that vertex functions for few particle systems provide a convenient medium for the analysis of reactions in the language of Feynman diagrams, analogously to elementary particle processes. The development of three-particle theory has provided considerably more impetus for the use of the language of three-body vertex functions through the possibility of their exact evaluation with only two-body input. While three-body vertices are probably superfluous for the description of only three-body processes, their practical usefulness often extends to reactions involving more than three-particle systems, as long as such systems can be meaningfully described in terms of not more than three particles playing the active role. This chapter reviews a simplified construction of three-body vertices. For a four system, the problem of normalization of the corresponding wave functions is so much more involved that at the present state of computer technology, there appears little chance of the exact evaluation of αdd and αtN vertex functions in terms of overlap integrals if wave functions calculated entirely in terms of N-N input potentials are to be used.
123745795
*recoil effects* in a model of higher baryon couplings. i. photoproduction
A recently proposed model (MM) of higher baryon couplings for P and V mesons is reformulated by reviewing the fuller possibilities of the "recoil term" in the primitive quark-meson interaction. While this introduces no basic change in the P-meson coupling structures, it yields an entirely new (L-1)-wave coupling of V mesons to J = L+12 baryons, which is capable of generating helicity-flip amplitudes. The advantage of this new coupling structure over the earlier one is demonstrated through the excellent reproduction of (i) the E1 angular distribution in Y * →Λγ decay and (ii) the appreciable magnitudes as well as energy variations of the asymmetry parameter ∑(θ) in pion photoproduction. In addition to a comparison of the two coupling structures (old and new), the present paper is also designed to study the role of still another parametric structure for the form factor - one which exhibits better convergence properties at higher energies than those discussed in MM. The additional processes studied in this connection are (i) η and X 0 photoproduction at intermediate energies (> 2 GeV), (ii) polarization of the recoil proton in η and π photoproduction, and (iii) π 0 photoproduction at high energies (∼ 6 GeV), in accordance with our earlier scheme of s-channel resonances. In connection with η photoproduction the roles of some pertinent I =12 resonances such as S 11 , P 11 , and G 17 are discussed, especially in relation to supermultiplet assignments.
119114701
Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
Newtonian gravity was formulated as a geometrodynamic theory as far back in 1930s by Elie Cartan in what is named aptly as Newton Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localisation of the Galilean Symmetry of nonrelativistic matter field theories.