61725309
The three-body problem: third generation and beyond?
121703466
THREE-BODY MODEL FOR STRIPPING AND THE VALIDITY OF THE DISTORTED-WAVE BORN APPROXIMATION
A model is proposed, according to which a "deuteron," consisting of two identical particles, interacts with a "core nucleus," taken as an infinitely massive point particle which can form a bound state with either of the two particles. Assuming factorable interactions between the particles of all the three pairs, exact expressions for the scattering and stripping amplitudes are obtained. A comparison with the corresponding distorted-wave Born approximation (DWBA) amplitudes, which can also be obtained in the model, shows that DWBA is valid within the model. The model also predicts that the partial-wave scattering amplitudes ${a}_{l}$ are small compared with the corresponding stripping amplitudes ${b}_{l}$. An (indirect) experimental test of this result is suggested on the basis of large angular momenta, which are needed to overcome the difficulties of finite nuclear size in actual situations.
123261827
RELATIVISTIC CORRECTIONS TO THE THREE-BODY PROBLEM.
14276078
Three-Quark Bethe-Salpeter vertex function under pairwise gluon-exchange-like interaction: application to n-p mass difference
A qqq BSE formalism based on an input 4-fermion Lagrangian of 'current' u, d quarks interacting pairwise via a gluon-exchange-like propagator in its nonperturbative regime, is employed for the construction of a relativistic qqq-wave function under the Covariant Instantaneity Ansatz (CIA). The chiral invariance of the input Lagrangian is automatically ensured by the vector character of the gluonic propagator, while the 'constituent' masses are the low momentum limits of the dynamical mass function m(p) generated by the standard mechanism of DB χ S in the solution of the Schwinger Dyson Equation (SDE). The CIA gives an exact reduction of the BSE to a 3D form which is appropriate for baryon spectroscopy, while the reconstructed 4D form identifies the hadron quark vertex function as the key ingredient for evaluating transition amplitudes via quark-loop integrals. In this paper the second stage of this 'two-tier' BSE formalism is extended from the 4D qq-meson to the 4D qqq-baryon vertex reconstruction through a reversal of steps offered by the CIA structure. As a first application of this 4D qqq wave function, we evaluate the quark loop integrals for the neutron (n) - proton (p) mass difference which receives contributions from two sources : i) the strong SU(2) effect arising from the u-d mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference works out at 1.28 MeV (vs. 1.29 expt), with two free parameters C 0 , ω 0 characterizing the infrared structure of the gluonic, which have been precalibrated from a common fit to qq and qqq spectra as well as several other observable quark loop integrals. A formal derivation, based on Green's function techniques for 3 spinless quarks, of the CIA structure of the 4D qqq-baryon vertex function as employed in the text, is given for completeness in Appendix B.
120123625
n-p mass difference in a model of higher baryon couplings
Abstract A unified model of PBB L and VBB L couplings recently proposed by one of us (ANM) is augmented by VDM to calculate the n-p mass difference. The J = L − 1 2 states of (56, 2 + ) are found crucial for bringing about the correct sign and magnitude.
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.
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.