Order Feynman Research Articles

The mesonic fluctuations and corrections in the chiral symmetry breaking vacuum

The mesonic quantum fluctuations and their corrections on the chiral condensate and pion polarization function are investigated in the self-consistent scheme of SU(2) Nambu-Jona-Lasinio model by exactly calculating the next-to-leading order (NLO) Feynman diagrams in $1/N_c$ expansion. While the fluctuations and corrections depend strongly on the meson's three-momentum cut-off $\Lambda_M$, no chiral symmetry restoration is found since the cancellation between the NLO and the one-quark-loop diagram with quark mass deviated from the mean-field value.

Exact evaluation of triplet photoproduction

The differential cross section of the triplet photoproduction (TPP), i.e., the pair production on an electron, has been evaluated by using the computer code HELAS in which all the eight lowest order Feynman graphs can be numerically treated without any approximation. It has been shown that the calculation with only two diagrams, called Borsellino diagrams, agrees very well with the full calculation in a wide kinematical region for photon energies between 50 and 550 MeV. For a possible application of TPP to the polarimetry of high energy linearly polarized photons, we show that the analyzing power can be enhanced by restricting the opening angle of the forward going e +e − pair.

Total and visible cross sections for multilepton events in e +e − collisions

We calculate cross section for e +e − scattering into four-lepton final states such as e +e −e +e −, e +e − μ + μ −, μ + μ − μ + μ −, μ + μ − τ + τ −. We also give exclusive cross sectionsfor all cases where one or more lepton tracks are at large angles to the beams. The calculations are performed using a Monte Carlo event generator which takes into account the complete set of relevant lowest order Feynman diagrams.

Asymptotic estimates of Feynman diagrams

We derive asymptotic estimates for the most likely value of generical very high order Feynman diagram.

Dual Amplitude and Quark Dynamics

We regard the usual quark diagram as the lowest order Feynman diagram describing hadron dynamics. In the lowest order amplitude a factor V is introduced to obtain a dual one. Then the quark mass and the upper bound of the meson trajectory intercept can be predicted. Further the physical meaning of V is studied. Firstly, the role of V in the amplitude is analytically investigated. Secondly, we seek a possibility that V may effectively represent an interacting between quarks. Assuming some Feynman diagrams which may represent a part of the role of V, a Regge trajectory is derived by the perturbative calculation. The trajectory is expanded about t=0 and it is compared with the trajectory of our dual amplitude. Then the intercept of the leading ordinary-trajectory satisfies α(0)=1/2.

Field Theoretic Description of (π+,p) and (p, π+) Reactions in Nuclei

A relativistic description of ( pi /sup +/,p) and (p, pi /sup +/) reactions using perturbative field theory is presented and an amplitude corresponding to the lowest order Feynman graphs is obtained. Form factors for the scattering processes enter naturally through nucleon wave functions or they can be left arbitrary in the absence of concrete knowledge. The method is applied to ( pi /sup +/,p) and (p, pi /sup +/) reacti ons in /sup 12/C, and predictions are compared with experiment. Treatment of initial- and final-state interactions is also indicated for the model. (auth)

The meson exchange current effect in radiative np capture

The pion exchange current contribution to the thermal neutron proton radiative capture cross section is calculated on the basis of potential theory by extracting a local “absorptive exchange potential” from the corresponding fourth order Feynman diagram with the deuteron nucleon vertex on the mass shell. Taking into account that the repulsive core of nucleon interaction leads to modifications not only of the wave functions (which include off-mass shell properties of the deuteron nucleon vertex) but also of this absorptive OPE potential a result is obtained which explains the main part (⋍ 2 3 ) of the well-known 10%-discrepancy between experiment and impulse approximation.

A parton approach to dual models

The problem of correspondence of very high order unrenormalized Feynman diagrams to the dual model is discussed. The very high order Feynman diagrams are investigated using a statistical formalism recently developed.

Polarization of the Recoil Proton for Proton Compton Scattering Below the Pion Production Threshold

Abstract The polarization of the recoil proton for Compton scattering on protons below the pion production threshold, which arises from fourth order Feynman diagrams, is calculated by using the second order Compton amplitude in the unitarity condition. It is assumed that the second order amplitude can be approximated by the one proton intermediate state contribution. The polarization does not exceed 0.1% in the entire range of the scattering angle.

Dual Resonance Amplitude Corresponding to Globular Feynman Diagrams

Following the conjecture on the correspondence between the dual resonance amplitude and the very high order Feynman diagram, we calculate the dual resonance amplitude cor­ responding to the globular Feynman diagram. We find that it develops essential singularities in the Lorentz-invariant variables. It has been suggested by several authors 1 l' 2 l that amplitudes in the dual res­ onance model can be obtained by taking the continuum limit of the F eynman amplitudes corresponding to the very high order planar diagrams. It seems rather peculiar that only the planar Feynman diagram can lead to the dual reso­ nance amplitude. In general any Feynman diagram can be drawn in a three­ dimensional topological space. However, we need higher dimensional topolo­ gical spaces in order to discuss the continuum limits of the very high order Feynman diagrams. For example, the Klein-bottle-like Feynman diagram can be drawn in the three-dimensional space before taking the continuum limit. But, once we take the continuum limit, we need the four-dimensional space to draw

The process of Σ - Λ conversion following the nuclear absorption of [formula omitted] with the production of A π −

The second order process of the Σ-Λ conversion following the nuclear absorption of a kaon from a K meso-atomic orbit with the production of a negative pion is discussed, and calculated from a second order Feynman diagram. The momentum distributions of the recoiling nucleus and of the pion are computed for the K absorption in 4He and in deuterium. A semi-quantitative agreement with the data is obtained in all the cases. No attempt is made to calculate the absolute values of the reaction rates in question. The need of more and better data is stressed. The available data tend to favour the assumption of the 2P capture over that of the 1S capture in the case of 4He, but it is insufficient to rule out any one of the two cases.

Exchange current and deuteron photodisintegration at threshold

The contribution from the meson exchange current to the deuteron photodisintegration amplitude at threshold is calculated by taking into account the next nearby singularities beyond the nucleon exchange poles in the crossed channels. The procedure is based on potential theory. Starting with the corresponding fourth order Feynman amplitude with the deuteron-nucleon vertex on the mass shell a local “exchange potential” is derived. Its contribution to the amplitude is calculated by using the Hulthén function for the initial deuteron state (thus including the off-mass shell properties of the deuteron-nucleon vertex) and the effective range approximation for the final scattering state. The result is combined with the direct γ-nucleon contribution calculated by Austern and Rost 1) and agrees with experiment within the limits of error.

A Note on the Analytic Property of a Fifth Order Feynman Graph

A Note on the Analytic Property of a Fifth Order Feynman Graph

Two-Component First-Order Wave Equations

It is shown that a suitable definition of the dotted spinors in terms of the undotted spinors allows the linearization of the two-component second order Feynman Gell-Mann wave equations. The linearized two-component first-order wave equations are similar to the original Jehle wave equations. They are covariant with respect to the restricted Lorentz group and are transformed into their complex conjugate wave equations by a reflection. Then it is shown that the current vector derived from them is a world vector.

Theory of K +-nucleon scattering

Dispersion relations for the KN interactions show that the ‘Born’ term is dominant in K +p scattering. Therefore we calculate the cross section and angular distribution for K +p scattering by perturbation theory using the lowest order Feynman graphs and, given certain parities and coupling constants, this fits the experimental data. The theory does not give good results for K +n scattering.

A simple non-local quantum electrodynamics

The Dirac-Maxwell equations are modified, according to Wataghin, by displacing the fields at the point of their interaction by introducing displacement parameters. When these parameters, which are taken to be small, tend to zero the original Dirac-Maxwell equations are obtained. The original charge renormalization program, the theory of Feynman « cut-off » and Yukawa’s non-local theory of particles with internal structure and the consequent convergent quantum electrodynamics can be considered as special cases of these modified DiracMaxwell equations. By combining the methods of these processes a convergent quantum electrodynamics, in which the original Feynman graph integrals are modified by the multiplication of a simple modifying factor, is obtained. This is illustrated by the calculations of second order Feynman graphs. It is then suggested that these equations can be considered to be free from the need of charge renormalization and the actual charge renormalization is due to the use of the Born approximation.