Chapter 4. Dispersion Theoretic Approach

Furuichi, Susumu

doi:10.1143/ptps.39.190

Cited by 13 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The projection formulae and the remaining spin algebra for the construction of the phase parameters can be found, for example, in Furuichi (1967). This then is the way by which the low-mass ( < 1 GeV) particle exchange contribution to the NN scattering amplitude has been calculated.…”

Section: Consider Then the Meson-nucleon Couplingmentioning

confidence: 99%

Mesons and two-nucleon potential

Cottingham

1978

Rep. Prog. Phys.

View full text Add to dashboard Cite

This article reviews the status of our knowledge of the low-energy nucleonnucleon interaction. I n particular we review the advances that have been made over the last 15 years in understanding the nuclear force. The theory is not fundamental but semi-phenomenological in that it correlates the force with the observed physics of mesons, their interactions with nucleons and with each other. However, it is successful in constructing the form of the nucleon-nucleon interaction outside the core region.

show abstract

Section: Consider Then the Meson-nucleon Couplingmentioning

confidence: 99%

Mesons and two-nucleon potential

Cottingham

1978

Rep. Prog. Phys.

View full text Add to dashboard Cite

show abstract

“…If this is the case, the contribution from higher resonances can be inferred as small and negative. 9 ) …”

Section: Letters To the Editormentioning

confidence: 99%

Effect of Higher πNResonances to Subtraction Constant in the $\pi\pi \to N\bar{N}$ Dispersion Relation

Furuichi

Watanabe

1967

Prog. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

After Chew, Goldberger, Low and Nambu 1 l (referred to as CGLN) many investigations have been carried out for pionnucleon scattering and the related processes, by using the unsubtracted pion-nucleon dispersion relation.Usually the imaginary parts, IrnA <±J and ImB<±MJ have been approximated only by the contribution from 33-resonance. The pion-nucleon scattering amplitude in this approximation _gives too large a contribution to the S-wave helicity amplitude f~+l 0 (t) for the NN~2n process, as. shown, for example, by the analyses of nucleon-nucleon scattering. 2 J As a method of suppressing such a large contribution, a kind of renormalization of f$+l 0 (0) =Co is attempted as a result of either the Cini-Fubini approximation to the Mandelstam representational or subtraction at t = 0 to the dispersion relation of f++Jo(t)Y By this procedure Co is reduced from 42 for the CGLN with 33-approximation to "-'0.tJ On leave of absence from Department of Physics, Nagoya University, Nagoya.*J The notation is the same as that in reference 1).On the other hand, Co is closely related with the subtraction constant of the pionnucleon dispersion relation in the forward direction. Menotti 5 J estimated Co from a subtraction constant of the pion-nucleon dispersion relation and obtained -1.9 ±3, which is consistent with the result of nucleon-nucleon scattering.In any case, such a small value for Co means that a new large constant contribution is introduced for the CGLN with 33approximation by adjustment of subtraction constants. In this note, we reexamine a similar problem by taking into account the contribution from higher pion-nucleon resonances, since the experimental results have rapidly increased very recently.As a first step, we estimate Co phenomenologically taking into account the experimental pion-nucleon scattering data. By extracting the S-wave amplitude with respect to the crossed t channel from the CGLN equation and taking the limit t_,.O, we obtain the formula = +l_ \ ds' P'W' 2 Q (s'-m 2 -1) n J s 1 -m 2 -1 m 1 2m (m+1) 2 Xa\;;;J (s')/4n+A<+l(m 2 +1, 0)/4n J, (1) where we use the neutral pion mass as the unit of masses and a~;J;l denotes the total nN cross section. The right-hand side of Eq. (1) can be estimated experimentally except for the last term A<+l(m 2 +1, 0) which is written as = =~ \ ds' IrnA<+l(s1 0). n J s 1 -m 2 -1 ' (2) <•+1)2 at

show abstract

“…2 ) In the analyses by the OBE model several methods have been used to calculate the scattering amplitudes which satisfy the unitarity conditions such as the K-matrix method, non-relativistic Schrodinger equation and dispersion relation. The K-matrix method has its characteristic in its simplicity, while the Schrodinger equation and dispersion relation involves the rescattering effects through virtual states which is usually ignored in the K-matrix approach.…”

Section: ~ I Introductionmentioning

confidence: 99%

Experimental Estimate for the Left-Hand-Cut Contributions in Nucleon-Nucleon Scattering

Furuich

Suemitsu²,

Watari

et al. 1968

Prog. Theor. Phys.

View full text Add to dashboard Cite

523In order to obtain the experimental values of the left-hand-cut contributions in the partial wave dispersion relation for nucleon-nucleon scattering, we calculated the right-hand-cut contributions ,from the experimental data following Kantor's procedure using the results of phase shift' analyses of nucleon-nucleon scattering in both elastic and inelastic regions. ~ I. IntroductionIt is well known that essential features of the nucleon-nucleon interaction below 310 Me V is well reproduced by the one-boson-exchange model (hereafter OBE model).1) On the other hand, the analyses of nucleon-nucleon interaction by the more orthodox field theoretic approach taking one-, two-, ... pion exchanges have been extensively made and the correlation between these two approaches has gradually been clarified. 2 ) In the analyses by the OBE model several methods have been used to calculate the scattering amplitudes which satisfy the unitarity conditions such as the K-matrix method, non-relativistic Schrodinger equation and dispersion relation. The K-matrix method has its characteristic in its simplicity, while the Schrodinger equation and dispersion relation involves the rescattering effects through virtual states which is usually ignored in the K-matrix approach. Each of these methods has its own merit and demerit. Among them, however, the dispersion t'heoretical approach seems to become most important and appropriate as the energy goes higher.The failure of the simple K-matrix model and the necessity of the physical effect corresponding to the right-hand-cut contributions in tpe OBE model are suggested from the analysis of the S waves.In a typical analysis of nucleon-nucleon scattering in terms of dispersion relation, some appro2timation is usually made for the left-hand-cut contributions

show abstract

Chapter 4. Dispersion Theoretic Approach

Cited by 13 publications

References 34 publications

Mesons and two-nucleon potential

Mesons and two-nucleon potential

Effect of Higher πNResonances to Subtraction Constant in the $\pi\pi \to N\bar{N}$ Dispersion Relation

Experimental Estimate for the Left-Hand-Cut Contributions in Nucleon-Nucleon Scattering

Contact Info

Product

Resources

About