Present State of Rigorous Analytic Properties of Scattering Amplitudes

Sommer, Gerald

doi:10.1002/prop.19700181102

Cited by 60 publications

(68 citation statements)

References 48 publications

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“…As the unitarity bounds of [39] are not sufficiently strong to enable us to discuss the subtractions occurring in the dispersion relations for the isospin-odd amplitudes, we invoke Regge-pole analysis, which yields more specific information about the asymptotic behaviour.…”

Section: Subtraction Constants and Saturationmentioning

confidence: 99%

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Baryon chiral perturbation theory in manifestly Lorentz invariant form

1999

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We show that in the presence of massive particles, such as nucleons, the standard low-energy expansion, in powers of meson momenta and light-quark masses, in general converges in only part of the low-energy region. The expansion of the scalar form factor σ(t), for instance, breaks down in the vicinity of t = 4M 2 π . In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region results only if the multiple internal-line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low-energy region, while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order p 4 .

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Section: Subtraction Constants and Saturationmentioning

confidence: 99%

“…To read off the contributions of the ∆ to the effective coupling constants of L (2) N , we expand the above expressions in powers of M and insert the result into (39). This leads to 14 :…”

Section: B Infrared Parts Of Some Loop Integralsmentioning

confidence: 99%

Baryon chiral perturbation theory in manifestly Lorentz invariant form

1999

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“…As the unitarity bounds of ref. [39] are too weak to discuss the subtractions occurring in the dispersion relations for the isospin odd amplitudes, we invoke Regge pole analysis, which yields more specific information about the asymptotic behaviour.…”

Section: Subtraction Constants and Saturationmentioning

confidence: 99%

Baryon chiral perturbation theory in manifestly Lorentz invariant form

1999

View full text Add to dashboard Cite

We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor σ(t), for instance, breaks down in the vicinity of t = 4M 2 π . In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order p 4 .

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“…The O p 2 amplitudes could be constructed as the most general invariant amplitudes satisfying the crossing, Bose and isospin symmetries and using the fact that they should be polynomials of the first order in the Mandelstam variables obeying (5) 17 . This form is independent of the power counting used:…”

Section: Kk → Kkmentioning

confidence: 99%

Dispersive approach to chiral perturbation theory

Zdrahal

Novotný

2008

Phys. Rev. D

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We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 → 2) scattering of all the pseudoscalar octet mesons (π, K, η). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented. * zdrahal@ipnp.troja.mff.cuni.cz † novotny@ipnp.troja.mff.cuni.cz 1 The standard power counting is based on the presumption that the value of B 0 is of order Λ. So there also appeared approaches extending the χPT to the case including the possibility of small B 0 too, which have a lesser predictive power connected with larger number of LEC -namely the generalised χPT [5]. 2 The only direct answer given by experiment is still the confirmation of the standard power counting in the 2 flavour case by the K l4 measurement at BNL [6].

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Present State of Rigorous Analytic Properties of Scattering Amplitudes

Abstract: The main (old and new) results about analyticity properties of two‐body transition amplitudes deducible from general local field theory are reviewed. Most of the proofs are included as well as a short chapter on applications.

Cited by 60 publications

References 48 publications

Baryon chiral perturbation theory in manifestly Lorentz invariant form

Baryon chiral perturbation theory in manifestly Lorentz invariant form

Baryon chiral perturbation theory in manifestly Lorentz invariant form

Dispersive approach to chiral perturbation theory

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