Analytic Properties of Partial Amplitudes in Meson-Nucleon Scattering

MacDowell, S. W.

doi:10.1103/physrev.116.774

Cited by 267 publications

(60 citation statements)

References 6 publications

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“…(15) the symmetry proposed by MacDowell in Ref. [30] is manifest: if the s −1/2 factor in T +− changes its sign while other terms remain fixed, then the S-wave amplitudes are transformed into the corresponding P-wave ones. That property is automatically fulfilled in perturbation theory, hence also satisfied here since we use perturbative amplitudes to evaluate the left-hand cut integrals.…”

Section: Left-hand Cut Contributions Implied By Bchpt At Tree-levelmentioning

confidence: 99%

New insights on low energy $$\pi N$$ π N scattering amplitudes

2018

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The S-and P-wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of treelevel perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to O( p 2 ). It is found that in S 11 and P 11 channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.

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Section: Left-hand Cut Contributions Implied By Bchpt At Tree-levelmentioning

confidence: 99%

New insights on low energy $$\pi N$$ π N scattering amplitudes

2018

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“…Let us stress once more that the functions Φ ab ± (s) only possess right-hand cuts, with discontinuities specified in terms of those of the partial waves, whereas the partial-wave projections themselves in general have a more complicated analytical structure [50][51][52][53].…”

Section: Two-loop Representation Of K ℓ4 Form Factorsmentioning

confidence: 99%

“…The form factors are regular and real in the interval between s = 0 and the positive value of s corresponding to the lowest-lying intermediate state. This singularity structure is transmitted to the partial waves (along, possibly, with other singularities produced by the projection procedure itself [50][51][52][53]). In the following, we will only need to know the discontinuities of the lowest partial waves along the positive s-axis at low energies, which are fixed by unitarity.…”

Section: Analyticity and Unitarity Propertiesmentioning

confidence: 99%

Isospin breaking in the phases of the K e4 form factors

2013

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Isospin breaking in the K ℓ4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the K ± → π + π − e ± νe channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S-and P -wave ππ phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only ππ rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a 0 0 and a 2 0 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K ± → π + π − e ± νe form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a 0 0 and a 2 0 , as well as for low-energy constants and order parameters of two-flavour χPT.

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“…Again we choose a very simple prescription capable of satisfying these constraints, namely (10) (Similarly for s;_ with ~+ replaced by ( flf,_-(~-l)Ef_) t -1) a is taken as an independent parameter in the range …”

Section: The Constraint (3) Becomesmentioning

confidence: 99%

Electromagnetic form factors of N∗ resonances and their determination from pion electroproduction

Devenish

Lyth

1975

Nuclear Physics B

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We show how Nft electromag netic form factors can be parametrise d ~n a simple way to take account of their known behaviour at threshold. Using such form factors and Breit-Wign ers to represent the final state interaction we calculate the imaginary parts of the invariant amplitudes for ·the process eN--+ eNn, the real parts are calculated from fixed t dispersion relations. The complete amplitudes are then fit to the coincidence data in the resonance region ( O< I ~·1 < 1.0 ~ ~ ~ W < 2 Ge..;} in order to determine the form factor parameters . Results are presented for the A 1 dependence of the resonant multipoles and in particular we find stable results critical discussion is given of the effect of theoretica l uncertaint ies on the results. We use our results to calculate the helicity asymmetry A on the resonant peaks seen in eN scattering and find that on the 2nd and 3rd peaks A changes sign in the vicinity of Although there is a lot of data for the total inelasti c cross section in the resonanc e region 1 only the properti es of the 1st resonanc e, the P 33 CI232), are well understo od. In the absence of data from polarise d targets res·ananc e informat ion could be used to examineBloom-G ilman duality (I) more fully, for example. The behaviou r of " the nucleon and N form factors also provides a very searchin g test of constitu ent models (2) The exclusiv e process of single plan electrop roductio n eN_. eN" is one of the most fruitful sources of informat ion on resonanc e structur e. The properti es of the P 33 (1232) have been largely determin ed by studying coincide nce data on ep_. ep rr~. Some coincide nce data exist at higher energies and a number of explanat ory calculat ions have been made using fixed t dispersi on relation techniqu es ~;vith some success (3) notable being the extractio n of the pion form factor from data on ~ '(4,5)~p ~ $"' il just above the resonanc e regionRecently the situatio n has improved in two ways which will enable real progress to be made on extract:i ng the detailed behaviou r of the N ir resonanc e form factors. The first and obvious one 1.s that a lot more coincide nce data on both ep-~ epl'i 0 and ep · ;..e,"n+ is availabl e in the resonanc e region and rr.uch more can be expected in the next few years. The second is that we now have reliable multipol e analyses of In this paper we will describe the determination of N • resonance form factors from coincidence data on eN_, eNK . Section II is devoted to the choice of form factors. Section III describes the method based on the resonance saturation of fixed t dispersion relations, with special attention to the uncertainties present in such an approach. We give a brief description of the data in section IV. The results are given 1n section V (numerical details in appendix B) and we conclude with a discussion of the results in section VI. II. Form FactorsThe subject of the choice of electromagnetic transition form factors for particles with spin has a long history (?), We will be guided by two principles, convenience...

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Analytic Properties of Partial Amplitudes in Meson-Nucleon Scattering

Cited by 267 publications

References 6 publications

New insights on low energy $$\pi N$$ π N scattering amplitudes

New insights on low energy $$\pi N$$ π N scattering amplitudes

Isospin breaking in the phases of the K e4 form factors

Electromagnetic form factors of N∗ resonances and their determination from pion electroproduction

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