A convergent set of integral equations for singlet proton-proton scattering

Ciulli, S.; Fischer, Ján

doi:10.1016/0029-5582(61)90413-8

Cited by 102 publications

(199 citation statements)

References 3 publications

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“…3), but fails to describe the experimental behavior of the Adler function in the low-energy domain Q 1 GeV, where the effects due to the pion mass become appreciable. Of course, in the framework of the massless APT, the infrared behavior of the Adler function can be greatly improved following the procedure introduced in [34]; this consists essentially in carrying out an appropriate resummation of threshold singularities, and introducing into (18) and (19) effects from nonperturbative light quark masses. The necessary nonperturbative information on the quark masses is furnished from the study of Schwinger-Dyson equations and quark condensates.…”

Section: Discussionmentioning

confidence: 99%

A novel integral representation for the Adler function

Нестеренко

Papavassiliou

2006

J. Phys. G: Nucl. Part. Phys.

137

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Abstract. New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result is found to be in reasonable agreement with the experimental prediction for the Adler function in the entire range of momenta 0 ≤ Q 2 < ∞.

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Section: Discussionmentioning

confidence: 99%

A novel integral representation for the Adler function

Нестеренко

Papavassiliou

2006

J. Phys. G: Nucl. Part. Phys.

137

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“…A specific type of conformal mapping technique has been proposed and introduced by Ciulli [21,22] and Pietarinen [23], and used in the Karlsruhe-Helsinki partial wave analysis [24] as an efficient expansion of invariant amplitudes. It was later used by a number of authors for solving various problems in scattering and field theory [25], but not applied to the pole search prior to our recent study [13].…”

Section: B Pietarinen Seriesmentioning

confidence: 99%

Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

et al. 2014

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We have applied a new approach to determine the pole positions and residues from pion photoproduction multipoles. The method is based on a Laurent expansion of the partial wave T-matrices, with a Pietarinen series representing the regular part of energy-dependent and single-energy photoproduction solutions. The method has been applied to multipole fits generated by the MAID and GWU/SAID groups. We show that the number and properties of poles extracted from photoproduction data correspond very well to results from πN elastic data and values cited by Particle Data Group (PDG). The photoproduction residues provide new information for the electromagnetic current at the pole position, which are independent of background parameterizations, as opposed to the Breit-Wigner representation. Finally, we present the photo-decay amplitudes from the current MAID and SAID solutions at the pole, for all four-star nucleon resonances below W = 2 GeV.

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“…Intuitively, one expects that a larger domain of convergence is related also to a better convergence rate. This expectation was confirmed by a mathematical result given in [22], which proves the existence of an "optimal conformal mapping" (OCM) for series expansions. It is the variable that maps the entire holomorphy domain of the expanded function onto a disk, and has the remarkable (less-known) property that by expanding in powers of this variable one obtains the series with the fastest largeorder convergence rate at all points inside the holomorphy domain.…”

Section: Non-power Perturbative Expansionsmentioning

confidence: 60%

Strong Coupling From the Tau Hadronic Width by Non-Power QCD Perturbation Theory

Caprini

2013

Mod. Phys. Lett. A

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Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalization-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the τ hadronic width, the contour-improved and the renormalization-group summed non-power expansions in the MS scheme lead to the prediction αs(M

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A convergent set of integral equations for singlet proton-proton scattering

Cited by 102 publications

References 3 publications

A novel integral representation for the Adler function

A novel integral representation for the Adler function

Pole positions and residues from pion photoproduction using the Laurent-Pietarinen expansion method

Strong Coupling From the Tau Hadronic Width by Non-Power QCD Perturbation Theory

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