Spectral representation for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>u</mml:mi></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>-channel exchange processes in a partial-wave decomposition

Lutz, Matthias; Kolomeitsev, E. É.; Korpa, C. L.

doi:10.1103/physrevd.92.016003

Cited by 15 publications

(15 citation statements)

References 49 publications

(149 reference statements)

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“…Among those are the Sato-Lee model [70], which has been extended by the EBAC [71][72][73] and ANL/Osaka collaborations [74] and extensively applied to analyze pion photo-and electroproduction data. The Dubna-Mainz-Taiwan (DMT) [75,76], Valencia [77], Jülich-Bonn [78,79] and GSI models [80][81][82] have been developed along similar lines. Theoretical constraints like unitarity and analyticity of the S-matrix are manifest in these approaches.…”

Section: Helicity Amplitudes Vs Transition Form Factorsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

436

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Helicity Amplitudes Vs Transition Form Factorsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

436

530

View full text Add to dashboard Cite

show abstract

“…Our starting point, is based directly on the general representation (2), which already established a suitable analytic continuation of the tree-level potential terms valid for arbitrary exchange masses. As was emphasized in our previous work [28] the reason why a one-loop diagram develops an anomalous threshold can be read off easily from its driving tree-level potential terms.…”

Section: Analytic Structure Of Partial-wave Scattering Amplitudesmentioning

confidence: 76%

“…where the cancellations in (29) follow from (23,28). We observe that owing to the identities (27,29) the two terms in (26) can be combined into a dispersion integral written in terms of the partially overlapping contours C c .…”

Section: Non-linear Integral Equation On Complex Contoursmentioning

confidence: 90%

“…To unfold the underlying physics of this non-perturbative domain of QCD novel approaches are required that combine the power of coupled-channel unitarity together with the micro-causality condition for hadronic degrees of freedom [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. While such frameworks exist for coupled-channel interactions that are dominated by short-range forces matters turn significantly more challenging in the presence of t-or u-channel long-range forces [20][21][22][23][24][25][26][27][28].…”

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confidence: 99%

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On coupled-channel dynamics in the presence of anomalous thresholds

Lutz

Korpa

2018

Phys. Rev. D

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We explore a general framework how to treat coupled-channel systems in the presence of overlapping left and right-hand cuts as well as anomalous thresholds. Such systems are studied in terms of a generalized potential, where we exploit the known analytic structure of t-and u-channel forces as the exchange masses get smaller approaching their physical values. Given an approximate generalized potential the coupled-channel reaction amplitudes are defined in terms of non-linear systems of integral equations. For large exchange masses, where there are no anomalous thresholds present, conventional N/D methods are applicable to derive numerical solutions to the latter. At a formal level a generalization to the anomalous case is readily formulated by use of suitable contour integrations with amplitudes to be evaluated at complex energies. However, it is a considerable challenge to find numerical solutions to anomalous systems set up on a set of complex contours.By a suitable deformations of left-hand and right-hand cut lines we managed to establish a framework of linear integral equations defined for real energies. Explicit expressions are derived for the driving terms that hold for an arbitrary number of channels. Our approach is illustrated in terms of a schematic 3-channel systems. It is demonstrated that despite the presence of anomalous thresholds the scattering amplitude can be represented in terms of 3 phase shifts and 3 in-elasticity parameters, as one would expect from the coupled-channel unitarity condition.

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“…An alternative approach is based on the spectral representation of the propagator of UP. It has a long history [24][25][26][27][28][29][30][31][32][33][34] and treats UP as a non-perturbative state or effective field (asymptotic free field [30,31]). For the first time, the hypothesis of continuous (smeared) mass of UP was suggested by Matthews and Salam [27].…”

Section: Introductionmentioning

confidence: 99%

Complex-Mass Definition and the Structure of Unstable Particle’s Propagator

Kuksa

2015

Advances in High Energy Physics

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The propagators of unstable particles are considered in framework of the convolution representation. Spectral function is found for a special case when the propagator of scalar unstable particle has Breit-Wigner form. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. We obtain the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition.

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Spectral representation foru- andt-channel exchange processes in a partial-wave decomposition

Cited by 15 publications

References 49 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

On coupled-channel dynamics in the presence of anomalous thresholds

Complex-Mass Definition and the Structure of Unstable Particle’s Propagator

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