QCD based quark description of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mo>−</mml:mo><mml:mi>π</mml:mi></mml:math>scattering up to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math>regions

Cotanch, Stephen R.; Maris, Pieter

doi:10.1103/physrevd.66.116010

Cited by 51 publications

(60 citation statements)

References 30 publications

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“…In Refs. [697,698] the rainbow-ladder expression for the ππ scattering amplitude in the forward limit t = 0 was calculated and the scattering lengths at threshold (s = 4m 2 π ) were extracted. (A similar calculation has been recently performed in the covariant spectator approach [699].)…”

Section: Applicationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

421

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: Applicationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

421

530

View full text Add to dashboard Cite

show abstract

“…The DSBSE approach to hadrons uses the BSE to describe mesons as quark-antiquark systems [58], a covariant Faddeev equation for a three-quark setup to study baryons [59][60][61], and more complicated equations to go beyond these configurations [62][63][64][65]. The covariant amplitudes are then used for the subsequent calculation of form factors or other transiton amplitudes [66][67][68][69][70][71][72][73][74][75][76][77].…”

Section: Essentials Of the Bethe-salpeter Equationmentioning

confidence: 99%

Charming quasi-exotic open-flavor mesons

Hilger

Krassnigg

2017

EPJ Web Conf.

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“…It has now been established that the choice of the transverse vertex has observable consequences at the hadronic level, despite the fact that the simple rainbowladder truncation is sufficient to reproduce a large body of existing experimental data on pseudoscalar and vector mesons such as their masses, charge radii, decay constants and scattering lengths, as well as their form factors and the valence quark distribution functions, [23][24][25][26][27][28][29][30][31][32][33]. For example, the conundrum of mass difference between opposite parity states can only be explained through corrections to the rainbow ladder truncations, [34], also see the review, [35].…”

Section: Sde For the Fermion Propagatormentioning

confidence: 99%

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

et al. 2013

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We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term, characterized by coupling strengths α and λ, respectively. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension γm = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors N f = N c f above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strengths, αc and λc, necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength α and the four-fermion coupling λ, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn in the phase space of (α, λ, N f ) to clearly depict the interplay of their relative strengths to separate the two phases. We also compute the β-functions (βα and β λ ), and observe that αc and λc are their respective ultraviolet fixed points. The power law part of the momentum dependence, describing the mass function, implies γm = 1 + s, which reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED. 11.30.Rd, 11.15.Tk Since the works of Maskawa and Nakajima as well as the Kiev group [1], it is well known that quenched quantum electrodynamics (QED) exhibits vacuum rearrangement, which triggers chiral symmetry breaking when the interaction strength α = e 2 /(4π) exceeds a critical value α c ∼ 1. α c was argued to be an ultraviolet stable fixed point defining the continuum limit in supercritical QED. Although these works were carried out for the bare vertex in the Landau gauge, principle qualitative conclusions were later shown to be robust even for the most general and sophisticated ansätze put forward henceforth for an arbitrary value of the covariant gauge parameter, see e.g., [2][3][4][5]. Bardeen, Leung and Love [6] demonstrated that the composite operatorψψ acquires large anomalous dimensions at α = α c . In fact, the mass anomalous dimension was shown to be γ m = 1, leading to the fact that the four-fermion interaction operator (ψψ) 2 acquires the scaling dimension of d = 2(3 − γ m ) = 4 instead of 6, and becomes renormalizable. This is an example of when an interaction which is irrelevant in a certain region of phase space (perturbative) might become relevant in another (non perturbative). Consequently, the four-fermion contact interaction becomes mar...

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QCD based quark description ofπ−πscattering up to theσandρregions

Cited by 51 publications

References 30 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Charming quasi-exotic open-flavor mesons

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

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