Scattering amplitudes in the light-front formalism

Cruz-Santiago, Christian A.; Kotko, Piotr; Staśto, Anna

doi:10.1016/j.ppnp.2015.07.002

Cited by 18 publications

(29 citation statements)

References 84 publications

(190 reference statements)

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“…[161][162][163][164][165][166] for reviews) take a different route in this respect. Motivated by the triviality of the vacuum in light-cone quantization, the goal is to calculate the eigenstates of the gauge-fixed QCD Hamiltonian directly by solving large-scale eigenvalue problems.…”

Section: Confinementmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

438

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: Confinementmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

438

530

View full text Add to dashboard Cite

show abstract

“…In this section, we apply the angular momentum conservation law in the lightfront formulation derived in Section 3.3 to present an explanation for the selection rule of the orbital angular momentum observed in [9][10]: in the n-th order perturbative expansion of a renormalizable theory, the change of orbital angular momentum between the initial and final states in the front form is constrained by |∆ l 3 | ≤ n.…”

Section: Selection Rule For Orbital Angular Momentum In the Front Formmentioning

confidence: 99%

“…This explains the vanishing amplitude M (+, +, ..., +) 10 at tree level [9] [11] : In 2 → n gluon scattering , the amplitude M (+, +, ..., +) = M (−− → +...+) has ∆ s 3 = n + 2. Conservation of angular momentum in the z-direction then gives ∆ l 3 = −(n + 2).…”

Section: Selection Rule For Orbital Angular Momentum In the Front Formmentioning

confidence: 99%

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Angular momentum conservation law in light-front quantum field theory

Chiu

Brodsky

2017

Phys. Rev. D

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We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the lightfront formulation. We explicitly show that j 3 , the z-component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.

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“…Instead, the recent review by Cruz-Santiago, Kotko, and Staśto [11] provides an excellent introduction to light-front calculations of scattering amplitudes.…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

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Scattering amplitudes in the light-front formalism

Cited by 18 publications

References 84 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Angular momentum conservation law in light-front quantum field theory

Nonperturbative light-front Hamiltonian methods

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