Light-front formulation of the standard model

Srivastava, Prem Prakash; Brodsky, Stanley J.

doi:10.1103/physrevd.66.045019

Cited by 63 publications

(75 citation statements)

References 42 publications

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“…For example in QED, vacuum graphs such as e + e − γ associated with the zero-point energy do not arise. In the Higgs theory, the usual Higgs vacuum expectation value is replaced with a k + = 0 zero mode [6]; however, the resulting phenomenology is identical to the standard analysis.…”

Section: Vacuum Effects and Light-front Quantizationmentioning

confidence: 99%

“…In the case of the Higgs model, the effect of the usual Higgs vacuum expectation value is replaced by a constant k + = 0 zero mode field. [6] • If one quantizes QCD in the physical lightcone gauge (LCG) A + = 0, then gluons only have physical angular momentum projections S z = ±1. The orbital angular momenta of quarks and gluons are defined unambiguously, and there are no ghosts.…”

Section: The Light-front Hamiltonian Approach To Qcdmentioning

confidence: 99%

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Light-Front Holography, AdS/QCD, and Hadronic Phenomena

Brodsky

Téramond

2010

Nuclear Physics B - Proceedings Supplements

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AdS/QCD, the correspondence between theories in a modified five-dimensional anti-de Sitter space and confining field theories in physical space-time, provides a remarkable semiclassical model for hadron physics. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate z with an invariant light-front coordinate ζ which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrödinger equation with a confining potential which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The mapping of electromagnetic and gravitational form factors in AdS space to their corresponding expressions in light-front theory confirms this correspondence. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. The distinction between static structure functions, such as the probability distributions computed from the square of the light-front wavefunctions, versus dynamical structure functions which include the effects of rescattering, is emphasized. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined. The Light-Front Hamiltonian Approach to QCDOne of the most important theoretical tools in atomic physics is the Schrödinger wavefunction, which describes the quantum-mechanical structure of an atomic system at the amplitude level. Light-front wavefunctions (LFWFs) play a similar role in quantum chromodynamics, providing a fundamental description of the structure and internal dynamics of hadrons in terms of their constituent quarks and gluons. The LFWFs of bound states in QCD are relativistic generalizations of the Schrödinger wavefunctions of atomic physics, but they are determined at fixed lightcone time τ = t + z/c -the "front form" introduced by Dirac [1] -rather than at fixed ordinary time t.When a flash from a camera illuminates a scene, each object is illuminated along the lightfront of the flash; i.e., at a given τ . Similarly, when a sample is illuminated by an x-ray source, each element of the target is struck at a given τ. In contrast, setting the initial condition using conventional instant time t requires simultaneous scattering of photons on each constituent. Thus it is natural to set boundary conditions at fixed τ and then evolve the system using the light-front (LF) Hamiltonian2 where M is the physical mass. Its eigenfunctions are the light-front eigenstates whose Fock state projections define the light-front wavefunctions. Given the LF Fock state wavefunctions ψ H n (x i , k ⊥i , λ i ), wherek ⊥i = 0, one can immediately compute observables such as hadronic form factors (overl...

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Section: Vacuum Effects and Light-front Quantizationmentioning

confidence: 99%

Section: The Light-front Hamiltonian Approach To Qcdmentioning

confidence: 99%

Light-Front Holography, AdS/QCD, and Hadronic Phenomena

Brodsky

Téramond

2010

Nuclear Physics B - Proceedings Supplements

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“…In this sense it is already normal-ordered. In the case of the Higgs theory, the usual Higgs vacuum expectation value is replaced by a classical k + = 0 background zero-mode field which is not sensed by the energy momentum tensor [56]. The phenomenology of the Higgs theory is unchanged.…”

Section: The Light-front Vacuummentioning

confidence: 99%

QCD on the Light-Front

2013

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Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3 , provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian HLF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of HLF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable ζ 2 = b 2 ⊥ x(1−x), which is conjugate to the invariant mass squared M 2 qq . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories M 2 (n, L, S) = 4κ 2 (n+L+S/2) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

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“…In the case of the electroweak theory, spontaneous symmetry breaking is realized in LF quantization by the appearance of zero modes of the Higgs field. Light-front quantization leads to an elegant ghost-free theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions, as well as the Goldstone boson equivalence theorem [4].…”

Section: Introductionmentioning

confidence: 99%

New Results in Light-Front Phenomenology

Brodsky¹

2004

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The light-front quantization of gauge theories in light-cone gauge provides a frameindependent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these nearconformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as s(x) =s(x),ū(x) =d(x). Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains "hidden color" states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.2

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Light-front formulation of the standard model

Cited by 63 publications

References 42 publications

Light-Front Holography, AdS/QCD, and Hadronic Phenomena

Light-Front Holography, AdS/QCD, and Hadronic Phenomena

QCD on the Light-Front

New Results in Light-Front Phenomenology

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