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Title: Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD

Abstract

We show how the string amplitude {Phi}(z) defined on the fifth dimension in AdS{sub 5} space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable z and an impact variable {zeta}, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schroedinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for spacelike Q{sup 2}. Only one parameter which sets the mass scale, {Lambda}{sub QCD}, is introduced.

Authors:
;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
877213
Report Number(s):
SLAC-PUB-11716
hep-ph/0602252; TRN: US0601302
DOE Contract Number:
AC02-76SF00515
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; BARYONS; BOUND STATE; DIMENSIONS; FORM FACTORS; GLUONS; HADRONS; MESONS; QUANTUM CHROMODYNAMICS; QUARKS; SCHROEDINGER EQUATION; SPACE-TIME; SPECTRA; Phenomenology-HEP,HEPPH, HEPTH

Citation Formats

Brodsky, Stanley J., and de Teramond, Guy F.. Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD. United States: N. p., 2006. Web. doi:10.2172/877213.
Brodsky, Stanley J., & de Teramond, Guy F.. Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD. United States. doi:10.2172/877213.
Brodsky, Stanley J., and de Teramond, Guy F.. Fri . "Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD". United States. doi:10.2172/877213. https://www.osti.gov/servlets/purl/877213.
@article{osti_877213,
title = {Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD},
author = {Brodsky, Stanley J. and de Teramond, Guy F.},
abstractNote = {We show how the string amplitude {Phi}(z) defined on the fifth dimension in AdS{sub 5} space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable z and an impact variable {zeta}, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schroedinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for spacelike Q{sup 2}. Only one parameter which sets the mass scale, {Lambda}{sub QCD}, is introduced.},
doi = {10.2172/877213},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Mar 03 00:00:00 EST 2006},
month = {Fri Mar 03 00:00:00 EST 2006}
}

Technical Report:

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  • A fundamental goal in QCD is to understand the non-perturbative structure of hadrons at the amplitude level--not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion,more » the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wavefunctions is discussed. A new type of jet production reaction, ''self-resolving diffractive interactions'' can provide direct information on the light-front wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.« less
  • We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector {omega}{sup {mu}}. The LFWFs with definite total angular momentum are eigenstates of a kinematic angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents M{sub 0}{sup 2} = ({Sigma}k{sup {mu}}){sup 2} and the light-cone momentum fractions x{sub i} = k{sub i}{omega}/p{omega} multiplied by invariants constructed from the spin matrices, polarization vectors,more » and {omega}{sup {mu}}. These properties are illustrated using known nonperturbative eigensolutions of the Wick-Cutkosky model. We analyze the LFWFs introduced by Chung and Coester to describe static and low momentum properties of the nucleons. They correspond to the spin-locking of a quark with the spin of its parent nucleon, together with a positive-energy projection constraint. These extra constraints lead to anomalous dependence of form factors on Q rather than Q{sup 2}. In contrast, the dependence of LFWFs on M{sub 0}{sup 2} implies that hadron form factors are analytic functions of Q{sup 2} in agreement with dispersion theory and perturbative QCD. We show that a model incorporating the leading-twist perturbative QCD prediction is consistent with recent data for the ratio of proton Pauli and Dirac form factors.« less
  • We show how the string amplitude {phi}(z) defined on the fifth dimension in AdS{sub 5} space can be precisely mapped to the light-front wave functions of hadrons in physical space-time. We find an exact correspondence between the holographic variable z and an impact variable {zeta}, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schroedinger equations for the bound states of massless quarks and gluons which exactly reproduce the anti-de Sitter conformal field theory results and give a realistic description of the light-quark meson and baryon spectrum as wellmore » as the form factors for spacelike Q{sup 2}. Only one parameter which sets the mass scale, {lambda}{sub QCD}, is introduced.« less
  • A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wavefunctions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, diffractive dissociation intomore » jets, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wavefunctions is discussed. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-cone partition function, summed over exponentially weighted light-cone energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-cone wavefunctions.« less
  • The light-cone Fock representation encodes the bound-state quark and gluon properties of hadrons, including their helicity and flavor correlations, in terms of universal process-independent and frame-independent wavefunctions. It also provides a physical factorization scheme for separating hard and soft contributions in both exclusive and inclusive hard processes. A new type of jet production reaction, self-resolving diffractive interactions can provide direct information on the light-cone wavefunctions of hadrons in terms of their QCD degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.