skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Structure functions at small x from worldlines: Unpolarized distributions

Abstract

The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world- line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small x .

Authors:
;
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1560902
Alternate Identifier(s):
OSTI ID: 1570678
Report Number(s):
BNL-212178-2019-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ; 054007
Grant/Contract Number:  
SC0012704
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Tarasov, Andrey, and Venugopalan, Raju. Structure functions at small x from worldlines: Unpolarized distributions. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.054007.
Tarasov, Andrey, & Venugopalan, Raju. Structure functions at small x from worldlines: Unpolarized distributions. United States. doi:10.1103/PhysRevD.100.054007.
Tarasov, Andrey, and Venugopalan, Raju. Tue . "Structure functions at small x from worldlines: Unpolarized distributions". United States. doi:10.1103/PhysRevD.100.054007.
@article{osti_1560902,
title = {Structure functions at small x from worldlines: Unpolarized distributions},
author = {Tarasov, Andrey and Venugopalan, Raju},
abstractNote = {The world-line representation of quantum field theory is a powerful framework for the computation of perturbative multi-leg Feynman amplitudes. In particular, in gauge theories, it provides an efficient way, via point particle Grassmann functional integrals, to compute spinor and color traces in these amplitudes. Further, semi-classical approximations to quantum mechanical world- line trajectories provide useful intuition in a wide range of dynamical problems. We develop here the world-line approach to compute deeply inelastic structure functions in the small x Regge limit of QCD. In a shockwave approximation valid in this limit, we show how one recovers the well-known dipole model for unpolarized structure functions. In a follow-up work, we will discuss the world-line computation of polarized structure functions at small x.},
doi = {10.1103/PhysRevD.100.054007},
journal = {Physical Review D},
number = 5,
volume = 100,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.100.054007

Figures / Tables:

FIG. 1 FIG. 1: a) Current-current correlator in an arbitrary background field; b) The same in the CGC shockwave background, where the spatial separation in $x$ shrinks to a point.

Save / Share:

Works referenced in this record:

Infrared finite S-matrix in the QCD coherent state basis
journal, January 1988


Asymptotic conditions and infrared divergences in quantum electrodynamics
journal, January 1971

  • Kulish, P. P.; Faddeev, L. D.
  • Theoretical and Mathematical Physics, Vol. 4, Issue 2
  • DOI: 10.1007/BF01066485

Small- x Asymptotics of the Quark Helicity Distribution
journal, January 2017


Scalar formalism for quantum electrodynamics
journal, June 1985

  • Hostler, Levere C.
  • Journal of Mathematical Physics, Vol. 26, Issue 6
  • DOI: 10.1063/1.526945

Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field
journal, May 1959


Constructing phase space distributions with internal symmetries
journal, March 2019


Field theory without Feynman diagrams: One-loop effective actions
journal, October 1992


Worldline path integrals for fermions with general couplings
journal, May 1996


Worldline construction of a covariant chiral kinetic theory
journal, July 2017


Gauge covariance of QCD coherent states
journal, January 1987


Intrinsic glue distribution at very small x
journal, May 1997

  • Jalilian-Marian, Jamal; Kovner, Alex; McLerran, Larry
  • Physical Review D, Vol. 55, Issue 9
  • DOI: 10.1103/PhysRevD.55.5414

The role of the axial anomaly in measuring spin-dependent parton distributions
journal, November 1988


Semihard processes in QCD
journal, November 1983


The Color Glass Condensate
journal, November 2010


Small-x behavior and parton saturation: A QCD model
journal, April 1990


Path integral approach to eikonal and next-to-eikonal exponentiation
journal, March 2009


BFKL pomeron in the next-to-leading approximation
journal, June 1998


Wong’s equations and the small x effective action in QCD
journal, January 2001


Operator expansion for high-energy scattering
journal, March 1996


The electron–ion collider: assessing the energy dependence of key measurements
journal, January 2019

  • Aschenauer, E. C.; Fazio, S.; Lee, J. H.
  • Reports on Progress in Physics, Vol. 82, Issue 2
  • DOI: 10.1088/1361-6633/aaf216

High gluon densities in heavy ion collisions
journal, February 2017


Wilson renormalization group for low x physics: Towards the high density regime
journal, November 1998


Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
journal, January 2011

  • Laenen, Eric; Magnea, Lorenzo; Stavenga, Gerben
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)141

Green’s function in the color field of a large nucleus
journal, August 1994


Particles with non abelian charges
journal, October 2013

  • Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)098

Webs in multiparton scattering using the replica trick
journal, November 2010

  • Gardi, Einan; Laenen, Eric; Stavenga, Gerben
  • Journal of High Energy Physics, Vol. 2010, Issue 11
  • DOI: 10.1007/JHEP11(2010)155

Path-integral representation for the relativistic particle propagators and BFV quantization
journal, November 1991


On Gauge Invariance and Vacuum Polarization
journal, June 1951


Particle spin dynamics as the grassmann variant of classical mechanics
journal, April 1977


Higher-twist corrections to gluon TMD factorization
journal, July 2017


Equivalence of the spinning superparticle descriptions with grassmann variables or with c-number spinors
journal, January 1989


Classical scalar and spinning particles interacting with external Yang-Mills fields
journal, June 1977


The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990


Anticommuting variables, internal degrees of freedom, and the Wilson loop
journal, January 1981


Erratum to: Helicity evolution at small x
journal, October 2016

  • Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)148

Perturbative quantum field theory in the string-inspired formalism
journal, December 2001


Field and particle equations for the classical Yang-Mills field and particles with isotopic spin
journal, February 1970


Classical description of a particle interacting with a non-Abelian gauge field
journal, April 1977

  • Balachandran, A. P.; Salomonson, Per; Skagerstam, Bo-Sture
  • Physical Review D, Vol. 15, Issue 8
  • DOI: 10.1103/PhysRevD.15.2308

Quantum Electrodynamics at Infinite Momentum: Scattering from an External Field
journal, March 1971

  • Bjorken, James D.; Kogut, John B.; Soper, Davison E.
  • Physical Review D, Vol. 3, Issue 6
  • DOI: 10.1103/PhysRevD.3.1382

Fock space distributions, structure functions, higher twists, and small x
journal, March 1999


Sub-eikonal corrections to scattering amplitudes at high energy
journal, January 2019


Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory
journal, March 2018


Worldline path integrals for fermions with scalar, pseudoscalar and vector couplings
journal, May 1996


The computation of loop amplitudes in gauge theories
journal, July 1992


The anomalous gluon contribution to polarized leptoproduction
journal, September 1988


Fusing gauge theory tree amplitudes into loop amplitudes
journal, February 1995


Small- x F 2 structure function of a nucleus including multiple Pomeron exchanges
journal, June 1999


Nonlinear gluon evolution in the color glass condensate: II
journal, May 2002


Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory
journal, July 2000


Unitarity at small Bjorken x
journal, June 2002


Coherent States of Fermi Operators and the Path Integral
journal, August 1978

  • Ohnuki, Y.; Kashiwa, T.
  • Progress of Theoretical Physics, Vol. 60, Issue 2
  • DOI: 10.1143/PTP.60.548

Sizable CP violation in the bosonized Standard Model
journal, May 2009


Nonlinear gluon evolution in the color glass condensate: I
journal, September 2001


Axial couplings on the world-line
journal, January 1996


Asymptotic coherent states and colour screening
journal, March 1986


A Lagrangian formulation of the classical and quantum dynamics of spinning particles
journal, January 1977


Gluon recombination and shadowing at small values of x
journal, May 1986


Computing quark and gluon distribution functions for very large nuclei
journal, March 1994


Yukawa couplings for the spinning particle and the world-line formalism
journal, May 1995


Wilson renormalization group for low x physics: Gluon evolution at finite parton density
journal, November 1998


Colour transparency and scaling properties of nuclear shadowing in deep inelastic scattering
journal, December 1991

  • Nikolaev, N. N.; Zakharov, B. G.
  • Zeitschrift f�r Physik C Particles and Fields, Vol. 49, Issue 4
  • DOI: 10.1007/BF01483577

Quark orbital angular momentum from Wigner distributions and light-cone wave functions
journal, June 2012


Second order fermions in gauge theories
journal, May 1995


Impact Parameter Space Interpretation for Generalized Parton Distributions
journal, January 2003


Small- x helicity evolution: An operator treatment
journal, March 2019


Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all
journal, September 2016


Limitations on using the operator product expansion at small values of x
journal, March 1997


Helicity evolution at small x
journal, January 2016

  • Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)072

Lagrangian and Hamiltonian descriptions of Yang-Mills particles
journal, June 1978


Pseudoclassical description of relativistic spinning particles with anomalous magnetic moment
journal, December 1982


Gluon distribution functions for very large nuclei at small transverse momentum
journal, April 1994


Worldline colour fields and non-Abelian quantum field theory
journal, January 2018


Quark imaging in the proton via quantum phase-space distributions
journal, April 2004


Local supersymmetry and Dirac particle propagator as a path integral
journal, August 1988


A mapping between Feynman and string motivated one-loop rules in gauge theories
journal, July 1992


    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.