Structure functions at small x from worldlines: Unpolarized distributions

Tarasov, Andrey; Venugopalan, Raju

doi:10.1103/PhysRevD.100.054007

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

Journal Article · 10 September 2019 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.100.054007 · OSTI ID:1560902

Tarasov, Andrey; Venugopalan, Raju

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Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0012704

OSTI ID:: 1560902

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 5 Vol. 100; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (79)

Asymptotic conditions and infrared divergences in quantum electrodynamics Kulish, P. P.; Faddeev, L. D. Theoretical and Mathematical Physics, Vol. 4, Issue 2 https://doi.org/10.1007/BF01066485	journal	January 1971
Colour transparency and scaling properties of nuclear shadowing in deep inelastic scattering Nikolaev, N. N.; Zakharov, B. G. Zeitschrift f�r Physik C Particles and Fields, Vol. 49, Issue 4 https://doi.org/10.1007/BF01483577	journal	December 1991
Field and particle equations for the classical Yang-Mills field and particles with isotopic spin Wong, S. K. Il Nuovo Cimento A, Vol. 65, Issue 4 https://doi.org/10.1007/BF02892134	journal	February 1970
Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach Laenen, Eric; Magnea, Lorenzo; Stavenga, Gerben Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)141	journal	January 2011
Helicity evolution at small x Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)072	journal	January 2016
Sub-eikonal corrections to scattering amplitudes at high energy Chirilli, Giovanni Antonio Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/JHEP01(2019)118	journal	January 2019
Higher-twist corrections to gluon TMD factorization Balitsky, I.; Tarasov, A. Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)095	journal	July 2017
Particles with non abelian charges Bastianelli, Fiorenzo; Bonezzi, Roberto; Corradini, Olindo Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)098	journal	October 2013
Erratum to: Helicity evolution at small x Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)148	journal	October 2016
Webs in multiparton scattering using the replica trick Gardi, Einan; Laenen, Eric; Stavenga, Gerben Journal of High Energy Physics, Vol. 2010, Issue 11 https://doi.org/10.1007/JHEP11(2010)155	journal	November 2010
Particle spin dynamics as the grassmann variant of classical mechanics Berezin, F. A.; Marinov, M. S. Annals of Physics, Vol. 104, Issue 2 https://doi.org/10.1016/0003-4916(77)90335-9	journal	April 1977
Semihard processes in QCD Gribov, L. Physics Reports, Vol. 100, Issue 1-2 https://doi.org/10.1016/0370-1573(83)90022-4	journal	November 1983
Pseudoclassical description of relativistic spinning particles with anomalous magnetic moment Barducci, A. Physics Letters B, Vol. 118, Issue 1-3 https://doi.org/10.1016/0370-2693(82)90611-6	journal	December 1982
Asymptotic coherent states and colour screening Catani, S.; Ciafaloni, M.; Marchesini, G. Physics Letters B, Vol. 168, Issue 3 https://doi.org/10.1016/0370-2693(86)90980-9	journal	March 1986
The anomalous gluon contribution to polarized leptoproduction Altarelli, G.; Ross, G. G. Physics Letters B, Vol. 212, Issue 3 https://doi.org/10.1016/0370-2693(88)91335-4	journal	September 1988
The role of the axial anomaly in measuring spin-dependent parton distributions Carlitz, R. D.; Collins, J. C.; Mueller, A. H. Physics Letters B, Vol. 214, Issue 2 https://doi.org/10.1016/0370-2693(88)91474-8	journal	November 1988
Equivalence of the spinning superparticle descriptions with grassmann variables or with c-number spinors Barut, A. O.; Pavšič, M. Physics Letters B, Vol. 216, Issue 3-4 https://doi.org/10.1016/0370-2693(89)91118-0	journal	January 1989
Yukawa couplings for the spinning particle and the world-line formalism Mondragón, Myriam; Nellen, Lukas; Schmidt, Michael G. Physics Letters B, Vol. 351, Issue 1-3 https://doi.org/10.1016/0370-2693(95)00337-K	journal	May 1995
Second order fermions in gauge theories Morgan, A. G. Physics Letters B, Vol. 351, Issue 1-3 https://doi.org/10.1016/0370-2693(95)00377-W	journal	May 1995
Axial couplings on the world-line Mondragón, Myriam; Nellen, Lukas; Schmidt, Michael G. Physics Letters B, Vol. 366, Issue 1-4 https://doi.org/10.1016/0370-2693(95)01392-X	journal	January 1996
Classical scalar and spinning particles interacting with external Yang-Mills fields Barducci, A.; Casalbuoni, R.; Lusanna, L. Nuclear Physics B, Vol. 124, Issue 1 https://doi.org/10.1016/0550-3213(77)90278-4	journal	June 1977
A Lagrangian formulation of the classical and quantum dynamics of spinning particles Brink, L.; Di Vecchia, P.; Howe, P. Nuclear Physics B, Vol. 118, Issue 1-2 https://doi.org/10.1016/0550-3213(77)90364-9	journal	January 1977
Anticommuting variables, internal degrees of freedom, and the Wilson loop Barducci, A.; Casalbuoni, R.; Lusanna, L. Nuclear Physics B, Vol. 180, Issue 1 https://doi.org/10.1016/0550-3213(81)90158-9	journal	January 1981
Gluon recombination and shadowing at small values of x Mueller, A. H.; Qiu, Jianwei Nuclear Physics B, Vol. 268, Issue 2 https://doi.org/10.1016/0550-3213(86)90164-1	journal	May 1986
Gauge covariance of QCD coherent states Catani, S.; Ciafaloni, M. Nuclear Physics B, Vol. 289 https://doi.org/10.1016/0550-3213(87)90392-0	journal	January 1987
Local supersymmetry and Dirac particle propagator as a path integral Fainberg, V. Ya.; Marshakov, A. V. Nuclear Physics B, Vol. 306, Issue 3 https://doi.org/10.1016/0550-3213(88)90018-1	journal	August 1988
Infrared finite S-matrix in the QCD coherent state basis Giavarini, Giorgio; Marchesini, Giuseppe Nuclear Physics B, Vol. 296, Issue 3 https://doi.org/10.1016/0550-3213(88)90031-4	journal	January 1988
Small-x behavior and parton saturation: A QCD model Mueller, A. H. Nuclear Physics B, Vol. 335, Issue 1 https://doi.org/10.1016/0550-3213(90)90173-B	journal	April 1990
The g1 problem: Deep inelastic electron scattering and the spin of the proton Jaffe, R. L.; Manohar, Aneesh Nuclear Physics B, Vol. 337, Issue 3 https://doi.org/10.1016/0550-3213(90)90506-9	journal	June 1990
Field theory without Feynman diagrams: One-loop effective actions Strassler, Matthew J. Nuclear Physics B, Vol. 385, Issue 1-2 https://doi.org/10.1016/0550-3213(92)90098-V	journal	October 1992
The computation of loop amplitudes in gauge theories Bern, Zvi; Kosower, David A. Nuclear Physics B, Vol. 379, Issue 3 https://doi.org/10.1016/0550-3213(92)90134-W	journal	July 1992
A mapping between Feynman and string motivated one-loop rules in gauge theories Bern, Zvi; Dunbar, David C. Nuclear Physics B, Vol. 379, Issue 3 https://doi.org/10.1016/0550-3213(92)90135-X	journal	July 1992
Fusing gauge theory tree amplitudes into loop amplitudes Bern, Zvi; Dixon, Lance; Dunbar, David C. Nuclear Physics B, Vol. 435, Issue 1-2 https://doi.org/10.1016/0550-3213(94)00488-Z	journal	February 1995
Operator expansion for high-energy scattering Balitsky, I. Nuclear Physics B, Vol. 463, Issue 1 https://doi.org/10.1016/0550-3213(95)00638-9	journal	March 1996
Worldline path integrals for fermions with scalar, pseudoscalar and vector couplings D'Hoker, Eric; Gagné, Darius G. Nuclear Physics B, Vol. 467, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00125-3	journal	May 1996
Worldline path integrals for fermions with general couplings D'Hoker, Eric; Gagné, Darius G. Nuclear Physics B, Vol. 467, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00126-5	journal	May 1996
Perturbative quantum field theory in the string-inspired formalism Schubert, Christian Physics Reports, Vol. 355, Issue 2-3 https://doi.org/10.1016/S0370-1573(01)00013-8	journal	December 2001
Limitations on using the operator product expansion at small values of x Mueller, A. H. Physics Letters B, Vol. 396, Issue 1-4 https://doi.org/10.1016/S0370-2693(97)00116-0	journal	March 1997
BFKL pomeron in the next-to-leading approximation Fadin, V. S.; Lipatov, L. N. Physics Letters B, Vol. 429, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00473-0	journal	June 1998
Nonlinear gluon evolution in the color glass condensate: I Iancu, Edmond; Leonidov, Andrei; McLerran, Larry Nuclear Physics A, Vol. 692, Issue 3-4 https://doi.org/10.1016/S0375-9474(01)00642-X	journal	September 2001
Nonlinear gluon evolution in the color glass condensate: II Ferreiro, Elena; Iancu, Edmond; Leonidov, Andrei Nuclear Physics A, Vol. 703, Issue 1-2 https://doi.org/10.1016/S0375-9474(01)01329-X	journal	May 2002
Unitarity at small Bjorken x Weigert, Heribert Nuclear Physics A, Vol. 703, Issue 3-4 https://doi.org/10.1016/S0375-9474(01)01668-2	journal	June 2002
Sizable CP violation in the bosonized Standard Model Hernandez, Andres; Konstandin, Thomas; Schmidt, Michael G. Nuclear Physics B, Vol. 812, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2008.12.021	journal	May 2009
Spin in Particle Physics Leader, Elliot https://doi.org/10.1017/CBO9780511524455	book	January 2001
Quantum Chromodynamics at High Energy Kovchegov, Yuri V.; Levin, Eugene Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology https://doi.org/10.1017/CBO9781139022187	book	September 2012
Worldline colour fields and non-Abelian quantum field theory Edwards, James P.; Corradini, Olindo EPJ Web of Conferences, Vol. 182 https://doi.org/10.1051/epjconf/201818202038	journal	January 2018
Scalar formalism for quantum electrodynamics Hostler, Levere C. Journal of Mathematical Physics, Vol. 26, Issue 6 https://doi.org/10.1063/1.526945	journal	June 1985
Path integral approach to eikonal and next-to-eikonal exponentiation Laenen, Eric; Stavenga, Gerben; White, Chris D. Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/054	journal	March 2009
High gluon densities in heavy ion collisions Blaizot, Jean-Paul Reports on Progress in Physics, Vol. 80, Issue 3 https://doi.org/10.1088/1361-6633/aa5435	journal	February 2017
The electron–ion collider: assessing the energy dependence of key measurements Aschenauer, E. C.; Fazio, S.; Lee, J. H. Reports on Progress in Physics, Vol. 82, Issue 2 https://doi.org/10.1088/1361-6633/aaf216	journal	January 2019
Spinning test-particles in general relativity. I Papapetrou, A. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 209, Issue 1097, p. 248-258 https://doi.org/10.1098/rspa.1951.0200	journal	October 1951
On Gauge Invariance and Vacuum Polarization Schwinger, Julian Physical Review, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRev.82.664	journal	June 1951
Classical description of a particle interacting with a non-Abelian gauge field Balachandran, A. P.; Salomonson, Per; Skagerstam, Bo-Sture Physical Review D, Vol. 15, Issue 8 https://doi.org/10.1103/PhysRevD.15.2308	journal	April 1977
Lagrangian and Hamiltonian descriptions of Yang-Mills particles Balachandran, A. P.; Borchardt, S.; Stern, A. Physical Review D, Vol. 17, Issue 12 https://doi.org/10.1103/PhysRevD.17.3247	journal	June 1978
Quantum Electrodynamics at Infinite Momentum: Scattering from an External Field Bjorken, James D.; Kogut, John B.; Soper, Davison E. Physical Review D, Vol. 3, Issue 6 https://doi.org/10.1103/PhysRevD.3.1382	journal	March 1971
Path-integral representation for the relativistic particle propagators and BFV quantization Fradkin, E. S.; Gitman, D. M. Physical Review D, Vol. 44, Issue 10 https://doi.org/10.1103/PhysRevD.44.3230	journal	November 1991
Computing quark and gluon distribution functions for very large nuclei McLerran, Larry; Venugopalan, Raju Physical Review D, Vol. 49, Issue 5 https://doi.org/10.1103/PhysRevD.49.2233	journal	March 1994
Gluon distribution functions for very large nuclei at small transverse momentum McLerran, Larry; Venugopalan, Raju Physical Review D, Vol. 49, Issue 7 https://doi.org/10.1103/PhysRevD.49.3352	journal	April 1994
Green’s function in the color field of a large nucleus McLerran, Larry; Venugopalan, Raju Physical Review D, Vol. 50, Issue 3 https://doi.org/10.1103/PhysRevD.50.2225	journal	August 1994
Non-Abelian Weizsäcker-Williams field and a two-dimensional effective color charge density for a very large nucleus Kovchegov, Yuri V. Physical Review D, Vol. 54, Issue 9 https://doi.org/10.1103/PhysRevD.54.5463	journal	November 1996
Intrinsic glue distribution at very small x Jalilian-Marian, Jamal; Kovner, Alex; McLerran, Larry Physical Review D, Vol. 55, Issue 9 https://doi.org/10.1103/PhysRevD.55.5414	journal	May 1997
Wilson renormalization group for low x physics: Towards the high density regime Jalilian-Marian, Jamal; Kovner, Alex; Leonidov, Andrei Physical Review D, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevD.59.014014	journal	November 1998
Wilson renormalization group for low x physics: Gluon evolution at finite parton density Jalilian-Marian, Jamal; Kovner, Alex; Weigert, Heribert Physical Review D, Vol. 59, Issue 1 https://doi.org/10.1103/PhysRevD.59.014015	journal	November 1998
Fock space distributions, structure functions, higher twists, and small x McLerran, Larry; Venugopalan, Raju Physical Review D, Vol. 59, Issue 9 https://doi.org/10.1103/PhysRevD.59.094002	journal	March 1999
Small- x F 2 structure function of a nucleus including multiple Pomeron exchanges Kovchegov, Yuri V. Physical Review D, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRevD.60.034008	journal	June 1999
Minding one’s P’s and Q’s: From the one loop effective action in quantum field theory to classical transport theory Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju Physical Review D, Vol. 62, Issue 4 https://doi.org/10.1103/PhysRevD.62.045020	journal	July 2000
Wong’s equations and the small x effective action in QCD Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju Physical Review D, Vol. 63, Issue 3 https://doi.org/10.1103/PhysRevD.63.036004	journal	January 2001
Quark imaging in the proton via quantum phase-space distributions Belitsky, A. V.; Ji, Xiangdong; Yuan, Feng Physical Review D, Vol. 69, Issue 7 https://doi.org/10.1103/PhysRevD.69.074014	journal	April 2004
Quark orbital angular momentum from Wigner distributions and light-cone wave functions Lorcé, Cédric; Pasquini, Barbara; Xiong, Xiaonu Physical Review D, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevD.85.114006	journal	June 2012
Worldline construction of a covariant chiral kinetic theory Mueller, Niklas; Venugopalan, Raju Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevD.96.016023	journal	July 2017
Chiral anomaly, Berry phase, and chiral kinetic theory from worldlines in quantum field theory Mueller, Niklas; Venugopalan, Raju Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevD.97.051901	journal	March 2018
Small- x helicity evolution: An operator treatment Kovchegov, Yuri V.; Sievert, Matthew D. Physical Review D, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevD.99.054032	journal	March 2019
Constructing phase space distributions with internal symmetries Mueller, Niklas; Venugopalan, Raju Physical Review D, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevD.99.056003	journal	March 2019
Small- x Asymptotics of the Quark Helicity Distribution Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D. Physical Review Letters, Vol. 118, Issue 5 https://doi.org/10.1103/PhysRevLett.118.052001	journal	January 2017
Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field Bargmann, V.; Michel, Louis; Telegdi, V. L. Physical Review Letters, Vol. 2, Issue 10 https://doi.org/10.1103/PhysRevLett.2.435	journal	May 1959
Electron-Ion Collider: The next QCD frontier: Understanding the glue that binds us all Accardi, A.; Albacete, J. L.; Anselmino, M. The European Physical Journal A, Vol. 52, Issue 9 https://doi.org/10.1140/epja/i2016-16268-9	journal	September 2016
Impact Parameter Space Interpretation for Generalized Parton Distributions Burkardt, Matthias International Journal of Modern Physics A, Vol. 18, Issue 02 https://doi.org/10.1142/S0217751X03012370	journal	January 2003
Coherent States of Fermi Operators and the Path Integral Ohnuki, Y.; Kashiwa, T. Progress of Theoretical Physics, Vol. 60, Issue 2 https://doi.org/10.1143/PTP.60.548	journal	August 1978
The Color Glass Condensate Gelis, Francois; Iancu, Edmond; Jalilian-Marian, Jamal Annual Review of Nuclear and Particle Science, Vol. 60, Issue 1 https://doi.org/10.1146/annurev.nucl.010909.083629	journal	November 2010