Singularities in twist-3 quark distributions

Aslan, Fatma P.; Burkardt, Matthias

doi:10.1103/physrevd.101.016010

Singularities in twist-3 quark distributions

Journal Article · Mon Jan 13 00:00:00 EST 2020 · Physical Review D

DOI:https://doi.org/10.1103/physrevd.101.016010· OSTI ID:1800852

Aslan, Fatma P. ^[1]; Burkardt, Matthias ^[2]

New Mexico State Univ., Las Cruces, NM (United States); OSTI
New Mexico State Univ., Las Cruces, NM (United States)

We find in one-loop calculations and spectator models that twist-3 generalized parton distributions exhibit discontinuities. In the forward limit, these discontinuities grow into Dirac delta functions which are essential to satisfy the sum rules involving twist-3 parton distribution functions (PDFs). Further, we calculate twist-3 quasi-PDFs as a function of longitudinal momentum and identify the Dirac delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to the infinite momentum frame.

View Accepted Manuscript (DOE)

Research Organization:: New Mexico State Univ., Las Cruces, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-96ER40965

OSTI ID:: 1800852

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 1 Vol. 101; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (57)

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD Müller, D.; Robaschik, D.; Geyer, B. Fortschritte der Physik/Progress of Physics, Vol. 42, Issue 2 https://doi.org/10.1002/prop.2190420202	journal	January 1994
Asymptotic behavior of the pion form factor in quantum chromodynamics Efremov, A. V.; Radyushkin, A. V. Theoretical and Mathematical Physics, Vol. 42, Issue 2 https://doi.org/10.1007/BF01032111	journal	February 1980
Generalized parton distributions in impact parameter space Diehl, M. The European Physical Journal C, Vol. 25, Issue 2 https://doi.org/10.1007/s10052-002-1016-9	journal	September 2002
Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation Kivel, N.; Mankiewicz, L. The European Physical Journal C, Vol. 21, Issue 4 https://doi.org/10.1007/s100520100760	journal	July 2001
Parton physics from large-momentum effective field theory Ji, XiangDong Science China Physics, Mechanics & Astronomy, Vol. 57, Issue 7 https://doi.org/10.1007/s11433-014-5492-3	journal	May 2014
Sum rules for forward virtual compton scattering Burkhardt, Hugh; Cottingham, W. N. Annals of Physics, Vol. 56, Issue 2 https://doi.org/10.1016/0003-4916(70)90025-4	journal	February 1970
Sum rules for spin-dependent electroproduction- test of relativistic constituent quarks Wandzura, S.; Wilczek, F. Physics Letters B, Vol. 72, Issue 2 https://doi.org/10.1016/0370-2693(77)90700-6	journal	December 1977
Scaling limit of deeply virtual compton scattering Radyushkin, A. V. Physics Letters B, Vol. 380, Issue 3-4 https://doi.org/10.1016/0370-2693(96)00528-X	journal	July 1996
Asymmetric gluon distributions and hard diffractive electroproduction Radyushkin, A. V. Physics Letters B, Vol. 385, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00844-1	journal	September 1996
Asymptotic freedom in parton language Altarelli, G.; Parisi, G. Nuclear Physics B, Vol. 126, Issue 2 https://doi.org/10.1016/0550-3213(77)90384-4	journal	August 1977
Parton distribution and decay functions Collins, John C.; Soper, Davison E. Nuclear Physics B, Vol. 194, Issue 3 https://doi.org/10.1016/0550-3213(82)90021-9	journal	January 1982
Chiral-odd parton distributions and Drell-Yan processes Jaffe, R. L.; Ji, Xiangdong Nuclear Physics B, Vol. 375, Issue 3 https://doi.org/10.1016/0550-3213(92)90110-W	journal	May 1992
Deeply virtual Compton scattering amplitude in the parton model Penttinen, M.; Polyakov, M. V.; Shuvaev, A. G. Physics Letters B, Vol. 491, Issue 1-2 https://doi.org/10.1016/S0370-2693(00)01035-2	journal	October 2000
DVCS amplitude with kinematical twist-3 terms Radyushkin, A. V.; Weiss, C. Physics Letters B, Vol. 493, Issue 3-4 https://doi.org/10.1016/S0370-2693(00)01155-2	journal	November 2000
Wandzura–Wilczek approximation for the twist-3 DVCS amplitude Kivel, N.; Polyakov, M. V.; Schäfer, A. Physics Letters B, Vol. 497, Issue 1-2 https://doi.org/10.1016/S0370-2693(00)01313-7	journal	January 2001
Wandzura–Wilczek approximation from generalized rotational invariance Anikin, I. V.; Teryaev, O. V. Physics Letters B, Vol. 509, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)00555-X	journal	June 2001
Twist-three observables in deeply virtual Compton scattering on the nucleon Belitsky, A. V.; Kirchner, A.; Müller, D. Physics Letters B, Vol. 510, Issue 1-4 https://doi.org/10.1016/S0370-2693(01)00608-6	journal	June 2001
Examination of Wandzura-Wilczek relation for g2(x, Q2) in pQCD Harindranath, A.; Zhang, Wei-Min Physics Letters B, Vol. 408, Issue 1-4 https://doi.org/10.1016/S0370-2693(97)00771-5	journal	September 1997
Twist-three effects in two-photon processes Belitsky, A. V.; Müller, D. Nuclear Physics B, Vol. 589, Issue 3 https://doi.org/10.1016/S0550-3213(00)00542-3	journal	November 2000
DVCS on the nucleon to the twist-3 accuracy Kivel, N.; Polyakov, M. V. Nuclear Physics B, Vol. 600, Issue 2 https://doi.org/10.1016/S0550-3213(01)00048-7	journal	April 2001
Theory of deeply virtual Compton scattering on the nucleon Belitsky, A. V.; Müller, D.; Kirchner, A. Nuclear Physics B, Vol. 629, Issue 1-3 https://doi.org/10.1016/S0550-3213(02)00144-X	journal	May 2002
Violation of sum rules for twist-3 parton distributions in QCD Burkardt, Matthias; Koike, Yuji Nuclear Physics B, Vol. 632, Issue 1-3 https://doi.org/10.1016/S0550-3213(02)00263-8	journal	June 2002
NLO corrections to the twist-3 amplitude in DVCS on a nucleon in the Wandzura–Wilczek approximation: quark case Kivel, N.; Mankiewicz, L. Nuclear Physics B, Vol. 672, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2003.08.029	journal	November 2003
Structure of light-front vacuum sector diagrams Mannheim, Philip D.; Lowdon, Peter; Brodsky, Stanley J. Physics Letters B, Vol. 797 https://doi.org/10.1016/j.physletb.2019.134916	journal	October 2019
The chirally-odd twist-3 distribution e ^a ( x ) Efremov, Anatoli Vasilievich; Schweitzer, Peter Journal of High Energy Physics, Vol. 2003, Issue 08 https://doi.org/10.1088/1126-6708/2003/08/006	journal	August 2003
Generalized parton correlation functions for a spin-1/2 hadron Meißner, Stephan; Metz, Andreas; Schlegel, Marc Journal of High Energy Physics, Vol. 2009, Issue 08 https://doi.org/10.1088/1126-6708/2009/08/056	journal	August 2009
Dynamics at Infinite Momentum Weinberg, Steven Physical Review, Vol. 150, Issue 4 https://doi.org/10.1103/PhysRev.150.1313	journal	October 1966
Asymptotic Sum Rules at Infinite Momentum Bjorken, J. D. Physical Review, Vol. 179, Issue 5 https://doi.org/10.1103/PhysRev.179.1547	journal	March 1969
Exclusive processes in perturbative quantum chromodynamics Lepage, G. Peter; Brodsky, Stanley J. Physical Review D, Vol. 22, Issue 9 https://doi.org/10.1103/PhysRevD.22.2157	journal	November 1980
Studies of the transverse spin-dependent structure function g 2 ( x , Q 2 ) Jaffe, R. L.; Ji, Xiangdong Physical Review D, Vol. 43, Issue 3 https://doi.org/10.1103/PhysRevD.43.724	journal	February 1991
Light-front quantization of the sine-Gordon model Burkardt, Matthias Physical Review D, Vol. 47, Issue 10 https://doi.org/10.1103/PhysRevD.47.4628	journal	May 1993
Deeply virtual Compton scattering Ji, Xiangdong Physical Review D, Vol. 55, Issue 11 https://doi.org/10.1103/PhysRevD.55.7114	journal	June 1997
Proof of factorization for deeply virtual Compton scattering in QCD Collins, John C.; Freund, Andreas Physical Review D, Vol. 59, Issue 7 https://doi.org/10.1103/PhysRevD.59.074009	journal	February 1999
Gauge invariance of the deeply virtual Compton scattering amplitude Anikin, I. V.; Pire, B.; Teryaev, O. V. Physical Review D, Vol. 62, Issue 7 https://doi.org/10.1103/PhysRevD.62.071501	journal	August 2000
Impact parameter dependent parton distributions and off-forward parton distributions for ζ→0 Burkardt, Matthias Physical Review D, Vol. 62, Issue 7 https://doi.org/10.1103/PhysRevD.62.071503	journal	September 2000
Deeply virtual Compton scattering amplitude at the tree level: Transversality, twist-3, and factorization Radyushkin, A. V.; Weiss, C. Physical Review D, Vol. 63, Issue 11 https://doi.org/10.1103/PhysRevD.63.114012	journal	April 2001
Deeply virtual Compton scattering on the nucleon: Study of the twist-3 effects Kivel, N.; Polyakov, M. V.; Vanderhaeghen, M. Physical Review D, Vol. 63, Issue 11 https://doi.org/10.1103/PhysRevD.63.114014	journal	May 2001
Twist-three analysis of photon electroproduction off the pion Belitsky, A. V.; Müller, D.; Kirchner, A. Physical Review D, Vol. 64, Issue 11 https://doi.org/10.1103/PhysRevD.64.116002	journal	November 2001
Erratum: Impact parameter dependent parton distributions and off-forward parton distributions for ζ → 0 [Phys. Rev. D 62 , 071503(R) (2000)] Burkardt, Matthias Physical Review D, Vol. 66, Issue 11 https://doi.org/10.1103/PhysRevD.66.119903	journal	December 2002
Chirally-odd twist-3 distribution function e a ( x ) in the chiral quark-soliton model Schweitzer, P. Physical Review D, Vol. 67, Issue 11 https://doi.org/10.1103/PhysRevD.67.114010	journal	June 2003
Nonperturbative origin of the delta-function singularity in the chirally odd twist-3 distribution function e ( x ) Wakamatsu, M.; Ohnishi, Y. Physical Review D, Vol. 67, Issue 11 https://doi.org/10.1103/PhysRevD.67.114011	journal	June 2003
Detailed QCD analysis of twist-3 effects in deeply virtual Compton scattering observables Freund, A. Physical Review D, Vol. 68, Issue 9 https://doi.org/10.1103/PhysRevD.68.096006	journal	November 2003
πN sigma term and chiral-odd twist-3 distribution function e(x) of the nucleon in the chiral quark soliton model Ohnishi, Y.; Wakamatsu, M. Physical Review D, Vol. 69, Issue 11 https://doi.org/10.1103/PhysRevD.69.114002	journal	June 2004
Quantum Field Theories in the Infinite-Momentum Frame. IV. Scattering Matrix of Vector and Dirac Fields and Perturbation Theory Yan, Tung-Mow Physical Review D, Vol. 7, Issue 6 https://doi.org/10.1103/PhysRevD.7.1780	journal	March 1973
Transverse force on quarks in deep-inelastic scattering Burkardt, Matthias Physical Review D, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevD.88.114502	journal	December 2013
One-loop matching for parton distributions: Nonsinglet case Xiong, Xiaonu; Ji, Xiangdong; Zhang, Jian-Hui Physical Review D, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevD.90.014051	journal	July 2014
Matching the quasiparton distribution in a momentum subtraction scheme Stewart, Iain W.; Zhao, Yong Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevD.97.054512	journal	March 2018
Twist-3 generalized parton distributions in deeply-virtual Compton scattering Aslan, Fatma; Burkardt, Matthias; Lorcé, Cédric Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevD.98.014038	journal	July 2018
Factorization theorem relating Euclidean and light-cone parton distributions Izubuchi, Taku; Ji, Xiangdong; Jin, Luchang Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.056004	journal	September 2018
Parton Physics on a Euclidean Lattice Ji, Xiangdong Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/PhysRevLett.110.262002	journal	June 2013
Gauge-Invariant Decomposition of Nucleon Spin Ji, Xiangdong Physical Review Letters, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevLett.78.610	journal	January 1997
Generalized parton distributions of the pion in a Bethe-Salpeter approach Noguera, S.; Theußl, L.; Vento, V. The European Physical Journal A, Vol. 20, Issue 3 https://doi.org/10.1140/epja/i2003-10174-3	journal	June 2004
Single-spin asymmetry parameter from deeply virtual Compton scattering of hadrons up to twist-3 accuracy: I. Pion case Anikin, I. V.; Binosi, D.; Medrano, R. The European Physical Journal A, Vol. 14, Issue 1 https://doi.org/10.1140/epja/iepja1332	journal	May 2002
Generalized parton distributions in impact parameter space Diehl, M. The European Physical Journal C, Vol. 31, Issue 2 https://doi.org/10.1140/epjc/s2003-01356-4	journal	November 2003
Genuine twist-3 contributions to the generalized parton distributionsfrom instantons Kiptily, D. V.; Polyakov, M. V. The European Physical Journal C, Vol. 37, Issue 1 https://doi.org/10.1140/epjc/s2004-01957-3	journal	September 2004
Perspectives on Higgs Physics II Kane, Gordon L. Advanced Series on Directions in High Energy Physics https://doi.org/10.1142/ASDHEP	book	November 1997
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

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