Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations

Ninomiya, Yu; Bentz, Wolfgang; Cloet, Ian C.

doi:10.1103/physrevc.96.045206

Title: Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations

Journal Article · Tue Oct 24 00:00:00 EDT 2017 · Physical Review C

DOI:https://doi.org/10.1103/physrevc.96.045206· OSTI ID:1430705

Ninomiya, Yu ^[1]; Bentz, Wolfgang ^[2]; Cloet, Ian C. ^[3]

Tokai Univ., Hiratsuka (Japan). Dept. of Physics. School of Science
Tokai Univ., Hiratsuka (Japan). Dept. of Physics. School of Science; RIKEN, Wako (Japan). Radiation Lab. Nishina Center
Argonne National Lab. (ANL), Argonne, IL (United States). Physics Division

In this paper, we present a covariant formulation and model calculations of the leading-twist time-reversal even transverse-momentum-dependent quark distribution functions (TMDs) for a spin-one target. Emphasis is placed on a description of these three-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even ρ meson TMDs in the framework provided by the Nambu–Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cutoff in the proper-time regularization scheme. In particular, the behaviors of the three-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Our results do not exhibit the familiar Gaussian behavior in the transverse momentum, and other results of interest include the finding that the tensor polarized TMDs—associated with spin-one hadrons—are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator γ⁺γ_Tγ₅ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the ρ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. Finally, a qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to existing experimental and theoretical results for the two-nucleon (deuteron) bound state.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States); Tokai Univ., Hiratsuka (Japan)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); ANL Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1430705

Alternate ID(s):: OSTI ID: 1402531

Journal Information:: Physical Review C, Vol. 96, Issue 4; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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References (59)

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II Nambu, Y.; Jona-Lasinio, G. Physical Review, Vol. 124, Issue 1 https://doi.org/10.1103/PhysRev.124.246	journal	October 1961
QCD evolution of the Sivers asymmetry Echevarria, Miguel G.; Idilbi, Ahmad; Kang, Zhong-Bo Physical Review D, Vol. 89, Issue 7 https://doi.org/10.1103/PhysRevD.89.074013	journal	April 2014
Deep inelastic scattering from arbitrary spin targets Jaffe, R. L.; Manohar, Aneesh Nuclear Physics B, Vol. 321, Issue 2 https://doi.org/10.1016/0550-3213(89)90347-7	journal	July 1989
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
Tensor-polarized structure function $b_{1}$ in the standard convolution description of the deuteron Cosyn, W.; Dong, Yu-Bing; Kumano, S. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074036	journal	April 2017
NJL-jet model for quark fragmentation functions Ito, T.; Bentz, W.; Cloët, I. C. Physical Review D, Vol. 80, Issue 7 https://doi.org/10.1103/PhysRevD.80.074008	journal	October 2009
Extended NJL model for light and heavy mesons without thresholds Ebert, Dietmar; Feldmann, Thorsten; Reinhardt, Hugo Physics Letters B, Vol. 388, Issue 1 https://doi.org/10.1016/0370-2693(96)01158-6	journal	November 1996
Numerical solution of Q2 evolution equations in a brute-force method Miyama, M.; Kumano, S. Computer Physics Communications, Vol. 94, Issue 2-3 https://doi.org/10.1016/0010-4655(96)00013-6	journal	April 1996
Spin-Dependent Structure Functions in Nuclear Matter and the Polarized EMC Effect Cloët, I. C.; Bentz, W.; Thomas, A. W. Physical Review Letters, Vol. 95, Issue 5 https://doi.org/10.1103/PhysRevLett.95.052302	journal	July 2005
Dressed quark mass dependence of pion and kaon form factors Ninomiya, Y.; Bentz, W.; Cloët, I. C. Physical Review C, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevC.91.025202	journal	February 2015
Convenient parametrization for deep inelastic structure functions of the deuteron Khan, Hafsa; Hoodbhoy, Pervez Physical Review C, Vol. 44, Issue 3 https://doi.org/10.1103/PhysRevC.44.1219	journal	September 1991
Tensor-polarized quark and antiquark distribution functions in a spin-one hadron Kumano, S. Physical Review D, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevD.82.017501	journal	July 2010
Quark-jet model for transverse momentum dependent fragmentation functions Bentz, W.; Kotzinian, A.; Matevosyan, H. H. Physical Review D, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevD.94.034004	journal	August 2016
Transverse polarisation of quarks in hadrons Barone, Vincenzo; Drago, Alessandro; Ratcliffe, Philip G. Physics Reports, Vol. 359, Issue 1-2 https://doi.org/10.1016/S0370-1573(01)00051-5	journal	March 2002
Baryon octet electromagnetic form factors in a confining NJL model Carrillo-Serrano, Manuel E.; Bentz, Wolfgang; Cloët, Ian C. Physics Letters B, Vol. 759 https://doi.org/10.1016/j.physletb.2016.05.065	journal	August 2016
Measurement of the Tensor Structure Function $b_{1}$ of the Deuteron Airapetian, A.; Akopov, N.; Akopov, Z. Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevLett.95.242001	journal	December 2005
The Nambu and Jona-Lasinio model: Its implications for Hadrons and Nuclei Vogl, U.; Weise, W. Progress in Particle and Nuclear Physics, Vol. 27 https://doi.org/10.1016/0146-6410(91)90005-9	journal	January 1991
Parton fragmentation functions Metz, A.; Vossen, A. Progress in Particle and Nuclear Physics, Vol. 91 https://doi.org/10.1016/j.ppnp.2016.08.003	journal	November 2016
Non-perturbative QCD effects in q T spectra of Drell-Yan and Z-boson production D’Alesio, Umberto; Echevarria, Miguel G.; Melis, Stefano Journal of High Energy Physics, Vol. 2014, Issue 11 https://doi.org/10.1007/JHEP11(2014)098	journal	November 2014
$π$ and $ρ$ structure functions from lattice QCD Best, C.; Göckeler, M.; Horsley, R. Physical Review D, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevD.56.2743	journal	September 1997
Quark distributions in the nucleon based on a relativistic three-body approach to the Nambu–Jona-Lasinio model Mineo, H.; Bentz, W.; Yazaki, K. Physical Review C, Vol. 60, Issue 6 https://doi.org/10.1103/PhysRevC.60.065201	journal	October 1999
Relativistic calculation of structure functions b1,2(x) of the deuteron Umnikov, A. Yu Physics Letters B, Vol. 391, Issue 1-2 https://doi.org/10.1016/S0370-2693(96)01440-2	journal	January 1997
Diquark confinement in an extended NJL model Hellstern, G.; Alkofer, R.; Reinhardt, H. Nuclear Physics A, Vol. 625, Issue 4 https://doi.org/10.1016/S0375-9474(97)00412-0	journal	November 1997
Chiral-odd and spin-dependent quark fragmentation functions and their applications Ji, Xiangdong Physical Review D, Vol. 49, Issue 1 https://doi.org/10.1103/PhysRevD.49.114	journal	January 1994
Extraction of partonic transverse momentum distributions from semi-inclusive deep-inelastic scattering, Drell-Yan and Z-boson production Bacchetta, Alessandro; Delcarro, Filippo; Pisano, Cristian Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/JHEP06(2017)081	journal	June 2017
Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. II. Parton model Hino, S.; Kumano, S. Physical Review D, Vol. 60, Issue 5 https://doi.org/10.1103/PhysRevD.60.054018	journal	August 1999
Numerical solution of Q2 evolution equation for the transversity distribution ΔTq Hirai, M.; Kumano, S.; Miyama, M. Computer Physics Communications, Vol. 111, Issue 1-3 https://doi.org/10.1016/S0010-4655(98)00028-9	journal	June 1998
Polarization phenomena in hadronic reactions Bourrely, C.; Leader, E.; Soffer, J. Physics Reports, Vol. 59, Issue 2 https://doi.org/10.1016/0370-1573(80)90017-4	journal	March 1980
Sum rule for the spin-dependent structure function $b_{1} (x)$ for spin-one hadrons Close, F. E.; Kumano, S. Physical Review D, Vol. 42, Issue 7 https://doi.org/10.1103/PhysRevD.42.2377	journal	October 1990
Unpolarised transverse momentum dependent distribution and fragmentation functions from SIDIS multiplicities Anselmino, M.; Boglione, M.; Gonzalez H., J. O. Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)005	journal	April 2014
The Deuteron Polarized Tensor Structure Function b ₁ Slifer, K. Journal of Physics: Conference Series, Vol. 543 https://doi.org/10.1088/1742-6596/543/1/012003	journal	October 2014
Novel effects in deep inelastic scattering from spin-one hadrons Hoodbhoy, Pervez; Jaffe, R. L.; Manohar, Aneesh Nuclear Physics B, Vol. 312, Issue 3 https://doi.org/10.1016/0550-3213(89)90572-5	journal	January 1989
Quark distributions in nuclear matter and the EMC effect Mineo, H.; Bentz, W.; Ishii, N. Nuclear Physics A, Vol. 735, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2004.02.011	journal	May 2004
b ₁ and the Angular Momentum Sum Rule in the Deuteron Liuti, S.; Kathuria, K. Journal of Physics: Conference Series, Vol. 543 https://doi.org/10.1088/1742-6596/543/1/012005	journal	October 2014
Deep inelastic leptoproduction of spin-one hadrons Bacchetta, A.; Mulders, P. J. Physical Review D, Vol. 62, Issue 11 https://doi.org/10.1103/PhysRevD.62.114004	journal	October 2000
Positivity bounds on spin-one distribution and fragmentation functions Bacchetta, A.; Mulders, P. J. Physics Letters B, Vol. 518, Issue 1-2 https://doi.org/10.1016/S0370-2693(01)01051-6	journal	October 2001
Electromagnetic structure of the deuteron Gilman, R.; Gross, Franz Journal of Physics G: Nuclear and Particle Physics, Vol. 28, Issue 4 https://doi.org/10.1088/0954-3899/28/4/201	journal	February 2002
Positivity Constraints for Spin-Dependent Parton Distributions Soffer, Jacques Physical Review Letters, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevLett.74.1292	journal	February 1995
Numerical solution of Q2 evolution equations for polarized structure functions Hirai, M.; Kumano, S.; Miyama, M. Computer Physics Communications, Vol. 108, Issue 1 https://doi.org/10.1016/S0010-4655(97)00129-X	journal	January 1998
$ρ$ meson form factors in a confining Nambu–Jona-Lasinio model Carrillo-Serrano, Manuel E.; Bentz, Wolfgang; Cloët, Ian C. Physical Review C, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevC.92.015212	journal	July 2015
The stability of nuclear matter in the Nambu–Jona-Lasinio model Bentz, W.; Thomas, A. W. Nuclear Physics A, Vol. 696, Issue 1-2 https://doi.org/10.1016/S0375-9474(01)01119-8	journal	December 2001
Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Nambu, Y.; Jona-Lasinio, G. Physical Review, Vol. 122, Issue 1 https://doi.org/10.1103/PhysRev.122.345	journal	April 1961
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
Transversity quark distributions in a covariant quark–diquark model Cloët, I. C.; Bentz, W.; Thomas, A. W. Physics Letters B, Vol. 659, Issue 1-2 https://doi.org/10.1016/j.physletb.2007.09.071	journal	January 2008
Pionic and hidden-color, six-quark contributions to the deuteron $b_{1}$ structure function Miller, Gerald A. Physical Review C, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevC.89.045203	journal	April 2014
Light meson form factors at near physical masses Owen, Benjamin J.; Kamleh, Waseem; Leinweber, Derek B. Physical Review D, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevD.91.074503	journal	April 2015
The Nambu—Jona-Lasinio model of quantum chromodynamics Klevansky, S. P. Reviews of Modern Physics, Vol. 64, Issue 3 https://doi.org/10.1103/RevModPhys.64.649	journal	July 1992
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
Simple relativistic model for the $b_{1}$ structure function of the $ρ$ meson Mankiewicz, Lech Physical Review D, Vol. 40, Issue 1 https://doi.org/10.1103/PhysRevD.40.255	journal	July 1989
Role of diquark correlations and the pion cloud in nucleon elastic form factors Cloët, Ian C.; Bentz, Wolfgang; Thomas, Anthony W. Physical Review C, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevC.90.045202	journal	October 2014
Electron Ion Collider: The Next QCD Frontier Accardi, A.; Albacete, J. L.; Anselmino, M. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-00275	text	January 2016
Transversity quark distributions in a covariant quark-diquark model Cloët, I. C.; Bentz, W.; Thomas, A. W. arXiv https://doi.org/10.48550/arxiv.0708.3246	text	January 2007
Rho meson form factors in a confining Nambu--Jona-Lasinio model Carrillo-Serrano, Manuel E.; Bentz, Wolfgang; Cloët, Ian C. arXiv https://doi.org/10.48550/arxiv.1504.08119	text	January 2015
Baryon Octet Electromagnetic Form Factors in a confining NJL model Carrillo-Serrano, Manuel E.; Bentz, Wolfgang; Cloët, Ian C. arXiv https://doi.org/10.48550/arxiv.1603.02741	text	January 2016
Parton Fragmentation Functions Metz, Andreas; Vossen, Anselm arXiv https://doi.org/10.48550/arxiv.1607.02521	text	January 2016
Positivity bounds on spin-one distribution and fragmentation functions Bacchetta, A.; Mulders, P. J. arXiv https://doi.org/10.48550/arxiv.hep-ph/0104176	text	January 2001
Chiral-Odd and Spin-Dependent Quark Fragmentation Functions and their Applications Ji, Xiangdong arXiv https://doi.org/10.48550/arxiv.hep-ph/9307235	text	January 1993
Extended NJL Model for light and heavy mesons without q-qbar thresholds Ebert, D.; Feldmann, T.; Reinhardt, H. arXiv https://doi.org/10.48550/arxiv.hep-ph/9608223	text	January 1996
Quark distributions in nuclear matter and the EMC effect Mineo, H.; Bentz, W.; Ishii, N. arXiv https://doi.org/10.48550/arxiv.nucl-th/0312097	text	January 2003

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