Abstract
An explicit evaluation of the two pion transverse momentum dependent parton distributions at leading twist is presented, in the framework of the Nambu-Jona Lasinio model with Pauli-Villars regularization. The transverse momentum dependence of the obtained distributions is generated solely by the dynamics of the model. Using these results, the so called generalized Boer-Mulders shift is studied and compared with recent lattice data. The obtained agreement is very encouraging, in particular because no additional parameter has been introduced. A more conclusive comparison would require a precise knowledge of the QCD evolution of the transverse momentum dependent parton distributions under scrutiny.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].
A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P.J. Mulders and M. Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum, JHEP 02 (2007) 093 [hep-ph/0611265] [INSPIRE].
V. Barone, F. Bradamante and A. Martin, Transverse-spin and transverse-momentum effects in high-energy processes, Prog. Part. Nucl. Phys. 65 (2010) 267 [arXiv:1011.0909] [INSPIRE].
R. Angeles-Martinez et al., Transverse momentum dependent (TMD) parton distribution functions: status and prospects, arXiv:1507.05267 [INSPIRE].
J.-C. Peng and J.-W. Qiu, Novel phenomenology of parton distributions from the Drell-Yan process, Prog. Part. Nucl. Phys. 76 (2014) 43 [arXiv:1401.0934] [INSPIRE].
D. Boer and P.J. Mulders, Time reversal odd distribution functions in leptoproduction, Phys. Rev. D 57 (1998) 5780 [hep-ph/9711485] [INSPIRE].
D. Boer, Investigating the origins of transverse spin asymmetries at RHIC, Phys. Rev. D 60 (1999) 014012 [hep-ph/9902255] [INSPIRE].
M. Engelhardt, P. Hägler, B. Musch, J. Negele and A. Schäfer, Lattice QCD study of the Boer-Mulders effect in a pion, arXiv:1506.07826 [INSPIRE].
M. Engelhardt, B. Musch, P. Hägler, J. Negele and A. Schäfer, Lattice study of the Boer-Mulders transverse momentum distribution in the pion, PoS LATTICE2013 (2014) 284 [arXiv:1310.8335] [INSPIRE].
B.U. Musch, P. Hägler, M. Engelhardt, J.W. Negele and A. Schäfer, Sivers and Boer-Mulders observables from lattice QCD, Phys. Rev. D 85 (2012) 094510 [arXiv:1111.4249] [INSPIRE].
Z. Lu and B.-Q. Ma, Non-zero transversity distribution of the pion in a quark-spectator-antiquark model, Phys. Rev. D 70 (2004) 094044 [hep-ph/0411043] [INSPIRE].
M. Burkardt and B. Hannafious, Are all Boer-Mulders functions alike?, Phys. Lett. B 658 (2008) 130 [arXiv:0705.1573] [INSPIRE].
L. Gamberg and M. Schlegel, Final state interactions and the transverse structure of the pion using non-perturbative eikonal methods, Phys. Lett. B 685 (2010) 95 [arXiv:0911.1964] [INSPIRE].
Z. Lu, B.-Q. Ma and J. Zhu, Boer-Mulders function of the pion in the MIT bag model, Phys. Rev. D 86 (2012) 094023 [arXiv:1211.1745] [INSPIRE].
T. Frederico, E. Pace, B. Pasquini and G. Salmè, Pion Generalized Parton Distributions with covariant and Light-front constituent quark models, Phys. Rev. D 80 (2009) 054021 [arXiv:0907.5566] [INSPIRE].
B. Pasquini and P. Schweitzer, Pion transverse momentum dependent parton distributions in a light-front constituent approach and the Boer-Mulders effect in the pion-induced Drell-Yan process, Phys. Rev. D 90 (2014) 014050 [arXiv:1406.2056] [INSPIRE].
S.P. Klevansky, The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Mod. Phys. 64 (1992) 649 [INSPIRE].
R.M. Davidson and E. Ruiz Arriola, Structure functions of pseudoscalar mesons in the SU(3) NJLS model, Phys. Lett. B 348 (1995) 163 [INSPIRE].
R.M. Davidson and E. Ruiz Arriola, Parton distributions functions of pion, kaon and eta pseudoscalar mesons in the NJLS model, Acta Phys. Polon. B 33 (2002) 1791 [hep-ph/0110291] [INSPIRE].
L. Theussl, S. Noguera and V. Vento, Generalized parton distributions of the pion in a Bethe-Salpeter approach, Eur. Phys. J. A 20 (2004) 483 [nucl-th/0211036] [INSPIRE].
E. Ruiz Arriola and W. Broniowski, Pion light cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model, Phys. Rev. D 66 (2002) 094016 [hep-ph/0207266] [INSPIRE].
A. Courtoy and S. Noguera, The Pion-photon transition distribution amplitudes in the Nambu-Jona Lasinio model, Phys. Rev. D 76 (2007) 094026 [arXiv:0707.3366] [INSPIRE].
A. Courtoy, Generalized Parton Distributions of Pions. Spin Structure of Hadrons, PhD. Thesis, Valencia University, Spain (2009) [arXiv:1010.2974] [INSPIRE].
S. Noguera and V. Vento, The pion transition form factor and the pion distribution amplitude, Eur. Phys. J. A 46 (2010) 197 [arXiv:1001.3075] [INSPIRE].
S. Noguera and S. Scopetta, The eta-photon transition form factor, Phys. Rev. D 85 (2012) 054004 [arXiv:1110.6402] [INSPIRE].
S. Noguera and V. Vento, Model analysis of the world data on the pion transition form factor, Eur. Phys. J. A 48 (2012) 143 [arXiv:1205.4598] [INSPIRE].
S.J. Brodsky, D.S. Hwang and I. Schmidt, Final state interactions and single spin asymmetries in semiinclusive deep inelastic scattering, Phys. Lett. B 530 (2002) 99 [hep-ph/0201296] [INSPIRE].
A. Courtoy, F. Fratini, S. Scopetta and V. Vento, A Quark model analysis of the Sivers function, Phys. Rev. D 78 (2008) 034002 [arXiv:0801.4347] [INSPIRE].
A. Courtoy, S. Scopetta and V. Vento, Model calculations of the Sivers function satisfying the Burkardt Sum Rule, Phys. Rev. D 79 (2009) 074001 [arXiv:0811.1191] [INSPIRE].
A. Courtoy, S. Scopetta and V. Vento, Analyzing the Boer-Mulders function within different quark models, Phys. Rev. D 80 (2009) 074032 [arXiv:0909.1404] [INSPIRE].
B. Pasquini and F. Yuan, Sivers and Boer-Mulders functions in Light-Cone Quark Models, Phys. Rev. D 81 (2010) 114013 [arXiv:1001.5398] [INSPIRE].
J.D. Bjorken and S. Drell, Relativistic Quantum Mechanics, McGraw-Hill, New York U.S.A. (1964).
W. Broniowski, E. Ruiz Arriola and K. Golec-Biernat, Generalized parton distributions of the pion in chiral quark models and their QCD evolution, Phys. Rev. D 77 (2008) 034023 [arXiv:0712.1012] [INSPIRE].
A. Courtoy and S. Noguera, Enhancement effects in exclusive ππ and ρπ production in γ∗γ scattering, Phys. Lett. B 675 (2009) 38 [arXiv:0811.0550] [INSPIRE].
J.S. Conway et al., Experimental Study of Muon Pairs Produced by 252 GeV Pions on Tungsten, Phys. Rev. D 39 (1989) 92 [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
F. Schlumpf, Charge form-factors of pseudoscalar mesons, Phys. Rev. D 50 (1994) 6895 [hep-ph/9406267] [INSPIRE].
P.L. Chung, F. Coester and W.N. Polyzou, Charge Form-Factors of Quark Model Pions, Phys. Lett. B 205 (1988) 545 [INSPIRE].
B.U. Musch, P. Hagler, J.W. Negele and A. Schafer, Exploring quark transverse momentum distributions with lattice QCD, Phys. Rev. D 83 (2011) 094507 [arXiv:1011.1213] [INSPIRE].
T.C. Rogers, An Overview of Transverse Momentum Dependent Factorization and Evolution, arXiv:1509.04766 [INSPIRE].
J. Collins and T. Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91 (2015) 074020 [arXiv:1412.3820] [INSPIRE].
V. Barone, A. Drago and P.G. Ratcliffe, Transverse polarisation of quarks in hadrons, Phys. Rept. 359 (2002) 1 [hep-ph/0104283] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.01061
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Noguera, S., Scopetta, S. Pion transverse momentum dependent parton distributions in the Nambu and Jona-Lasinio model. J. High Energ. Phys. 2015, 102 (2015). https://doi.org/10.1007/JHEP11(2015)102
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)102