Lattice QCD study of the Boer-Mulders effect in a pion
Abstract
The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentumdependent parton distribution functions (TMDs). Our work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. The primary goal is to gain insight into the behavior of TMDs as a function of a Collins-Soper evolution parameter, $$\hat{ζ}$$, which quantifies the rapidity difference between the hadron momentum and a vector describing the trajectory of the struck quark, e.g., in a semiinclusive deep-inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass mπ = 518 MeV, utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. Aided by the lower mass of the pion, compared to the nucleon studied previously, the present investigation of pion TMD observables constitutes an important step towards the quantitative study of the physically important regime of large relative rapidity where the dependence on $$\hat{ζ}$$ appears to approach a limit. Even though matching to perturbative evolution equations in $$\hat{ζ}$$ is not yet available, extrapolations based on Ansätze containing inverse powers of $$\hat{ζ}$$ yield stable results with an uncertainty as low as 20%, and both upper and lower bounds for the asymptotics are obtained. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is indicated.
- Authors:
-
- New Mexico State Univ., Las Cruces, NM (United States)
- Univ. of Regensburg, Regensburg (Germany)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); New Mexico State Univ., Las Cruces, NM (United States); University of California, Berkeley, CA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division; USDOE Office of Science (SC), National Energy Research Scientific Computing Center (NERSC)
- OSTI Identifier:
- 1505597
- Alternate Identifier(s):
- OSTI ID: 1239861
- Grant/Contract Number:
- FG02-94ER40818; AC02-05CH11231; FG02-96ER40965; AC05-06OR23177
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Engelhardt, M., Hägler, P., Musch, B., Negele, J., and Schäfer, A. Lattice QCD study of the Boer-Mulders effect in a pion. United States: N. p., 2016.
Web. doi:10.1103/physrevd.93.054501.
Engelhardt, M., Hägler, P., Musch, B., Negele, J., & Schäfer, A. Lattice QCD study of the Boer-Mulders effect in a pion. United States. https://doi.org/10.1103/physrevd.93.054501
Engelhardt, M., Hägler, P., Musch, B., Negele, J., and Schäfer, A. Tue .
"Lattice QCD study of the Boer-Mulders effect in a pion". United States. https://doi.org/10.1103/physrevd.93.054501. https://www.osti.gov/servlets/purl/1505597.
@article{osti_1505597,
title = {Lattice QCD study of the Boer-Mulders effect in a pion},
author = {Engelhardt, M. and Hägler, P. and Musch, B. and Negele, J. and Schäfer, A.},
abstractNote = {The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentumdependent parton distribution functions (TMDs). Our work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. The primary goal is to gain insight into the behavior of TMDs as a function of a Collins-Soper evolution parameter, $\hat{ζ}$, which quantifies the rapidity difference between the hadron momentum and a vector describing the trajectory of the struck quark, e.g., in a semiinclusive deep-inelastic scattering (SIDIS) process. The lattice calculation, performed at the pion mass mπ = 518 MeV, utilizes a definition of TMDs via hadronic matrix elements of a quark bilocal operator with a staple-shaped gauge connection; in this context, the evolution parameter is related to the staple direction. By parametrizing the aforementioned matrix elements in terms of invariant amplitudes, the problem can be cast in a Lorentz frame suited for the lattice calculation. Aided by the lower mass of the pion, compared to the nucleon studied previously, the present investigation of pion TMD observables constitutes an important step towards the quantitative study of the physically important regime of large relative rapidity where the dependence on $\hat{ζ}$ appears to approach a limit. Even though matching to perturbative evolution equations in $\hat{ζ}$ is not yet available, extrapolations based on Ansätze containing inverse powers of $\hat{ζ}$ yield stable results with an uncertainty as low as 20%, and both upper and lower bounds for the asymptotics are obtained. In passing, the similarity between the Boer-Mulders effects extracted in the pion and the nucleon is indicated.},
doi = {10.1103/physrevd.93.054501},
journal = {Physical Review D},
number = 5,
volume = 93,
place = {United States},
year = {Tue Mar 01 00:00:00 EST 2016},
month = {Tue Mar 01 00:00:00 EST 2016}
}
Web of Science
Works referenced in this record:
Exclusive processes in position space and the pion distribution amplitude
journal, May 2008
- Braun, V. M.; Müller, D.
- The European Physical Journal C, Vol. 55, Issue 3
Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering
journal, April 2008
- Collins, J. C.; Rogers, T. C.; Staśto, A. M.
- Physical Review D, Vol. 77, Issue 8
The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
journal, February 1996
- Mulders, P. J.; Tangerman, R. D.
- Nuclear Physics B, Vol. 461, Issue 1-2
Scalar pion form factor in two-flavor lattice QCD
journal, May 2014
- Gülpers, Vera; von Hippel, Georg; Wittig, Hartmut
- Physical Review D, Vol. 89, Issue 9
Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering
journal, May 2002
- Collins, John C.
- Physics Letters B, Vol. 536, Issue 1-2
QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum
journal, February 2005
- Ji, Xiangdong; Ma, Jian-Ping; Yuan, Feng
- Physical Review D, Vol. 71, Issue 3
Parameterization of the quark–quark correlator of a spin-<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> hadron
journal, July 2005
- Goeke, K.; Metz, A.; Schlegel, M.
- Physics Letters B, Vol. 618, Issue 1-4
Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering
journal, October 2011
- Boer, D.; Gamberg, L.; Musch, B. U.
- Journal of High Energy Physics, Vol. 2011, Issue 10
Exploring quark transverse momentum distributions with lattice QCD
journal, May 2011
- Musch, B. U.; Hägler, Ph.; Negele, J. W.
- Physical Review D, Vol. 83, Issue 9
QCD evolution of the Sivers function
journal, February 2012
- Aybat, S. M.; Collins, J. C.; Qiu, J. W.
- Physical Review D, Vol. 85, Issue 3
Transverse single-spin asymmetry and cross section for and mesons at large Feynman in collisions at
journal, September 2012
- Adamczyk, L.; Agakishiev, G.; Aggarwal, M. M.
- Physical Review D, Vol. 86, Issue 5
Measurement of Single- and Double-Spin Asymmetries in Deep Inelastic Pion Electroproduction with a Longitudinally Polarized Target
journal, December 2010
- Avakian, H.; Bosted, P.; Burkert, V. D.
- Physical Review Letters, Vol. 105, Issue 26
Light hadrons with improved staggered quarks: Approaching the continuum limit
journal, November 2004
- Aubin, C.; Bernard, C.; DeTar, C.
- Physical Review D, Vol. 70, Issue 9
Parton Physics on a Euclidean Lattice
journal, June 2013
- Ji, Xiangdong
- Physical Review Letters, Vol. 110, Issue 26
Lattice calculation of the pion form factor with Ginsparg-Wilson-type fermions
journal, February 2006
- Capitani, Stefano; Gattringer, Christof; Lang, C. B.
- Physical Review D, Vol. 73, Issue 3
Single Spin Asymmetries in Charged Pion Production from Semi-Inclusive Deep Inelastic Scattering on a Transversely Polarized Target at
journal, August 2011
- Qian, X.; Allada, K.; Dutta, C.
- Physical Review Letters, Vol. 107, Issue 7
The Boer-Mulders Transverse Momentum Distribution in the Pion and its Evolution in Lattice QCD
journal, January 2015
- Engelhardt, M.; Musch, B.; Hägler, P.
- International Journal of Modern Physics: Conference Series, Vol. 37
Pion form factors from two-flavor lattice QCD with exact chiral symmetry
journal, August 2009
- Aoki, S.; Chiu, T. W.; Fukaya, H.
- Physical Review D, Vol. 80, Issue 3
Soft factor subtraction and transverse momentum dependent parton distributions on the lattice
journal, April 2015
- Ji, Xiangdong; Sun, Peng; Xiong, Xiaonu
- Physical Review D, Vol. 91, Issue 7
Spin Structure of the Pion
journal, September 2008
- Brömmel, D.; Diehl, M.; Göckeler, M.
- Physical Review Letters, Vol. 101, Issue 12
Intrinsic quark transverse momentum in the nucleon from lattice QCD
journal, December 2009
- Hägler, Ph.; Musch, B. U.; Negele, J. W.
- EPL (Europhysics Letters), Vol. 88, Issue 6
Equality of two definitions for transverse momentum dependent parton distribution functions
journal, February 2013
- Collins, John; Rogers, Ted
- Physical Review D, Vol. 87, Issue 3
Lattice calculation of parton distributions
journal, July 2015
- Alexandrou, Constantia; Cichy, Krzysztof; Drach, Vincent
- Physical Review D, Vol. 92, Issue 1
Observation of the Naive- -Odd Sivers Effect in Deep-Inelastic Scattering
journal, October 2009
- Airapetian, A.; Akopov, N.; Akopov, Z.
- Physical Review Letters, Vol. 103, Issue 15
Lattice QCD Studies of Transverse Momentum-Dependent Parton Distribution Functions
journal, April 2015
- Engelhardt, M.; Musch, B.; Hägler, P.
- Few-Body Systems, Vol. 56, Issue 6-9
Back-to-back jets in QCD
journal, December 1981
- Collins, John C.; Soper, Davison E.
- Nuclear Physics B, Vol. 193, Issue 2
Intrinsic transverse momentum and the polarized Drell-Yan process
journal, April 1995
- Tangerman, R. D.; Mulders, P. J.
- Physical Review D, Vol. 51, Issue 7
Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons
journal, January 2014
- Airapetian, A.; Akopov, N.; Akopov, Z.
- Physics Letters B, Vol. 728
Are all Boer–Mulders functions alike?
journal, January 2008
- Burkardt, Matthias; Hannafious, Brian
- Physics Letters B, Vol. 658, Issue 4
The pion form factor from lattice QCD with two dynamical flavours
journal, May 2007
- Brömmel, D.; Diehl, M.; Göckeler, M.
- The European Physical Journal C, Vol. 51, Issue 2
Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006
- Detmold, William; Lin, C. -J. David
- Physical Review D, Vol. 73, Issue 1
Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone
journal, July 2012
- Echevarría, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio
- Journal of High Energy Physics, Vol. 2012, Issue 7
Sivers and Boer-Mulders observables from lattice QCD
journal, May 2012
- Musch, B. U.; Hägler, Ph.; Engelhardt, M.
- Physical Review D, Vol. 85, Issue 9
Studies of transverse momentum dependent parton distributions and Bessel weighting
journal, March 2015
- Aghasyan, M.; Avakian, H.; De Sanctis, E.
- Journal of High Energy Physics, Vol. 2015, Issue 3
Measurement of transverse-single-spin asymmetries for midrapidity and forward-rapidity production of hadrons in polarized collisions at and 62.4 GeV
journal, July 2014
- Adare, A.; Afanasiev, S.; Aidala, C.
- Physical Review D, Vol. 90, Issue 1
Foundations of Perturbative QCD
book, May 2011
- Collins, John
- Cambridge Monographs on Particle Physics, Nuclear Physics, and Cosmology
Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution
journal, June 2011
- Aybat, S. Mert; Rogers, Ted C.
- Physical Review D, Vol. 83, Issue 11
Time-reversal odd distribution functions in leptoproduction
journal, May 1998
- Boer, D.; Mulders, P. J.
- Physical Review D, Vol. 57, Issue 9
Lattice computations of the pion form factor
journal, September 2005
- Bonnet, Frederic D. R.; Edwards, Robert G.; Fleming, George T.
- Physical Review D, Vol. 72, Issue 5
Pseudoscalar and vector meson form factors from lattice QCD
journal, May 2007
- Hedditch, J. N.; Kamleh, W.; Lasscock, B. G.
- Physical Review D, Vol. 75, Issue 9
Nucleon structure from mixed action calculations using flavors of asqtad sea and domain wall valence fermions
journal, November 2010
- Bratt, J. D.; Edwards, R. G.; Engelhardt, M.
- Physical Review D, Vol. 82, Issue 9
Collins and Sivers asymmetries for pions and kaons in muon–deuteron DIS
journal, March 2009
- Alekseev, M.; Alexakhin, V. Yu.; Alexandrov, Yu.
- Physics Letters B, Vol. 673, Issue 2
Electromagnetic form factor of the pion from twisted-mass lattice QCD at
journal, April 2009
- Frezzotti, R.; Lubicz, V.; Simula, S.
- Physical Review D, Vol. 79, Issue 7
Flavor structure of the nucleon sea from lattice QCD
journal, March 2015
- Lin, Huey-Wen; Chen, Jiunn-Wei; Cohen, Saul D.
- Physical Review D, Vol. 91, Issue 5
Nucleon generalized parton distributions from full lattice QCD
journal, May 2008
- Hägler, Ph.; Schroers, W.; Bratt, J.
- Physical Review D, Vol. 77, Issue 9
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
journal, August 2008
- Bacchetta, Alessandro; Boer, Daniël; Diehl, Markus
- Journal of High Energy Physics, Vol. 2008, Issue 08
Production of dimuons from high-energy polarized proton-proton collisions
journal, May 1979
- Ralston, John P.; Soper, Davidson E.
- Nuclear Physics B, Vol. 152, Issue 1
The Electromagnetic form Factor of the Pion: Results from the Lattice
journal, December 2013
- Brandt, Bastian B.
- International Journal of Modern Physics E, Vol. 22, Issue 12
The Chroma Software System for Lattice QCD
journal, March 2005
- Edwards, Robert G.; Joó, Bálint
- Nuclear Physics B - Proceedings Supplements, Vol. 140
A high-statistics measurement of transverse spin effects in dihadron production from muon–proton semi-inclusive deep-inelastic scattering
journal, September 2014
- Adolph, C.; Akhunzyanov, R.; Alekseev, M. G.
- Physics Letters B, Vol. 736
Exclusive processes in position space and the pion distribution amplitude
text, January 2008
- Braun, Vladimir M.; Müller, Dieter
- Universität Regensburg
Studies of Transverse Momentum Dependent Parton Distributions and Bessel Weighting
text, January 2015
- Aghasyan, M.; Avakian, H.; De Sanctis, E.
- Universität Regensburg
Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons
text, January 2014
- The Hermes, Collaboration; Schäfer, Andreas
- Universität Regensburg
Are all Boer-Mulders functions alike?
text, January 2007
- Burkardt, Matthias; Hannafious, Brian
- arXiv
Nucleon Generalized Parton Distributions from Full Lattice QCD
text, January 2007
- Hägler, Ph.; Schroers, W.; Bratt, J.
- arXiv
Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
text, January 2007
- Collins, J. C.; Rogers, T. C.; Staśto, A. M.
- arXiv
Collins and Sivers asymmetries for pions and kaons in muon-deuteron DIS
text, January 2008
- Collaboration, The COMPASS; Alekseev, M.; Alexakhin, V. Yu.
- arXiv
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
text, January 2008
- Bacchetta, Alessandro; Boer, Daniel; Diehl, Markus
- arXiv
Observation of the Naive-T-odd Sivers Effect in Deep-Inelastic Scattering
text, January 2009
- Collaboration, The HERMES
- arXiv
Exploring quark transverse momentum distributions with lattice QCD
text, January 2010
- Musch, Bernhard U.; Hägler, Philipp; Negele, John W.
- arXiv
Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
text, January 2011
- Boer, Daniel; Gamberg, Leonard; Musch, Bernhard
- arXiv
Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
text, January 2011
- Echevarria, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio
- arXiv
Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons
preprint, January 2013
- Collaboration, The HERMES; Airapetian, A.; Akopov, N.
- arXiv
The electromagnetic form factor of the pion: Results from the lattice
text, January 2013
- Brandt, Bastian B.
- arXiv
A high-statistics measurement of transverse spin effects in dihadron production from muon-proton semi-inclusive deep-inelastic scattering
text, January 2014
- Adolph, C.; Akhunzyanov, R.; Alekseev, M. G.
- arXiv
Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice
text, January 2014
- Ji, Xiangdong; Sun, Peng; Xiong, Xiaonu
- arXiv
Sivers Asymmetry with QCD Evolution
text, January 2014
- Echevarria, Miguel G.; Idilbi, Ahmad; Kang, Zhong-Bo
- arXiv
Deep-inelastic scattering and the operator product expansion in lattice QCD
text, January 2005
- Detmold, William; Lin, C. -J. David
- arXiv
The pion form factor from lattice QCD with two dynamical flavours
text, January 2006
- Brömmel, D.; Diehl, M.; Göckeler, M.
- arXiv
Pseudoscalar and vector meson form factors from lattice QCD
text, January 2007
- Hedditch, J. N.; Kamleh, W.; Lasscock, B. G.
- arXiv
QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
text, January 2004
- Ji, Xiangdong; Ma, Jian-ping; Yuan, Feng
- arXiv
Time-reversal odd distribution functions in leptoproduction
text, January 1997
- Boer, D.; Mulders, P. J.
- arXiv
Works referencing / citing this record:
Predicting the light-front holographic TMDs of the pion
journal, September 2019
- Ahmady, Mohammad; Mondal, Chandan; Sandapen, Ruben
- Physical Review D, Vol. 100, Issue 5
Where do we stand with a 3-D picture of the proton?
journal, June 2016
- Bacchetta, Alessandro
- The European Physical Journal A, Vol. 52, Issue 6
Hadrons and nuclei
journal, November 2019
- Detmold, William; Edwards, Robert G.; Dudek, Jozef J.
- The European Physical Journal A, Vol. 55, Issue 11
Pion nucleus Drell–Yan process and parton transverse momentum in the pion
journal, August 2018
- Ceccopieri, Federico Alberto; Courtoy, Aurore; Noguera, Santiago
- The European Physical Journal C, Vol. 78, Issue 8
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results
journal, June 2019
- Cichy, Krzysztof; Constantinou, Martha
- Advances in High Energy Physics, Vol. 2019
Nonperturbative Renormalization of Nonlocal Quark Bilinears for Parton Quasidistribution Functions on the Lattice Using an Auxiliary Field
text, January 2018
- Green, Jeremy; Jansen, Karl; Steffens, Fernanda
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Nucleon transverse momentum-dependent parton distributions in lattice QCD: Renormalization patterns and discretization effects
text, January 2017
- Yoon, Boram; Engelhardt, Michael; Gupta, Rajan
- Universität Regensburg
Novel quark smearing for hadrons with high momenta in lattice QCD
text, January 2016
- Bali, Gunnar S.; Lang, Bernhard; Musch, Bernhard U.
- arXiv
Pion nucleus Drell-Yan process and parton transverse momentum in the pion
text, January 2018
- Ceccopieri, Federico Alberto; Courtoy, Aurore; Noguera, Santiago
- arXiv
Renormalization of Wilson-line operators in the presence of nonzero quark masses
text, January 2018
- Spanoudes, G.; Panagopoulos, H.
- arXiv
Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD
text, January 2018
- Ebert, Markus A.; Stewart, Iain W.; Zhao, Yong
- arXiv
A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
text, January 2018
- Cichy, Krzysztof; Constantinou, Martha
- arXiv
Predicting the light-front holographic TMDs of the pion
text, January 2019
- Ahmady, Mohammad; Mondal, Chandan; Sandapen, Ruben
- arXiv