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Title: 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 m π = 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:
 [1];  [2];  [2];  [3];  [2]
  1. New Mexico State Univ., Las Cruces, NM (United States)
  2. Univ. of Regensburg, Regensburg (Germany)
  3. 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); Univ. 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) (SC-26); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). 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. doi: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. doi: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 = {2016},
month = {3}
}

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