Nucleon transverse momentumdependent parton distributions in lattice QCD: Renormalization patterns and discretization effects
Abstract
Lattice QCD calculations of transverse momentumdependent parton distribution functions (TMDs) in nucleons are presented in this paper, based on the evaluation of nucleon matrix elements of quark bilocal operators with a stapleshaped gauge connection. Both timereversal odd effects, namely, the generalized Sivers and BoerMulders transverse momentum shifts, as well as timereversal even effects, namely, the generalized transversity and one of the generalized wormgear shifts, are studied. Results are obtained on two different n _{f} = 2 + 1 flavor ensembles with approximately matching pion masses but very different discretization schemes: domainwall fermions (DWF) with lattice spacing a = 0.084 fm and pion mass 297 MeV, and Wilsonclover fermions with a = 0.114 fm and pion mass 317 MeV. Comparison of the results on the two ensembles yields insight into the length scales at which lattice discretization errors are small, and into the extent to which the renormalization pattern obeyed by the continuum QCD TMD operator continues to apply in the lattice formulation. For the studied TMD observables, the results are found to be consistent between the two ensembles at sufficiently large separation of the quark fields within the operator, whereas deviations are observed in the local limit and in themore »
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 New Mexico State Univ., Las Cruces, NM (United States). Dept. of Physics
 Deutsches ElektronenSynchrotron (DESY), Zeuthen (Germany)
 Univ. of Regensburg (Germany). Inst. of Theoretical Physics
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
 Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN/BNL Research Center
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); New Mexico State Univ., Las Cruces, NM (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of Regensburg (Germany)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); LANL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); German Research Foundation (DFG)
 OSTI Identifier:
 1415395
 Alternate Identifier(s):
 OSTI ID: 1409722
 Report Number(s):
 LAUR1724472
Journal ID: ISSN 24700010
 Grant/Contract Number:
 AC5206NA25396; AC0205CH11231; AC0506OR23177; FG0296ER40965; SC0011090; FC0206ER41444; ACI1053575; SFBTRR 55
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 9; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice QCD; particles & fields; nuclear physics
Citation Formats
Yoon, Boram, Engelhardt, Michael, Gupta, Rajan, Bhattacharya, Tanmoy, Green, Jeremy R., Musch, Bernhard U., Negele, John W., Pochinsky, Andrew V., Schäfer, Andreas, and Syritsyn, Sergey N. Nucleon transverse momentumdependent parton distributions in lattice QCD: Renormalization patterns and discretization effects. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.094508.
Yoon, Boram, Engelhardt, Michael, Gupta, Rajan, Bhattacharya, Tanmoy, Green, Jeremy R., Musch, Bernhard U., Negele, John W., Pochinsky, Andrew V., Schäfer, Andreas, & Syritsyn, Sergey N. Nucleon transverse momentumdependent parton distributions in lattice QCD: Renormalization patterns and discretization effects. United States. doi:10.1103/PhysRevD.96.094508.
Yoon, Boram, Engelhardt, Michael, Gupta, Rajan, Bhattacharya, Tanmoy, Green, Jeremy R., Musch, Bernhard U., Negele, John W., Pochinsky, Andrew V., Schäfer, Andreas, and Syritsyn, Sergey N. 2017.
"Nucleon transverse momentumdependent parton distributions in lattice QCD: Renormalization patterns and discretization effects". United States.
doi:10.1103/PhysRevD.96.094508.
@article{osti_1415395,
title = {Nucleon transverse momentumdependent parton distributions in lattice QCD: Renormalization patterns and discretization effects},
author = {Yoon, Boram and Engelhardt, Michael and Gupta, Rajan and Bhattacharya, Tanmoy and Green, Jeremy R. and Musch, Bernhard U. and Negele, John W. and Pochinsky, Andrew V. and Schäfer, Andreas and Syritsyn, Sergey N.},
abstractNote = {Lattice QCD calculations of transverse momentumdependent parton distribution functions (TMDs) in nucleons are presented in this paper, based on the evaluation of nucleon matrix elements of quark bilocal operators with a stapleshaped gauge connection. Both timereversal odd effects, namely, the generalized Sivers and BoerMulders transverse momentum shifts, as well as timereversal even effects, namely, the generalized transversity and one of the generalized wormgear shifts, are studied. Results are obtained on two different nf = 2 + 1 flavor ensembles with approximately matching pion masses but very different discretization schemes: domainwall fermions (DWF) with lattice spacing a = 0.084 fm and pion mass 297 MeV, and Wilsonclover fermions with a = 0.114 fm and pion mass 317 MeV. Comparison of the results on the two ensembles yields insight into the length scales at which lattice discretization errors are small, and into the extent to which the renormalization pattern obeyed by the continuum QCD TMD operator continues to apply in the lattice formulation. For the studied TMD observables, the results are found to be consistent between the two ensembles at sufficiently large separation of the quark fields within the operator, whereas deviations are observed in the local limit and in the case of a straight link gauge connection, which is relevant to the studies of parton distribution functions. Finally and furthermore, the lattice estimates of the generalized Sivers shift obtained here are confronted with, and are seen to tend towards, a phenomenological estimate extracted from experimental data.},
doi = {10.1103/PhysRevD.96.094508},
journal = {Physical Review D},
number = 9,
volume = 96,
place = {United States},
year = 2017,
month =
}

Lattice QCD calculations of nucleon transverse momentumdependent parton distributions using clover and domain wall fermions
Here, we present a lattice QCD calculation of transverse momentum dependent parton distribution functions (TMDs) of protons using stapleshaped Wilson lines. For timereversal odd observables, we calculate the generalized Sivers and BoerMulders transverse momentum shifts in SIDIS and DY cases, and for Teven observables we calculate the transversity related to the tensor charge and the generalized wormgear shift. The calculation is done on two different n _{f} = 2+1 ensembles: domainwall fermion (DWF) with lattice spacing 0:084fm and pion mass of 297 MeV, and clover fermion with lattice spacing 0:114 fm and pion mass of 317 MeV. The results frommore » 
Nucleon transverse momentumdependent parton distributions from domain wall fermion calculations at 297 MeV pion mass
Here, lattice QCD calculations of transverse momentumdependent parton distributions (TMDs) in a nucleon are performed based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing stapleshaped gauge connections. A parametrization of the matrix elements in terms of invariant amplitudes serves to cast them in the Lorentz frame preferred for the lattice calculation. Using a RBC/UKQCD domain wall fermion ensemble corresponding to a pion mass of 297 MeV, on a lattice with spacing 0.084 fm, selected TMD observables are accessed and compared to previous exploration at heavier pion masses on coarser lattices. 
Renormalization, Wilson lines, and transversemomentumdependent partondistribution functions
We perform an analysis of transversemomentum dependent partondistribution functions, making use of their renormalization properties in terms of their leadingorder anomalous dimensions. We show that the appropriate Wilson line in the light cone gauge, associated with such quantities, is a cusped one at light cone infinity. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transversemomentum dependent partondistribution functions an additional soft counter term (gauge link) along that cusped transverse contour. We demonstrate that this is tantamount to an 'intrinsic (Coulomb) phase', which accumulates the full gauge history of the colorcharged particle.