Volume 346 - 23rd International Spin Physics Symposium (SPIN2018) - Parallel Session: Structure of the Nucleon: TMDs (A. Bacchetta, J. Drachenberg and B. Parsamyan)
Quark orbital angular momentum in the proton evaluated using a direct derivative method
M. Engelhardt,* J. Green, N. Hasan, S. Krieg, S. Meinel, J. Negele, A. Pochinsky, S. Syritsyn
*corresponding author
Full text: pdf
Pre-published on: 2019 August 19
Published on: 2019 August 23
Abstract
Quark orbital angular momentum (OAM) in the proton can be calculated directly given a Wigner function encoding the simultaneous distribution of quark transverse positions and momenta. This distribution can be accessed via proton matrix elements of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position). To generate the weighting by quark transverse position needed to calculate OAM, a derivative with respect to momentum transfer is consequently required. This derivative is evaluated using a direct derivative method, i.e., a method in which the momentum derivative of a correlator is directly sampled in the lattice calculation, as opposed to extracting it a posteriori from the numerical correlator data. The method removes the bias stemming from estimating the derivative a posteriori that was seen to afflict a previous exploratory calculation. Data for Ji OAM generated on a clover ensemble at pion mass $m_{\pi } = 317\, \mbox{MeV}$ are seen to agree with the result obtained via the traditional Ji sum rule method. By varying the gauge connection in the quark bilocal operator, also Jaffe-Manohar OAM is extracted, and seen to be enhanced significantly compared to Ji OAM.
DOI: https://doi.org/10.22323/1.346.0047
Open Access