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It is suggested in the paper by A.J. Chambers {it et al.} (Phys. Rev. Lett. 118, 242001 (2017), arXiv:1703.01153) that the time-ordered current-curent correlator in the nucleon calculated on the lattice is to be identified as the forward Compton amplitude so that it is related to the sum of the even moments of the structure function as in the Minkowski space in the continuum. We point out two problems with this identification. First of all, the current-current correlator defined in the Euclidean space is not analytic everywhere on the rest of the complex $ u$ or $omega$ plane, besides the cuts on the real axis. As such, there is no dispersion relation to relate it to its imaginary part and hence the moments of the structure function. On the lattice, there is an additional difficulty in that the higher dimensional local operators from the operator production expansion (OPE) of the current-current product can mix with lower dimensional higher-twist operators which leads to divergences in the powers of inverse lattice spacing. This mixing needs to be removed before their matrix elements can be identified as the moments of the structure function.
Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far
We have reported elsewhere in this conference on our continuing project to determine non-perturbative Wilson coefficients on the lattice, as a step towards a completely non-perturbative determination of the nucleon structure. In this talk we discuss
We investigate the Operator Product Expansion (OPE) on the lattice by directly measuring the product <Jmu Jnu> (where J is the vector current) and comparing it with the expectation values of bilinear operators. This will determine the Wilson coeffici
We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover
We present first results for Wilson coefficients of operators up to first order in the covariant derivatives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude $mathcal{W}_{mu u}(a,p,q)$ of massless quar