Abstract
We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $\gamma^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.
Highlights
One of the more curious experimental results over a generation ago was that of the EMC Collaboration [1]
In order to give an indication of the structure of the final expression in four dimensions after the implementation of the Larin method we note that in the Landau gauge for Nf 1⁄4 3 we have
We have evaluated the two loop quark 2-point function with the flavor singlet axial vector current inserted at nonzero momentum at the nonexceptional symmetric point
Summary
One of the more curious experimental results over a generation ago was that of the EMC Collaboration [1]. By contrast in lattice language there are disconnected contributions to the proton correlation function when probed with the axial vector current in the flavor singlet case While the latter have been incorporated in the lattice simulations [27,31], their omission in the matching to the continuum in [31], albeit due to taking only one loop data, means that the effect of the chiral anomaly has not been taken into account. In other words the central values measured on the lattice for the hadronic matrix element will not have accommodated the discrepancy in the continuum difference between the flavor nonsinglet and singlet operators This is due to the lack of a two loop computation of the relevant Green’s function containing the flavor singlet axial vector current.
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