content_image/348529.jpg content_image/348536.jpg content_image/348537.jpg
<img src='content_image/348529.jpg'>

suppressed by an additional factor of α$_{s}$ and thus well below ± 0 . 0001. 

## C. Non-conserved current 

The discretization effect may also come from the non-conserved local current J loc ν in (13), which is represented by the term Δ J $_{µν}$( Q ) in (10). 

We estimate its leading contribution Δ J $_{µν}$( Q ) = ( δ$_{µν}$ ˆ Q $^{2}$− ˆ Q$_{µ}$ ˆ Q$_{ν}$ ) Q 2 $_{ν}$F J $_{11}$( Q ) in the expansion (13) in terms of small aQ$_{µ}$ , by solving linear equations (10) for different sets of µ and ν . We find that the maximum magnitude of ( δ$_{µν}$ ˆ Q 2 − ˆ Q$_{µ}$ ˆ Q$_{ν}$ ) Q 2 $_{ν}$F V + A 11 ( Q ) is less than 1% of Π$_{V}$$_{+}$$_{A}$( Q ) in the fit range 0 . 463 ≤ ( aQ ) 2 ≤ 0 . 994. 

The contribution of Δ J $_{µν}$( Q ) may also be estimated by looking at a difference between VPFs obtained with µ = ν (diag) and with µ ̸ = ν (offd) components, i.e. 

<img src='content_image/348536.jpg'>

<img src='content_image/348537.jpg'>

respectively. Figure 6 shows Π diag V ( Q ) − Π offd V ( Q ) as a function of ( aQ ) $^{2}$. The maximum magnitude of the difference in the range 0 . 463 ≤ ( aQ ) 2 ≤ 0 . 994 is 0.003, which is the same 

