RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions

RI/(S)MOM renormalizations of overlap quark bilinears with different levels of hypercubic smearing

“…While if we use the MOM scheme, a good window for Z MS S,P (2 GeV; a 2 p 2 ) can be found, in which the a 2 p 2 -dependence can be well fitted by a linear function and is attributed to O(a 2 p 2 ) discretization effects. Similar observations were made in a more recent work [11], in which both the SMOM and MOM schemes were used to obtain the RCs for overlap quark bilinears on both domain-wall fermion and Highly Improved Staggered Quark (HISQ) configurations.…”

“…for "thin", HYP1 and HYP2, respectively. Since the uncertainty of Z WI A using the "thin" link is much larger than the other cases, we repeat the calculation with Coulomb wall source [11] to improve the statistics, and obtain Z WI A,thin = 1.4403( 6) which is consistent with that listed in Eq. ( 22) but has much smaller uncertainty.…”

“…5,9] as that in Ref. [11] for ensemble 64I and use a third order polynomial, then we obtain χ 2 /dof = 41.4/17 = 2.4 and Z MS S (2 GeV)/Z A = 0.9657(88), where the error has been enlarged by χ 2 /dof.…”

“…The values in the sea quark massless limit are from linear extrapolations, whose errors are enlarged by χ 2 /dof (if > 1). [17,10,11]. The truncation error in the conversion ratio from MOM to MS is found to be 0.67%, which is smaller than the 1.5% in [17] and the 2.29% in [11].…”

“…[17,10,11]. The truncation error in the conversion ratio from MOM to MS is found to be 0.67%, which is smaller than the 1.5% in [17] and the 2.29% in [11]. One reason is that here the lower limit of |p| used in the a 2 p 2extrapolation is about 5.3 GeV, which is higher than the 4 GeV in [17] and the 3 GeV in [11].…”