Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point

Abstract

We extend the Rome-Southampton regularization independent momentumsubtraction renormalization scheme(RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Green's functions with the insertion of quark bilinear operators are computed with scalar, pseudoscalar, vector, axial-vector and tensor operators at one-loop order in perturbative QCD. We call this new scheme RI/SMOM, where the S stands for "symmetric". Conversion factors are derived, which connect the RI/SMOM scheme and the MS scheme and can be used to convert results obtained in lattice calculations into the MS scheme. Such a symmetric subtraction point involves nonexceptional momenta implying a lattice calculation with substantially suppressed contamination from infrared effects. Further, we find that the size of the one-loop corrections for these infrared improved kinematics is substantially decreased in the case of the pseudoscalar and scalar operator, suggesting a much better behaved perturbative series. Therefore it should allow us to reduce the error in the determination of the quark mass appreciably.

K→ππΔI=3/2decay amplitude in the

“…The momenta in such RI-SMOM schemes are chosen so that there are no "exceptional" channels, i.e. no channels in which the square of the momenta is small [13]. (This is in contrast with the original RI-MOM scheme [14,15] in which p 1 = p 2 .)…”

“…(RI-SMOM) schemes [13] as described in detail in [2] and briefly summarized below. The matching between the RI-SMOM and MS schemes is necessarily performed in perturbation theory and is currently known at one-loop order.…”

Three loop renormalization of 3-quark operators in QCD

“…However, one reason for not choosing to explicitly include, say, RI ′ results rests in the fact that as noted in [14] the definition of such schemes is not unique for Lorentz structure beyond the simplest quark mass operator. Indeed in the tensor current case a scheme alternative, [14], to the original one of [11,13] appeared to converge quicker at two loops. Only a three loop calculation would give more insight into this.…”

“…Indeed with the current loop calculation technology this invariably means three loops through the use of the Mincer package, [7,8]. As highlights of this bridge we mention quark current renormalization for zero momentum operator insertions, [9,10], and more recently at non-zero momentum insertion, [11,12,13,14,15]. The latter are known at two loops at the symmetric subtraction point for the MS scheme.…”

“…The latter are known at two loops at the symmetric subtraction point for the MS scheme. However, in both cases results have been determined in the regularization invariant (RI), [16,17], class of schemes which includes RI ′ and RI ′ /SMOM, [11], where SMOM indicates momentum subtraction at the symmetric point. These are schemes which are devised for lattice regularization in order to minimize the use of derivatives, which is computationally intense, in extracting renormalization constants as well as amplitudes.…”