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Register a new userA massive momentum-subtraction scheme
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A new renormalization scheme is defined for fermion bilinears in QCD at non vanishing quark masses. This new scheme, denoted RI/mSMOM, preserves the benefits of the nonexceptional momenta introduced in the RI/SMOM scheme, and allows a definition of renormalized composite fields away from the chiral limit. Some properties of the scheme are investigated by performing explicit one-loop computation in dimensional regularization.
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We introduce a new massive renormalization scheme, denoted mSMOM, as a modification of the existing RI/SMOM scheme. We use SMOM for defining renormalized fermion bilinears in QCD at non-vanishing fermion mass. This scheme has properties similar to those of the SMOM scheme, such as the use of non-exceptional symmetric momenta, while in contrast to SMOM, it defines the renormalized fields away from the chiral limit. Here we discuss some of the properties of mSMOM, and present non-perturbative arguments for deriving some renormalization constants. The results of a 1-loop calculation in dimensional regularization are briefly summarised to illustrate some properties of the scheme.
We extend the Rome-Southampton regularization independent momentum-subtraction renormalization scheme(RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Greens 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 MSbar scheme and can be used to convert results obtained in lattice calculations into the MSbar 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.
The momentum space subtraction (MOM) scheme is one of the most frequently used renormalization schemes in perturbative QCD (pQCD) theory. In the paper, we make a detailed discussion on the gauge dependence of the pQCD prediction under the MOM scheme. Conventionally, there is renormalization scale ambiguity for the fixed-order pQCD predictions, which assigns an arbitrary range and an arbitrary error for the fixed-order pQCD prediction. The principle of maximum conformality (PMC) adopts the renormalization group equation to determine the magnitude of the coupling constant and hence determines an effective momentum flow of the process, which is independent to the choice of renormalization scale. There is thus no renormalization scale ambiguity in PMC predictions. To concentrate our attention on the MOM gauge dependence, we first apply the PMC to deal with the pQCD series. We adopt the Higgs boson decay width, $Gamma(Hto gg)$, up to five-loop QCD contributions as an example to show how the gauge dependence behaves before and after applying the PMC. It is found that the Higgs decay width $Gamma (Hto gg)$ depends very weakly on the choices of the MOM schemes, being consistent with the renormalization group invariance. It is found that the gauge dependence of $Gamma(Hto gg)$ under the $rm{MOMgg}$ scheme is less than $pm1%$, which is the smallest gauge dependence among all the mentioned MOM schemes.
We introduce the simplest minimal subtraction method for massive $lambda phi^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the partial-$p$ operation in every diagram of the two-point vertex part in order to separate it into a sum of squared mass and external momentum, respectively, with different coefficients. Then, the loop integral which is the coefficient of the quadratic mass can be solved entirely in terms of the mass, no longer depending upon the external momentum, using the {it parametric dissociation transform}. It consists in the choice of a certain set of fixed values of Feynman parameters replaced inside the remaining loop integral after solving the internal subdiagrams. We check the results in the diagrammatic computation of critical exponents at least up to two-loop order using a flat metric with Euclidean signature.
The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.
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