Related papers: Two-loop renormalization of three-quark operators …
We consider renormalization of four-fermion operators in the critical QED and $SU(N_c)$ version of Gross--Neveu--Yukawa model in non-integer dimensions. Since the number of mixing operators is infinite, the diagonalization of an anomalous…
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\bar{\psi}\Gamma\psi$, where $\Gamma$ corresponds to the Vector, Axial-Vector and Tensor Dirac operators, in the lattice formulation of…
The prescription for the $\gamma_5$-matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.
General analyses of $B$-physics processes beyond the Standard Model require accounting for operator mixing in the renormalization-group evolution from the matching scale down to the typical scale of $B$ physics. For this purpose the…
We consider a gauge-invariant, mass-independent prescription for renormalizing composite operators, regularized on the lattice, in the spirit of the coordinate space (X-space) renormalization scheme. The prescription involves only Green's…
We compute the ratio between the scale $\Lambda_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{MS-bar}$. To this end, the one-loop relation between the lattice coupling $g_0$ and the coupling…
Recently certain nonlocal operators were proposed to provide quark masses for the holographic model of QCD developed by Sakai and Sugimoto. The properties of these operators at strong coupling are examined in detail using holographic…
We calculate the two-loop QCD mixing of the dimension-five flavor-changing operators that arise in the Standard Model after integrating out the $W$, $Z$ and Higgs bosons and the top-quark, i.e.~the mixing among gluonic and photonic magnetic…
We present the result of a calculation for the third and fourth moments of the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD with full color and flavour structures. We discuss also a general expressions for…
Renormalization group evolution of QCD composite light-cone operators, built from two and more quark and gluon fields, is responsible for the logarithmic scaling violations in diverse physical observables. We analyze spectra of anomalous…
In this study, we explore the renormalization of a comprehensive set of gauge-invariant gluon nonlocal operators on the lattice. We calculate the renormalization factors for these operators in the modified Minimal Subtraction $(\rm…
We derive explicit transformation formulae relating the renormalized quark mass and field as defined in the MS-bar scheme with the corresponding quantities defined in any other scheme. By analytically computing the three-loop quark…
We perform a dedicated study of the $q \bar{q}$-initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order $\alpha$ and…
Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\Delta F = 1$ and $\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with…
In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic continuation approach, and minimal-subtraction scheme to…
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous…
In this work, we compute the anomalous dimensions of the $\phi^Q$ operator in six-dimensional cubic scalar theory. The renormalization analysis is carried out within the framework of the Operator Product Expansion method, while the…
We present a comprehensive QCD sum rules analysis at next-to-leading order for all types of $J^P=0^{+}$ four-quark states composed of $u$, $d$, and $s$ quarks. The eigenvectors of the renormalization matrix are chosen to be the renormalized…
Using the virial theorem of the heavy-quark effective theory, we show that the mixing of the operator for the heavy-quark kinetic energy with the identity operator is forbidden at the one-loop order by Lorentz invariance. This explains why…