Related papers: Operator Product Expansion and Calculation of the …
The semi-analytical $O(\alpha_s^4)$ expression for the renormalization group $\beta$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the existing information…
We recalculate the contributions of individual six loop graphs to the $\beta$-function for a three dimensional scalar theory with an arbitrary sextic scalar potential. Previously this was calculated by Hager who specialised to a theory with…
We construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of potentials and for arbitrary inverse temperatures $ {\rm Re}\,\beta>0 $ and number of eigenvalues $ N $. Using matching…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
The complete two-loop expression for the jet function J(p^2,mu) of soft-collinear effective theory is presented, including non-logarithmic terms. Combined with our previous calculation of the soft function S(omega,mu), this result provides…
We present a brief description of the determination of the two-loop spin-dependent time-like splitting functions relevant for the NLO evolution of polarized fragmentation functions. Our calculation based on the analytic continuation of the…
We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling $\alpha_s$ for the non-singlet contributions to Adler $D$-function and Bjorken polarized sum rule calculated previously in the $\MSbar$-scheme…
We present a general method for extracting the Gell Mann-Low logarithmic derivative of an effective charge of an observable directly from data as a mean for empirically verifying the universal terms of the QCD $\beta$-function. Our method…
The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at the double pole at $s=1$. In this article, we derive a new…
We calculate boundary operator product expansion coefficients for boundary operators in the first column of the Kac table in conformal field theories. For c=0 we give closed form expressions for all such coefficients. Then we generalize to…
The order $\alpha_s$ corrections to the Wilson coefficients of the dipole operators ($O_7,O_8$) at the matching scale $\mu =m_W$ are a crucial ingredient for a complete next- to-leading logarithmic calculation of the branching ratio for $b…
General one-loop formulas for loop-induced processes $\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in the paper. Analytic expressions evaluated in this work are valid for a class of Higgs Extensions…
We investigate the convergence of the derivative expansion of the exact renormalization group, by using it to compute the beta function of scalar field theory. We show that the derivative expansion of the Polchinski flow equation converges…
This research note deals with the evaluation of some generalized beta-type integral operators involving the multi-index Mittag-Leffler function $E_{\epsilon_{i}),(\omega_{i})}(z)$. Further, we derive a new family of beta-type integrals…
By considering corrections to the asymptotic scaling functions of the photon and electron in quantum electrodynamics with $\Nf$ flavours, we solve the skeleton Dyson equations at $O(1/\Nf)$ in the large $\Nf$ expansion at the…
We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for…
The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function…
In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established.…
In this paper we study the renormalization of the product of two operators $O_1=-\frac{1}{4} G^{\mu \nu}G_{\mu \nu}$ in QCD. An insertion of two such operators $O_1(x)O_1(0)$ into a Greens function produces divergent contact terms for…
The renormalization-group functions of the two-dimensional n-vector \lambda \phi^4 model are calculated in the five-loop approximation. Perturbative series for the \beta-function and critical exponents are resummed by the Pade-Borel-Leroy…