Related papers: Three-loop massive tadpoles and polylogarithms thr…
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases…
The real and imaginary part of the vacuum polarisation function $\Pi(q^2)$ induced by a massive quark is calculated in perturbative QCD up to order $\alpha_s^2$. The method is described and the results are presented. This extends the…
We calculate analytically a class of three-loop vacuum diagrams with two different mass values, one of which is one-third as large as the other, using the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization scheme.…
We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved…
In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3-2*ep dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
The mass spectra of ground-state triply heavy baryons are systematically unscrambled and computed in QCD sum rules. With a tentative $(QQ)-(Q')$ configuration for $QQQ'$, the interpolating currents representing the triply heavy baryons are…
In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta.…
I present analytical expressions for the cusp anomalous dimension in QCD through three loops in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
An efficient method to calculate tadpole diagrams is proposed. Its capability is demonstrated by analytically evaluating two four-loop tadpole diagrams of current interest in the literature, including their $O(\epsilon)$ terms in…
We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…
We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…
Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master…
An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these…
The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…
We introduce systems of objects and operators in linear monoidal categories called $\hat \Psi$-systems. A $\hat \Psi$-system satisfying several additional assumptions gives rise to a topological invariant of triples (a closed oriented…
Closed classes of three-valued logic generated by periodic symmetric funtions that equal $1$ in tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence and finite bases existence for these…
We calculate the complete three-loop O(alpha_s^3) anomalous dimension matrix for the dimension-five dipole operators that arise in the Standard Model after integrating out the top quark and the heavy electroweak bosons. Our computation…