Related papers: Structural Relations between Nested Harmonic Sums
``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised…
A geometric relationship between loop quantum gravity and partitioned (triangulated) string theory is discussed. Combinatorial analysis reveals that three spatial and three curvature dimensions, intrinsic to the partitioned string, are…
We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the…
The contributions $\propto n_f$ to the $O(\alpha_s^3)$ massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit $Q^2 \gg m^2$ are computed for the structure function $F_2(x,Q^2)$ and transversity for…
We define discrete nested sums over integer points for symbols on the real line, which obey stuffle relations whenever they converge. They relate to Chen integrals of symbols via the Euler-MacLaurin formula. Using a suitable holomorphic…
We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space R^{m+1} was constructed recently, including a higher dimensional analogue of the logarithmic function in the complex…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
We extend the recent one loop analysis of the ultraviolet completion of the $CP(N)$ nonlinear $\sigma$ model in six dimensions to two loop order in the MSbar scheme for an arbitrary covariant gauge. In particular we compute the anomalous…
When relating the strong coupling $\alpha_s$, measured at the scale of the $Z$ boson mass, to its numerical value at some higher energy, for example the scale of Grand Unification, it is important to include higher order corrections both in…
The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with…
Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous…
We show that at certain values of QCD condensates the nucleon QCD sum rules with "pole+continuum" model for the hadron spectrum obtain an unphysical solution. This provides constrains for the values of condensates to be consistent with…
We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both…
A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes,…
It is shown that harmonic functions from a simply connected domain in R^3 to R^3 cannot always be expressed as a sum of a monogenic (hyperholomorphic) function and an antimonogenic function, in contrast to the situation for complex numbers…
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 develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
We investigate the level sets of harmonic functions on $(\mathbb{R}^{3}\setminus \{0\},g)$. Drawing inspiration from Miao, we adopt the method developed by Munteanu-Wang to derive a monotonic quantity associated with the level sets of…
For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic…