Related papers: Note on Cyclic Sum and Combination Sum of Color-or…
The objects of our interest are the so-called $A$-permutations, which are permutations whose cycle length lie in a fixed set $A$. They have been extensively studied with respect to the uniform or the Ewens measure. In this paper, we extend…
In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with…
The basis of renormalon calculus is briefly discussed. The method is applied to study QCD predictions for three sum rules of deep-inelastic scattering, namely for the Gross-Llewellyn Smith, Bjorken polarized and unpolarized sum rules. It is…
We undertake a detailed investigation into the structure of permutations in monotone grid classes whose row-column graphs do not contain components with more than one cycle. Central to this investigation is a new decomposition, called the…
Feynman diagrams for gluon tree amplitudes are studied in the Feynman gauge and in any number of spacetime dimensions. The color-kinematics combinations $\Delta=n_s-n_t-n_u$ of numerators are explicitly calculated for $N=4,5,6$ gluons to…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the…
The identity between expressions for the coefficient functions of the Bjorken and Ellis-Jaffe sum rules is derived in the conformal invariant limit of massless U(1) theory, namely in the perturbative quenched QED model, and in the same…
A new relation between $\rho$-meson mass, weak $\pi$-meson decay constant, quark and gluon condensates is derived from the QCD sum rules. As a byproduct an explanation for the dominance of $\rho\rho$-decay for the $f_0(1370)$-meson is…
Results for four-, five-, and six-parton tree amplitudes for massive quark-antiquark scattering with gluons are calculated using the recursion relations of Britto, Cachazo, Feng, and Witten. The required diagrams are generated using shifts…
We analyze the B->KK decays with the soft-gluon corrections by using the QCD light-cone sum rules (LCSR). Although QCD factorization approach calculates the leading order factorization parts and the radiative corrections from hard- gluon…
New sum rules for $B\to \pi,K $ and $B\to \rho,K^*$ form factors are derived from the correlation functions expanded near the light-cone in terms of B-meson distribution amplitudes. The contributions of quark-antiquark and…
We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems:…
We present first results of resumming soft gluon effects in a simulation of high energy collisions beyond the leading-colour approximation. We work to all orders in QCD perturbation theory using a new parton branching algorithm. This…
The unintegrated quark and gluon distributions in the pion and nucleon are analysed using the CCFM equations in the single-loop approximation. We utilise the transverse-coordinate (or impact-parameter) representation which diagonalises the…
We study in detail the general structure and further properties of the tree-level amplitudes in the SU(N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU(N) fields U(x), write…
We use, for the first time, ab initio coupled-cluster theory to compute the spectral function of the uniform electron gas at a Wigner-Seitz radius of $r_\mathrm{s}=4$. The coupled-cluster approximations we employ go significantly beyond the…
Gaussian QCD sum-rules are ideally suited to the study of mixed states of gluonium (glueballs) and quark ($q\bar q$) mesons because of their capability to resolve widely-separated states of comparable strength. The analysis of the Gaussian…
We present nonlinear (NL) and higher twist (HT) corrections to the color dipole model (CDM) bounds at low values of $x$ and $Q^{2}$ using the parameterization method. Consistency between the bounds at this region describe that a transition…
In this paper we consider the following conjecture, proposed by Brian Alspach, concerning partial sums in finite cyclic groups: given a subset $A$ of $\mathbb{Z}_n\setminus \{0\}$ of size $k$ such that $\sum_{z\in A} z\not= 0$, it is…