Related papers: Analytic Continuation of Mellin Transforms up to t…
We present the analytic form of all leading-color two-loop five-parton helicity amplitudes in QCD. The results are analytically reconstructed from exact numerical evaluations over finite fields. Combining a judicious choice of variables…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading order in a 1/Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation…
In this thesis, major developments in the publicly available program SecDec are presented, extending the numerical evaluation of multi-loop multi-scale integrals from Euclidean to physical kinematics. The power of this new feature is shown…
Splitting functions govern the scale evolution of parton distribution functions. Through a Mellin transformation, they are related to anomalous dimensions of twist-two operators in the operator product expansion. We study off-shell operator…
We establish asymptotic estimates of Mathieu-type series defined by sequences with power-logarithmic or factorial behavior. By taking the Mellin transform, the problem is mapped to the singular behavior of certain Dirichlet series, which is…
The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For Mellin bandlimited functions it becomes an exact quadrature formula. Our main aim is to study…
We review the status of the calculation of the time-like splitting functions for the evolution of fragmentation functions to the next-to-next-to-leading order in perturbative QCD. By employing relations between space-like and time-like…
We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution…
We study the $\phi$ meson at finite temperature and finite momentum using QCD sum rules. The presence of medium breaks the Lorentz invariance, and induces distinct in-medium modifications of the transverse and longitudinal modes at finite…
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…
Finite size scaling studies of monopole condensation in noncompact quenched lattice $QED$ indicate an authentic second order phase transition lying in the universality class of four dimensional percolation. Since the upper critical…
We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…
We discuss analytic continuation as a tool to extract the cumulants of the quark number fluctuations in the strongly interacting medium from lattice QCD simulations at imaginary chemical potentials. The method is applied to $N_f = 2+1$ QCD,…
We propose to associate to a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequence in terms of the Mellin…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
Mean square estimates for $Z_2(s) = \int_1^\infty |\zeta(1/2+ix)|^4x^{-s}dx (\Re s > 1)$ are discussed, and some related Mellin transforms of quantities connected with the fourth power moment of $|\zeta(1/2+ix)|^4$.
We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings $\mathcal{A}_{\nu}(Q^2)$ for complex or real squared momenta $Q^2$. These couplings are holomorphic analogs of the powers $a(Q^2)^{\nu}$ of the…
In this paper we discuss the definition, the construction and the implementation of \textit{generalised antenna functions} for final-state radiation up to Next-to-Next-to-Leading Order (NNLO) in QCD. Generalised antenna functions…
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…