Searcharxiv⌕ Search

arXiv subjects

Johannes Blümlein

Publications and source records attributed to Johannes Blümlein.

At least 37 records · Page 2Linked to original sources
arXiv2014

Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums

The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented. The ultimate goal of this project is the automatic evaluation of MB representations for multiloop scalar and tensor Feynman integrals through infinite sums, preferably with analytic solutions. We shortly describe a strategy of further algebraic summation.

hep-ph↗
arXiv2014

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.

hep-th↗
arXiv2014

Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $τ=2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version to the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and $V$-type graphs, belonging to the genuine 3-loop topologies. In case of the $V$-type graphs with five massive propagators new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of $\sim 30$ square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for $N \in \mathbb{C}$. Integrals with a power-like divergence in $N$--space $\propto a^N, a \in \mathbb{R}, a > 1,$ for large values of $N$ emerge. They still possess a representation in $x$--space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.

hep-ph↗
arXiv2014

The $O(α_s^2)$ Heavy Quark Corrections to Charged Current Deep-Inelastic Scattering at large Virtualities

We calculate the $O(α_s^2)$ heavy flavor corrections to charged current deep-inelastic scattering at large scales $Q^2 \gg m^2$. The contributing Wilson coefficient are given as convolutions between massive operator matrix elements and massless Wilson coefficients. Foregoing results in the literature are extended and corrected. Numerical results are presented for the kinematic region of the HERA data.

hep-ph↗
arXiv2013

Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements

3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation technologies provided by the package {\sf Sigma} and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with $ξ\in \{1,1/2,2\}$ emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of $N$. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region $Q^2 \gg m^2$.

hep-ph↗
arXiv2013

Harmonic Sums, Polylogarithms, Special Numbers, and their Generalizations

In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.

math-ph↗
arXiv2013

Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms

In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by rational (or real) numerator weights also different from $\pm 1$. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincaré iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the $S$-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of $S$-sum expressions. Finally, we calculate algebraic relations for infinite $S$-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package {\tt HarmonicSums}.

math-ph↗
arXiv2012

The Theory of Deeply Inelastic Scattering

The nucleon structure functions probed in deep-inelastic scattering at large virtualities form an important tool to test Quantum Chromdynamics (QCD) through precision measurements of the strong coupling constant $α_s(M_Z^2)$ and the different parton distribution functions. The exact knowledge of these quantities is also of importance for all precision measurements at hadron colliders. During the last two decades very significant progress has been made in performing precision calculations. We review the theoretical status reached for both unpolarized and polarized lepton-hadron scattering based on perturbative QCD.

hep-ph↗
arXiv2012

Why Precision?

Precision measurements together with exact theoretical calculations have led to steady progress in fundamental physics. A brief survey is given on recent developments and current achievements in the field of perturbative precision calculations in the Standard Model of the Elementary Particles and their application in current high energy collider data analyses.

hep-ph↗
arXiv2012

The $O(α_s^3 n_f T_F^2 C_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements

The $O(α_s^3 n_f T_F^2 C_{A,F})$ terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable $N$. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of $N$ is provided.

hep-ph↗
arXiv2011

Two-loop QED Operator Matrix Elements with Massive External Fermion Lines

The two-loop massive operator matrix elements for the fermionic local twist--2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter $ε= D - 4$. We investigate the hypothesis of Ref. \cite{BBN} that the 2--loop QED initial state corrections to $e^+e^-$ annihilation into a virtual neutral gauge boson, except power corrections of $O((m_f^2/s)^k), k \geq 1$, can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell-Yan process.

hep-ph↗
arXiv2011

Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincaré--iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of $N$ is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument $x=1$, resp., for the cyclotomic harmonic sums at $N \rightarrow \infty$, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight {\sf w = 1,2} sums up to cyclotomy {\sf l = 20}.

math-ph↗
arXiv2011

New Exclusion Limits for Dark Gauge Forces from Beam-Dump Data

We re-analyze proton beam dump data taken at the U70 accelerator at IHEP Serpukhov with the $ν$-calorimeter I experiment in 1989 to set mass-coupling limits for dark gauge forces. The corresponding data have been used for axion and light Higgs particle searches in Refs. before. We determine new mass and coupling exclusion bounds for dark gauge bosons.

hep-ex↗
arXiv2010

QCD Analysis of the Polarized Deep-Inelastic World Data

The results of a recent next-to-leading order QCD analysis of the world data on polarized deep inelastic scattering are reported. New parameterizations are derived for the quark and gluon distributions, accounting for the massive Wilson coefficient for the charm quarks, and the value of $α_s(M_z^2)$ is determined with correlated errors. We obtain $α_s^{\rm NLO}(M_Z^2)= 0.1132 {array}{l} + 0.0056 -0.0095 {array}$. Limits on potential higher twist contributions to the structure function $g_1(x,Q^2)$ are derived. We also compare to the results obtained by other groups.

hep-ph↗
arXiv2010

The QCD Coupling and Parton Distributions at High Precision

A survey is given on the present status of the nucleon parton distributions and related precision calculations and precision measurements of the strong coupling constant $α_s(M_Z^2)$. We also discuss the impact of these quantities on precision observables at hadron colliders.

hep-ph↗
arXiv2010

QCD Analysis of Polarized Deep Inelastic Scattering Data

A QCD analysis of the world data on polarized deep inelastic scattering is presented in next--to--leading order, including the heavy flavor Wilson coefficient in leading order in the fixed flavor number scheme. New parameterizations are derived for the quark and gluon distributions and the value of $α_s(M_z^2)$ is determined. The impact of the variation of both the renormalization and factorization scales on the distributions and the value of $α_s$ is studied. We obtain $α_s^{\rm NLO}(M_Z^2) = 0.1132~~\begin{array}{l} + 0.0056 \\ -0.0095 \end{array}$. The first moments of the polarized twist--2 parton distribution functions are calculated with correlated errors to allow for comparisons with results from lattice QCD simulations. Potential higher twist contributions to the structure function $g_1(x,Q^2)$ are determined and found to be compatible with zero both for proton and deuteron targets.

hep-ph↗
arXiv2009

Heavy Flavor Contributions to DIS Structure Functions at $O(α_s^3)$

We calculate moments of the $O(α_s^3)$ heavy flavor contributions to the Wilson coefficients of the structure function $F_2(x,Q^2)$ in the region $Q^2\gg m^2$. The massive Wilson coefficients are obtained as convolutions of massive operator matrix elements (OMEs) and the known light flavor Wilson coefficients. The calculation of moments of the massive OMEs involves a first independent recalculation of moments of the fermionic contributions to all 3--loop anomalous dimensions of the unpolarized twist--2 local composite operators stemming from the light--cone expansion. The expressions for the massive OMEs are now known for general values of the Mellin variable $N$ apart of one coefficient in the constant term, for which only a series of moments is computed.

hep-ph↗