Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil

Charm in Deep-Inelastic Scattering

We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions $F^c_2$, $F^c_L$ and $F^c_3$ to NNLO

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as in its successor, the DLMF, but their proofs were lost. We use generating functions and symbolic summation techniques to produce new proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl

Landwirt*innen nutzen Citizen Science Praktiken zur Unterstützung der Artenvielfalt am Land

Das EU-Projekt FRAMEwork fördert bottom-up Innovationen getragen von Landwirt*innen via elf "Farmer Cluster" in neun Ländern Europas. Anhand zweier Farmer Cluster im Mostviertel und im Burgenland in Österreich veranschaulicht das Poster zwei komplementäre Citizen Science Praktiken, die einen evidenzbasierten, lokal eingebetteten, gemeinschaftlichen Ansatz zum Schutz und zur Verbesserung der biologischen Vielfalt unterstützen und strukturiertes Monitoring mit adaptiven Landmanagementpraktiken kombinieren

Simplifying Multiple Sums in Difference Fields

In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package \SigmaP\ by discovering and proving new harmonic number identities extending those from (Paule and Schneider, 2003). In addition, the newly developed package \texttt{EvaluateMultiSums} is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.Comment: Uses svmult.cls, to appear as contribution in the book "Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions" (www.Springer.com

New parton distributions in fixed flavour factorization scheme from recent deep-inelastic-scattering data

We present our QCD analysis of the proton structure function $F_2^p(x,Q^2)$ to determine the parton distributions at the next-to-leading order (NLO). The heavy quark contributions to $F_2^i(x,Q^2)$, with $i$ = $c$, $b$ have been included in the framework of the `fixed flavour number scheme' (FFNS). The results obtained in the FFNS are compared with available results such as the general-mass variable-flavour-number scheme (GM-VFNS) and other prescriptions used in global fits of PDFs. In the present QCD analysis, we use a wide range of the inclusive neutral-current deep-inelastic-scattering (NC DIS) data, including the most recent data for charm $F_2^c$, bottom $F_2^b$, longitudinal $F_L$ structure functions and also the reduced DIS cross sections $\sigma_{r,NC}^\pm$ from HERA experiments. The most recent HERMES data for proton and deuteron structure functions are also added. We take into account ZEUS neutral current $e^ \pm p$ DIS inclusive jet cross section data from HERA together with the recent Tevatron Run-II inclusive jet cross section data from CDF and D{\O}. The impact of these recent DIS data on the PDFs extracted from the global fits are studied. We present two families of PDFs, {\tt KKT12} and {\tt KKT12C}, without and with HERA `combined' data sets on $e^{\pm}p$ DIS. We find these are in good agreement with the available theoretical models.Comment: 23 pages, 26 figures and 4 tables. V3: Only few comments and references added in the replaced version, results unchanged. Code can be found at http://particles.ipm.ir/links/QCD.ht

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes

We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.Comment: 46 page

Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders exactly for any value of the 't Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtained several new orders of the strong coupling expansion of the BFKL pomeron intercept. As a by-product we formulated a prescription for the correct analytical continuation in S which opens a way for deriving the BFKL regime of twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2 and D_2 on page 29 we corrected the rational part of the strong coupling predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table

From polygons and symbols to polylogarithmic functions

We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple polylogarithm in terms of the combinatorial properties of an associated rooted decorated polygon. We also outline a systematic approach to constructing a function corresponding to a given symbol, and illustrate it in the particular case of harmonic polylogarithms up to weight four. Furthermore, part of the ambiguity of this process is highlighted by exhibiting a family of non-trivial elements in the kernel of the symbol map for arbitrary weight.Comment: 75 pages. Mathematica files with the expression of all HPLs up to weight 4 in terms of the spanning set are include