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C. Schneider

Publications and source records attributed to C. Schneider.

162 records · Page 9Linked to original sources
arXiv2013

New Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

We report on recent results obtained for the 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering (DIS) at general values of the Mellin variable $N$ at larger scales of $Q^2$. These concern contributions to the gluonic ladder-topologies, the transition matrix elements in the variable flavor scheme of $O(n_f T_F^2)$ and $O(T_F^2)$, and first results on higher 3-loop topologies. The knowledge of the heavy flavor Wilson coefficients at 3-loop order is of importance to extract the parton distribution functions and $α_s(M_Z^2)$ in complete NNLO QCD analyses of the world precision data on the structure function $F_2(x,Q^2)$.

hep-ph↗
arXiv2012

Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals

Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter $n$. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist--Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in $n$. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all $n$ solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

cs.SC↗
arXiv2012

Microcavity controlled coupling of excitonic qubits

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. The most relevant mechanism of coherent coupling of distant qubits is coupling via the electromagnetic field. Here, we demonstrate the controlled coherent coupling of spatially separated excitonic qubits via the photon mode of a solid state microresonator. This is revealed by two-dimensional spectroscopy of the sample's coherent response, a sensitive and selective probe of the coherent coupling. The experimental results are quantitatively described by a rigorous theory of the cavity mediated coupling within a cluster of quantum dots excitons. Having demonstrated this mechanism, it can be used in extended coupling channels - sculptured, for instance, in photonic crystal cavities - to enable a long-range, non-local wiring up of individual emitters in solids.

quant-ph↗
arXiv2012

Evaluation of Multi-Sums for Large Scale Problems

A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme.

math-ph↗
arXiv2012

New Heavy Flavor Contributions to the DIS Structure Function $F_2(x,Q^2)$ at $O(α_s^3)

We report on recent results obtained for the massive Wilson coefficients which contribute to the structure function $F_2(x,Q^2)$ at $O(α_s^3)$ in the region $Q^2/m^2 \gsim 10$. In the calculation new species of harmonic sums and harmonic polylogarithms generated by cyclotomic polynomials arise in intermediary results which are briefly discussed.

hep-ph↗
arXiv2011

Multi-dimensional laser spectroscopy of exciton-polaritons with spatial light modulators

We describe an experimental system that allows one to easily access the dispersion curve of exciton-polaritons in a microcavity. Our approach is based on two spatial light modulators (SLM), one for changing the excitation angles (momenta), and the other for tuning the excitation wavelength. We show that with this setup, an arbitrary number of states can be excited accurately and that re-configuration of the excitation scheme can be done at high speed.

cond-mat.mes-hall↗
arXiv2010

Conditional phase shift from a quantum dot in a pillar microcavity

Large conditional phase shifts from coupled atom-cavity systems are a key requirement for building a spin photon interface. This in turn would allow the realisation of hybrid quantum information schemes using spin and photonic qubits. Here we perform high resolution reflection spectroscopy of a quantum dot resonantly coupled to a pillar microcavity. We show both the change in reflectivity as the quantum dot is tuned through the cavity resonance, and measure the conditional phase shift induced by the quantum dot using an ultra stable interferometer. These techniques could be extended to the study of charged quantum dots, where it would be possible to realise a spin photon interface.

quant-ph↗
arXiv2010

The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity

The contributions $\propto n_f$ to the $O(α_s^3)$ 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 general values of the Mellin variable $N$. Here, for two matrix elements, $A_{qq,Q}^{\sf PS}(N)$ and $A_{qg,Q}(N)$, the complete result is obtained. A first independent computation of the contributions to the 3--loop anomalous dimensions $γ_{qg}(N)$, $γ_{qq}^{\sf PS}(N$ and $γ_{qq}^{\sf NS,(TR)}(N)$ is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.

hep-ph↗
arXiv2010

Heavy Flavor DIS Wilson coefficients in the asymptotic regime

We report on results for the heavy flavor contributions to $F_2(x,Q^2)$ in the limit $Q^2\gg m^2$ at {\sf NNLO}. By calculating the massive $3$--loop operator matrix elements, we account for all but the power suppressed terms in $m^2/Q^2$. Recently, the calculation of fixed Mellin moments of all $3$--loop massive operator matrix elements has been finished. We present new all--$N$ results for the $O(n_f)$--terms, thereby confirming the corresponding parts of the $3$--loop anomalous dimensions. Additionally, we report on first genuine $3$--loop results of the ladder--type diagrams for general values of the Mellin variable $N$.

hep-ph↗
arXiv2010

Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams

By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2--loop and 3--loop massive single scale Feynman diagrams with local operator insertion.

math-ph↗
arXiv2009

From Moments to Functions in Quantum Chromodynamics

Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.

hep-ph↗
arXiv2009

Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space. It is often easier to calculate fixed moments for these quantities compared to a direct attempt to derive them in terms of harmonic sums and their generalizations involving the Mellin parameter $N$. Starting from a sufficiently large number of given moments, we establish linear recurrence relations of lowest possible order with polynomial coefficients of usually high degree. Then these recurrence equations are solved in terms of d'Alembertian solutions where the involved nested sums are represented in optimal nested depth. Given this representation, it is then an easy task to express the result in terms of harmonic sums. In this process we compactify the result such that no algebraic relations occur among the sums involved. We demonstrate the method for the QCD unpolarized anomalous dimensions and massless Wilson coefficients to 3--loop order treating the contributions for individual color coefficients. For the most complicated subproblem 5114 moments were needed in order to produce a recurrence of order 35 whose coefficients have degrees up to 938. About four months of CPU time were needed to establish and solve the recurrences for the anomalous dimensions and Wilson coefficients on a 2 GHz machine requiring less than 10 GB of memory. No algorithm is known yet to provide such a high number of moments for 3--loop quantities. Yet the method presented shows that it is possible to establish and solve recurrences of rather large order and and degree, occurring in physics problems, uniquely, fast and reliably with computer algebra.

hep-ph↗
arXiv2008

High-resolution X-ray spectroscopy of the evolving shock in the 2006 outburst of RS Ophiuchi

The evolution of the 2006 outburst of the recurrent nova RS Ophiuchi was followed with 12 X-ray grating observations with Chandra and XMM-Newton. We present detailed spectral analyses using two independent approaches. From the best dataset, taken on day 13.8 after outburst, we reconstruct the temperature distribution and derive elemental abundances. We find evidence for at least two distinct temperature components on day 13.8 and a reduction of temperature with time. The X-ray flux decreases as a power-law, and the power-law index changes from -5/3 to -8/3 around day 70 after outburst. This can be explained by different decay mechanisms for the hot and cool components. The decay of the hot component and the decrease in temperature are consistent with radiative cooling, while the decay of the cool component can be explained by the expansion of the ejecta. We find overabundances of N and of alpha-elements, which could either represent the composition of the secondary that provides the accreted material or that of the ejecta. The N overabundance indicates CNO-cycled material. From comparisons to abundances for the secondary taken from the literature, we conclude that 20-40% of the observed nitrogen could originate from the outburst. The overabundance of the alpha-elements is not typical for stars of the spectral type of the secondary in the RS Oph system, and white dwarf material might have been mixed into the ejecta. However, no direct measurements of the alpha-elements in the secondary are available, and the continuous accretion may have changed the observable surface composition.

astro-ph↗
arXiv2007

Feynman integrals and difference equations

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called Pi-Sigma-fields. We test the implementaion of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics.

math-ph↗
arXiv2007

Difference Equations in Massive Higher Order Calculations

The calculation of massive 2--loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter $N$. We report on the solution of these sums through higher order difference equations using the summation package {\tt Sigma}.

math-ph↗