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J. Blümlein

Publications and source records attributed to J. Blümlein.

At least 37 records · Page 2Linked to original sources
arXiv2022

The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2, F_L, xF_3$ and $g_1$

We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2), F_L(x,Q^2), x F_3(x,Q^2)$ in the $\overline{\sf MS}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial--vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three--loop Wilson coefficients are calculated for the first time. As a by--product we also obtain the quarkonic three--loop anomalous dimensions from the $O(1/\varepsilon)$ terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable $x$ are provided.

hep-ph↗
arXiv2022

Gravity in binary systems at the fifth and sixth post-Newtonian order

Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective One-Body Hamiltonian, extending the applicability of our results to the late inspiral and merger phases.

gr-qc↗
arXiv2022

Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses

We compute the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop (and 5th post-Newtonian) approximation to the harmonic coordinates effective action in a direct calculation. The computation is performed using effective field methods based on Feynman diagrams in momentum-space in $d = 3 - 2\varepsilon$ space dimensions. We also reproduce the previous results including the 4th post-Newtonian order.

gr-qc↗
arXiv2022

The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach

Within an effective field theory method to general relativity, we calculate the fifth-order post--Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in--in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, $q_{82}, q_{63}, q_{44}, \bar{d_5}$ and $a_6$, can all be determined from the local contributions to periastron advance $K^{\rm loc,h}(\hat{E},j)$, without further assumptions on the structure of the symmetric mass ratio, $ν$, of the expansion coefficients of the scattering angle $χ_k$. The $O(ν^2)$ contributions to the 5 PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables.

gr-qc↗
arXiv2022

The 3-loop anomalous dimensions from off-shell operator matrix elements

We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature.

hep-ph↗
arXiv2022

High Precision QED Initial State Corrections for $e^+ e^- \rightarrow γ^*/Z^*$ Annihilation

The precise knowledge of the QED initial state corrections is of instrumental importance in studying high luminosity measurements in $e^+e^-$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC\_ee. Logarithmic corrections of up to $O(α^6 L^5)$ are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like $e^+ e^- \rightarrow γ^*/Z^*$ and also the forward-backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far.

hep-ph↗
arXiv2022

The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms

We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and difference ring theory, based on integration-by-parts relations. This method also constitutes one way to compute the QCD anomalous dimensions. The presented higher order contributions to these operator matrix elements occur as building blocks in the corresponding higher order calculations up to four--loop order. All contributing quantities can be expressed in terms of harmonic sums in Mellin--$N$ space or by harmonic polylogarithms in $z$--space. We also perform comparisons to the literature.

hep-ph↗
arXiv2021

Hypergeometric Structures in Feynman Integrals

Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We solve these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series. The expansion coefficients can be determined using either the package {\tt Sigma} in the case of linear difference equations or by applying heuristic methods in the case of partial linear difference equations. In the present context a new type of sums occurs, the Hurwitz harmonic sums, and generalized versions of them. The code {\tt HypSeries} transforming classes of differential equations into analytic series expansions is described. Also partial difference equations having rational solutions and rational function solutions of Pochhammer symbols are considered, for which the code {\tt solvePartialLDE} is designed. Generalized hypergeometric functions, Appell-,~Kampé de Fériet-, Horn-, Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We illustrate the algorithms by examples.

math-ph↗
arXiv2021

The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three--loop order in the M--scheme by using the traditional method of space--like off--shell massless operator matrix elements, being a gauge--dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non--singlet splitting function $ΔP_{\rm qq}^{(2), \rm s, NS}$ and compare the final results to the literature, also including predictions for the region of small values of Bjorken $x$.

hep-ph↗
arXiv2021

The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements

We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{\rm NS}^{\rm \pm tr}$ for transversity directly. We compare our results to the literature.

hep-ph↗
arXiv2021

The N$^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F^{\rm NS}_2(x,Q^2)$ and $g_1^{\rm NS}(x,Q^2)$

We present the scheme-invariant unpolarized and polarized flavor non-singlet evolution equation to N$^3$LO for the structure functions $F_2(x,Q^2)$ and $g_1(x,Q^2)$ including the charm- and bottom quark effects in the asymptotic representation. The corresponding evolution is based on the experimental measurement of the non-singlet structure functions at a starting scale $Q_0^2$. In this way the evolution does only depend on the strong coupling constant $α_s(M_Z)$ or the QCD scale $Λ_{\rm QCD}$ and the charm and bottom quark masses $m_c$ and $m_b$ and provides one of the cleanest ways to measure the strong coupling constant in future high luminosity deep-inelastic scattering experiments. The yet unknown parts of the 4-loop anomalous dimensions introduce only a marginal error in this analysis.

hep-ph↗
arXiv2021

The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering

We compute the logarithmic contributions to the polarized massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the polarized massive operator matrix elements needed in the variable flavor number scheme. The calculation is performed in the Larin scheme. For the massive operator matrix elements $A_{qq,Q}^{(3),\rm PS}$ and $A_{qg,Q}^{(3),\rm S}$ the complete results are presented. The expressions are given in Mellin-$N$ space and in momentum fraction $z$-space.

hep-ph↗
arXiv2021

The Large Hadron-Electron Collider at the HL-LHC

The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

hep-ex↗
arXiv2021

Analytic integration methods in quantum field theory: an Introduction

A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind.

hep-th↗
arXiv2021

Iterated integrals over letters induced by quadratic forms

An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer--Poincaré letters is presented. These quantities emerge in analytic single and multi--scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities.

hep-th↗
arXiv2021

The QED Initial State Corrections to the Forward-Backward Asymmetry of $e^+e^- \to γ^*/Z^{0*}$ to Higher Orders

The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow γ^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(α^6 L^6)$ extending the known corrections up to $O(α^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical results are presented for various energies around the $Z$-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC$\_$ee.

hep-ph↗
arXiv2021

The 6th Post-Newtonian Potential Terms at $O(G_N^4)$

We calculate the potential contributions of the Hamiltonian in harmonic coordinates up 6PN for binary mass systems to $O(G_N^4)$ and perform comparisons to recent results in the literature \cite{Bern:2021dqo} and \cite{Bini:2020nsb}.

gr-qc↗