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J. Blümlein

Publications and source records attributed to J. Blümlein.

At least 91 records · Page 5Linked to original sources
arXiv2017

Strange sea determination from collider data

We consider determinations of the strange sea in the nucleon based on the QCD analyses of data collected at the LHC with focus on the recent high-statistics ATLAS measurement of the $W^\pm$- and $Z$-boson production. We study the effect of different functional forms for parameterization of the parton distribution functions and the combination of various data sets in the analysis. We compare to earlier strange sea determinations and discuss ways to improve them in the future.

hep-ph↗
arXiv2017

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $ρ$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-$N$ space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as $_2F_1$ Gauß hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using $q$-product and series representations implied by Jacobi's $\vartheta_i$ functions and Dedekind's $η$-function. The corresponding representations can be traced back to polynomials out of Lambert--Eisenstein series, having representations also as elliptic polylogarithms, a $q$-factorial $1/η^k(τ)$, logarithms and polylogarithms of $q$ and their $q$-integrals. Due to the specific form of the physical variable $x(q)$ for different processes, different representations do usually appear. Numerical results are also presented.

hep-th↗
arXiv2017

Running of the Charm-Quark Mass from HERA Deep-Inelastic Scattering Data

Combined HERA data on charm production in deep-inelastic scattering have previously been used to determine the charm-quark running mass $m_c(m_c)$ in the MSbar renormalisation scheme. Here, the same data are used as a function of the photon virtuality $Q^2$ to evaluate the charm-quark running mass at different scales to one-loop order, in the context of a next-to-leading order QCD analysis. The scale dependence of the mass is found to be consistent with QCD expectations.

hep-ph↗
arXiv2017

Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses

Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, $η= m_c^2/m_b^2 \sim 1/10$, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two--mass case is different from the single mass case derived in \cite{Bierenbaum:2009mv}. We present the moments $N=2,4$ and $6$ for all contributing operator matrix elements, expanding in the ratio $η$. We calculate the analytic results for general values of the Mellin variable $N$ in the flavor non-singlet case, as well as for transversity and the matrix element $A_{gq}^{(3)}$. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element $A_{gg}$. As it turns out, the expansion in $η$ is usually inapplicable for general values of $N$. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

hep-ph↗
arXiv2017

The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$

We calculate the unpolarized twist-2 three-loop splitting functions $P_{qg}^{(2)}(x)$ and $P_{gg}^{(2,\rm N_F)}(x)$ and the associated anomalous dimensions using massive three-loop operator matrix elements. While we calculate $P_{gg}^{(2,\rm N_F)}(x)$ directly, $P_{qg}^{(2)}(x)$ is computed from 1200 even moments, without any structural prejudice, using a hierarchy of recurrences obtained for the corresponding operator matrix element. The largest recurrence to be solved is of order 12 and degree 191. We confirm results in the foregoing literature.

hep-ph↗
arXiv2017

Parton Distribution Functions, $α_s$ and Heavy-Quark Masses for LHC Run II

We determine a new set of parton distribution functions (ABMP16), the strong coupling constant $α_s$ and the quark masses $m_c$, $m_b$ and $m_t$ in a global fit to next-to-next-to-leading order (NNLO) in QCD. The analysis uses the $\overline{\mathrm{MS}}$ scheme for $α_s$ and all quark masses and is performed in the fixed-flavor number scheme for $n_f=3, 4, 5$. Essential new elements of the fit are the combined data from HERA for inclusive deep-inelastic scattering (DIS), data from the fixed-target experiments NOMAD and CHORUS for neutrino-induced DIS, and data from Tevatron and the LHC for the Drell-Yan process and the hadro-production of single-top and top-quark pairs. The theory predictions include new improved approximations at NNLO for the production of heavy quarks in DIS and for the hadro-production of single-top quarks. The description of higher twist effects relevant beyond the leading twist collinear factorization approximation is refined. At NNLO we obtain the value $α_s^{(n_f=5)}(M_Z) = 0.1147 \pm 0.0008$.

hep-ph↗
arXiv2016

The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^+-W^-}(x,Q^2)$ and $F_2^{W^+-W^-}(x,Q^2)$

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure functions $F_L^{W^+}(x,Q^2)-F_L^{W^-}(x,Q^2)$ and $F_2^{W^+}(x,Q^2)-F_2^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production, also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the unpolarized Bjorken sum rule and Adler sum rule are discussed.

hep-ph↗
arXiv2016

A Critical Appraisal and Evaluation of Modern PDFs

We review the present status of the determination of parton distribution functions (PDFs) in the light of the precision requirements for the LHC in Run 2 and other future hadron colliders. We provide brief reviews of all currently available PDF sets and use them to compute cross sections for a number of benchmark processes, including Higgs boson production in gluon-gluon fusion at the LHC. We show that the differences in the predictions obtained with the various PDFs are due to particular theory assumptions made in the fits of those PDFs. We discuss PDF uncertainties in the kinematic region covered by the LHC and on averaging procedures for PDFs, such as advocated by the PDF4LHC15 sets, and provide recommendations for the usage of PDF sets for theory predictions at the LHC.

hep-ph↗
arXiv2016

Summary of workshop on Future Physics with HERA Data

Recent highlights from the HERA experiments, Hermes, H1 and ZEUS, are reviewed and ideas for future analyses to fully exploit this unique data set are proposed. This document is a summary of a workshop on future physics with HERA data held at DESY, Hamburg at the end of 2014. All areas of HERA physics are covered and contributions from both experimentalists and theorists are included. The document outlines areas where HERA physics can still make a significant contribution, principally in a deeper understanding of QCD, and its relevance to other facilities. Within the framework of the Data Preservation in High Energy Physics, the HERA data have been preserved for analyses to take place over a timescale of 10 years and more. Therefore, although an extensive list of possibilities is presented here, safe storage of the data ensures that it can also be used in the far future should new ideas and analyses be proposed.

hep-ex↗
arXiv2015

High-precision $α_s$ measurements from LHC to FCC-ee

This document provides a writeup of all contributions to the workshop on "High precision measurements of $α_s$: From LHC to FCC-ee" held at CERN, Oct. 12--13, 2015. The workshop explored in depth the latest developments on the determination of the QCD coupling $α_s$ from 15 methods where high precision measurements are (or will be) available. Those include low-energy observables: (i) lattice QCD, (ii) pion decay factor, (iii) quarkonia and (iv) $τ$ decays, (v) soft parton-to-hadron fragmentation functions, as well as high-energy observables: (vi) global fits of parton distribution functions, (vii) hard parton-to-hadron fragmentation functions, (viii) jets in $e^\pm$p DIS and $γ$-p photoproduction, (ix) photon structure function in $γ$-$γ$, (x) event shapes and (xi) jet cross sections in $e^+e^-$ collisions, (xii) W boson and (xiii) Z boson decays, and (xiv) jets and (xv) top-quark cross sections in proton-(anti)proton collisions. The current status of the theoretical and experimental uncertainties associated to each extraction method, the improvements expected from LHC data in the coming years, and future perspectives achievable in $e^+e^-$ collisions at the Future Circular Collider (FCC-ee) with $\cal{O}$(1--100 ab$^{-1}$) integrated luminosities yielding 10$^{12}$ Z bosons and jets, and 10$^{8}$ W bosons and $τ$ leptons, are thoroughly reviewed. The current uncertainty of the (preliminary) 2015 strong coupling world-average value, $α_s(m_Z)$ = 0.1177 $\pm$ 0.0013, is about 1\%. Some participants believed this may be reduced by a factor of three in the near future by including novel high-precision observables, although this opinion was not universally shared. At the FCC-ee facility, a factor of ten reduction in the $α_s$ uncertainty should be possible, mostly thanks to the huge Z and W data samples available.

hep-ph↗
arXiv2015

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable $N$ and the dimensional parameter $\varepsilon$. Given these representations, the desired Laurent series expansions in $\varepsilon$ can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of $N$ are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of $V$-topologies.

hep-ph↗
arXiv2015

The O(α_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure function $xF_3^{W^+}(x,Q^2)+xF_3^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the Gross-Llewellyn Smith sum rule are discussed.

hep-ph↗
arXiv2015

The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function $g_1(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$ and the momentum fraction $x$, and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function $g_2(x,Q^2)$ in the twist-2 approximation are also given.

hep-ph↗
arXiv2014

Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering

The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities $Q^2$. We also describe a series of mathematical, computer-algebraic and combinatorial methods and special function spaces, needed to perform these calculations. Finally, we briefly discuss the status of measuring $α_s(M_Z)$, the charm quark mass $m_c$, and the parton distribution functions at next-to-next-to-leading order from the world precision data on deep-inelastic scattering.

hep-ph↗
arXiv2014

3-loop heavy flavor Wilson coefficients in deep-inelastic scattering

We present our most recent results on the calculation of the heavy flavor contributions to deep-inelastic scattering at 3-loop order in the large $Q^2$ limit, where the heavy flavor Wilson coefficients are known to factorize into light flavor Wilson coefficients and massive operator matrix elements. We describe the different techniques employed for the calculation and show the results in the case of the heavy flavor non-singlet and pure singlet contributions to the structure function $F_2(x,Q^2)$.

hep-ph↗
arXiv2014

3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$

Contributions to heavy flavour transition matrix elements in the variable flavour number scheme are considered at 3-loop order. In particular a calculation of the diagrams with two equal masses that contribute to the massive operator matrix element $A_{gg,Q}^{(3)}$ is performed. In the Mellin space result one finds finite nested binomial sums. In $x$-space these sums correspond to iterated integrals over an alphabet containing also square-root valued letters.

hep-ph↗