arXiv subjects
Publications and source records attributed to J. Blümlein.
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the $O(n_f T_F^2 C_{F,A})$ and $O(T_F^2 C_{F,A})$ gluonic corrections, two-mass quarkonic moments, and ladder- and Benz-topologies. We also discuss technical aspects of the calculations.
The physics programme and the design are described of a new collider for particle and nuclear physics, the Large Hadron Electron Collider (LHeC), in which a newly built electron beam of 60 GeV, up to possibly 140 GeV, energy collides with the intense hadron beams of the LHC. Compared to HERA, the kinematic range covered is extended by a factor of twenty in the negative four-momentum squared, $Q^2$, and in the inverse Bjorken $x$, while with the design luminosity of $10^{33}$ cm$^{-2}$s$^{-1}$ the LHeC is projected to exceed the integrated HERA luminosity by two orders of magnitude. The physics programme is devoted to an exploration of the energy frontier, complementing the LHC and its discovery potential for physics beyond the Standard Model with high precision deep inelastic scattering measurements. These are designed to investigate a variety of fundamental questions in strong and electroweak interactions. The physics programme also includes electron-deuteron and electron-ion scattering in a $(Q^2, 1/x)$ range extended by four orders of magnitude as compared to previous lepton-nucleus DIS experiments for novel investigations of neutron's and nuclear structure, the initial conditions of Quark-Gluon Plasma formation and further quantum chromodynamic phenomena. The LHeC may be realised either as a ring-ring or as a linac-ring collider. Optics and beam dynamics studies are presented for both versions, along with technical design considerations on the interaction region, magnets and further components, together with a design study for a high acceptance detector. Civil engineering and installation studies are presented for the accelerator and the detector. The LHeC can be built within a decade and thus be operated while the LHC runs in its high-luminosity phase. It thus represents a major opportunity for progress in particle physics exploiting the investment made in the LHC.
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.
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.
We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the $O(α^2)$ initial state corrections to $e^+e^-$ annihilation into a virtual boson for large cms energies $s \gg m_e^2$ into massive operator matrix elements and the massless Wilson coefficients of the Drell-Yan process adapting the color coefficients to the case of QED, as proposed by Berends et. al. in Ref. [1]. Our calculations show explicitly that the representation proposed in Ref. [1] works at one-loop order and up to terms linear in $\ln(s/m^2_e)$ at two-loop order. However, the two-loop constant part contains a few structural terms, which have not been obtained in previous direct calculations.
We report on recent results obtained for the massive operator matrix elements which contribute to the massive Wilson coefficients in deep-inelastic scattering for $Q^2 \gg m_i^2$ in case of sub-processes with two fermion lines and different mass assignment.
We study the impact of Tevatron jet data on a global fit of parton distribution functions and on the determination of the value of the strong coupling constant. The consequences are illustrated for cross sections of Higgs boson production at Tevatron and the LHC.
We provide a fast and precise Mellin-space implementation of the $O(α_s)$ heavy flavor Wilson coefficients for charged current deep inelastic scattering processes. They are of importance for the extraction of the strange quark distribution in neutrino-nucleon scattering and the QCD analyses of the HERA charged current data. Errors in the literature are corrected. We also discuss a series of more general parton parameterizations in Mellin space.
We summarize the results of recent determinations of $α_s(M_Z^2)$ in NNLO QCD analyses of the deep-inelastic world data.
The inclusive production cross sections for $W^+, W^-$ and $Z^0$-bosons form important benchmarks for the physics at hadron colliders. We perform a detailed comparison of the predictions for these standard candles based on recent next-to-next-to-leading order (NNLO) parton parameterizations and new analyses including the combined HERA data, compare to all available experimental results, and discuss the predictions for present and upcoming RHIC, SPS, Tevatron and LHC energies. The rates for gauge boson production at the LHC can be rather confidently predicted with an accuracy of better than about 10% at NNLO. We also present detailed NNLO predictions for the Higgs boson production cross sections for Tevatron and LHC energies (1.96, 7, 8, 14 TeV), and propose a possible method to monitor the gluon distribution experimentally in the kinematic region close to the mass range expected for the Higgs boson. The production cross sections of the Higgs boson at the LHC are presently predicted with an accuracy of about 10--17%. The inclusion of the NNLO contributions is mandatory for achieving such accuracies since the total uncertainties are substantially larger at NLO.
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.
The logarithmic contributions to the massive twist-2 operator matrix elements for deep-inelastic scattering are calculated to $O(α_s^3)$for general values of the Mellin variable $N$.
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 $N$.
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.
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolating between the zero-mass 4-flavor scheme at asymptotically large values of momentum transfer $Q^2$ and the 3-flavor scheme prescription of Buza-Matiounine-Smith-van Neerven (BMSN) at the value of $Q^2 = m_c^2$. The results in the GMVFN scheme are compared with those of the fixed-flavor scheme and other prescriptions used in global fits of PDFs. The strong coupling constant is measured at an accuracy of $\approx 1.5%$. We obtain at NNLO $α_s(M_Z^2) = 0.1135 \pm 0.0014$ in the fixed-flavor scheme and $α_s(M_Z^2) = 0.1129 \pm 0.0applying the BMSN-prescription. The implications for important standard candle and hard scattering processes at hadron colliders are illustrated. Predictions for cross sections of $W^{\pm}$- and $Z$-boson, the top-quark pair- and Higgs-boson production at the Tevatron and the LHC based on the 5-flavor PDFs of the present analysis are provided.014$
We provide a data mine of proven results for multiple zeta values (MZVs) of the form $ζ(s_1,s_2,...,s_k)=\sum_{n_1>n_2>...>n_k>0}^\infty \{1/(n_1^{s_1} >... n_k^{s_k})\}$ with weight $w=\sum_{i=1}^k s_i$ and depth $k$ and for Euler sums of the form $\sum_{n_1>n_2>...>n_k>0}^\infty t\{(ε_1^{n_1} >...ε_1 ^{n_k})/ (n_1^{s_1} ... n_k^{s_k}) \}$ with signs $ε_i=\pm1$. Notably, we achieve explicit proven reductions of all MZVs with weights $w\le22$, and all Euler sums with weights $w\le12$, to bases whose dimensions, bigraded by weight and depth, have sizes in precise agreement with the Broadhurst--Kreimer and Broadhurst conjectures. Moreover, we lend further support to these conjectures by studying even greater weights ($w\le30$), using modular arithmetic. To obtain these results we derive a new type of relation for Euler sums, the Generalized Doubling Relations. We elucidate the "pushdown" mechanism, whereby the ornate enumeration of primitive MZVs, by weight and depth, is reconciled with the far simpler enumeration of primitive Euler sums. There is some evidence that this pushdown mechanism finds its origin in doubling relations. We hope that our data mine, obtained by exploiting the unique power of the computer algebra language {\sc form}, will enable the study of many more such consequences of the double-shuffle algebra of MZVs, and their Euler cousins, which are already the subject of keen interest, to practitioners of quantum field theory, and to mathematicians alike.
We calculate the two- and three-loop massive operator matrix elements (OMEs) contributing to the heavy flavor Wilson coefficients of transversity. We obtain the complete result for the two-loop OMEs and compute the first thirteen Mellin moments at three-loop order. As a by-product of the calculation, the moments N=1 to 13 of the complete two-loop and the $T_F$-part of the three-loop transversity anomalous dimension are obtained.
In deep-inelastic processes the heavy flavor Wilson coefficients factorize for $Q^2 \gg m^2$ into the light flavor Wilson coefficients of the corresponding process and the massive operator matrix elements (OMEs). We calculate the $O(α_s^2)$ and $O(α_s^3)$ massive OME for the flavor non-singlet transversity distribution. At $O(α_s^2)$ the OME is obtained for general values of the Mellin variable $N$, while at $O(α_s^3)$ the moments $N = 1$ to 13 are computed. The terms $\propto T_F$ of the 3--loop transversity anomalous dimension are obtained and results in the literature are confirmed. We discuss the relation of these contributions to the Soffer bound for transversity.