282 research outputs found

    Subleading Logarithmic QED Initial State Corrections to e+e−→γ∗/Z0∗e^+e^- \rightarrow \gamma^*/{Z^{0}}^* to O(α6L5)O(\alpha^6 L^5)

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    Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process e+e−→γ∗/Z∗e^+e^- \rightarrow \gamma^*/Z^* for the first three logarithmic contributions from O(α3L3),O(α3L2),O(α3L)O(\alpha^3 L^3), O(\alpha^3 L^2), O(\alpha^3 L) to O(α5L5),O(α5L4),O(α5L3)O(\alpha^5 L^5), O(\alpha^5 L^4), O(\alpha^5 L^3) and compare their effects to the leading contribution O(α6L6)O(\alpha^6 L^6) and one more subleading term O(α6L5)O(\alpha^6 L^5). The calculation is performed in the limit of large center of mass energies squared s≫me2s \gg m_e^2. These terms supplement the known corrections to O(α2)O(\alpha^2), which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two--loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen--Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight {\sf w = 6} of argument zz and (1−z)(1-z) and in Mellin NN space by generalized harmonic sums. Numerical results are presented on the position of the ZZ peak and corrections to the ZZ width, ΓZ\Gamma_Z. The corrections calculated result into a final theoretical accuracy for δMZ\delta M_Z and δΓZ\delta \Gamma_Z which is estimated to be of O(30 keV) at an anticipated systematic accuracy at the FCC\_ee of \sim 100 keV. This precision cannot be reached, however, by including only the corrections up to O(α3)O(\alpha^3).Comment: 58 pages, 3 Figure

    Forfeiture of Attorney\u27s Fees Under RICO and CCE

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    We present the matching relations of the variable flavor number scheme at next-to-leading order, which are of importance to define heavy quark partonic distributions for the use at high energy colliders such as Tevatron and the LHC. The consideration of the two-mass effects due to both charm and bottom quarks, having rather similar masses, are important. These effects have not been considered in previous investigations. Numerical results are presented for a wide range of scales. We also present the corresponding contributions to the structure function F2(x,Q2)F_2(x,Q^2)

    The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization

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    We calculate the two-mass contribution to the 3-loop vacuum polarization of the gluon in Quantum Chromodynamics at virtuality p2=0p^2 = 0 for general masses and also present the analogous result for the photon in Quantum Electrodynamics.Comment: 5 pages Late

    The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

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    We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions F2F_2 and FLF_L we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

    The O(α2)O(\alpha^2) Initial State QED Corrections to e+e−e^+e^- Annihilation to a Neutral Vector Boson Revisited

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    We calculate the non-singlet, the pure singlet contribution, and their interference term, at O(α2)O(\alpha^2) due to electron-pair initial state radiation to e+e−e^+ e^- annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit s≫me2s \gg m_e^2 we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in m2/sm^2/s. In this way, we also confirm the validity of the factorization of massive partons in the Drell-Yan process. We also add non-logarithmic terms at O(α2)O(\alpha^2) which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in e+e−e^+e^- annihilation into γ∗/Z∗\gamma^*/Z^* at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file

    The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element Agg,Q(3)A_{gg,Q}^{(3)}

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    We calculate the two-mass QCD contributions to the massive operator matrix element Agg,QA_{gg,Q} at O(αs3)\mathcal{O} (\alpha_s^3) in analytic form in Mellin NN- and zz-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin NN-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to zz-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.Comment: 99 pages LATEX, 2 Figure

    The two-mass contribution to the three-loop pure singlet operator matrix element

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    We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function F2(x,Q2)F_2(x,Q^2) at O(αs3)O(\alpha_s^3) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.Comment: 28 papges Latex, 3 figure

    The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

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    We report on our latest results in the calculation of the two--mass contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and Agq,QA_{gq,Q} OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME Agg,QA_{gg,Q} are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two--mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.Comment: 20 pages Latex, 5 Figures, different style file

    The QED initial state corrections to the forward-backward asymmetry of e+^{+} e−^{-} → γ∗^{∗}/Z0∗^{0∗} to higher orders

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    The QED initial state corrections are calculated to the forward-backward asymmetry for e+^{+} e−^{-} → γ∗^{∗}/Z0∗^{0∗} in the leading logarithmic approximation to O(α6^{6}L6^{6}) extending the known corrections up to O(α2^{2}L2^{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

    The QED Initial State Corrections to the Forward-Backward Asymmetry of e+e−→γ∗/Z0∗e^+e^- \to \gamma^*/Z^{0*} to Higher Orders

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    The QED initial state corrections are calculated to the forward-backward asymmetry for e+e−→γ∗/Z0∗e^+e^- \rightarrow \gamma^*/{Z^{0}}^* in the leading logarithmic approximation to O(α6L6)O(\alpha^6 L^6) extending the known corrections up to O(α2L2)O(\alpha^2 L^2) in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-NN and momentum fraction zz-space. Numerical results are presented for various energies around the ZZ-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC_\_ee.Comment: Dedicated to the Memory of Tini Veltman, who made it possible to probe the Standard Model at high precisio
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