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ABSTRACT: In this paper we compute the four-loop corrections to the QED photon
self-energy Pi(Q^2) in the two limits of q=0 and Q^2->infinity. These results
are used to explicitly construct the conversion relations between the QED
charge renormalized in on-shell(OS) and MSbar scheme. Using these relations and
results of Baikov et al. [1] we construct the momentum dependent part of
Pi(Q^2,m,alpha) at large Q^2 at five loops in both MSbar and OS schemes. As a
direct consequence we arrive at the full result for the QED beta-function in
the OS scheme at five loops. These results are applied, in turn, to
analytically evaluate a class of asymptotic contributions to the muon anomaly
at five and six loops.
07/2012;
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ABSTRACT: Recent theoretical and experimental improvements in the determination of charm and bottom quark masses are discussed. A new and improved evaluation of the contribution from the gluon condensate $\langle \frac{\alpha_s}{\pi} G^2\rangle$ to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for $b\bar b$ production is presented, together with a study of the parametric uncertainty from the $\alpha_s$-dependence of our results. The final results, $m_c(3\,\text{GeV})=986(13)\,$MeV and $m_b(m_b)=4163(16)\,$MeV, represent, together with a closely related lattice determination $m_c(3\;{\rm GeV})=986(6)\,$MeV, the presently most precise determinations of these two fundamental Standard Model parameters. A critical analysis of the theoretical and experimental uncertainties is presented. Comment: 12 pages, presented at Quarks~2010, 16th International Seminar of High Energy Physics, Kolomna, Russia, June 6-12, 2010
10/2010;
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ABSTRACT: Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass, $m_c(3 {\rm GeV})= 0.986(13) {\rm GeV}$, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark, $m_b(10 {\rm GeV})= 3.610(16) {\rm GeV}$, corresponding to $m_b(m_b)= 4.163(16) {\rm GeV}$, makes use both of the new data and the new perturbative results and is consistent with the earlier determination. Comment: 5 pages
07/2009;
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I. Allison,
E. Dalgic,
C. T. H. Davies,
E. Follana,
R. R. Horgan,
K. Hornbostel,
G. P. Lepage,
C. McNeile,
J. Shigemitsu,
H. Trottier,
R. M. Woloshyn,
K. G. Chetyrkin,
J. H. Kuhn,
M. Steinhauser, C. Sturm
[show abstract]
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ABSTRACT: We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_\msb(M_Z,n_f=5)=0.1174(12). The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for e+e- annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.
06/2008;
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ABSTRACT: The four-loop QCD corrections to the electroweak rho parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing "nonsinglet" piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. The inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass are thus stabilized.
Physical Review Letters 10/2006; 97(10):102003. · 7.37 Impact Factor
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ABSTRACT: New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed.
European Physical Journal C 09/2006; 48(1):107-110. · 3.63 Impact Factor
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ABSTRACT: The four-loop QCD corrections to the electroweak $\rho$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized.
06/2006;
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[show abstract]
[hide abstract]
ABSTRACT: New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass. Implications for the value of the quark masses are briefly discussed.
05/2006;
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ABSTRACT: We report about recent progress in computing four-loop massive correlators. The expansion of these correlators in the external momentum leads to vacuum integrals. The calculation of these vacuum integrals can be used to determine Taylor expansion coefficients of the vacuum polarization function and decoupling functions in perturbative Quantum chromodynamics. New results at four-loop order for the lowest Taylor expansion coefficient of the vacuum polarization function and for the decoupling relation are presented.
05/2006;
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ABSTRACT: It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ep-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Pade approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schr\"oder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.
02/2006;
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ABSTRACT: We present the matching condition for the strong coupling contant alpha_s at a heavy quark threshold to four loops in the modified minimal subtraction scheme. Our results lead to further decrease of the theoretical uncertainty of the evolution of the strong coupling constant through heavy quark thresholds. Using a low energy theorem we furthermore derive the effective coupling of the Higgs boson to gluons (induced by a virtual heavy quark) in four- and (partially) through five-loop approximation.
01/2006;
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ABSTRACT: The vacuum polarization due to a virtual heavy quark pair and specifically the coefficients of its Taylor expansion in the external momentum are closely related to moments of the cross section for quark-antiquark pair production in electron-positron annihilation. Relating measurement and theoretically calculated Taylor coefficients, an accurate value for charm- and bottom-quark mass can be derived, once corrections from perturbative QCD are sufficiently well under control. Up to three-loop order these have been evaluated previously. We now present a subset of four-loop contributions to the lowest two moments, namely those from diagrams which involve two internal loops from massive and massless fermions coupled to virtual gluons, hence of order
as3 nf2\alpha_s^3 n_f^2
. The calculation demonstrates the applicability of Laportaas3\alpha_s^3
contribution.
European Physical Journal C 03/2005; 40(3):361-366. · 3.63 Impact Factor
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[show abstract]
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ABSTRACT: The vacuum polarization due to a virtual heavy quark pair and specifically the coefficients of its Taylor expansion in the external momentum are closely related to moments of the cross section for quark-antiquark pair production in electron-positron annihilation. Relating measurement and theoretically calculated Taylor coefficients, an accurate value for charm- and bottom-quark mass can be derived, once corrections from perturbative QCD are sufficiently well under control. Up to three-loop order these have been evaluated previously. We now present a subset of four-loop contributions to the lowest two moments, namely those from diagrams which involve two internal loops from massive and massless fermions coupled to virtual gluons, hence of order alphas^3 nf^2. The calculation demonstrates the applicability of Laporta's algorithm to four-loop vacuum diagrams with both massive and massless propagators and should be considered a first step towards the full evaluation of the order alphas^3 contribution.
01/2005;
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[show abstract]
[hide abstract]
ABSTRACT: It is shown that for every problem within dimensional regularization, using the integration-by-parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ϵ-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Padé approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schröder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.
Nuclear Physics B.
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[show abstract]
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ABSTRACT: We present the matching condition for the strong coupling constant at a heavy quark threshold to four loops in the modified minimal subtraction scheme. Our results lead to further decrease of the theoretical uncertainty of the evolution of the strong coupling constant through heavy quark thresholds. Using a low energy theorem we furthermore derive the effective coupling of the Higgs boson to gluons (induced by a virtual heavy quark) in four- and (partially) through five-loop approximation.
Nuclear Physics B.
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[show abstract]
[hide abstract]
ABSTRACT: We report about recent progress in computing four-loop massive correlators. The expansion of these correlators in the external momentum leads to vacuum integrals. The calculation of these vacuum integrals can be used to determine Taylor expansion coefficients of the vacuum polarization function and decoupling functions in perturbative Quantum chromodynamics. New results at four-loop order for the lowest Taylor expansion coefficient of the vacuum polarization function and for the decoupling relation are presented.
Nuclear Physics B - Proceedings Supplements.
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I. Allison,
E. Dalgic,
CTH Davies,
E. Follana,
RR Horgan,
K. Hornbostel,
GP Lepage,
C. McNeile,
J. Shigemitsu,
H. Trottier,
RM Woloshyn,
KG Chetyrkin,
JH Kuehn,
M. Steinhauser, C. Sturm
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ABSTRACT: We have constructed an ϵ-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak ρ-parameter. Using transformation rules from the ϵ-finite basis to the standard “minimal-number-of-lines” basis, we obtain as a by-product analytical expressions for few leading terms of the ϵ-expansion of all members of the standard basis. The new master integrals have been computed with the help of the Padé method and by use of difference equations independently.
Nuclear Physics B.
