2,178 research outputs found

    Low-energy moments of non-diagonal quark current correlators at four loops

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    We compute the leading four physical terms in the low-energy expansions of heavy-light quark current correlators at four-loop order. As a by-product we reproduce the corresponding top-induced non-singlet correction to the electroweak rho parameter.Comment: 13 pages, no figures. Extended discussion and added reference

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

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    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=32εd = 3 - 2\varepsilon space dimensions. We also reproduce the previous results including the 4th post-Newtonian order.Comment: 15 pages, 4 figure

    Four-loop relation between the MSˉ\bar{\rm MS} and on-shell quark mass

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    In this contribution we discuss the four-loop relation between the on-shell and MSˉ\bar{\rm MS} definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the MSˉ\bar{\rm MS} quark mass and various threshold mass definitions and discuss the uncertainty at next-to-next-to-next-to-leading order.Comment: 9 pages, 2 figures, to appear in the proceedings of the 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders

    Quark mass relations to four-loop order

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    We present results for the relation between a heavy quark mass defined in the on-shell and MSˉ\bar{\rm MS} scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MSˉ\bar{\rm MS} quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MSˉ\bar{\rm MS} heavy quark masses.Comment: 6 pages, v2: references added, typos in eq.(16) fixed, matches published versio

    Matching the heavy-quark fields in QCD and HQET at four loops

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    The QCD/HQET matching coefficient for the heavy-quark field is calculated up to four loops. It must be finite; this requirement produces analytical results for some terms in the four-loop on-shell heavy-quark field renormalization constant which were previously only known numerically. The effect of a non-zero lighter-flavor mass is calculated up to three loops. A class of on-shell integrals with two masses is analyzed in detail. By specifying our result to QED, we obtain the relation between the electron field and the Bloch--Nordsieck field with four-loop accuracy.Comment: 20 pages. v2: ref. [48] added, small changes in the text, corresponds to the journal versio

    (g2)μ(g-2)_\mu at four loops in QED

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    We review the four-loop QED corrections to the anomalous magnetic moment of the muon. The fermionic contributions with closed electron and tau contributions are discussed. Furthermore, we report on a new independent calculation of the universal four-loop contribution and compare with existing results.Comment: 6 pages, Contribution to the proceedings of the International workshop on e+e- collisions from Phi to Psi 2017, v2: references adde

    MS\overline{\rm MS}-on-shell quark mass relation up to four loops in QCD and a general SU(N)(N) gauge group

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    In this paper we compute the relation between heavy quark masses defined in the modified minimal subtraction and on-shell scheme. Detailed results are presented for all coefficients of the SU(Nc)(N_c) colour factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Some of the about 380 master integrals are computed analytically, others with high numerical precision based on Mellin-Barnes representations, and the rest numerically with the help of {\tt FIESTA}. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the MS\overline{\rm MS} quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quark. We discuss the dependence on the renormalization and factorization scale.Comment: 53 pages, 11 figures, v2: minor changes, references added, corresponds to published versio

    The ρ\rho parameter at three loops and elliptic integrals

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    We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the ρ\rho parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.Comment: 14 pages Latex, 7 figures, to appear in the Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, Po

    The Heavy Quark Form Factors at Two Loops

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    We compute the two-loop QCD corrections to the heavy quark form factors in case of the vector, axial-vector, scalar and pseudo-scalar currents up to second order in the dimensional parameter ϵ=(4D)/2\epsilon = (4-D)/2. These terms are required in the renormalization of the higher order corrections to these form factors.Comment: 131 pages, 3 figure
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