2,187 research outputs found
Low-energy moments of non-diagonal quark current correlators at four loops
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
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 space
dimensions. We also reproduce the previous results including the 4th
post-Newtonian order.Comment: 15 pages, 4 figure
Four-loop relation between the and on-shell quark mass
In this contribution we discuss the four-loop relation between the on-shell
and definition of heavy quark masses which is applied to the
top, bottom and charm case. We also present relations between the 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
We present results for the relation between a heavy quark mass defined in the
on-shell and 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
quark mass to next-to-next-to-next-to-leading order accuracy.
These relations play an important role in the accurate determination of the
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
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
at four loops in QED
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
-on-shell quark mass relation up to four loops in QCD and a general SU gauge group
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 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
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 parameter at three loops and elliptic integrals
We describe the analytic calculation of the master integrals required to
compute the two-mass three-loop corrections to the 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
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 . 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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