The analytical value of the electron (g − 2) at order α3 in QED

Abstract

We have evaluated in closed analytical form the contribution of the three-loop non-planar 'triple-cross' diagrams contributing to the electron (g-2) in QED; its value, omitting the already known infrared divergent part, is

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

“…We carry out the calculation by employing the technique based on the Laporta algorithm [75][76][77][78] and the differential equation method [79][80][81][82][83][84][85][86], already used in [73,74]. The calculation of the leading color coefficient in the gluon fusion does not require the calculation of any new master integrals beyond the ones obtained in the two previous works, such that we do not discuss the calculational method in full detail.…”

Calculating three-loop diagrams in heavy quark effective theory with integration-by-parts recurrence relations

“…Reduction of two-loop propagator integrals with generic masses and momentum to a finite set of bases integrals has been achieved [12]. First three-loop on-shell calculations have been done recently [11,13].…”

Algebraic algorithms for multiloop calculations The first 15 years. What's next?

“…replaced with + N i 's with required N i ≥ 0 (or even with some N i < 0 if the integer part of the i -th original power was already positive), and with Q on the r.h.s. This is similar to explicit solution of recurrent relations in the conventional algorithms [3], [12].…”

“…Consider integrals of the form d Contrast this with the "algebraic calculability" of [14] which attempts to normalize the spectacular success achieved in the case of massless self-energies which was merely a matter of luck. A situation much more like what I envisaged in the beginning occured in the case of anomalous magnetic moment where everything reduces to 18 independent integrals [12].…”

“…The Drilling Through The Moon With A Colossal Auger -such was the subject of Mr. Lund's speech!… [11] The range of applications of algebraic algorithms of the conventional type (differential identities in momentum space [1]) continues to expand (cf. the recent applications to the electron magnetic moment [12] and to the effective heavy quark theories [13]). What I'd like to discuss now is the case of integrals with several external parameters (s, t , masses etc.…”