The analytical value of the corner-ladder graphs contribution to the electron (g − 2) in QED

Laporta, S.

doi:10.1016/0370-2693(94)01401-w

Cited by 30 publications

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“…, I 18 . The Laurent expansions in ǫ = (4 − D)/2 of the master integrals were calculated in analytical form, by direct calculation (the simpler ones) or by using identities which relate the coefficients of expansions to values of integrals in 4 dimensions already known from previous work [5,6,7,8]. Subsequently, in Ref.[9], we found that the QED contribution of all three-loop graphs can be reduced to a linear combination of the same master integrals, which are therefore the only master integrals needed in the three-loop calculation.…”

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High-precision ϵ-expansions of three-loop master integrals contributing to the electron g–2 in QED

Laporta

2001

Physics Letters B

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In this paper we calculate at high-precision the Laurent expansions in ǫ = (4 − D)/2 of the 17 master integrals which appeared in the analytical calculation of 3-loop QED contribution to the electron g-2, using difference and differential equations. The coefficients of the expansions so obtained are in perfect agreement with all the analytical expressions already known. The values of coefficients not previously known will be used in the high-precision calculation of the 4-loop QED contribution to the electron g-2.PACS number(s): 12.20.Ds Specific calculations and limits of quantum electrodynamics.The g-2 of the electron is probably one of the most precise test of QED. Over the years, the continuous improvements in the precision of experimental determinations have demanded correspondent improvements of the theoretical predictions. Let us recall the current status of calculations of QED contribution to the electron g-2. One-and two-loop contributions are known in closed analytical form for a long time. The calculation of three-loop contribution in closed analytical form was completed more recently[1], after many years of hard work. Four-loop contribution is known at present only numerically[2], with a precision of about 2.5%, obtained using Monte-Carlo integration methods. At present this precision is adequate for comparison with current experimental determinations. Anyway, there is the need of a new independent high-precision calculation, in order to cross-check the current numerical value and to improve considerably its precision, in view of future experiments.A technique which turned out to be useful in g-2 calculations is integration-by-parts [3,4]. The contribution to g-2 of a graph, expressed in the form of a combination of many different integrals with different powers in the numerator and in the denominator, is reduced to a linear combination of a small set of "master integrals" by using identities obtained by integrating-by-parts in D-dimension space-time. The master integrals must be calculated analytically or numerically in the limit D → 4 by some method.In Ref.[1] this technique was applied to the analytical calculation of the contribution to the electron g-2 of the last family of three-loop graphs still not known analytically, the so-called triple-cross graphs; the contributions of all the other three-loop graphs were already obtained in analytical form by other methods. The contribution of triple-cross graphs to the g-2 was reduced to a combination of 18 master integrals, called I 1 , I 2 , . . . , I 18 . The Laurent expansions in ǫ = (4 − D)/2 of the master integrals were calculated in analytical form, by direct calculation (the simpler ones) or by using identities which relate the coefficients of expansions to values of integrals in 4 dimensions already known from previous work [5,6,7,8]. Subsequently, in Ref.[9], we found that the QED contribution of all three-loop graphs can be reduced to a linear combination of the same master integrals, which are therefore the only master integrals needed in the...

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High-precision ϵ-expansions of three-loop master integrals contributing to the electron g–2 in QED

Laporta

2001

Physics Letters B

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“…As the previous graphs were the last graphs for which the analytical value of the anomaly was still missing, on account the previously known results [4,5,6,7] (5) By using the best numerical value of a e (4 − loop) = −1.557(70) , Ref. [8], and 1/α = 137.0359979(32) , Ref.…”

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“…(11), one finds for instance (16) Similarly, in Ref. [7] the following 7-denominator integral was evaluated…”

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

1996

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“…21 compares the contributions and uncertainties for g/2. The leading constants for second [64], third [65,66,67] and fourth [68,69,70,71,72] orders,…”

Section: New Determination Of the Fine Structure Constantmentioning

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Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant

Gabrielse¹

2009

The Spin

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The analytical value of the corner-ladder graphs contribution to the electron (g − 2) in QED

Cited by 30 publications

References 11 publications

High-precision ϵ-expansions of three-loop master integrals contributing to the electron g–2 in QED

High-precision ϵ-expansions of three-loop master integrals contributing to the electron g–2 in QED

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

Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant

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