Heavy-quark form factors in the large $$\beta _0$$ β 0 limit

Grozin, Andrey

doi:10.1140/epjc/s10052-017-5021-4

Cited by 10 publications

(4 citation statements)

References 35 publications

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“…[47]. The large β 0 limit for massive form factors has been considered in [56] and in [57], where the three-loop scalar and pseudo-scalar form factors were computed in the static limit.…”

Section: Introductionmentioning

confidence: 99%

Automated solution of first order factorizable systems of differential equations in one variable

et al. 2019

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We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the coefficient matrix of the differential equations. These systems appear in a large variety of higher order calculations in perturbative Quantum Field Theories. We apply this method to calculate the master integrals of the three-loop massive form factors for different currents, as an illustration, and present the results for the vector form factors in detail. Here the solution space emerging is given by the cyclotomic harmonic polylogarithms and their associated special constants. No special basis representation of the master integrals is needed. The algorithm can be applied as well to more general cases factorizing at first order, which are based on more general alphabets, iterated integrals and associated constants.

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“…[47]. The large β 0 limit for massive form factors has been considered in [56] and in [57], where the three-loop scalar and pseudo-scalar form factors were computed in the static limit.…”

Section: Introductionmentioning

confidence: 99%

Automated solution of first order factorizable systems of differential equations in one variable

et al. 2019

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“…In a parallel and independent computation in [16], the authors also have obtained both the colorplanar and complete light quark non-singlet three-loop massive form factors for the aforementioned currents. In [17], the large β 0 limit has been considered.…”

Section: Introductionmentioning

confidence: 99%

Massive three loop form factor in the planar limit

Rana¹,

Ablinger²,

Bluemlein³

et al. 2018

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)

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We present the color planar and complete light quark QCD contributions to the three loop heavy quark form factors in the case of vector, axial-vector, scalar and pseudo-scalar currents. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for any first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.

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“…(6) via the 2 F 1 function whose ε expansion is known to all orders [12]. The expansion in euclidean case is given there (there is a typo in the journal version corrected in the version 4 in arXiv); the Minkowski case is given by the formula (41) in [13]. Our result (22) at l 1 ¼ l 2 ¼ 0 agrees with the formula (B.10) in [13] (it contains 3 further expansion terms).…”

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confidence: 99%