The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements

Blümlein, J.; Marquard, P.; Schneider, C.; Schönwald, K.

doi:10.48550/arxiv.2107.06267

Cited by 6 publications

(18 citation statements)

References 73 publications

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“…For completeness, we have included the most important structure function g 1 in spin-dependent DIS, for its coefficient functions and splitting functions at NNLO see refs. [70][71][72][73][74].…”

Section: Notation Formalism and Calculationsmentioning

confidence: 99%

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

Davies¹,

Kom²,

Moch³

et al. 2022

Preprint

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We present a comprehensive study of high-energy double logarithms in inclusive DIS. They appear parametrically as α n s ln 2n−k x at the n-th order in perturbation theory in the splitting functions for the parton evolution and the coefficient functions for the hard scattering process, and represent the leading corrections at small x in the flavour non-singlet case. We perform their resummation, in terms of modified Bessel functions, to all orders in full QCD up to NNLL accuracy, and partly to N 3 LL and beyond in the large-n c limit, and provide fixed-order expansions up to five loops. In the flavour-singlet sector, where these double logarithms are sub-dominant at small x compared to single-logarithmic α n s x −1 ln n−k x BFKL contributions, we construct fixed-order expansions up to five loops at NNLL accuracy in full QCD. The results elucidate the analytic small-x structure underlying inclusive DIS results in fixed-order perturbation theory and provide important information for present and future numerical and analytic calculations of these quantities. c 83997239 1944 − 2253859 81 ζ 2 + 13220 9 ζ 3 + 48070 3 ζ 4 + 64 ζ 3 ζ 2 − 4312 3 ζ 5 + 176 ζ 2 3 − 1444 ζ 6 + n f C F n 3 c − 5138330 243 + 267860 27 ζ 2 − 4336 3 ζ 3 − 28432 9 ζ 4 + 128 ζ 3 ζ 2 + 1504 3 ζ 5 − 64 ζ 2 3 − 248 ζ 6 + n 2 f C F n 2 c 760669 243 − 9076 9 ζ 2 + 2000 9 ζ 3 + 1408 9 ζ 4 + n 3 f C F n c − 12826 81

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Section: Notation Formalism and Calculationsmentioning

confidence: 99%

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

Davies¹,

Kom²,

Moch³

et al. 2022

Preprint

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“…with the spherical factor S ε given in Eq. ( 13) of [11]. The bare coupling constant â and the gauge parameter ξ are defined in Eqs.…”

Section: The Unrenormalized Polarized Operator Matrix Elements and De...mentioning

confidence: 99%

“…One of the important ingredients to this is the knowledge of the the polarized singlet anomalous dimensions to highest possible order. The polarized non-singlet anomalous dimensions are known to 3-loop order [10,11] and the polarized singlet anomalous dimensions were calculated to first [12][13][14][15][16], second [17][18][19] and third order in [20,21], using different computation techniques. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper we use the traditional approach of massless off-shell operator matrix elements (OMEs), allowing the direct calculation, as before for the non-singlet case and the three-loop anomalous dimensions of transversity in Ref. [11]. However, for this method the computational framework is gauge dependent.…”

Section: Introductionmentioning

confidence: 99%

“…To some extent different steps in the computation technology are the same as in the non-singlet case, cf. [11] which will be referred to this paper and we only will describe new additional elements in the present paper. 2 At the phenomenological side we mention that, unlike the singlet case, the flavor non-singlet description of the structure functions g NS 1,2 (x, Q 2 ) is well explored to three-loop order, also including the heavy flavor contributions [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Blümlein,

Marquard,

Schneider

et al. 2021

Preprint

Self Cite

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Future high luminosity polarized deep-inelastic scattering experiments will improve both the knowledge of the spin sub-structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three-loop order in the M-scheme by using the traditional method of space-like off-shell massless operator matrix elements, being a gauge-dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non-singlet splitting function ∆P(2),s,NS qq and compare the final results to the literature, also including predictions for the region of small values of Bjorken x.

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The infrared structure of perturbative gauge theories

et al. 2023

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The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements

Cited by 6 publications

References 73 publications

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

The infrared structure of perturbative gauge theories

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