Quark and gluon form factors in four-loop QCD

Lee, Roman N.; von Manteuffel, Andreas; Schabinger, Robert M.; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

doi:10.48550/arxiv.2202.04660

Cited by 4 publications

(7 citation statements)

References 86 publications

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“…On top of all the necessary ingredients for N 4 LL resummation, we also include the 4-loop hard function, which we have extracted from the 4-loop form factor calculation of ref. [101]. Figure 2 shows our results as a function of the scattering angle χ through different logarithmic orders.…”

Section: Numerical Resultsmentioning

confidence: 97%

“…In eq. ( 14), J 0 is the Bessel function arising from the Fourier transform due to the azymuthal symmetry of the EEC measurement, H q q is the quark color singlet SCET hard function, which is related to the IR finite part of the quark form factors [92][93][94][95][96][97][98][99][100][101] and can be extracted up to 4 loops from the recent result of ref. [101], and J q is the quark EEC jet function which is known up to N 3 LO [50,51].…”

Section: Eec In the Back-to-back Limitmentioning

confidence: 99%

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The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

Duhr¹,

Mistlberger²,

Vita³

2022

Preprint

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Section: Numerical Resultsmentioning

confidence: 97%

Section: Eec In the Back-to-back Limitmentioning

confidence: 99%

The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

Duhr¹,

Mistlberger²,

Vita³

2022

Preprint

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“…The four loop cusp anomalous dimension in QCD can be found in [37,38]. The numerical-analytical expressions for virtual and soft anomalous dimensions were obtained in [38][39][40]42]. Based on these results, we obtain the full expressions for rapidity anomalous dimensions, albeit with some color coefficients a numerical value (see in Tab.…”

Section: A2 Anomalous Dimensionsmentioning

confidence: 92%

“…Very recently all matter dependent terms were obtained in [38] (using previous results e.g. [93,94]), and finally the full four loop form factors were computed [41][42][43].…”

Section: Summary Of Perturbative Data For Anomalous Dimensionsmentioning

confidence: 99%

“…In the last several years, there has been remarkable progress in extending calculations of a number of key gauge theory quantities to the four loop level. These include the β-function [20][21][22][23], the anomalous dimensions of twist-2 operators [24][25][26][27], the cusp anomalous dimension [24,[27][28][29][30][31][32][33][34][35][36][37][38], the quark and gluon collinear anomalous dimensions [29-32, 34, 35, 35, 38-40], and most recently the full form factors [41][42][43]. These anomalous dimensions govern the behavior of scattering amplitudes and cross sections in infrared limits, allowing the resummation of logarithms that appear in these limits, and which often invalidate a fixed order perturbative expansion, to N 4 LL.…”

Section: Introductionmentioning

confidence: 99%

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The Four Loop QCD Rapidity Anomalous Dimension

Moult¹,

Zhu²,

Zhu³

2022

Preprint

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The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the β-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to O( ). Combined with recent perturbative data from the study of on-shell form factors and splitting functions, this allows us to derive the four loop rapidity anomalous dimension in QCD.

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Singlet and non-singlet three-loop massive form factors

Fael,

Lange,

Schönwald

et al. 2022

Preprint

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We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy s which allows to cover the whole kinematic range for negative and positive values of s. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.

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Quark and gluon form factors in four-loop QCD

Cited by 4 publications

References 86 publications

The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

The Four Loop QCD Rapidity Anomalous Dimension

Singlet and non-singlet three-loop massive form factors

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