Four-loop cusp anomalous dimension in QED

Abstract

The 4-loop $C_F^3{T}_F{n}_l$ and 5-loop $C_F^4{T}_F{n}_l$ terms in the HQET field anomalous dimension ${\gamma }_h$ are calculated analytically (the 4-loop one agrees with the recent numerical result [arXiv:1801.08292]). The 4-loop $C_F^3{T}_F{n}_l$ and 5-loop $C_F^4{T}_F{n}_l$ terms in the cusp anomalous dimension $\Gamma (\phi )$ are calculated analytically, exactly in $\phi$ (the $\phi \to \infty$ asymptotics of the 4-loop one agrees with the recent numerical result [arXiv:1707.08315]). Combining these results with the recent 4-loop $d_{FF}{n}_l$ contributions to ${\gamma }_h$ and to the small-$\phi$ expansion of $\Gamma (\phi )$ up to ${\phi }^4$ [arXiv:1708.01221] (recently extended to ${\phi }^6$ [arXiv:1807.05145]) we now have the complete analytical 4-loop result for the Bloch--Nordsieck field anomalous dimension in QED, and the small-$\phi$ expansion of the 4-loop QED cusp anomalous dimension up to ${\phi }^6$.

9 pages; v2: minor typos fixed; v3: some explanations and 3 references added; v4: QED cusp anomalous dimension extended to ${\phi }^6$, comparison with the quark-antiquark potential added, several typos fixed, 3 references added

References in corpus (6)

• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The three-loop cusp anomalous dimension in QCD
• On the Casimir scaling violation in the cusp anomalous dimension at small angle
• Four-loop wave function renormalization in QCD and QED
• Matching heavy-quark fields in QCD and HQET at three loops

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• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
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• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
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• Planar master integrals for four-loop form factors
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• The Fully-Differential Gluon Beam Function at NNLO
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• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• Four-loop massive cusp anomalous dimension in QCD: a calculation from asymptotics
• Matching the heavy-quark fields in QCD and HQET at four loops
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• Precision QCD phenomenology of exotic spin-2 search at the LHC
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