Pseudo-scalar form factors at three loops in QCD

Ahmed, Taushif; Gehrmann, Thomas; Mathews, Prakash; Rana, N. C.; Ravindran, V.

doi:10.1007/jhep11(2015)169

Cited by 45 publications

(79 citation statements)

References 119 publications

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“…in Ref. [32], the one-loop coefficients differ by terms of Oðϵ 0 Þ, whereas at the two-loop level these differences are of Oðϵ −2 Þ. After subtracting the IR divergences and taking the physical limit ϵ → 0, however, we obtain the same (regularization-scheme independent) results.…”

Section: Uv Renormalized Form Factorssupporting

confidence: 59%

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γ5 in the four-dimensional helicity scheme

Gnendiger

Signer

2018

Phys. Rev. D

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We investigate the regularization-scheme dependent treatment of γ 5 in the framework of dimensional regularization, mainly focusing on the four-dimensional helicity scheme (FDH). Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the FDH scheme constitutes a viable and efficient alternative compared to more traditional approaches. In addition, we extend the considerations to the two-loop level and compute the pseudoscalar form factors of quarks and gluons in FDH. We provide the necessary operator renormalization and discuss at a practical level how the complexity of intermediate calculational steps can be reduced in an efficient way.

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Section: Uv Renormalized Form Factorssupporting

confidence: 59%

“…(2.2), see e.g. [32] and references therein. In the following we consider the form factors up to two loops for (i) different dimensional schemes, i.e.…”

Section: Pseudoscalar Form Factors In Fdhmentioning

confidence: 99%

γ5 in the four-dimensional helicity scheme

Gnendiger

Signer

2018

Phys. Rev. D

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“…The renormalization of the quantity F G;Q appearing in Eq. (2.17) involves the mixing of the gluonic operator GG with another operator, namely, ∂ μψ γ μ γ 5 ψ, as discussed in [32,46,47], where ψ indicates all quark flavors including the massive one. We get,…”

Section: Renormalizationmentioning

confidence: 99%

Heavy quark form factors at two loops

et al. 2018

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“…The calculation of the FFs follows closely the steps used in the derivation of the 3-loop spin-2 and pseudo-scalar FFs in QCD [17,18]. In contrast to the most popular method of on-shell unitarity for computing the scattering amplitudes in N = 4 SYM, we use the conventional Feynman diagrammatic approach, which carries its own advantages in light of following the regularization scheme, to accomplish the job.…”

Section: Calculation Of the Form Factorsmentioning

confidence: 99%

Konishi form factor at three loops in N=4 supersymmetric Yang-Mills theory

Ahmed¹,

Banerjee²,

Dhani³

et al. 2017

Phys. Rev. D

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We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in N = 4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (DR) scheme. We show that it satisfies KG equation in DR scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in N = 4. PACS numbers: 12.38BxThe ability to accomplish the challenging job of calculating quantities is of fundamental importance in any potential mathematical theory. In quantum field theory (QFT), this manifests itself in the quest for computing the multi-loop and multi-leg scattering amplitudes under the glorious framework of age-old perturbation theory. The fundamental quantities to be calculated in any gauge theory are the scattering amplitudes or the correlation functions. Recently, there have been surge of interest to study form factors (FFs) as they connect fully on-shell amplitudes and correlation functions. The FFs are a set of quantities which are constructed out of the scattering amplitudes involving on-shell states consisting of elementary fields and an off-shell state described through a composite operator. These are operator matrix elements of the form p σ1 1 , · · · , p σ l l |O|0 where, O represents a gauge invariant composite operator which generates a multiparticle on-shell state |p σ1 1 , · · · , p σ l l upon operating on the vacuum of the theory. p i are the momenta and σ i encapsulate all the other quantum numbers of the particles. More precisely, FFs are the amplitudes of the processes where classical current or field, coupled through gauge invariant composite operator O, produces some quantum state. Studying these quantities not only help to understand the underlying ultraviolet and infrared structures of the theory, but also enable us to calculate the anomalous dimensions of the associated composite operator.The Sudakov FFs (l = 2) in N = 4 maximally supersymmetric Yang-Mills (SYM) theory [1, 2] were initially considered by van Neerven in [3], almost three decades back, where a half-BPS operator belonging to the stressenergy supermultiplet, that contains the conserved currents of N = 4 SYM, was investigated to 2-loop order:Very recently, this was extended to 3-loop in [4]. We will represent scalar and pseudo-scalar fields by φ a m and χ a m ...

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Pseudo-scalar form factors at three loops in QCD

Cited by 45 publications

References 119 publications

γ5 in the four-dimensional helicity scheme

γ5 in the four-dimensional helicity scheme

Heavy quark form factors at two loops

Konishi form factor at three loops in N=4 supersymmetric Yang-Mills theory

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