Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities

Groote, S.; Körner, J. G.

doi:10.1016/j.nuclphysb.2018.11.023

Cited by 10 publications

(4 citation statements)

References 28 publications

(37 reference statements)

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“…It is thereby a mixed momentum-space and coordinatespace amplitude. We remark that such mixed amplitudes, although quite complex, may have further interesting applications in quantum-field theoretic calculations [58,59,90]. We were able to carry out the calculation analytically up to and including the averaging over the direction of the muon momentum.…”

Section: Discussionmentioning

confidence: 99%

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Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Asmussen

Chao

Gérardin

et al. 2023

J. High Energ. Phys.

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Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor g of the muon to deviate from the value of two predicted by Dirac’s theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon (g − 2). Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.

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Section: Discussionmentioning

confidence: 99%

“…in eq. (2.11) in terms of position-space propagators [57][58][59] and use the method of Gegenbauer polynomials [60][61][62][63][64][65][66][67][68][69] to perform the angular integrals and average over the direction of the muon momentum [70] (see also refs. [69,71]).…”

Section: Jhep04(2023)040mentioning

confidence: 99%

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Asmussen

Chao

Gérardin

et al. 2023

J. High Energ. Phys.

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“…In this appendix, we report several equations which are useful to transform our results from position to momentum space. Some of them are taken from [50]…”

Section: Appendix D: Useful Fourier Transformsmentioning

confidence: 99%

Dipole picture and the nonrelativistic expansion

Escobedo

Lappi

2020

Phys. Rev. D

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We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. This process offers one of the best ways to obtain information about gluon distributions at small x, in ultraperipheral heavy ion collisions and in deep inelastic scattering. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. In this paper, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium light-cone wave function in light-cone gauge. Using these corrections we recover results for the NLO decay width of quarkonium to e + e − and we check that the non-relativistic expansion is consistent with ERBL evolution and with B-JIMWLK evolution of the target. The results presented here will allow computing the exclusive quarkonium production rate at NLO once the one loop photon wave function with massive quarks, currently under investigation, is known. I. INTRODUCTIONThe partonic structure of hadrons and nuclei in the limit of high collision energies, or equivalently small momentum fractions x, is poorly constrained by existing experimental data. It is believed that at high enough energies the properties of small-x gluons are dominated by gluon saturation, i.e. the dominance of nonlinear interactions in the gluon field. In order to fully understand the behavior of small x gluons, a variety of different experimental measurements are needed. Of particular importance here is exclusive quarkonium production mediated by real or virtual photons. Such measurements are currently made in ultraperipheral heavy ion collisions [1] at the LHC and at RHIC. Exclusive measurements will also be an important part of the program at a future electron-ion-collider [2]. Exclusive quarkonium production is an important process for several reasons. As an exclusive process it depends on the gluon density quadratically and is thus more sensitive to nonlinearities than inclusive cross sections. Exclusive processes can, depending on exactly what final state of the target one measures, be sensitive to separately the average and the fluctuations of the gluon density in the target [3][4][5][6]. On the other hand, the heavy quark masses cut away nonperturbative long distance contributions and make the use of a weak coupling framework safer than for light quark processes [7,8].The dipole picture of DIS [9-13] (a specialization of the light cone perturbation theory framework of [14] to the DIS process) provides a convenient framework to study deep inelastic scattering at high energy. In particular one expresses both inclusive and exclusive cross sections in terms of the same fundamental quantity, the dipole scattering amplitude, which gives this picture more predictive power than collinear factorization. With light quarks several recent advances have taken cal...

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“…Pioneering work in this area was done in Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], where the simplest elliptic Feynman integral, the two-loop equal-mass sunrise diagram, was evaluated. These initial works have incited an active research field into elliptic Feynman integrals .…”

Section: Introductionmentioning

confidence: 99%

The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO

Prausa

Usovitsch

2021

J. High Energ. Phys.

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We present an analytic three-loop result for the leading color contribution to the Higgs-gluon form factor in QCD. The leading color contribution is given at next-to-next-to-leading order by the $$ {N}_c^2 $$ N c 2 -term in QCD with Nc colors. The main focus of this article lies on the evaluation of the relevant Feynman integrals with a special emphasis on the elliptic sector.

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Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities

Cited by 10 publications

References 28 publications

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Dipole picture and the nonrelativistic expansion

The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO

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