New Technique for Vertex Graphs

Levine, Michael J.; Roskies, R.

doi:10.1103/physrevlett.30.772

“…In this paper we will show that also the non-factorizable diagrams can be calculated using the hadronic vacuum polarization in the space-like region by making use of the hyperspherical integration method. This method was exploited for instance to evaluate parts of the QED three-loop contributions to the electron g−2 [37][38][39][40][41][42], and more recently to calculate the pion pole contribution to a HLBL µ [43,44] and in the dispersive approach to the HLBL [45,46].…”

Section: Introductionmentioning

confidence: 99%

Hadronic corrections to μ-e scattering at NNLO with space-like data

Fael

¹

2019

J. High Energ. Phys.

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The Standard Model prediction for µ-e scattering at Next-to-Next-to-Leading Order (NNLO) contains non-perturbative QCD contributions given by diagrams with a hadronic vacuum polarization insertion in the photon propagator. By taking advantage of the hyperspherical integration method, we show that the subset of hadronic NNLO corrections where the vacuum polarization appears inside a loop, the irreducible diagrams, can be calculated employing the hadronic vacuum polarization in the space-like region, without making use of the R ratio and time-like data. We present the analytic expressions of the kernels necessary to evaluate numerically the two types of irreducible diagrams: the two-loop vertex and box corrections. As a cross check, we evaluate these corrections numerically and we compare them with the results given by the traditional dispersive approach and with analytic two-loop vertex results in QED.

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“…It is worth noting that equation ( 34) is identical to the result of the mapping the integration range 0 x < 1 in equation ( 12) onto the kinematic interval 0 Q 2 < ∞ reported in references [69,73,74] and to the result of straightforward calculation [75] performed within the technique [49][50][51][52].…”

Section: The 'Spacelike' Kernel Functionsmentioning

confidence: 64%

“…Here the perturbative results for the function R(s) are usually complemented by the low-energy experimental data on the R-ratio of electron-positron annihilation into hadrons, that constitutes the data-driven method of evaluation of a HVP μ . In turn, the 'spacelike' and 'timelike' kernel functions can be calculated within various techniques, such as the mass operator approach [46][47][48], the hyperspherical approach [49][50][51][52], the dispersive method [53][54][55][56][57], and the asymptotic expansion method [11,58,59]. The 'timelike' kernel functions have been extensively studied over the past decades, whereas the corresponding 'spacelike' kernel functions remain largely unavailable.…”

Section: Introductionmentioning

confidence: 99%

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Нестеренко

¹

2022

J. Phys. G: Nucl. Part. Phys.

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The complete set of relations, which mutually express the spacelike and timelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a μ HVP in terms of each other, is obtained. By making use of the derived relations the explicit expression for the next-to-leading order spacelike kernel function, which enters the representation for a μ HVP involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for a μ HVP involving the Adler function, is calculated numerically. The obtained results can be employed in the assessments of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment in the framework of the spacelike methods, such as lattice studies, MUonE project, and others.

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“…( 12) onto the kinematic interval 0 ≤ Q 2 < ∞ reported in Refs. [33,36] and to the result of straightforward calculation [37] performed within the technique [12][13][14][15]. In turn, the explicit form of the kernel function K…”

Section: The "Spacelike" Kernel Functionsmentioning

confidence: 99%

“…Here the perturbative results for the function R(s) are usually complemented by the lowenergy experimental data on the R-ratio of electron-positron annihilation into hadrons, that constitutes the data-driven method of evaluation of a HVP µ . In turn, the "spacelike" and "timelike" kernel functions can be calculated within various techniques, such as the mass operator approach [9][10][11], the hyperspherical approach [12][13][14][15], the dispersive method [16][17][18][19][20], and the asymptotic expansion method [21][22][23]. The "timelike" kernel functions have been extensively studied over the past decades, whereas the corresponding "spacelike" kernel functions remain largely unavailable.…”

Section: Introductionmentioning

confidence: 99%

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Nesterenko

2021

Preprint

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The hadronic vacuum polarization contributions to the muon anomalous magnetic moment are studied. Specifically, the complete set of relations, which express the corresponding kernel functions K Π (Q 2 ), K D (Q 2 ), and K R (s) in terms of each other, is obtained. By making use of the derived relations the explicit expression for the functionThe obtained results can be employed in the assessments of the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in the framework of the spacelike methods, such as lattice studies, MUonE project, and others.

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New Technique for Vertex Graphs

Cited by 20 publications

References 5 publications

Hadronic corrections to μ-e scattering at NNLO with space-like data

Hadronic corrections to μ-e scattering at NNLO with space-like data

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

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