An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment

Groote, S.; Körner, Jürgen; Pivovarov, A. A.

doi:10.1007/s10052-002-0958-2

Cited by 16 publications

(16 citation statements)

References 47 publications

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“…(2.2). As suggested by Groote et al [46], however, one can exploit generating integral representations of r n and r n log(r) to express the pure polynomial and log terms in the asymptotic expansion of the kernel function in terms of Π. Using Eqs.…”

Section: Contribution (A)mentioning

confidence: 99%

Higher-order hadronic-vacuum-polarization contribution to the muon g−2 from lattice QCD

et al. 2018

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We introduce a new method for calculating the O(α 3 ) hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab-initio lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function Π(q 2 ), or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously-published results for the Taylor coefficients of Π(q 2 ) that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain 10 10 a HVP,HO µ = −9.3(1.3), in agreement with, but with a larger uncertainty than, determinations from e + e − → hadrons data plus dispersion relations.

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Section: Contribution (A)mentioning

confidence: 99%

Higher-order hadronic-vacuum-polarization contribution to the muon g−2 from lattice QCD

et al. 2018

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“…Such estimates are normally in good agreement with the result of the rigorous analysis. To estimate the hadronic contribution at two-loop level we use, for the three light quarks u, d and s, the value m u = m d = m s = m ef f ∼ 180 MeV adopted to describe in the lowest order the hadronic contribution to the muon anomalous magnetic moment [57]. The numerical results for the light-quark contribution at KLOE energies are included in the third column of Table 2.…”

Section: Numerical Analysismentioning

confidence: 99%

Calculation of the two-loop heavy-flavor contribution to Bhabha scattering

Bonciani

Ferroglia

Penin

2008

J. High Energy Phys.

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We describe in detail the calculation of the two-loop corrections to the QED Bhabha scattering cross section due to the vacuum polarization by heavy fermions. Our approach eliminates one mass scale from the most challenging part of the calculation and allows us to obtain the corrections in a closed analytical form. The result is valid for arbitrary values of the heavy fermion mass and the Mandelstam invariants, as long as s, t, u ≫ m 2 e .High energy electron-positron or Bhabha scattering [1] is among the most important and carefully studied processes in particle physics. It provides a very efficient tool for luminosity determination at electron-positron colliders and thus mediates the process of extracting physical information from the raw experimental data [2]. The small-angle Bhabha scattering is particularly effective as a luminosity monitor at high-energy colliders. 4 The large-angle Bhabha scattering is used to measure the luminosity at colliders operating at the center-of-mass energy, √ s, of a few GeV, such as BABAR/PEP-II, BELLE/KEKB, BES/BEPC, KLOE/DAΦNE, and CMD, SND/VEPP-2M [5]. 5 Moreover, it will be also used to disentangle the luminosity spectrum at the ILC [6,7]. Bhabha scattering involves stable charged leptons both in the initial and the final states and, therefore, it can be measured experimentally with very high precision. At LEP, the experimental error in the luminosity measurement has been reduced to 0.4 permille [8] and it is expected to be even smaller at the ILC: the goal of the TESLA forward calorimeter collaboration is to reach the experimental accuracy of 0.1 permille in the first year of run [9]. Finally, at the low-energy accelerators DAΦNE and VEPP-2M the cross section of the large-angle scattering is measured with the accuracy of about 1 permille [10,11]. In the phenomenologically most interesting cases of low energy or small angle scattering, the Bhabha cross section is QED dominated, with the electroweak and hadronic effects being strongly suppressed. Therefore, it can be reliably computed in perturbative QED, with the accuracy limited only by uncalculated high order corrections. These properties make in such a way that Bhabha scattering is an ideal "standard candle" for electron-positron colliders.Realistic simulations of the Bhabha events, which take into account the detector geometry and experimental cuts, are performed by means of sophisticated Monte Carlo generators, such as BHLUMI [12], BABAYAGA [5,13], BHAGENF [14], BHWIDE [15], MCGPJ [16], and SABSPV [17]. To match the experimental needs, the two-loop QED corrections must be included into the theoretical analysis and incorporated into the event generators. Since the theoretical accuracy directly affects the luminosity determination and may jeopardize the high-precision physics program at electron-positron colliders, remarkable efforts were devoted to the study of the radiative corrections. The one-loop corrections have been known in the full electroweak theory for a long time [18]. The two-loop electroweak corrections ar...

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“…In principle, to calculate the gauge invariant matrix element corresponding to the of l.h.s. of ( 14) it is possible to use the expression for the dynamical mass given in any gauge, but in that case the factor p 2n will be modified for more complicated weight function providing invariance of the answer 4 .…”

Section: The Instanton Effective Quark Modelmentioning

confidence: 99%

“…Very similar arguments lead the author of[30] to the conclusion that finiteness of all transverse momenta moments of the quark distributions guarantees the exponential fall-of of the cross sections 4. If one would naively use the dynamical quark mass corresponding to popular singular gauge then one finds the problem with convergence of the integrals in(14), because in this gauge there is only powerlike asymptotics of M (p) ∼ p −6 at large p 2 .…”

mentioning

confidence: 95%

$VA\widetilde{V}$ correlator within the instanton vacuum model

Dorokhov

2005

Eur. Phys. J. C

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The correlator of vector and nonsinglet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of QCD vacuum. In general the correlator has two Lorentz structures: longitudinal w L and transversal w T with respect to axial-vector index. Within the instanton model the saturation of the anomalous w L structure is demonstrated. It is known that in the chiral limit the transversal structure w T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w T at arbitrary momentum transfer q and show the absence of power corrections to this structure at large q 2 . Instead there arise the exponential corrections to w T at large q 2 reflecting nonlocal properties of QCD vacuum. The slope of w T at zero virtuality, the QCD vacuum magnetic susceptibility of the quark condensate and its momentum dependence are estimated.

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An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment

Cited by 16 publications

References 47 publications

Higher-order hadronic-vacuum-polarization contribution to the muon g−2 from lattice QCD

Higher-order hadronic-vacuum-polarization contribution to the muon g−2 from lattice QCD

Calculation of the two-loop heavy-flavor contribution to Bhabha scattering

$VA\widetilde{V}$ correlator within the instanton vacuum model

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