Vacuum Polarization

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Ulrich D Jentschura - One of the best experts on this subject based on the ideXlab platform.

  • relativistic reduced mass and recoil corrections to Vacuum Polarization in muonic hydrogen muonic deuterium and muonic helium ions
    Physical Review A, 2011
    Co-Authors: Ulrich D Jentschura
    Abstract:

    The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Z{alpha}){sup 4} {mu}{sup 3}/m{sub N}{sup 2} is evaluated for muonic hydrogen and deuterium and muonic helium ions ({mu} is the reduced mass and m{sub N} is the nuclear mass). Relativistic corrections to Vacuum Polarization of order {alpha}(Z{alpha}){sup 4}{mu} are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to Vacuum Polarization of order {alpha}(Z{alpha}){sup 5} ln{sup 2}(Z{alpha}){mu}{sup 2}/m{sub N} is obtained in leading logarithmic approximation. The results emphasize the need for a unified treatment of relativistic corrections to Vacuum Polarization in muonic hydrogen, muonic deuterium, and muonic helium ions, where the mass ratio of the orbiting particle to the nuclear mass is larger than the fine-structure constant.

  • relativistic reduced mass and recoil corrections to Vacuum Polarization in muonic hydrogen muonic deuterium and muonic helium ions
    Physical Review A, 2011
    Co-Authors: Ulrich D Jentschura
    Abstract:

    The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order $(Z\ensuremath{\alpha}){}^{4} \ensuremath{\mu}{}^{3}/{m}_{N}^{2}$ is evaluated for muonic hydrogen and deuterium and muonic helium ions ($\ensuremath{\mu}$ is the reduced mass and ${m}_{N}$ is the nuclear mass). Relativistic corrections to Vacuum Polarization of order $\ensuremath{\alpha}(Z\ensuremath{\alpha}){}^{4}\ensuremath{\mu}$ are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to Vacuum Polarization of order $\ensuremath{\alpha}(Z\ensuremath{\alpha}){}^{5} \mathrm{ln}{}^{2}(Z\ensuremath{\alpha})\ensuremath{\mu}{}^{2}/{m}_{N}$ is obtained in leading logarithmic approximation. The results emphasize the need for a unified treatment of relativistic corrections to Vacuum Polarization in muonic hydrogen, muonic deuterium, and muonic helium ions, where the mass ratio of the orbiting particle to the nuclear mass is larger than the fine-structure constant.

  • binding two loop Vacuum Polarization corrections to the bound electron g factor
    Physical Review A, 2009
    Co-Authors: Ulrich D Jentschura
    Abstract:

    We commence the evaluation of the one- and two-loop binding corrections to the $g$ factor for an electron in a hydrogenlike system of order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{5}$ and consider diagrams with closed fermion loops. The one-loop Vacuum-Polarization correction is rederived and confirmed. For the two-loop Vacuum-Polarization correction, due to a specific gauge-invariant set of diagrams with closed fermion loops, we find a correction $\ensuremath{\delta}g=7.442{(\ensuremath{\alpha}/\ensuremath{\pi})}^{2}{(Z\ensuremath{\alpha})}^{5}$. Based on the numerical trend of the coefficients inferred from the gauge-invariant subset, we obtain a numerically large tentative estimate for the complete two-loop binding correction to the $g$ factor (sum of self-energy and Vacuum Polarization).

Antonin Portelli - One of the best experts on this subject based on the ideXlab platform.

  • electromagnetic finite size effects to the hadronic Vacuum Polarization
    Physical Review D, 2019
    Co-Authors: Johan Bijnens, James Harrison, Andreas Juttner, Nils Hermanssontruedsson, T Janowski, Antonin Portelli
    Abstract:

    In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach subpercent accuracy on the hadronic-Vacuum-Polarization contribution. This requires the inclusion of O(α) electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the QEDL finite-volume corrections to the two-pion contribution to the hadronic Vacuum Polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order 1/L3 where L is the spatial extent. A 1/L2 term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar U(1) gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic Vacuum Polarization in infinite volume using a basis of 2-loop master integrals.

  • calculation of the hadronic Vacuum Polarization contribution to the muon anomalous magnetic moment
    Physical Review Letters, 2018
    Co-Authors: T Blum, P A Boyle, Vera Gulpers, Andreas Juttner, Christoph Lehner, Antonin Portelli, Taku Izubuchi, Luchang Jin, Chulwoo Jung, Justus Tobias Tsang
    Abstract:

    We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic Vacuum Polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a_{μ}^{HVP LO}=715.4(18.7)×10^{-10}. By supplementing lattice data for very short and long distances with R-ratio data, we significantly improve the precision to a_{μ}^{HVP LO}=692.5(2.7)×10^{-10}. This is the currently most precise determination of a_{μ}^{HVP LO}.

  • isospin breaking corrections to meson masses and the hadronic Vacuum Polarization a comparative study
    Journal of High Energy Physics, 2017
    Co-Authors: P A Boyle, Vera Gulpers, James Harrison, Andreas Juttner, Christoph Lehner, Antonin Portelli, C T Sachrajda
    Abstract:

    We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic Vacuum Polarization in an exploratory study on a 64 × 243 lattice with an inverse lattice spacing of a −1 = 1.78 GeV and an isospin symmetric pion mass of m π = 340 MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than 1% for the up quark and 0.1% for the strange quark, although it should be noted that this is obtained using unphysical light quark masses. In addition to the results themselves, we compare the precision which can be reached for the same computational cost using each method. Such a comparison is also made for the meson electromagnetic mass-splittings.

  • isospin breaking corrections to meson masses and the hadronic Vacuum Polarization a comparative study
    arXiv: High Energy Physics - Lattice, 2017
    Co-Authors: P A Boyle, Vera Gulpers, James Harrison, Andreas Juttner, Christoph Lehner, Antonin Portelli, C T Sachrajda
    Abstract:

    We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic Vacuum Polarization in an exploratory study on a $64\times24^3$ lattice with an inverse lattice spacing of $a^{-1}=1.78$ GeV and an isospin symmetric pion mass of $m_\pi=340$ MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than $1\%$ for the up quark and $0.1\%$ for the strange quark, although it should be noted that this is obtained using unphysical light quark masses. In addition to the results themselves, we compare the precision which can be reached for the same computational cost using each method. Such a comparison is also made for the meson electromagnetic mass-splittings.

  • calculation of the hadronic Vacuum Polarization disconnected contribution to the muon anomalous magnetic moment
    Physical Review Letters, 2016
    Co-Authors: T Blum, P A Boyle, Andreas Juttner, Christoph Lehner, Taku Izubuchi, Luchang Jin, K Maltman, Marina Marinkovic, Antonin Portelli
    Abstract:

    We report the first lattice QCD calculation of the hadronic Vacuum Polarization (HVP) disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique that enables the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 48^{3}×96 physical-pion-mass lattice generated by the RBC and UKQCD Collaborations. We find the leading-order hadronic Vacuum Polarization a_{μ}^{HVP(LO)disc}=-9.6(3.3)(2.3)×10^{-10}, where the first error is statistical and the second systematic.

T Blum - One of the best experts on this subject based on the ideXlab platform.

  • calculation of the hadronic Vacuum Polarization contribution to the muon anomalous magnetic moment
    Physical Review Letters, 2018
    Co-Authors: T Blum, P A Boyle, Vera Gulpers, Andreas Juttner, Christoph Lehner, Antonin Portelli, Taku Izubuchi, Luchang Jin, Chulwoo Jung, Justus Tobias Tsang
    Abstract:

    We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic Vacuum Polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a_{μ}^{HVP LO}=715.4(18.7)×10^{-10}. By supplementing lattice data for very short and long distances with R-ratio data, we significantly improve the precision to a_{μ}^{HVP LO}=692.5(2.7)×10^{-10}. This is the currently most precise determination of a_{μ}^{HVP LO}.

  • calculation of the hadronic Vacuum Polarization disconnected contribution to the muon anomalous magnetic moment
    Physical Review Letters, 2016
    Co-Authors: T Blum, P A Boyle, Andreas Juttner, Christoph Lehner, Taku Izubuchi, Luchang Jin, K Maltman, Marina Marinkovic, Antonin Portelli
    Abstract:

    We report the first lattice QCD calculation of the hadronic Vacuum Polarization (HVP) disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique that enables the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 48^{3}×96 physical-pion-mass lattice generated by the RBC and UKQCD Collaborations. We find the leading-order hadronic Vacuum Polarization a_{μ}^{HVP(LO)disc}=-9.6(3.3)(2.3)×10^{-10}, where the first error is statistical and the second systematic.

  • calculation of the hadronic Vacuum Polarization disconnected contribution to the muon anomalous magnetic moment
    Physical Review Letters, 2016
    Co-Authors: T Blum, P A Boyle, Andreas Juttner, Christoph Lehner, Antonin Portelli, Kim Maltman, Taku Izubuchi, Luchang Jin, Marina Marinkovic, M Spraggs
    Abstract:

    We report the first lattice QCD calculation of the hadronic Vacuum Polarization disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique which enabled the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 483×96 physical-pion-mass lattice generated by the RBC and UKQCD collaborations. We find aHVP (LO) DISC?=?9.6(3.3)(2.3)×10?10, where the first error is statistical and the second systematic.

  • hadronic Vacuum Polarization with twisted boundary conditions
    Physical Review D, 2013
    Co-Authors: Christopher Aubin, T Blum, Maarten Golterman, Santiago Peris
    Abstract:

    The leading-order hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over the subtracted hadronic Vacuum Polarization. This integral is dominated by euclidean momenta of order the muon mass, i.e., momenta not accessible on current lattice volumes with periodic boundary conditions. Twisted boundary conditions can in principle help in accessing momenta of any size even in a finite volume, but their use leads to a modification of the Ward-Takahashi identity that normally guarantees transversality of the Vacuum Polarization. As a result, the Vacuum Polarization contains a non-transversal, quadratically divergent term, which arises as an artifact of using twisted boundary conditions in a finite volume. In this article, we show how to determine and remove this term from the Vacuum Polarization.

  • model independent parametrization of the hadronic Vacuum Polarization and g 2 for the muon on the lattice
    Physical Review D, 2012
    Co-Authors: Christopher Aubin, T Blum, Maarten Golterman, Santiago Peris
    Abstract:

    The leading hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over euclidean momentum of the hadronic Vacuum Polarization. This integral is dominated by momenta of order the muon mass. Since the finite volume in lattice QCD makes it difficult to compute the Vacuum Polarization at a large number of low momenta with high statistics (combined with the fact that one cannot compute it at zero momentum), a parametrization of the Vacuum Polarization is required to extrapolate the data. A much used functional form is based on vector meson dominance, which introduces model dependence into the lattice computation of the magnetic moment. Here we introduce a model-independent extrapolation method, and present a few first tests of this new method.

Herbert Weigel - One of the best experts on this subject based on the ideXlab platform.

  • emerging translational variance Vacuum Polarization energy of the kink
    Advances in High Energy Physics, 2017
    Co-Authors: Herbert Weigel
    Abstract:

    We propose an efficient method to compute the Vacuum Polarization energy of static field configurations that do not allow decomposition into symmetric and antisymmetric channels in one space dimension. In particular, we compute the Vacuum Polarization energy of the kink soliton in the model. We link the dependence of this energy on the position of the center of the soliton to the different masses of the quantum fluctuations at negative and positive spatial infinity.

  • emerging translational variance Vacuum Polarization energy of the mathbf phi 6 kink
    arXiv: High Energy Physics - Theory, 2017
    Co-Authors: Herbert Weigel
    Abstract:

    We propose an efficient method to compute the Vacuum Polarization energy of static field configurations that do not allow a decomposition into symmetric and anti-symmetric channels in one space dimension. In particular we compute the Vacuum Polarization energy of the kink soliton in the $\phi^6$ model. We link the dependence of this energy on the position of the center of the soliton to the different masses of the quantum fluctuations at negative and positive spatial infinity.

  • Vacuum Polarization energy for general backgrounds in one space dimension
    Physics Letters B, 2017
    Co-Authors: Herbert Weigel
    Abstract:

    Abstract For field theories in one time and one space dimensions we propose an efficient method to compute the Vacuum Polarization energy of static field configurations that do not allow a decomposition into symmetric and anti-symmetric channels. The method also applies to scenarios in which the masses of the quantum fluctuations at positive and negative spatial infinity are different. As an example we compute the Vacuum Polarization energy of the kink soliton in the ϕ 6 model. We link the dependence of this energy on the position of the soliton to the different masses.

Savely G. Karshenboim - One of the best experts on this subject based on the ideXlab platform.

  • hadronic Vacuum Polarization contribution to various qed observables
    European Physical Journal D, 2021
    Co-Authors: Savely G. Karshenboim, Valery A. Shelyuto
    Abstract:

    Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic Vacuum Polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of $$a_\mu $$ . This experimental value can be considered as an indirect determination of the hVP contribution to $$a_\mu $$ and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of $$a_\mu $$ values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for $$Z\le 10$$ . We also consider the NLO contribution of the muonic Vacuum Polarization to the Lamb shift in hydrogen-like atoms. With the $$a_\mu $$ puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for $$a_\mu $$ and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions.

  • Radiative corrections to the hadronic Vacuum Polarization contribution to the muonium hyperfine interval
    Physical Review D, 2018
    Co-Authors: Valery A. Shelyuto, Savely G. Karshenboim, S. Eidelman
    Abstract:

    Muonium is a purely leptonic system, but the accuracy of the theoretical QED prediction for its hyperfine interval is limited in part by hadronic effects. Here we consider radiative corrections to the leading hadronic Vacuum Polarization term, since their size is larger than the uncertainty in the calculation of the leading hadronic term itself. The total hadronic contribution of relative order of a in comparison with the leading hadronic term is found to be 4.97(19) Hz. The hadronic uncertainty sets an "ultimate" limit on the use of the 1s hyperfine interval in muonium as a QED variable.

  • relativistic recoil effects on energy levels in a muonic atom a grotch type calculation of the second order Vacuum Polarization contributions
    Physical Review A, 2014
    Co-Authors: Savely G. Karshenboim, Evgeny Yu Korzinin, Vladimir G Ivanov
    Abstract:

    Adjusting a previously developed Grotch-type approach to a perturbative calculation of the electronic Vacuum-Polarization effects in muonic atoms, we find here the two-loop Vacuum-Polarization relativistic recoil correction of order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{4}{m}^{2}/M$ in light muonic atoms. The result is in perfect agreement with the one previously obtained within the Breit-type approach. We also discuss here simple approximations of the irreducible part of the two-loop Vacuum-Polarization dispersion density, which are applied to test our calculations and could be useful for other evaluations with an uncertainty better than 1%.

  • relativistic recoil effects for energy levels in a muonic atom within a grotch type approach ii an application to the one loop electronic Vacuum Polarization
    Physical Review A, 2014
    Co-Authors: Vladimir G Ivanov, Evgeny Yu Korzinin, Savely G. Karshenboim
    Abstract:

    We continue our account of relativistic recoil effects in muonic atoms and present explicitly analytic results at first order in electron-Vacuum-Polarization effects. The results are obtained within a Grotch-type approach based on an effective Dirac equation. Some expressions are cumbersome and we investigate their asymptotic behavior. Previously, relativistic two-body effects due to the one-loop electron Vacuum Polarization were studied by several groups. Our results found here are consistent with the previous result derived within a Breit-type approach (including ours) and disagree with a recent attempt to apply a Grotch-type approach.

  • Vacuum Polarization in muonic and antiprotonic atoms the fine structure at medium z
    arXiv: Atomic Physics, 2006
    Co-Authors: Yu E Korzinin, Vladimir G Ivanov, Savely G. Karshenboim
    Abstract:

    Effects of Vacuum Polarization modify the energy levels in atoms with an orbiting particle heavier than an electron. The dominant effect is due to the Uehling potential. In this paper we consider the relativistic corrections to the energy levels caused by the Uehling potential and in particular the fine structure in muonic and antiprotonic atoms. We derive general expressions and consider in detail specific regions of parameters which allow simple asymptotic expansion. We take into account the recoil effects and anomalous magnetic moment in the case of an antiproton as the orbiting particle.