Hadronic vacuum polarization contribution to a μ from full lattice QCD
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Chakraborty, Bipasha↗
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The Epstein–Glaser causal approach to the light-front QED{sub 4}. II: Vacuum polarization tensor
In this work we show how to construct the one-loop vacuum polarization for light-front QED{sub 4} in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in the literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the Epstein–Glaser causal theory, it is shown that the fermionic propagator does not have instantaneous term, and with this propagator we calculate the one-loop vacuum polarization, from this calculation it follows the same result as those obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind our obtaining the same result whether we consider or not the instantaneous fermionic propagator term. - Highlights: • We develop the Epstein–Glaser causal approach for light-front field theory. • We evaluate in detail the vacuum polarization at one-loop for the light-front QED. • We discuss the subtle issues of the Instantaneous part of the fermionic propagator in the light-front. • We evaluate the vacuum polarization at one-loop for the light-front QED with the Instantaneous fermionic part.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Representing the vacuum polarization on de Sitter
Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Vacuum polarization throughout general subtracted black hole spacetimes
Here we compute the vacuum polarization of a massless minimally coupled scalar field in a background given by a black hole with subtracted geometry. Extending previous results for the horizon of rotating black holes with no charge, we obtain an analytical expression for the vacuum polarization that is valid throughout the spacetime and for arbitrary rotation and charge parameters. The vacuum polarization diverges at the inner horizon, and the quantum state cannot be extended to the inside of it.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Computing the hadronic vacuum polarization function by analytic continuation
We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method leads to the desired hadronic vacuum polarization function in Minkowski spacetime. We present with the example of the leading-order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Calculation of the Hadronic Vacuum Polarization Disconnected Contribution to the Muon Anomalous Magnetic Moment
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Three-pion contribution to hadronic vacuum polarization
We address the contribution of the 3π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e + e - → 3π amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon (g - 2) μ , both to its absolute value and uncertainty. It is largely dominated by the narrow resonances ω and Φ, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for (g - 2) μ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying γ* → 3π amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various e + e - → 3π data sets. Overall, we obtain a$3π\atop{μ}$|≤1.8 GeV = 46.2(6)(6) × 10 -10 as our best estimate for the total 3π contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2π channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to a$HVP\atop{μ}$ = 692.3(3.3) × 10 -10 when the remainder is taken from the literature, and thus reaffirming the (g-2) μ anomaly at the level of at least 3.4σ. As side products, we find for the vacuum-polarization-subtracted masses M ω = 782.63(3)(1) MeV and M Φ = 1019.20(2)(1) MeV, confirming the tension to the ω mass as extracted from the 2π channel.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Vacuum polarization in a strong external field
Vacuum polarization in the field of a high-Z finite-size nucleus is examined, and the polarization charge density in coordinate space of order alpha(Z alpha)exp n not less than 3 is calculated. Energy-level shifts of K- and L-shell electrons in hydrogenlike systems are given.
Soff, Gerhard↗
Searching for minicharged particles via birefringence, dichroism and Raman spectroscopy of the vacuum polarized by a high-intensity laser wave
Absorption and dispersion of probe photons in the field of a high-intensity circularly polarized laser wave are investigated. The optical theorem is applied for determining the absorption coefficients in terms of the imaginary part of the vacuum polarization tensor. Compact expressions for the vacuum refraction indices and the photon absorption coefficients are obtained in various asymptotic regimes of interest. The outcomes of this analysis reveal that, far from the region relatively close to the threshold of the two-photon reaction, the birefringence and dichroism of the vacuum are small and, in some cases, strongly suppressed. On the contrary, in a vicinity of the region in which the photo-production of a pair occurs, these optical properties are manifest with lasers of moderate intensities. We take advantage of such a property in the search of minicharged particles by considering high-precision polarimetric experiments. In addition, Raman-like electromagnetic waves resulting from the inelastic part of the vacuum polarization tensor are suggested as an alternative form for finding exclusion limits on these hypothetical charge carriers. The envisaged parameters of upcoming high-intensity laser facilities are used for establishing upper bounds on the minicharged particles. -- Highlights: •Via dichroism and birefringence of the vacuum by a strong laser wave, minicharged particles can be probed. •The discovery potential is the highest in a vicinity of the first pair production threshold. •As alternative observable, Raman scattered waves are put forward.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear theory of intense laser-plasma interactions modified by vacuum polarization effects
The classical nonlinear theory of laser-plasma interactions is corrected by taking account of the vacuum polarization effects. A set of wave equations are obtained by using the Heisenberg-Euler Lagrangian density and the derivative correction with the first-order quantum electrodynamic effects. A model more suitable to formulate the interactions of ultra-strong lasers and high-energy-density plasmas is developed. In the result, some environments in which the effects of vacuum polarization will be enhanced are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Relativistic reduced-mass and recoil corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions
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.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e - → π + π - channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e - → 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e- → 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives for the total 3π contribution to the anomalous magnetic moment of the muon, of which ${a}^{FSR}_\mu [3\pi]$ = 0.51(1) x 10 -10 and ${a}^{\rho - \omega}_\mu [3\pi]$ = -2.68(70) x 10 -10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e + e - → 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782.70(3) MeV, M Φ = 1019.21(2) MeV, Γ ω = 8.71(3) MeV, and Γ Φ = 4.27(1) MeV.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The effects of vacuum polarization on thermonuclear reaction rates
Added to the pure Coulomb potential, the contribution from vacuum polarization increases the barrier, reducing the wave function (u) for reacting nuclei within the range of nuclear forces. The cross section and reaction rate are then reduced accordingly by a factor proportional to u squared. The effect is treated by evaluating the vacuum polarization potential as a small correction to the Coulomb term, then computing u in a WKB formulation. The calculation is done analytically employing the small r power-series expansion for the Uehling potential to express the final result in terms of convenient parameters. At a temperature of 1.4 x 10 to the 7th K the (negative) correction is 1.3 percent for the fundamental fusion process p + p yields d + e(+) + nu.
Gould, Robert J.↗
Polarized vacuum ultraviolet and X-radiation
The most intense source of polarized vacuum UV and X radiation is synchrotron radiation, which exhibits a degree of partially polarized light between about 80-100%. However, the radiation transmitted by vacuum UV monochromators can also be highly polarized. The Seya-Namioka type of monochromator can produce partially polarized radiation between 50-80%. For certain experiments it is necessary to know the degree of polarization of the radiation being used. Also, when synchrotron radiation and a monochromator are combined the polarization characteristic of both should be known in order to make full use of these polarization properties. The polarizing effect of monochromators (i.e., diffraction gratings) have been measured at the Seya angle and at grazing angles for various spectral orders. Experimental evidence is presented which shows that the reciprocity law holds for polarization by reflection where the angle of incidence and diffraction are unequal. These results are reviewed along with the techniques for measuring the degree of polarization.
Samson, J. A. R.↗
Update of Euclidean windows of the hadronic vacuum polarization
We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional subleading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find 𝑎$^{W}_{μ}$ = 235.56(65)(50) × 10 −10 , which is in 3.8𝜎 tension with the recently published dispersive result of 𝑎$^{W}_{μ}$ =229.4(1.4) × 10 −10 [G. Colangelo, A. X. El-Khadra, M. Hoferichter, A. Keshavarzi, C. Lehner, P. Stoffer, and T. Teubner, Phys. Lett. B 833, 137313 (2022)] and in agreement with other recent lattice determinations. We also provide a result for the standard short-distance window. The results reported here are unchanged compared to our presentation at the Edinburgh workshop of the g-2 Theory Initiative in 2022 [C. Lehner, Talk Presented at the 5th Plenary Meeting of the g-2 Theory Initiative in Edinburgh (2022)].
Lattice QCD↗
Towards a real-time computation of timelike hadronic vacuum polarization and light-by-light scattering: Schwinger Model tests
Hadronic vacuum polarization (HVP) and light-by-light scattering (HLBL) are crucial for evaluating the Standard Model predictions concerning the muon’s anomalous magnetic moment. However, direct first-principle lattice gauge theory-based calculations of these observables in the timelike region remain challenging. Discrepancies persist between lattice quantum chromodynamics (QCD) calculations in the spacelike region and dispersive approaches relying on experimental data parametrization from the timelike region. Here, we introduce a methodology employing 1+1-dimensional quantum electrodynamics (QED), i.e. the Schwinger Model, to investigate the HVP and HLBL. To that end, we use both tensor network techniques, specifically matrix product states, and classical emulators of digital quantum computers. Demonstrating feasibility in a simplified model, our approach sets the stage for future endeavors leveraging digital quantum computers.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Vacuum polarization in Coulomb field revisited
Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonic hydrogen the result obtained here reasonably agrees with that given in literature.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Utility of a hybrid approach to the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
An accurate calculation of the leading-order hadronic vacuum polarization (LOHVP) contribution to the anomalous magnetic moment of the muon ( a μ ) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator G ( t ) , where G ( t ) can be calculated using lattice QCD or, with dispersion relations, from experimental data for e + e − → hadrons . The BMW/DMZ collaboration recently presented a hybrid approach in which G ( t ) is calculated using lattice QCD for most of the contributing t range, but using experimental data for the largest t (lowest energy) region. Here we study the advantages of varying the position t = t 1 separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of t 1 , providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favor the CMD-3 cross section data for e + e − → π + π − over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for a μ and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of t 1 values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own. Published by the American Physical Society 2025
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗