Next to the $π^0$ pole, $η$ and $η'$ intermediate states give rise to the leading singularities of the hadronic light-by-light tensor, resulting in sizable contributions to the anomalous magnetic moment of the muon $a_μ$. The strength of the poles is determined by the respective transition form factors (TFFs) to two (virtual) photons. We present a calculation of these TFFs that implements a number of low- and high-energy constraints, including the $η^{(\prime)}\toγγ$ decay widths, $η^{(\prime)}\toπ^+π^-γ$ spectra, chiral symmetry for the $η^{(\prime)}\to 2(π^+π^-)$ amplitudes, vector-meson couplings, and asymptotic limits. Crucially, we investigate the role of the leading left-hand singularity generated by the exchange of the $a_2$ tensor meson, yielding, for the first time, an estimate of the associated factorization-breaking corrections. Our final results, $a_μ^{η\text{-pole}}=14.7(9)\times 10^{-11}$ and $a_μ^{η'\text{-pole}}=13.5(7)\times 10^{-11}$, conclude a dedicated effort to evaluate the pseudoscalar-pole contributions to hadronic light-by-light scattering using dispersion relations, amounting to a combined $a_μ^{\text{PS-poles}}=91.2^{+2.9}_{-2.4}\times 10^{-11}$.
Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at ${\mathcal O}(α^4)$. Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to $\lesssim 1\times 10^{-11}$ and thus negligible a…
We discuss the hadronic contributions to the muon anomalous magnetic moment. They are dominated by light quark contributions which are constrained by the mechanism of chiral symmetry breaking. Using the leading order result based on $e^+ e^-$ scattering data, we show that the next-to-leading order contributions in the fine structure constant $α$ can be reliably calculated. Extending this idea to the hadronic four-point function we give a prediction for the light-by-light contribution.
Recently, it was shown that insertions of hadronic vacuum polarization at O(alpha^4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g-2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.
We present the status of the MUonE experimental proposal which aims at determining the leading order hadronic contribution to the muon g-2 by measuring the hadronic part of the photon vacuum polarization in the spacelike region. The challenges posed by this measurement on the detector, the proposed solution, and the status of this proposal will be discussed.
The MUonE proposal at the CERN SPS consists in extracting the value of the hadronic vacuum polarization self-energy function (HVP) from its contribution to the differential cross-section of elastic muon-electron scattering. The HVP contribution to the muon anomalous magnetic moment can then be obtained from a weighted integral of the measured HVP self-energy function. This, however, requires a knowledge of the HVP function in its full integration domain. This paper discusses a procedure to reconstruct the HVP function in the regions not directly accessible to measurement. The method is based o…
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a lot of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions.
In view of the current 3 - 4 $σ$ deviation between theoretical and experimental values for the muon's anomalous magnetic moment, we review the ongoing efforts in constraining the hadronic light-by-light contribution to $a_μ$ by using dispersive techniques combined with a dedicated experimental program to obtain the required hadronic input.
Contributions of hadronic effects to the muonium physics and anomalous magnetic moment of muon are considered. Special attention is paid to higher-order effects and the uncertainty related to the hadronic contribution to the hyperfine structure interval in the ground state of muonium.
We report on our progress toward the computation of the $π^0$, $η$ and $η^{\prime}$ transition form factors using staggered quarks on $N_f=2+1+1$ gauge ensembles generated by the Budapest-Marseille-Wuppertal collaboration. These form factors are essential ingredients to evaluate the pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Preliminary results for the pseudoscalar-pole contributions are presented, at finite lattice spacing, for all three light mesons.
We present a calculation of the hadronic vacuum polarization (HVP) tensor within the framework of Dyson--Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, $a_μ$. We find $a_μ^{HVP}= 6760\times 10^{-11}$ which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of $a_…
We present simple analytic expressions to compute the hadronic vacuum polarization contribution to the muon $g$-2 in the space-like region up to next-to-next-to-leading order. These results can be employed in lattice QCD calculations of this contribution as well as in space-like determinations based on scattering data, like that expected from the proposed MUonE experiment at CERN.
The Standard Model prediction for muon-electron scattering beyond leading order requires the inclusion of QCD contributions which cannot be computed perturbatively. At next-to- and next-to-next-to-leading order, they arise from one- and two-loop diagrams with hadronic vacuum polarization insertions in the photon propagator. We present their evaluation using the dispersive approach with hadronic $e^+e^-$ annihilation data and estimate their uncertainty. We find that these corrections are crucial for the analysis of future high-precision muon-electron scattering data, like those of the recently …
We give a status report on the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment from the Dyson-Schwinger approach. We discuss novel, model-independent properties of the light-by-light amplitude: we give its covariant decomposition in view of electromagnetic gauge invariance and Bose symmetry, and we identify the relevant kinematic regions that are probed under the integral. The decomposition of the amplitude at the quark level and the importance of its various diagrams are discussed and related to model approaches.
I present a preliminary calculation of the hadronic vacuum polarization for 2+1 flavors of improved Kogut-Susskind quarks by utilizing a set of gauge configurations recently generated by the MILC collaboration. The polarization function $Π(q^2)$ is then used to calculate the lowest order (in $α_{QED}$) hadronic contribution to the muon anomalous magnetic moment.
Hadronic light-by-light scattering in the anomalous magnetic moment of the muon $a_μ$ is one of two hadronic effects limiting the precision of the Standard Model prediction for this precision observable, and hence the new-physics discovery potential of direct experimental determinations of $a_μ$. In this contribution, we report on recent progress in the calculation of this effect achieved both via dispersive and lattice QCD methods.
We discuss hadronic effects in the muonium hyperfine structure and derive an expression for the hadronic contribution to the hfs interval in form of the one-dimensional integral of the cross section of e+e- annihilation into hadrons. Higher-order hadronic contributions are also considered.
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.
We extend our analysis of the leading hadronic contribution to the anomalous magnetic moment of the muon using the mixed representation method to study its chiral behavior. We present results derived from local-conserved two-point lattice vector correlation functions, computed on a subset of light two-flavor ensembles made available to us through the CLS effort with pion masses as low as 190 MeV. The data is analyzed also using the more standard four-momentum method. Both methods are systematically compared as the calculations approach the physical point.
The hadronic contributions to the anomalous magnetic moment of the muon which are relevant for the confrontation between theory and experiment at the present level of accuracy, are evaluated within the same framework: the constituent chiral quark model. This includes the contributions from the dominant hadronic vacuum polarization as well as from the next--to--leading order hadronic vacuum polarization, the contributions from the hadronic light-by-light scattering, and the contributions from the electroweak hadronic $Zγγ$ vertex. They are all evaluated as a function of only one free parameter:…
We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was mistaken.
Some short-distance properties of the fourth-rank hadronic vacuum polarization tensor are re-examined.Their consequences are critically discussed in the context of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.
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 $a^{\text{HVP}}_μ$ 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 $a^{\text{HVP}}_μ$ involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for $a^{\text{…
We give a short overview of the theory of the muon anomalous magnetic moment with emphasis on the hadronic light-by-light and the pion loop contribution. We explain the difference between the hidden local symmetry and full VMD pion loop and discuss leading logarithms in the anomalous sector of 2-flavour chiral perturbation theory.
The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.
We present a refined calculation of the quark-loop contribution to hadronic light-by-light scatter- ing that focuses upon the impact of the transverse components of the quark-photon vertex. These structures are compared and contrasted with those found within the extended NJL-models. We discuss similarities and differences between the two approaches and further clarify the important role of momentum dependent dressing functions. As expected we find that the transverse structures of the quark-photon vertex lead to a suppression of the quark-loop contribution to the anomalous magnetic moment of t…
We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of Möbius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_μ^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$
The lowest order hadronic contribution to the $g-2$ factor of the muon is analyzed in the framework of the operator product expansion at short distances, and a QCD finite energy sum rule designed to quench the role of the $e^+ e^-$ data. This procedure reduces the discrepancy between experiment and theory, $Δa_μ\equiv a^{EXP}_μ- a^{SM}_μ$, from $Δa_μ= 28.7 (8.0) \times 10^{-10}$ to $Δa_μ= 19.2 (8.0) \times 10^{-10}$, i.e. without changing the uncertainty.
The contributions to the muon anomalous magnetic moment from hadronic vacuum polarization and from hadronic light-by-light scattering are reexamined within the frame work of chiral perturbation theory; the $1/N_c$-expansion; and the extended Nambu Jona-Lasinio model of low-energy QCD.
We give the first estimate of charmless scalar meson emitting weak hadronic decays of 0 $\Lembda_{b}^{0}$, $Ξ_{b}^{0}$ and $Ξ_{b}^{-}$ bottom baryons employing the pole model and consequently predict their branching ratios.
The well-known discrepancy in the muon $g-2$ between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon $g-2$ using full QCD.
We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, $a_μ= (g_μ-2)/2$. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain $a_μ^{{\rm LBL},π^0} = +56 \times 10^{-11}$.
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 intr…
The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_μ$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_μ|_{uds} =686 \pm 26$, and in the heavy-quark sector $a^{HAD}_μ|_{c} =14.4 \pm 0.1$, and $a^{HAD}_μ|_{b} =0.29 \pm 0.01$, resulting in $a^{HAD}_μ= 701 \pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this …
We propose a novel approach to determine the leading hadronic corrections to the muon g-2. It consists in a measurement of the effective electromagnetic coupling in the space-like region extracted from Bhabha scattering data. We argue that this new method may become feasible at flavor factories, resulting in an alternative determination potentially competitive with the accuracy of the present results obtained with the dispersive approach via time-like data.
The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment can be estimated by computing constituent quark loops. Such an estimate is very sensitive to the numerical values of the constituent quark masses. These can be fixed by computing the hadronic vacuum polarization contribution to the muon magnetic anomaly within the same model. In this Letter, we demonstrate the stability of this framework against first-order perturbative QCD corrections.
The contribution of hadronic vacuum polarization (HVP) to the hyperfine splitting of the muonium ground state is evaluated with the account of modern experimental data on the cross section of $e^+e^- \to$ annihilation into hadrons.
A model for verifying a consistency of the next-to-leading order hadronic contributions to the muon anomalous magnetic moment with those of the leading order is proposed. A part of the next-to-leading order hadronic contributions related to the vacuum polarization is rather accurately reproduced in the model. I find a new numerical value for the light-by-light hadronic contribution that leads to agreement with recent experimental result for the muon anomalous magnetic moment.
Using the gauge/gravity duality, we compute the leading order hadronic (HLO) contribution to the anomalous magnetic moment of muon, amu(HLO). Holographic renormalization is used to obtain a finite vacuum polarization. We find amu(HLO) =470.5 x 10^{-10} in AdS/QCD with two light flavors, which is compared with the currently revised BABAR data estimated from e^+ e^- -> pi^+ pi^- events, amu(HLO)[pipi]=(514.1 +- 3.8) x 10^{-10}.
We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental da…
The contribution of hadronic vacuum polarization to the Lamb shift in muonic hydrogen is evaluated with the account of modern experimental data on the cross section of $e^+e^-$ annihilation into hadrons. The numerical value of this contribution to the (2P-2S) shift in muonic hydrogen is equal to 10.77 $μeV$.
The hadronic light-by-light contribution to a_{mu}, the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a_{mu}, and to a sizeable reduction of the discrepancy between the present experimental value of a_{mu} and its theoretical counterpart in the standard model…
We computed the hadronic vacuum-polarization contributions to the muon anomalous magnetic moment $a_μ(hadr.)$ by using the QCD model with infinite number of vector mesons [1,2]. The result is $a_μ(hadr.) = 663(23) \times 10^{-10}$. }
We reevaluate the hadronic vacuum polarisation contributions to the muon magnetic anomaly and to the running of the electromagnetic coupling constant at the Z-boson mass. We include newest e+e- to hadrons cross-section data (among others) from the BABAR and VEPP-2000 experiments. For the muon (g-2)/2 we find for the lowest-order hadronic contribution (693.1 +- 3.4) 10^-10, improving the precision of our previous evaluation by 21%. The full Standard Model prediction differs by 3.5 sigma from the experimental value. The five-quark hadronic contribution to alpha(mZ) is evaluated to be (276.0 +- 0…
The current status of the muon anomalous magnetic moment problem is briefly presented. The corrections to muon anomaly coming from the effects of hadronic vacuum polarization, Z*γγ* effective vertex and light-by-light scattering are estimated within the instanton model of QCD vacuum.
The contribution of hadronic vacuum polarization to the hyperfine splitting of the muonic hydrogen ground state is calculated with the account of experimental data on the cross section of e^+e^-\to annihilation into hadrons and the dipole parameterization of electromagnetic proton form factors.
We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass Möbius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_μ^{\rm HLbL} = 7.87(3.06)_\text{stat}(1.77)_\text{sys}\times 10^{-10}$. Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to e…
The hadronic light-by-light scattering contribution to the muon g-2 is the most troublesome component of its theoretical prediction; (1) it cannot be determined from the other measurable quantities, (2) the dimensional argument and the estimation based on hadronic models imply that the magnitude of this contribution may be comparable to the discrepancy between the standard model prediction and the experimental value. The direct approach to evaluate the hadronic light-by-light scattering contribution requires the evaluation of the correlation function of {\it four} hadronic electromagnetic curr…
The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.
There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, a_mu (LBL,had). Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a_mu (LBL,had) is overestimated. Interpolating, thi…
We reanalyze the two-loop electroweak hadronic contributions to the muon g-2 that may be enhanced by large logarithms. The present evaluation is improved over those already existing in the literature by the implementation of the current algebra Ward identities and the inclusion of the correct short-distance QCD behaviour of the relevant hadronic Green's function.
Extensive Air Showers are complex macroscopic objects initiated by single ultra-high energy particles. They are the result of millions of high energy reactions in the atmosphere and can be described as the superposition of hadronic and electromagnetic cascades. The hadronic cascade is the air shower backbone, and it is mainly made of pions. Decays of neutral pions initiate electromagnetic cascades, while the decays of charged pions produce muons which leave the hadronic core and travel many kilometers almost unaffected. Muons are smoking guns of the hadronic cascade: the energy, transverse mom…
{}From the study of the multiple muon events in deep underground detectors, it is possible to extract information about the spectrum and composition of the primary cosmic rays. In this work the number of TeV muons produced by a primary cosmic ray of a given energy and zenith angle is computed using analytic and montecarlo methods, for a family of simplified models as description of the properties of hadronic interactions. The effects of the uncertainties in our knowledge of the hadronic cross sections in the calculation of TeV muons are discussed.
