Hadronic Contribution Research Articles

Theory-Driven Evolution of the Weak Mixing Angle.

We present the first purely theoretical calculation of the weak mixing angle in the MS[over ¯] scheme at low energies by combining results from lattice QCD with perturbation theory. We discuss its correlation with the hadronic contribution to the anomalous magnetic moment of the muon and to the energy dependence of the electromagnetic coupling. We also compare the results with calculations using cross-section data as input. Implications for the standard model prediction of the mass of the W boson are also discussed.

Model-independent extrapolation of MUonE data with Padé and D-Log approximants

The MUonE experiment is designed to extract the hadronic contribution to the electromagnetic coupling in the spacelike region Δαhad(t) from elastic eμ scattering. The leading-order hadronic vacuum polarization contribution to the muon g−2, aμHVP,LO, can then be obtained from a weighted integral over Δαhad(t). This, however, requires knowledge of Δαhad(t) in the whole domain of integration, which cannot be achieved by experiment. In this work, we propose to use Padé and D-Log Padé approximants as a systematic and model-independent method to fit and reliably extrapolate the future MUonE experimental data, extracting aμHVP,LO with a conservative but competitive uncertainty, using no or very limited external information. The method relies on fundamental analytic properties of the two-point correlator underlying aμHVP,LO and provides lower and upper bounds for the result for aμHVP,LO. We demonstrate the reliability of the method using toy datasets generated from a model for Δαhad(t) reflecting the expected statistics of the MUonE experiment. Published by the American Physical Society 2024

Time-kernel for lattice determinations of NLO hadronic vacuum polarization contributions to the muon g-2

We study the time-momentum representation of the kernel needed to compute the hadronic vacuum polarization contribution to the muon g-2 in the space-like region at next-to-leading order. For small values of the time, we present analytical series expansions; for large values of the time, we present numerical series expansions which overcome the problems showed by naïve asymptotic expansions. These results are to be employed in lattice QCD determination of the hadronic vacuum polarization contribution to the muon g-2 at next-to-leading order.

The detector for the MUonE experiment at CERN

The comparison between the measurement and the Standard Model prediction of the anomalous magnetic moment of the muon (aμ) is a way to search for physics beyond the Standard Model. Recently, the Fermilab Muon g−2 experiment measured aμ with a precision of 200 parts per billion (ppb), while the theoretical prediction of aμ is limited by the uncertainty in the leading-order hadronic vacuum-polarization contribution (aμHLO) as the two calculation methods, namely the dispersive approach and the lattice QCD, yield different results. The MUonE experiment proposes an alternative and independent way to precisely measure aμHLO through a unique direct measurement, which can be used to cross-check the theoretical value.

Hadron Contribution of Light-by-Light Scattering to Hyperfine Splitting in Muonium

Hadron Contribution of Light-by-Light Scattering to Hyperfine Splitting in Muonium

Maximizing the physics potential of B±→π±μ+μ− decays

We present a method that maximizes the experimental sensitivity to new physics contributions in B±→π±μ+μ− decays. This method relies on performing an unbinned maximum likelihood fit to both the measured dimuon q2 distribution of B±→π±μ+μ− decays, and theory calculations at spacelike q2, where QCD predictions are most reliable. Using known properties of the decay amplitude we employ a dispersion relation to describe the nonlocal hadronic contributions across spacelike and timelike q2 regions. The fit stability and the sensitivity to new physics couplings and new sources of CP-violation are studied for current and future data-taking scenarios, with the LHCb experiment as an example. The proposed method offers a precise and reliable way to search for new physics in these decays. Published by the American Physical Society 2024

Measurement of the e+e−→π+π− cross section from threshold to 1.2 GeV with the CMD-3 detector

The cross section of the process e+e−→π+π− has been measured in the center of mass energy range from 0.32 to 1.2 GeV with the CMD-3 detector at the electron-positron collider VEPP-2000. The measurement is based on a full dataset collected below 1 GeV during three data taking seasons, corresponding to an integrated luminosity of about 62 pb−1. In the dominant ρ-resonance region, a systematic uncertainty of 0.7% has been reached. At energies around ϕ-resonance the π+π− production cross section was measured for the first time with high beam energy resolution. The forward-backward charge asymmetry in the π+π− production has also been measured. It shows a strong deviation from the theoretical prediction based on the conventional scalar quantum electrodynamics framework, and it is in good agreement with the generalized vector-meson-dominance and dispersive-based predictions. The impact of the presented results on the evaluation of the hadronic contribution to the anomalous magnetic moment of muon is discussed. Published by the American Physical Society 2024

Measurement of the Pion Form Factor with CMD-3 Detector and Its Implication to the Hadronic Contribution to Muon (g-2).

The cross section of the process e^{+}e^{-}→π^{+}π^{-} has been measured in the center-of-mass energy range from 0.32 to 1.2GeV with the CMD-3 detector at the electron-positron collider VEPP-2000. The measurement is based on an integrated luminosity of about 88 pb^{-1}, of which 62 pb^{-1} represent a complete dataset collected by CMD-3 at center-of-mass energies below 1GeV. In the dominant region near the ρ resonance a systematic uncertainty of 0.7% was achieved. The implications of the presented results for the evaluation of the hadronic contribution to the anomalous magnetic moment of the muon are discussed.

On electroweak corrections to neutral current Drell–Yan with the POWHEG BOX

Motivated by the requirement of a refined and flexible treatment of electroweak corrections to the neutral current Drell–Yan process, we report on recent developments on various input parameter/renormalization schemes for the calculation of fully differential cross sections, including both on-shell and MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{ \\mathrm MS}$$\\end{document} schemes. The latter are particularly interesting for direct determinations of running couplings at the highest LHC energies. The calculations feature next-to-leading order precision with additional higher order contributions from universal corrections such as Δα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varDelta \\alpha $$\\end{document} and Δρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varDelta \\rho $$\\end{document}. All the discussed input parameter/renormalization scheme options are implemented in the package of POWHEG-BOX-V2 dedicated to the neutral current Drell–Yan simulation, i.e. Z_ew-BMNNPV, which is used to obtain the presented numerical results. In particular, a comprehensive analysis on physical observables calculated with different input parameter/renormalization schemes is presented, addressing the Z peak invariant mass region as well as the high energy window. We take the opportunity of reporting also on additional improvements and options introduced in the package Z_ew-BMNNPV after svn revision 3376, such as different options for the treatment of the hadronic contribution to the running of the electromagnetic coupling and for the handling of the unstable Z resonance.

Lepton pair production in muon-nucleus scattering

The MUonE experiment aims at providing a novel determination of the leading hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering. Since the initial-state electrons are bound in a low-Z atomic target, the interaction between the incoming muons and the nuclei is expected to be the main source of experimental background. In this article, we study the production of a real lepton pair from the muon-nucleus scattering, discussing its numerical impact in the MUonE kinematic configuration. The process is described as a scattering of a muon in an external Coulomb field with the addition of a form factor to describe the nuclear charge distribution. The calculation is implemented in the fully differential Monte Carlo event generator Mesmer, without introducing any approximation on the angular variables.

Hadronic vacuum polarization: Comparing lattice QCD and data-driven results in systematically improvable ways

The precision with which hadronic vacuum polarization (HVP) is obtained determines how accurately important observables, such as the muon anomalous magnetic moment aμ or the low-energy running of the electromagnetic coupling α, are predicted. The two most precise approaches for determining HVP are dispersive relations combined with e+e−→hadrons cross section data and lattice QCD. However, the results obtained in these two approaches display significant tensions, whose origins are not understood. Here we present a framework that sheds light on this issue and—if the two approaches can be reconciled—allows them to be combined. Via this framework, we test the hypothesis that the tensions can be explained by modifying the R-ratio in different intervals of center-of-mass energy s. As ingredients, we consider observables that have been precisely determined in both approaches. These are the leading hadronic contributions to aμ, to the so-called intermediate window observable, and to the running of α between spacelike virtualities 1 and 10 GeV2 (for which only a preliminary lattice result exists). Our tests take into account all uncertainties and correlations, as well as uncertainties on uncertainties in the lattice results. For instance, using this framework we show that results obtained in the two approaches can be made to agree, for all three observables, by modifying the ρ peak in the experimental spectrum. More specifically, we show that this requires a common ∼5% increase in the contributions of the peak to each of the three observables. This result is robust against the presence or absence of the running of α in the comparison. However, such an increase is much larger than the uncertainties on the measured R-ratio. We also discuss a variety of generalizations of the methods used here, as well as the limits in the information that can be extracted from the R-ratio via a finite set of observables. Published by the American Physical Society 2024

Hadronic vacuum polarization in the muon g − 2: the short-distance contribution from lattice QCD

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon g – 2, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${x}_{0}^{4}$$\\end{document}-behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with 2 + 1 flavours of O(a)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range 130 – 420 MeV. Our estimate at the physical point contains a full error budget and reads \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\left({a}_{\\mu }^{{\ ext{hvp}}}\\right)}^{{\ ext{SD}}}$$\\end{document} = 68.85(14)stat (42)syst·10−10, which corresponds to a relative precision of 0.7%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization.

Determination of short- and long-distance contributions in B0→K*0μ+μ− decays

An amplitude analysis of the B0→K*0μ+μ− decay is presented. The analysis is based on data collected by the LHCb experiment from proton-proton collisions at s=7, 8 and 13 TeV, corresponding to an integrated luminosity of 4.7 fb−1. For the first time, Wilson coefficients and nonlocal hadronic contributions are accessed directly from the unbinned data, where the latter are parametrized as a function of q2 with a polynomial expansion. Wilson coefficients and nonlocal hadronic parameters are determined under two alternative hypotheses: the first relies on experimental information alone, while the second one includes information from theoretical predictions for the nonlocal contributions. Both models obtain similar results for the parameters of interest. The overall level of compatibility with the Standard Model is evaluated to be between 1.8 and 1.9 standard deviations when looking at the C9 Wilson coefficient alone, and between 1.3 and 1.4 standard deviations when considering the full set of C9,C10,C9′ and C10′ Wilson coefficients. The ranges reflect the theoretical assumptions made in the analysis. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Data-driven estimates for light-quark-connected and strange-plus-disconnected hadronic g−2 window quantities

A number of discrepancies have emerged between lattice computations and data-driven dispersive evaluations of the RBC/UKQCD intermediate-window-hadronic contribution to the muon anomalous magnetic moment. It is therefore interesting to obtain data-driven estimates for the light-quark-connected and strange-plus-disconnected components of this window quantity, allowing for a more detailed comparison between the lattice and data-driven approaches. The aim of this paper is to provide these estimates, extending the analysis to several other window quantities, including two windows designed to focus on the region in which the two-pion contribution is dominant. Clear discrepancies are observed for all light-quark-connected contributions considered, while good agreement with lattice results is found for strange-plus-disconnected contributions to the quantities for which corresponding lattice results exist. The largest of these discrepancies is that for the RBC/UKQCD intermediate window, where, as previously reported, our data-driven result, aμW1,lqc=198.9(1.1)×10−10, is in significant tension with the results of 8 different recent lattice determinations. Our strategy is the same as recently employed in obtaining data-driven estimates for the light-quark-connected and strange-plus-disconnected components of the full leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. Updated versions of those earlier results are also presented, for completeness. Published by the American Physical Society 2024

A prototype electromagnetic calorimeter for the MUonE experiment: status and first performance results

The MUonE experiment proposes a novel approach to determine the leading hadronic contribution to the muon g-2, from a precise measurement of the differential cross section of the μ-e elastic scattering, achievable by using the CERN SPS muon beam onto atomic electrons of a light target. The detector layout is modular, consisting of an array of identical tracking stations, each one made of a light target and silicon strip planes, followed by an electromagnetic calorimeter made of PbWO4 crystals with APD readout, placed after the last station, and a muon filter. The scattering particles are tracked without any magnetic field, and the event kinematics can be defined in a large phase space region from the expected correlation of the outgoing particle angles. The ambiguity affecting a specific region, with electron and muon outgoing with similar deflection angles, can be solved by identifying the electron track as the one with extrapolation matching the calorimeter cluster or the muon track by associating it to hits in the muon filter. The role of the calorimeter will be important for background estimate and reduction, and to assess systematic errors, providing some useful redundancy and allowing for alternative selections.Beam tests are carried out at CERN with a prototype calorimeter to determine its calibration with both high energy (20–150 GeV) and low energy electrons (1–10 GeV). In late summer a pilot run is scheduled with up to three tracking stations and the calorimeter integrated within a common triggerless readout system. The main motivations for the MUonE calorimeter are discussed, and the status and first performance results will be presented.

Determining the Origin of Very-high-energy Gamma Rays from Galactic Sources by Future Neutrino Observations

Recently, the Large High Altitude Air Shower Observatory (LHAASO) identified 12 gamma-ray sources emitting gamma rays with energies above 100 TeV, making them potential PeV cosmic-ray accelerators (PeVatrons). Neutrino observations are crucial in determining whether the gamma-ray radiation process is of hadronic or leptonic origin. In this paper, we study three detected sources, LHAASO J1908+0621, LHAASO J2018+3651, and LHAASO J2032+4102, which are also the most promising Galactic high-energy neutrino candidate sources with the lowest pretrial p-value based on the stacking searches testing for excess neutrino emission by the IceCube Neutrino Observatory. We study the lepto-hadronic scenario for the observed multiband spectra of these LHAASO sources considering the possible counterpart source of the LHAASO sources. The very-high-energy gamma rays are entirely attributed to the hadronic contribution; therefore, the most optimistic neutrino flux can be derived. Then, we evaluate the statistical significance (p-value) as a function of the observation time of IceCube and the next-generation IceCube-Gen2 neutrino observatory, respectively. Our results tend to disfavor that all gamma rays above 100 GeV from LHAASO J1908+0621 are of purely hadronic origin based on current IceCube observations, but the purely hadronic origin of gamma rays above 100 TeV is still possible. By IceCube-Gen2, the origin of gamma rays above 100 TeV from LHAASO J1908+0621 can be further determined at a 5σ significance level within a running time of ∼3 yr. For LHAASO J2018+3651 and LHAASO J2032+4102, the required running time of IceCube-Gen2 is ∼10 yr (3σ) and ∼10 yr (5σ), respectively. Future observations by the next-generation neutrino telescope will be crucial to understanding the particle acceleration and radiation processes inside the sources.

Hadronic contribution to the Muon 𝑔 − 2 with emphasis on photon-photon fusion processes

The current status of muon 𝑔 − 2 is briefly reviewed, particularly for its hadronic contributions, hadronic vacuum polarization (HVP) and hadronic light-by-light (HLbL), using the data-driven and dispersive approach. As the subprocess of HLbL, the photon-photon fusion to hadrons, especially to π+π−π0 process, is studied in detail.

Coordinate-space calculation of QED corrections to the hadronic vacuum polarization contribution to (g − 2)μ with SU(3) flavor symmetry

Lattice QCD (LQCD) has proven to be an important tool in understanding the tension between the experimental value for the anomalous magnetic moment of the muon (g − 2)μ and its prediction from the standard model. The lattice provides a non-perturbative method for evaluating the hadronic contributions to (g − 2)μ, which contributes the largest amount to the uncertainty of the theoretical prediction. Among these the hadronic vacuum polarization aμHVP is the dominant contribution. In order to match the uncertainty of the experiment, lattice QCD needs to reach sub-percent precision. This requires the calculation of QED corrections to aμHVP, which are represented by additional Feynman diagrams. We present a lattice calculation of the UV-finite (2+2) diagram at the SU(3) flavor symmetric point and compare this to the pseudoscalar meson exchange model with a vector-meson dominance parametrization of the transition form factor.

MUonE experiment

The anomalous magnetic moment of the muon has been a long stand ing issue in the field of particle physics. The recent results by Fermilab have pointed to a possible discrepancy of 4.2σ with respect to the Standard Model prediction. Although the future measurements will undoubtedly strengthen this result, the large uncertainty of the prediction, caused by a non-perturbative hadronic contribution, remains an issue. The MUonE experiment is designed to provide an independent, precise measurement of this contribution by employ ing a series of tracking stations and low-Z targets, to precisely determine the shape of differential cross-section of an elastic µ + e → µ + e scattering. It is expected to increase the result’s significance to at least 7σ, thus solidifying the discovery. The design of the detector allows also for New Physics searches with a signature of displaced vertices.

Perturbative contributions to Δα5MZ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right) $$\\end{document}

We compute a theoretically driven prediction for the hadronic contribution to the electromagnetic running coupling at the Z scale using lattice QCD and state-of-the-art perturbative QCD. We obtainΔα5MZ2=279.5±0.9±0.59×10−4Mainz CollaborationΔα5MZ2=278.42±0.22±0.59×10−4BMWCollaboration,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\displaystyle \\begin{array}{cc}\\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right)=\\left[279.5\\pm 0.9\\pm 0.59\\right]\ imes {10}^{-4}& \\left(\ extrm{Mainz}\\ \ extrm{Collaboration}\\right)\\\\ {}\\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right)=\\left[278.42\\pm 0.22\\pm 0.59\\right]\ imes {10}^{-4}& \\left(\ extrm{BMW}\\ \ extrm{Collaboration}\\right),\\end{array}} $$\\end{document}where the first error is the quoted lattice uncertainty. The second is due to perturbative QCD, and is dominated by the parametric uncertainty on α̂s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\hat{\\alpha}}_s $$\\end{document}, which is based on a rather conservative error. Using instead the PDG average, we find a total error on Δα5MZ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right) $$\\end{document} of 0.4 × 10−4. Furthermore, with a particular emphasis on the charm quark contributions, we also update Δα5MZ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right) $$\\end{document} when low-energy cross-section data is used as an input, obtaining Δα5MZ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\Delta {\\alpha}^{(5)}\\left({M}_Z^2\\right) $$\\end{document} = [276.29 ± 0.38 ± 0.62] × 10−4. The difference between lattice QCD and cross-section-driven results reflects the known tension between both methods in the computation of the anomalous magnetic moment of the muon. Our results are expressed in a way that will allow straightforward modifications and an easy implementation in electroweak global fits.