Hadronic Contribution Research Articles

Towards muon-electron scattering at NNLO

The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The theoretical formulation for the fixed-order NNLO photonic radiative corrections is described and the impact of the numerical results obtained with the corresponding Monte Carlo code is discussed for typical event selections of the MUonE experiment. In particular, the gauge-invariant subsets of corrections due to electron radiation as well as to muon radiation are treated exactly. The two-loop contribution due to diagrams where at least two virtual photons connect the electron and muon lines is approximated taking inspiration from the classical Yennie-Frautschi-Suura approach. The calculation and its Monte Carlo implementation pave the way towards the realization of a simulation code incorporating the full set of NNLO corrections matched to multiple photon radiation, that will be ultimately needed for data analysis.

New physics at the MUonE experiment at CERN

A confirmation of the long-standing muon $g$-2 discrepancy requires both experimental and theoretical progress. On the theory side, the hadronic corrections are under close scrutiny, as they induce the leading uncertainty of the Standard Model prediction. Recently, the MUonE experiment has been proposed at CERN to provide a new determination of the leading hadronic contribution to the muon $g$-2 via the measurement of the differential cross section of muon-electron scattering. The precision expected at this experiment raises the question whether possible new-physics (NP) could affect its measurements. We address this issue studying possible NP signals in muon-electron collisions due to heavy or light mediators, depending on whether their mass is higher or lower than ${\cal O} (1{\rm GeV})$. We analyze the former in a model-independent way via an effective field theory approach, whereas for the latter we focus on scenarios with light scalar and vector bosons. Using existing experimental bounds, we show that possible NP effects in muon-electron collisions are expected to lie below MUonE's sensitivity. This result confirms and reinforces the physics case of the MUonE proposal.

Constraints between Δαhad(MZ2) and (gμ−2)HVP

I discuss the possibility of estimating the shift $\delta\Delta\alpha(M_Z^2)$ on the running of the EM-coupling to the $M_Z$ scale, induced by the discrepancy $\Delta a_{\mu}$ between two precise determinations of the hadronic vacuum polarization contribution to $g_{\mu}-2$. It is shown that the size of $\Delta a_{\mu}$ implies rigorous bounds on the $\delta\Delta\alpha(M_Z^2)$-shift. Any extra contribution to this minimal shift necessarily depends on the specific shape of the underlying spectral function $\frac{1}{\pi}\Imm\Delta(t)$ responsible for the $\Delta a_{\mu}$-discrepancy. I show that, in the case of a quark model, the total $\Delta\alpha(M_Z^2)$-shift remains small. I also discuss the scenario where $\frac{1}{\pi}\Imm\Delta(t)$ is a constant in a finite $t$-region and show that in this case, up to a $t_{\rm max}\precsim 5~\GeV^2$, the size of the total $\delta\Delta\alpha_{\rm had}^{(5)}(M_Z^2)$-shift, remains below or of the order of the present error value on $\Delta\alpha_{\rm had}^{(5)}(M_Z^2)$.

Implications of the new LHCb angular analysis of B→K*μ+μ− : Hadronic effects or new physics?

The new angular analysis of the decay $B \to K^* \ell^+ \ell^-$ recently presented by the LHCb Collaboration still indicates some tensions with the Standard Model predictions. There are several ongoing analyses to solve the problem of separating hadronic and New Physics effects in this decay, but the significance of the observed tensions in the angular observables in $B \to K^* \mu^+\mu^-$ is still dependent on a theory guesstimate of the hadronic contributions to these decays. Using the new data from LHCb we offer two tests which make a statistical comparison to determine whether the most favoured explanation of the anomalies is New Physics or underestimated hadronic effects. We then analyse the usefulness of these tests in two future scenarios. Finally, we update our global fits to all available $b \to s $ data and discuss the impact of the new LHCb measurements.

Muon g−2 and Δα connection

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, $a_{\mu}=\left(g_{\mu}-2\right)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total $e^+e^- \rightarrow \text{hadrons}$ cross section, $\sigma_{\rm had}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, $a_{\mu}^{\rm had,\,VP}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2)$, which enters natural relations and global EW fits. The EW fit prediction of $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02722(41)$ agrees well with $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\Delta a_{\mu}=a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM}$ than currently expected. Postulating that the $\Delta a_{\mu}$ difference may be due to missing $\sigma_{\rm had}(s)$ contributions, implications for $M_W$, $\sin^2 \! \theta^{\rm lep}_{\rm eff}$ and $M_H$ obtained from global EW fits are investigated. Shifts in $\sigma_{\rm had}(s)$ needed to bridge $\Delta a_{\mu}$ are found to be excluded above $\sqrt{s} \gtrsim 0.7$ GeV at the 95\%CL. Moreover, prospects for $\Delta a_{\mu}$ originating below that energy are deemed improbable given the required increases in the cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, $a_e^{\rm SM}$, the ratio $R_{e/\mu} = (m_\mu/m_e)^2 (a_{e}^{\rm had,\,LO\,VP}/a_{\mu}^{\rm had,\,LO\,VP})$ and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2

A variant of QCD with the coupling suppressed in the infrared (IR) regime, as suggested by large-volume lattice calculations of the Landau gauge gluon and ghost dressing functions, is considered. The coupling is further restricted by the condition of approximate coincidence with perturbative QCD in the high momentum regime, and by the τ-lepton semihadronic decay rate in the intermediate momentum regime, the rate which is evaluated by a renormalon-motivated resummation method. The obtained coupling turns out to be free of Landau singularities. The D = 4, 6 condensate values of the Adler function are then extracted by application of the Borel sum rules to the OPAL and ALEPH (V + A)-channel data of τ-decay, and the corresponding V-channel condensate values are deduced as well. We then show that the correct value of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, , is reproduced by regularizing the D = 4, 6 OPE terms in the V-channel Adler function with IR-regularization masses , suggesting the internal consistency of the presented QCD framework.

IceCube Search for High-energy Neutrino Emission from TeV Pulsar Wind Nebulae

Abstract Pulsar wind nebulae (PWNe) are the main gamma-ray emitters in the Galactic plane. They are diffuse nebulae that emit nonthermal radiation. Pulsar winds, relativistic magnetized outflows from the central star, shocked in the ambient medium produce a multiwavelength emission from the radio through gamma-rays. Although the leptonic scenario is able to explain most PWNe emission, a hadronic contribution cannot be excluded. A possible hadronic contribution to the high-energy gamma-ray emission inevitably leads to the production of neutrinos. Using 9.5 yr of all-sky IceCube data, we report results from a stacking analysis to search for neutrino emission from 35 PWNe that are high-energy gamma-ray emitters. In the absence of any significant correlation, we set upper limits on the total neutrino emission from those PWNe and constraints on hadronic spectral components.

Isospin mass differences of singly heavy baryons

We study the isospin mass differences of singly heavy baryons, based on a pion mean-field approach. We consider both the electromagnetic interactions and the hadronic contributions that arise from the mass difference of the up and down quarks. The relevant parameters have been already fixed by the baryon octet. In addition, we introduce the strong hyperfine interactions between the light quarks inside a chiral soliton and the Coulomb interactions between the chiral soliton and a heavy quark. The numerical results are in good agreement with the experimental data. In particular, the results for the neutral mass relations, which contain only the electromagnetic contributions, are in remarkable agreement with the data, which implies that the pion mean field approach provides a good description of the singly heavy baryons.

Thermal Neutron-Induced SEUs in the LHC Accelerator Environment

In addition to high-energy hadrons, which include neutrons, protons, and pions above 20 MeV, thermal neutrons (ThNs) are a major concern in terms of soft error rate (SER) for electronics operating in the large hadron collider (LHC) accelerator at the European Organization for Nuclear Research (CERN). Most of the electronic devices still contain Boron-10 inside their structure, which makes them sensitive to ThNs. The LHC radiation environment in different tunnel and shielded areas is analyzed through measurements and FLUKA simulations, showing that the ThN fluence can be considerably higher than the high-energy one, up to a factor of 50. State-of-the-art commercial-off-the-shelf (COTS) components such as SRAM, field-programmable gate arrays (FPGA), and Flash memories of different technologies are studied to derive the expected single-event upset (SEU) rate due to ThNs, relative to the high-energy hadron contribution. We find that for the studied parts and most of the accelerator applications, ThNs are the dominating source of upsets with respect to the high energy particles yielding even to neglect the latter in some cases. Indeed, they can induce, in electronics, up to more than 90% of the total upsets. The estimation is performed also for ground-level and avionic applications, and although in general, ThNs are not the main source of SER, in Flash memories they can play the same role as high energy neutrons. Related radiation hardness assurance (RHA) considerations for the qualification of components and systems against ThNs are presented.

Geometry optimization of a muon-electron scattering detector

A high-statistics determination of the differential cross section of elastic muon-electron scattering as a function of the transferred four-momentum squared, dσel(μe→μe)/dq2, has been argued to provide an effective constraint to the hadronic contribution to the running of the fine-structure constant, Δαhad, a crucial input for precise theoretical predictions of the anomalous magnetic moment of the muon. An experiment called ‘‘MUonE’’ is being planned at the north area of CERN for that purpose. We consider the geometry of the detector proposed by the MUonE collaboration and offer a few suggestions on the layout of the passive target material and on the placement of silicon strip sensors, based on a fast simulation of elastic muon-electron scattering events and the investigation of a number of possible solutions for the detector geometry. The employed methodology for detector optimization is of general interest as it may be applied to the design of task-specific detectors for high-energy physics, nuclear physics, and astro-particle physics applications.

MUonE sensitivity to new physics explanations of the muon anomalous magnetic moment

The MUonE experiment aims at a precision measurement of the hadronic vacuum polarization contribution to the muon g − 2, via elastic muon-electron scattering. Since the current muon g − 2 anomaly hints at the potential existence of new physics (NP) related to the muon, the question then arises as to whether the measurement of hadronic vacuum polarization in MUonE could be affected by the same NP as well. In this work, we address this question by investigating a variety of NP explanations of the muon g − 2 anomaly via either vector or scalar mediators with either flavor-universal, non-universal or even flavor-violating couplings to electrons and muons. We derive the corresponding MUonE sensitivity in each case and find that the measurement of hadronic vacuum polarization at the MUonE is not vulnerable to any of these NP scenarios.

Consistency of hadronic vacuum polarization between lattice QCD and the R ratio

There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, and charm sea quark gauge ensembles generated in the staggered formalism by the MILC collaboration. We study the continuum limit using inverse lattice spacings from $a^{-1}\approx 1.6$ GeV to $3.5$ GeV, identical to recent studies by FNAL/HPQCD/MILC and Aubin et al. and similar to the recent study of BMW. Our calculation exhibits a tension for the particularly interesting window result of $a_\mu^{\rm ud, conn.,isospin, W}$ from $0.4$ fm to $1.0$ fm with previous results obtained with a different discretization of the vector current on the same gauge configurations. Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention. In this work we also provide results for $a_\mu^{\rm ud,conn.,isospin}$, $a_\mu^{\rm s,conn.,isospin}$, $a_\mu^{\rm SIB,conn.}$ for the total contribution and a large set of windows. For the total contribution, we find $a_\mu^{\rm HVP~LO}=714(27)(13) 10^{-10}$, $a_\mu^{\rm ud,conn.,isospin}=657(26)(12) 10^{-10}$, $a_\mu^{\rm s,conn.,isospin}=52.83(22)(65) 10^{-10}$, and $a_\mu^{\rm SIB,conn.}=9.0(0.8)(1.2) 10^{-10}$, where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD.

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 and UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find a_{μ}^{HLbL}=7.87(3.06)_{stat}(1.77)_{sys}×10^{-10}. Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to explain the difference between the standard model and the BNL experiment.

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

We study isospin-1 P-wave $\pi\pi$ scattering in lattice QCD with two flavours of O($a$) improved Wilson fermions. For pion masses ranging from $m_\pi=265$ MeV to $m_\pi=437$ MeV, we determine the energy spectrum in the centre-of-mass frame and in three moving frames. We obtain the scattering phase shifts using L\"uscher's finite-volume quantisation condition. Fitting the dependence of the phase shifts on the scattering momentum to a Breit-Wigner form allows us to determine the resonance parameters $m_\rho$ and $g_{\rho\pi\pi}$. By combining the scattering phase shifts with the decay matrix element of the vector current, we calculate the timelike pion form factor, $F_\pi$, and compare the results to the Gounaris-Sakurai representation of the form factor in terms of the resonance parameters. In addition, we fit our data for the form factor to the functional form suggested by the Omn\`es representation, which allows for the extraction of the charge radius of the pion. As a further application, we discuss the long-distance behaviour of the vector correlator, which is dominated by the two-pion channel. We reconstruct the long-distance part in two ways: one based on the finite-volume energies and matrix elements and the other based on $F_\pi$. It is shown that this part can be accurately constrained using the reconstructions, which has important consequences for lattice calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment.

A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to varvec{alpha }({{varvec{m}}}_{{varvec{Z}}}^2)

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^- rightarrow mathrm{hadrons} cross-section data together with a phenomenological fit of the threshold region in the evaluation of the dispersion integrals. The precision in the individual datasets cannot be fully exploited due to discrepancies that lead to additional systematic uncertainty in particular between BABAR and KLOE data in the dominant pi ^+pi ^- channel. For the muon (g-2)/2, we find for the lowest-order hadronic contribution (694.0 pm 4.0)cdot 10^{-10}. The full Standard Model prediction differs by 3.3sigma from the experimental value. The five-quark hadronic contribution to alpha (m_Z^2) is evaluated to be (276.0pm 1.0)cdot 10^{-4}.

Swift Observations of Mrk 421 in Selected Epochs. III. Extreme X-Ray Timing/Spectral Properties and Multiwavelength Lognormality during 2015 December–2018 April

Abstract We present the results from the timing and spectral study of Mrk 421 based mainly on the Swift data in the X-ray energy range obtained during the time interval 2015 December–2018 April. The most extreme X-ray flaring activity on long-term, daily, and intraday timescales was observed during the 2 month period that started in 2017 December, when the 0.3–10 keV flux exceeded a level of 5 × 10−9 erg cm−2 s−1, recorded only twice previously. While the TeV-band and X-ray variabilities were mostly correlated, the source often varied in a complex manner in the MeV–GeV and radio–UV energy ranges, indicating that the multifrequency emission of Mrk 421 could not always be generated in a single zone. The longer-term flares at X-rays and γ-rays showed a lognormal character, possibly indicating a variability imprint of the accretion disk onto the jet. A vast majority of the 0.3–10 keV spectra were consistent with the log-parabolic model, showing relatively low spectral curvature and correlations between the different spectral parameters, predicted in the case of the first- and second-order Fermi processes. The position of the synchrotron spectral energy distribution peak showed an extreme variability on diverse timescales between the energies E p < 0.1 and >15 keV, with 15% of the spectra peaking at the hard X-ray, and was related to the peak height as with α ∼ 0.6, which is expected for the transition from Kraichnan-type turbulence into the “hard sphere” one. The 0.3–300 GeV spectra showed features of the hadronic contribution, jet–star interaction, and upscatter in the Klein–Nishina regime in different time intervals.

G−2 of charged leptons, α(MZ2) , and the hyperfine splitting of muonium

Following updates in the compilation of $e^+e^-\rightarrow{\rm hadrons}$ data, this work presents re-evaluations of the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the electron ($a_e$), muon ($a_\mu$) and tau lepton ($a_\tau$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\alpha(M_Z^2)$. Combining the results for the hadronic vacuum polarisation contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of $a_\mu$ and its Standard Model prediction amounts to $\Delta a_{\mu} = (28.02 \pm 7.37) \times 10^{-10}$, corresponding to a muon $g-2$ discrepancy of $3.8\sigma$.

Lattice calculation of the hadronic leading order contribution to the muon g − 2

The persistent discrepancy of about 3.5 standard deviations between the experimental measurement and the Standard Model prediction for the muon anomalous magnetic moment, aµ, is one of the most promising hints for the possible existence of new physics. Here we report on our lattice QCD calculation of the hadronic vacuum polarisation contribution $ a_\mu ^{{\rm{hvp}}} $, based on gauge ensembles with Nf = 2 + 1 flavours of O(a) improved Wilson quarks. We address the conceptual and numerical challenges that one encounters along the way to a sub-percent determination of the hadronic vacuum polarisation contribution. The current status of lattice calculations of $ a_\mu ^{{\rm{hvp}}} $ is presented by performing a detailed comparison with the results from other groups.

Non-thermal emission in lobes of radio galaxies – III. 3C 98, Pictor A, DA 240, Cygnus A, 3C 326, and 3C 236

ABSTRACTRecent analyses of the broad spectral energy distributions (SEDs) of extensive lobes of local radio galaxies have confirmed the leptonic origin of their Fermi/Large Area Telescope γ-ray emission, significantly constraining the level of hadronic contribution. SEDs of distant (DL > 125 Mpc) radio-galaxy lobes are currently limited to the radio and X-ray bands, hence give no information on the presence of non-thermal (NT) protons but are adequate to describe the properties of NT electrons. Modelling lobe radio and X-ray emission in 3C 98, Pictor A, DA 240, Cygnus A, 3C 326, and 3C 236, we fully determine the properties of intralobe NT electrons and estimate the level of the related γ-ray emission from Compton scattering of the electrons off the superposed cosmic microwave background, extragalactic background light, and source-specific radiation fields.

The “Physics Beyond Colliders” Projects for the CERN M2 Beam

Physics Beyond Colliders is an exploratory study aimed at exploiting the full scientific potential of CERN’s accelerator complex up to 2040 and its scientific infrastructure through projects complementary to the existing and possible future colliders. Within the Conventional Beam Working Group (CBWG), several projects for the M2 beam line in the CERN North Area were proposed, such as a successor for the COMPASS experiment, a muon programme for NA64 dark sector physics, and the MuonE proposal aiming at investigating the hadronic contribution to the vacuum polarisation. We present integration and beam optics studies for 100 – 160 GeV/c muon beams as well as an outlook for improvements on hadron beams, which include RFseparated options and low-energy antiproton beams and radiation studies for high intensity beams. In addition, necessary beam instrumentation upgrades for beam particle identification and momentum measurements are discussed.