Search

The apparent tensions emerging from the comparison of experimental data of the anomalous magnetic moments of the muon and electron to the Standard Model predictions ($\Delta a_{\mu,e}$) could be interpreted as a potential signal of New Physics. Models encompassing a light vector boson have been known to offer a satisfactory explanation to $\Delta a_{\mu}$, albeit subject to stringent experimental constraints. Here we explore a minimal extension of the Standard Model via a leptophilic vector boson $Z^\prime$, under the hypothesis of strictly flavour-violating couplings of the latter to leptons. The most constraining observables to this ad-hoc construction emerge from lepton flavour universality violation (in $Z$ and $\tau$ decays) and from rare charged lepton flavour violating transitions. Once these are accommodated, one can saturate the tensions in $\Delta a_{\mu}$, but $\Delta a_{e}$ is predicted to be Standard Model-like. We infer prospects for several observables, including leptonic $Z$ decays and several charged lepton flavour violating processes. We also discuss potential signatures of the considered $Z^\prime$ at a future muon collider, emphasising the role of the $\mu^+\mu^- \to\tau^+\tau^- $ forward-backward asymmetry as a key probe of the model., Comment: 36 pages, 15 figures, v3: minor changes, few clarifications added, results and conclusions unchanged, matches version published in EPJC

It has been recently shown that the discrepancy between the theoretical and experimental values of the anomalous magnetic moment of the muon can be fully accommodated by considering the contribution of few Kaluza-Klein (KK) states of the gauged lepton number with masses lighter than the LEP energy, consistently with present experimental limits. In this article, we construct the minimal embedding of the Standard Model (SM) into D-brane configurations with a gauged lepton number. In order to give rise to such KK modes, the lepton number gauge boson must live on an abelian $U(1)_L$ brane extended along at least one "large" extra dimension in the bulk, with a compactification scale $M_L\sim\mathcal{O}(10-10^2~{\rm GeV})$ for a string scale $M_s\sim 10~{\rm TeV}$. As a consequence, $U(1)_L$ cannot participate to the hypercharge linear combination. We show that the minimal realisation of this framework contains five stacks of branes: the SM color $U(3)_c$, weak $U(2)_w$ and abelian $U(1)$ stacks extended effectively only in four dimensions, the bulk $U(1)_L$, as well as a fifth $U(1)^{'}$ brane. With these five abelian factors, one finds besides the hypercharge a second anomaly-free linear combination which does not couple to the SM spectrum, both in the non-supersymmetric case as well as in the minimal supersymmetric extension of the model. It is also shown how the right-handed neutrino can be implemented in the spectrum, and how fermions arising from the two non-SM branes and coupled to the SM through the $U(1)_L$ KK modes can provide Dark Matter candidates. Finally, the possibility of breaking Lepton Flavour Universality is studied by replacing $U(1)_L$ with a brane gauging only the muonic lepton number, avoiding most experimental constraints and enlarging the parameter space for explaining the discrepancy on the muon magnetic moment., Comment: 20 pages. Published version

We are very grateful to the Fermilab Directorate and the Fermilab Theoretical Physics Department for their financial and logistical support of the first workshop of the Muon g -2 Theory Initiative (held near Fermilab in June 2017) [123], which was crucial for its success, and indeed for the successful start of the Initiative. Financial support for this workshop was also provided by the Fermilab Distinguished Scholars program, the Universities Research Association through a URA Visiting Scholar award, the Riken Brookhaven Research Center, and the Japan Society for the Promotion of Science under Grant No. KAKEHNHI-17H02906. We thank Shoji Hashimoto, Toru Iijima, Takashi Kaneko, and Shohei Nishida for hosting the HVP workshop at KEK [124] and the KEK Theory Center and the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics for providing logistical and financial support. The HLbL workshop at the University of Connecticut [125] was hosted by the University of Connecticut Physics Department. We also gratefully acknowledge support for the second plenary workshop in Mainz [126] from the Deutsche Forschungsgemeinschaft via the Cluster of Excellence "Precision Physics, Fundamental Interactions and Structure of Matter'' (PRISMA), the Collaborative Research Centre "The low-energy frontier of the Standard Model'' (SFB 1044), as well as the Helmholtz Institute Mainz. And finally, we thank the Institute for Nuclear Theory at the University of Washington for hosting the third plenary workshop [127] and for its kind hospitality and stimulating research environment. This workshop was supported in part by the U.S. Department of Energy, Office of Science, under Award Nos. DE-FG02-00ER41132, DE-SC0020106, and by the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics. This review benefited from discussions with O. Cata, N. Christ, L.Y. Dai, H. Davoudiasl, S. Fayer, S. Ganguly, A. Gasparian, S. Hashimoto, T. Iijima, K. Kampf, D. Kawall, I. Larin, Z. Pagel, M. Petschlies, A. Rebhan, K. Schilcher, K. Shimomura, E. Shintani, D. Steffen, S. Tracz, C. Tu, and T. Yamazaki. The work in this paper was supported by CNRS, by Conacyt (Ciencia Basica 2015) under Grant No. 250628, by CONACyT-Mexico under Grant No. CB2014-22117, by Coordinacion de la Investigacion Cientifica (CIC-UMSNH) under Grant No. 4.10, by Danmarks Frie Forskningsfond under Grant No. 8021-00122B, by Deutsche Forschungsgemeinschaft Collaborative Research Centers CRC 1044, CRC 1044 -204404729, CRC 110, and under Grant No. HI 2048/1-1, Prisma Cluster for Excellence PRISMA+ EXC2118/1, STO/876/6-1, by European Research Council under the European Union's Horizon 2020 research and innovation programme under Grant Agreement Nos. 668679, 757646, 771971-SIMDAMA, 813942, by the European Union H2020-MSCA-COFUND2016 under Grant No. 754510, by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 843134, by European Union EuroPLEx Grant H2020-MSCA-ITN-2018-813942, by European Union STRONG 2020 project under Grant Agreement No. 824093, by the Excellence Initiative of Aix-Marseille University -A*MIDEX, a French "Investissements d'Avenir" program, through the Chaire d'Excellence program and the OCEVU Laboratoire d'Excellence (ANR-11-LABX-0060), by the Fermilab Distinguished Scholars program, by Fondo SEP-Cinvestav under Grant No. 142, Fundacao para a Ciencia e a Tecnologia under Grant No. SFRH/BPD/109443/2015, by Generalitat de Catalunya under Grant No. 2017SGR1069, by the Helmholtz Association (German Federal Ministry of Education and Research), by the Helmholtz-Institut Mainz, by the Istituto Nazionale di Fisica Nucleare (INFN), by the Isaac Newton Trust, by the Japan Society for the Promotion of Science under Grant Nos. KAKENHI-15H05742, 16K05317, 16K05323, 16K05338, 17H01133, 17H02906, 18H05226, 19K21872, 20K03926, 20K03960, by Junta de Andalucia under Grant No. A-FQM-467-UGR18, by KEK, by Ministerio de Ciencia e Innovacion under Grant No. CICYTFEDER-FPA2017-86989-P, by Ministerio de Industria, Economia y Competitividad under Grant Nos. FPA2016-78220-C3-3-P, FPA2017-86989-P, PGC2018-094857-B-I00, SEV-2016-0588, SEV-2016-0597, by Laboratoires d'Excellence FIRST-TF grants, a French "Investissements d'Avenir'' program, by the Ministry of Science and Higher Education of the Russian Federation under Grant Agreement No. 14.W03.31.0026, by the National Research Foundation of South Africa, by the Natural Sciences and Engineering Research Council of Canada, by the Portuguese Science Foundation (FCT) Investigator Grant IF/00898/2015, by the Romanian Ministry of Education and Research under Grant No. PN19060101, by the Russian Science Foundation under Grant No. RSF 18-12-00128, by the Secretaria d'Universitats i Recerca del Departament d'Economia i Coneixement de la Generalitat de Catalunya under Grant No. 2017 SGR 1069, by the Swedish Research Council under Grant Nos. 2016-05996, 2019-03779, by the Swiss National Science Foundation under Grant Nos. PP00P2_176884, PCEFP2_181117, by The Leverhulme Trust under Grant No. ECF-2019-223, by the UK Science and Technology Facilities Council (STFC) under Grant Nos. ST/N504130/1, ST/P000290/1, ST/P00055X/1, ST/P000630/1, ST/P000711/1, ST/P000746/1, ST/S000879/1, ST/S000925/1, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Nos. DE-SC0009919, DE-SC0009998, DE-SC0010005, DE-SC0010120, DE-SC0010339, DE-SC0012391, DE-SC0012704, DE-SC0013682, DE-SC0013895, DE-SC0015655, by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Nos. DE-AC02-05CH11231, DE-FG02-00ER41132, DE-FG02-97ER41020, by the U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, "Incubation Platform for Intensity Frontier", by the U.S. National Science Foundation under Grant Nos. NSF-PHY-1316222, PHY14-14614, PHY17-19626, and PHY19-23131, and by the U.S. National Institute of Standards and Technology (NIST) Precision Measurement Grant Program under Award No. 60NANB16D271. This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics., We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including with negligible numerical uncertainty. The electroweak contribution is suppressed by and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at and is due to hadronic vacuum polarization, whereas at the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads and is smaller than the Brookhaven measurement by 3.7. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future – which are also discussed here – make this quantity one of the most promising places to look for evidence of new physics., Fermilab Directorate, Fermilab Theoretical Physics Department, Fermilab Distinguished Scholars program, Universities Research Association through a URA Visiting Scholar award, Riken Brookhaven Research Center, Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT) Japan Society for the Promotion of Science KAKEHNHI-17H02906 KAKENHI-15H05742 16K05317 16K05323 16K05338 17H01133 17H02906 18H05226 19K21872 20K03926 20K03960, High Energy Accelerator Research Organization (KEK), U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, Deutsche Forschungsgemeinschaft via the Cluster of Excellence "Precision Physics, Fundamental Interactions and Structure of Matter'' (PRISMA), Collaborative Research Centre "The low-energy frontier of the Standard Model'' SFB 1044, Helmholtz Institute Mainz, United States Department of Energy (DOE) DE-FG02-00ER41132 DE-SC0020106, Centre National de la Recherche Scientifique (CNRS), Conacyt (Ciencia Basica 2015) 250628, Consejo Nacional de Ciencia y Tecnologia (CONACyT) CB2014-22117, Coordinacion de la Investigacion Cientifica (CIC-UMSNH) 4.10, Danmarks Frie Forskningsfond 8021-00122B, German Research Foundation (DFG) CRC 1044 CRC 1044 -204404729 CRC 110 HI 2048/1-1, Prisma Cluster for Excellence PRISMA+ EXC2118/1 STO/876/6-1, European Research Council (ERC) 668679 757646 771971-SIMDAMA 813942, European Union (EU) 754510, European Union (EU) 843134, European Union EuroPLEx Grant H2020-MSCA-ITN-2018-813942, European Union STRONG 2020 project 824093, French National Research Agency (ANR), OCEVU Laboratoire d'Excellence ANR-11-LABX-0060, Fondo SEP-Cinvestav 142, Portuguese Foundation for Science and Technology SFRH/BPD/109443/2015, Generalitat de Catalunya 2017SGR1069, Helmholtz Association (German Federal Ministry of Education and Research), Istituto Nazionale di Fisica Nucleare (INFN), Isaac Newton Trust, Junta de Andalucia A-FQM-467-UGR18, Instituto de Salud Carlos III Spanish Government CICYTFEDER-FPA2017-86989-P, Ministerio de Industria, Economia y Competitividad FPA2016-78220-C3-3-P FPA2017-86989-P PGC2018-094857-B-I00 SEV-2016-0588 SEV-2016-0597, Laboratoires d'Excellence FIRST-TF grants, Ministry of Science and Higher Education of the Russian Federation 14.W03.31.0026, National Research Foundation - South Africa, Natural Sciences and Engineering Research Council of Canada (NSERC) CGIAR, Portuguese Science Foundation (FCT) Investigator Grant IF/00898/2015, Romanian Ministry of Education and Research PN19060101, Russian Science Foundation (RSF) RSF 18-12-00128, Generalitat de Catalunya 2017 SGR 1069, Swedish Research Council 2016-05996 2019-03779, Swiss National Science Foundation (SNSF) PP00P2_176884 PCEFP2_181117, Leverhulme Trust ECF-2019-223, UK Research & Innovation (UKRI) Science & Technology Facilities Council (STFC) ST/N504130/1 ST/P000290/1 ST/P00055X/1 ST/P000630/1 ST/P000711/1 ST/P000746/1 ST/S000879/1 ST/S000925/1, United States Department of Energy (DOE) DE-SC0009919 DE-SC0009998 DE-SC0010005 DE-SC0010120 DE-SC0010339 DE-SC0012391 DE-SC0012704 DE-SC0013682 DE-SC0013895 DE-SC0015655, United States Department of Energy (DOE) DE-FG02-00ER41132 DE-AC02-05CH11231 DE-FG02-97ER41020 DE-AC02-07CH11359, U.S.-Japan Science and Technology Cooperation Program in High Energy Physics, "Incubation Platform for Intensity Frontier", National Science Foundation (NSF) NSF-PHY-1316222 PHY14-14614 PHY17-19626 PHY19-23131, U.S. National Institute of Standards and Technology (NIST) Precision Measurement Grant 60NANB16D271

The European physical journal / C 82(5), 474 (2022). doi:10.1140/epjc/s10052-022-10402-0, The electroweak (EW) sector of the Minimal Supersymmetric extension of the Standard Model (MSSM), assuming the lightest neutralino as Dark Matter (DM) candidate, can account for a variety of experimental results. This includes the DM direct detection limits, the searches for EW superpartners at the LHC, and in particular the discrepancy between the experimental result for the anomalous magnetic moment of the muon, $(g-2)_\mu $, and its Standard Model (SM) prediction. The new “MUON G-2” result, combined with the older BNL result on $(g-2)_\mu $, yields a deviation from the SM prediction of $\Delta a_\mu = ({25.1}\pm {5.9}) \times 10^{-10}$, corresponding to ${4.2}\,\sigma $. Using this updated bound, together with the other constraints, we calculate the MSSM prediction for the mass of the W boson, $M_W$. We assume contributions only from the EW sector, i.e. the colored sector of the MSSM, in agreement with the search limits, is taken to be heavy. We investigate five scenarios, distinguished by the mechanisms which yield a relic DM density in agreement with the latest Planck bounds. We find that with the new $(g-2)_\mu $ result taken into account and depending on the scenario, values up to are reached. The largest values are obtained for wino DM and in the case of slepton co-annihilation, where points well within the $1\,\sigma $ range of the experimental world average of $M_W^{\mathrm {exp}}= 80.379 \pm 0.012 \,\, \mathrm {GeV}$ are reached, whereas the SM predicts a too small value of $M_W^{\mathrm {SM}}= 80.353 \,\, \mathrm {GeV}$. We analyze the dependence of $M_W^{\mathrm {MSSM}}$ on the relevant masses of the EW superpartners and demonstrate that future $M_W$ measurements, e.g. at the ILC, could distinguish between various MSSM realizations. Sizable contributions to $M_W^{\mathrm {MSSM}}$ are associated with a relatively light $\tilde{\chi }_{1}^0$, accompanied by either a light chargino or a light smuon, setting interesting targets for future collider searches., Published by Springer, Heidelberg

The dispersive approaches to the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment $a_\mu$ are described. The main issues are discussed followed by perspectives in the next years., Comment: 4 pages, 1 figure, 1 table, contribution to the 2022 QCD session of the 56th Rencontres de Moriond

We present a lattice calculation of the leading order (LO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment for the connected light and strange quarks, $a^{\rm W}_{{\rm con}, l/s}$ in the widely used window $t_0=0.4~\mathrm{fm}$, $t_1=1.0~\mathrm{fm}$, $\Delta=0.15~\mathrm{fm}$, and also of $a^{\rm S}_{{\rm con}, l/s}$ in the short distance region. We use overlap fermions on 4 physical-point ensembles. Two 2+1 flavor RBC/UKQCD ensembles use domain wall fermions (DWF) and Iwasaki gauge actions at $a = 0.084$ and 0.114 fm, and two 2+1+1 flavor MILC ensembles use the highly improved staggered quark (HISQ) and Symanzik gauge actions at $a = 0.088$ and 0.121 fm. We have incorporated infinite volume corrections from 3 additional DWF ensembles at ${\rm L}$ = 4.8, 6.4 and 9.6 fm and physical pion mass. For $a^{\rm W}_{{\rm con}, l}$, we find that our results on the two smaller lattice spacings are consistent with those using the unitary setup, but those at the two coarser lattice spacings are slightly different. Eventually, we predict $a^{\rm W}_{{\rm con}, l}=206.7(1.5)(1.0)$ and $a^{\rm W}_{{\rm con}, s}=26.8(0.1)(0.3)$, using linear extrapolation in $a^2$, with systematic uncertainties estimated from the difference of the central values from the RBC/UKQCD and MILC ensembles., Comment: matched to the version accepted by PRD

The mini-proceedings of the STRONG2020 Virtual Workshop "Space-like and Time-like determination of the Hadronic Leading Order contribution to the Muon $g-2$", November 24--26 2021, are presented. This is the first workshop of the STRONG2020 WP21: JRA3-PrecisionSM: Precision Tests of the Standard Model (http://www.strong-2020.eu/joint-research-activity/jra3-precisionsm.html). The workshop was devoted to review of the working group activitity on: $(\it i)$ Radiative Corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^+ e^-$ collisions; $(\it ii)$ Annotated database for $e^+e^-$ into hadrons processes at low energy; $(\it iii)$ Radiative Corrections and Monte Carlo tools for $\mu$-$e$ elastic scattering., Comment: 43 pages, 21 contributions. Editors: A. Kup\'s\'c and G. Venanzoni

42 pp. (2022)., A search for new heavy scalars with flavour-violating decays in final states with multiple leptons and $b$-tagged jets is presented. The results are interpreted in terms of a general two-Higgs-doublet-model involving an additional scalar with couplings to the top-quark and the three up-type quarks ($\rho_{tt}$, $\rho_{tc}$, and $\rho_{tu}$). The targeted signals lead to final states with either a same-sign top-quark pair, three top-quarks, or four top-quarks. The search is based on a dataset of proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$^{-1}$. Events are categorised depending on the multiplicity of light charged leptons (electrons or muons), total lepton charge, and a deep-neural-network-based categorisation to enhance the purity of each of the signals. A mild excess is observed over the Standard Model expectation corresponding to a local significance of 2.81 standard deviations for a signal with $m_{H}=1000$ GeV and $\rho_{tt}=0.32$, $\rho_{tc}=0.05$, and $\rho_{tu}=0.85$. Exclusion limits at 95% confidence are set on the mass and couplings of the heavy Higgs boson. Masses of an additional scalar boson $m_{H}$ between 200-630 (200-840) GeV with couplings $\rho_{tt}=0.4$, $\rho_{tc}=0.2$, and $\rho_{tu}=0.2$ are observed (expected) to be excluded at 95% confidence level. Additional interpretations are provided in models of $R$-parity violating supersymmetry, motivated by the recent flavour and $(g-2)_\mu$ anomalies.

29 pp. (2022)., This note presents a search for a new $Z'$ vector gauge boson with the ATLAS experiment at the Large Hadron Collider using $pp$ collision data collected at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 139 fb$^{-1}$. The new gauge boson $Z'$ is predicted by $L_{\mu}-L_{\tau}$ models %to address the observed anomalies of the muon $g-2$ and rare B decay measurements. to address observed phenomena that can not be explained by the Standard Model. The search examines the four-muon (4$\mu$) final state, using a deep learning neural network classifier to separate the $Z'$ signal from the Standard Model background events. The di-muon invariant masses in the $4\mu$ events are used to extract the $Z'$ resonance signature. No significant excess of events is observed over the predicted background. Upper limits from 0.425 to 2.04 fb, at a 95\% confidence level, are set on the production cross-section times the decay branching fraction of $pp \rightarrow Z'\mu\mu \rightarrow 4\mu$ for the $Z'$ mass ranging from 5 to 75 GeV. Corresponding common coupling strengths, $g_{Z'}$, of the $Z'$ boson to the second and third generation leptons above 0.003 - 0.2 have been excluded.

The long-standing muon g-2 anomaly can be explained by heavy new physics particles through chirally-enhanced contributions. It has been recently proposed that a muon collider running at center-of-mass energies of several TeV could test these new physics scenarios in a model-independent way, through the study of high-energy processes such as mu+ mu- --> h gamma. In this work, we validate these findings, based on effective field theories, by considering renormalizable simplified models and by computing this one-loop process in full generality. Furthermore, we explore the interplay of direct and indirect high-energy searches to pin down the details of the underlying new physics model accommodating the muon g-2 anomaly.

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 on the so-called transfer theorems, due to Flajolet and Odlyzko, which we explain and adapt to HVP., 32 pages, 9 figures. Typos and wording corrected. Version to appear in JHEP

Recently, the Budapest-Marseille-Wuppertal collaboration achieved sub-percent precision in the evaluation of the lowest-order hadronic vacuum polarization contribution to the muon $g_\mu-2$ (arXiv:hep-lat/2002.12347v3). At this level of precision, isospin-symmetric QCD is not sufficient. In this contribution we review how QED and strong-isospin-breaking effects have been included in our work. Isospin breaking is implemented by expanding the relevant correlation functions to second order in the electric charge $e$ and to first order in $m_u-m_d$. The correction terms are then computed using isospin-symmetric configurations. The choice of this approach allows us to better distribute the available computing resources among the various contributions., Comment: talk presented at the 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

The 38th International Symposium on Lattice Field Theory, Lattice 2021, Zoom/Gather@Massachusetts Institute of Technology, USA, 26 Jul 2021 - 30 Jul 2021; Proceedings of Science / International School for Advanced Studies (LATTICE2021), 519 (2022). doi:10.22323/1.396.0519, We report on our computation of the pion transition form factor ${\cal F}_{P\rightarrow \gamma^*\gamma^*}$ from twisted mass lattice QCD in order to determine the numerically dominant light pseudoscalar pole contribution in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon $a_\mu =(g-2)_\mu$. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion-pole contribution with kinematic setup for the pion at rest., Published by SISSA, Trieste

The $\eta$ and $\eta^{\prime}$ mesons are nearly unique in the particle universe since they are almost Goldstone bosons and the dynamics of their decays are strongly constrained. The integrated $\eta$-meson samples collected in earlier experiments amount to $\sim10^{9}$ events. A new experiment, REDTOP (Rare Eta Decays To Probe New Physics), is being proposed, with the intent of collecting a data sample of order 10$^{14}$ $\eta$ (10$^{12}$ $\eta^{\prime}$) for studying very rare decays. Such statistics are sufficient for investigating several symmetry violations, and for searching for particles and fields beyond the Standard Model. In this work we present several studies evaluating REDTOP sensitivity to processes that couple the Standard Model to New Physics through all four of the so-called \emph{portals}: the Vector, the Scalar, the Axion and the Heavy Lepton portal. The sensitivity of the experiment is also adequate for probing several conservation laws, in particular $CP$, $T$ and Lepton Universality, and for the determination of the $\eta$ form factors, which is crucial for the interpretation of the recent measurement of muon $g-2$.

We show that the observed anomalies in the lepton sector can be explained in extensions of the Standard Model that are natural and, therefore, resolve the Higgs sector hierarchy problem. The scale of new physics is around the TeV and Technicolor-like theories are ideal candidate models., 5 pages, 2 figures

In April 2021, scientists active in muon physics met to discuss and work out the physics case for the new High-Intensity Muon Beams (HIMB) project at PSI that could deliver of order $10^{10}$\,s$^{-1}$ surface muons to experiments. Ideas and concrete proposals were further substantiated over the following months and assembled in the present document. The high intensities will allow for completely new experiments with considerable discovery potential and unique sensitivities. The physics case is outstanding and extremely rich, ranging from fundamental particle physics via chemistry to condensed matter research and applications in energy research and elemental analysis. In all these fields, HIMB will ensure that the facilities S$\mu$S and CHRISP on PSI's High Intensity Proton Accelerator complex HIPA remain world-leading, despite the competition of muon facilities elsewhere., Comment: 116 pages, 42 figures

We present a likelihood analysis of the general two Higgs doublet model, using the most important currently measured flavour observables, in view of the anomalies in charged current tree-level and neutral current one-loop rare decays of $B$ mesons in $b\to c l \overline{\nu}$ and $b\to s\mu^{+}\mu^{-}$ transitions, respectively. We corroborate that the model explains the latter and it is able to simultaneously fit the experimental values of the $R(D)$ ratio at $1\sigma$, but it can not accommodate the $R(D^{*})$ and $F_{L}(D^{*})$ observables. We find that the fitted values for the angular observables in $b\to s\mu^{+}\mu^{-}$ transitions exhibit better agreement with the general two Higgs double model in comparison to the SM. We also make predictions for future collider observables $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(h\to bs)$, $\mathrm{BR}(h\to \tau\mu)$, $\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$, $\mathrm{BR}(B^{+}\rightarrow K^{+}\tau^{+}\tau^{-})$ and the flavour violating decays of the $\tau$ lepton, $\mathrm{BR}(\tau\rightarrow3\mu)$ and $\mathrm{BR}(\tau\to\mu\gamma)$. The model predicts values of $\mathrm{BR}(t\to ch)$, $\mathrm{BR}(B_{s}\rightarrow\tau^{+}\tau^{-})$ and $\mathrm{BR}(B^{+}\rightarrow K^{+}\tau^{+}\tau^{-})$ that are out of reach of future experiments, but its predictions for $\mathrm{BR}(h\to bs)$ and $\mathrm{BR}(h\to \tau\mu)$ are within the future sensitivity of the HL-LHC or the ILC. We also find that the predictions for the $\tau\rightarrow3\mu$ and $\tau\to\mu\gamma$ decays are well within the projected limits of the Belle II experiment. Finally, using the latest measurement of the Fermilab Muon $g-2$ Collaboration, we performed a simultaneous fit to $\Delta a_{\mu}$ constrained by the charged anomalies, finding solutions at the $1\sigma$ level. Once the neutral anomalies are included, however, a simultaneous explanation is unfeasible., Comment: 49 pages, 18 figures, new references, fixed typos

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory.

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory., 38 pages, 6 figures. Accepted for publication in PRD

Amplitudes of the form $\gamma^*(q^2)\to \gamma P_1P_2$ appear as sub-processes in the computation of the muon $g-2$. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at $q^2=m^2_\phi$. Starting from an exact parameter-free dispersive representation for the $S$-wave satisfying QCD asymptotic constraints and Low's soft photon theorem we derive, in an effective theory spirit, a two-channel Omn\`es integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of $P_1P_2=\pi\eta$, we show that a very good fit of the KLOE data can be achieved with two real parameters, using a $T$-matrix previously determined from $\gamma\gamma$ scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the $T$-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the $I=1$ scalar form factors and to the $a_0(980)$ resonance complex pole are presented., Comment: 47 pages,13 figures [v2: version accepted for publication]

In this talk recent progress in studying the short-distance properties of the hadronic light-by-light contribution to the muon $g-2$ is described. The intermediate and short-distance part is a major contributor to the error of the theoretical prediction as described in the recent white paper [1]. We have shown that the massless quark-loop is the first term in a systematic expansion at short-distances, a result already used in the white paper. Newer results conclude that both nonperturbative and perturbative corrections are under control. The talk describes these developments and how they fit in the total theoretical prediction for the muon $g-2$., Comment: 6 pages, talk presented at PANIC21, 22nd Particles and Nuclei International Conference, 5-10 September 2021

Experimental data have provided intriguing hints for the violation of lepton flavour universality (LFU), including $B\to D^{(*)}\tau\nu/B\to D^{(*)}\ell\nu$, the anomalous magnetic moment of the muon and $b\!\to\! s\ell^+\ell^-$ with a significance of $\!>3\,\sigma$, $>\!4\,\sigma$ and $>\!5\,\sigma$, respectively. Furthermore, in a recent re-analysis of 2018 Belle data, it was found that the forward-backward asymmetry ($\Delta A_{\rm FB}$) of $B \to D^{*}\mu\bar \nu$ vs $B\to D^{*}e\bar \nu$ disagrees with the SM prediction by $\approx\!\!4\,\sigma$, providing an additional sign of LFU violation. We show that a tensor operator is necessary to significantly improve the agreement with data in $\Delta A_{\rm FB}$ while respecting the bounds from other $b\to c\ell\nu$ observables. Importantly, this tensor operator can only be induced (at tree-level within renormalizable models) by a scalar leptoquark. Furthermore, among the two possible representations, the $SU(2)_L$-singlet $S_1$ and the doublet $S_2$, which can interestingly both also account for the anomalous magnetic moment of the muon, only $S_1$ can provide a good fit. Even though the constraints from (differences of) other angular observables prefer a smaller value of $\Delta A_{\rm FB}$ than the current central one, this scenario is significantly preferred (nearly $4 \sigma$) over the SM hypothesis, and is compatible with constraints such as $B\to K^*\nu\nu$ and electroweak precision bounds. Therefore, if the $\Delta A_{\rm FB}$ anomaly is confirmed, it would provide circumstantial evidence for scalar leptoquarks and pave the way for a natural connection with all other anomalies pointing towards LFU violation., Comment: 7 pages, 3 figures, 1 table, matches journal version

The European physical journal / C 82(2), 184 (2022). doi:10.1140/epjc/s10052-022-10096-4, The generic hidden local symmetry (HLS) model has recently given rise to its $\hbox {BHLS}_2$ variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a modification of the covariant derivative at the root of the HLS approach. However, the description of the $\tau $ dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector ($e^+ e^- \rightarrow \pi ^+ \pi ^-/\pi ^+ \pi ^-\pi ^0/ \pi ^0 \gamma /\eta \gamma /K^+ K^-/K_L K_S$) is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the $[\pi ^0,\eta ,{\eta ^\prime }]$ system within this extended $\hbox {BHLS}_2$ ($\hbox {EBHLS}_2$) scope. This mechanism, an extension of the usual ���t Hooft determinant term, only affects the kinetic energy part of the $\hbox {BHLS}_2$ Lagrangian. One thus obtains a fair account for the $\tau $ dipion spectra which complements the fair account of the annihilation channels already reached. The Belle dipion spectrum is found to provide evidence in favor of a violation of the conserved vector current (CVC) in the $\tau $ lepton decay; this evidence is enforced by imposing the conditions $=ip_\mu f_q \delta _{q q^\prime }, \{ [q {\overline{q}}], q=u,d,s\}$ on $\hbox {EBHLS}_2$ axial current matrix elements. $\hbox {EBHLS}_2$ is found to recover the usual (completed) formulae for the [$\pi ^0,~\eta ,~{\eta ^\prime }$] mixing parameters, and the global fits return mixing parameter values in agreement with expectations and better uncertainties. Updating the muon hadronic vacuum polarization (HVP), one also argues that the strong tension between the KLOE and BaBar pion form factors imposes to provide two solutions, namely $a_\mu ^{HVP-LO}(\mathrm{KLOE})=687.48 \pm 2.93$ and $a_\mu ^{HVP-LO}(\mathrm{BaBar})=692.53 \pm 2.95$, in units of $10^{-10}$, rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance $> 5.4\sigma $ (KLOE) and $> 4.1\sigma $ (BaBar), with fit probabilities favoring the former., Published by Springer, Heidelberg

We demonstrate that the discrepancy between the anomalous magnetic moment measured at BNL and Fermilab and the Standard Model prediction could be explained within the context of low-scale gravity and large extra-dimensions. The dominant contribution to $(g-2)_\mu$ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. We show that the KK contribution to $(g-2)_\mu$ is universal with the string scale entering as an effective cutoff. The KK tower provides a unequivocal distinctive signal which will be within reach of the future muon smasher., Comment: Matching journal version; addendum in arXiv:2110.01247

The process $e^+e^-\to \pi^+\pi^-\pi^0\gamma$ is studied at a center-of-mass energy near the $\Upsilon(4S)$ resonance using a data sample of 469 fb$^{-1}$ collected with the BABAR detector at the PEP-II collider. We have performed a precise measurement of the $e^+e^-\to \pi^+\pi^-\pi^0$ cross section in the center-of-mass energy range from 0.62 to 3.5 GeV. In the energy regions of the $\omega$ and $\phi$ resonances, the cross section is measured with a systematic uncertainty of 1.3\%. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $e^+e^-\to \pi^+\pi^-\pi^0$ cross section from threshold to 2.0 GeV is $(45.86 \pm 0.14 \pm 0.58)\times 10^{-10}$. From the fit to the measured $3\pi$ mass spectrum we have determined the resonance parameters $\Gamma(\omega\to e^+e^-){\cal B}(\omega\to \pi^+\pi^-\pi^0)=(0.5698\pm0.0031\pm0.0082) \mbox{ keV}$, $\Gamma(\phi\to e^+e^-){\cal B}(\phi\to \pi^+\pi^-\pi^0)=(0.1841\pm0.0021\pm0.0080) \mbox{ keV}$, and ${\cal B}(\rho\to 3\pi)=(0.88\pm 0.23\pm 0.30)\times 10^{-4}$. The significance of the $\rho\to 3\pi$ signal is greater than $6\sigma$. For the $J/\psi$ resonance we have measured the product ${\Gamma(J/\psi\to e^+e^-){\cal B}(J/\psi\to 3\pi)}=(0.1248\pm0.0019\pm0.0026)\mbox{ keV}$., Comment: 35 pages, 28 figures, corrected cross section in Table IV

The 38th International Symposium on Lattice Field Theory, LATTICE2021, Zoom/Gather@Massachusetts Institute of Technology, USA, 26 Jul 2021 - 30 Jul 2021; Proceedings of Science / International School for Advanced Studies (LATTICE2021), 106 (2021). doi:10.22323/1.396.0106, he anomalous magnetic moment of the muon $a_{\mu}$ and the running of the electromagnetic coupling $\alpha$ play a fundamental role in beyond Standard Model (SM) physics searches. Non-perturbative hadronic contributions to both quantities, which are related to the hadronic vacuum polarization (HVP) function consisting of two electromagnetic currents, are a main source of uncertainty in the SM prediction. We compute the HVP function in lattice QCD+QED applying the time-momentum representation method. We expand the relevant correlation functions around the isosymmetric limit. In particular, we focus on leading isospin breaking effects taking quark-connected contributions into account, which we evaluate on isosymmetric $N_{\mathrm{f}}=2+1$ QCD gauge ensembles generated by the CLS initiative with non-perturbatively $O(a)$-improved Wilson fermions., Published by SISSA, Trieste

The prediction for the quartic coupling of the SM-like Higgs boson constrains the parameter space of SUSY models, even in scenarios where all of the new-particle masses are above the scale probed so far by the LHC. We study the implications of the Higgs-mass prediction on a recently-proposed SUSY model that features two pairs of Higgs doublets, and provides a solution to the g-2 anomaly thanks to a suitable enhancement of the muon Yukawa coupling., Comment: 22 pages, 3 PDF figures; v2: references added, discussion of figure 2 expanded. Version to be published in EPJC

Leptoquarks (LQs) have attracted increasing attention within recent years, mainly since they can explain the flavor anomalies found in $R(D^{(*)})$, $b \rightarrow s \ell^+ \ell^-$ transitions and the anomalous magnetic moment of the muon. In this article, we lay the groundwork for further automated analyses by presenting the complete Lagrangian and the corresponding set of Feynman rules for scalar leptoquarks. This means we consider the five representations $\Phi_1, \Phi_{\tilde1}, \Phi_2, \Phi_{\tilde2}$ and $\Phi_3$ and include the triple and quartic self-interactions, as well as couplings to the Standard Model (SM) fermions, gauge bosons and the Higgs. The calculations are performed using FeynRules and all model files are publicly available online at https://gitlab.com/lucschnell/SLQrules.

Given current discrepancy in muon $g-2$ and future dedicated efforts to measure muon electric dipole moment (EDM) $d_\mu$, we assess the indirect constraints imposed on $d_\mu$ by the EDM measurements performed with heavy atoms and molecules. We notice that the dominant muon EDM effect arises via the muon-loop induced 'light-by-light' $CP$-odd amplitude $\propto{\bf B}{\bf E}^3$, and in the vicinity of a large nucleus the corresponding parameter of expansion can be significant, $eE_{\rm nucl}/m_\mu^2 \sim 0.04$. We compute the $d_\mu$-induced Schiff moment of the $^{199}$Hg nucleus, and the linear combination of $d_e$ and semileptonic $C_S$ operator (dominant in this case) that determine the $CP$-odd effects in ThO molecule. The results, $d_\mu(^{199}{\rm Hg}) < 6\times 10^{-20}e$cm and $d_\mu({\rm ThO}) < 2\times 10^{-20}e$cm, constitute approximately three- and nine-fold improvements over the limits on $d_\mu$ extracted from the BNL muon beam experiment.

The measurement of exclusive $e^+e^-$ to hadrons processes is a significant part of the physics program of $BABAR$ experiment, aimed to improve the calculation of the hadronic contribution to the muon $g-2$ and to study the intermediate dynamics of the processes. We present the most recent results obtained by using the full data set of about 470\,fb$^{-1}$ collected by the BABAR detector at the PEP-II $e^+e^-$ collider at a center-of-mass energy of about 10.6 GeV. In particular, we report the results on $e^+e^-$ annihilation into six- and seven-pion final states. The study of the very rich dynamics of these processes can help to understand the difference seen between the QCD prediction and the sum of exclusive cross sections in the energy region around 2 GeV, thus improving the precision on the total hadronic cross section and of the $g-2$ calculation. Additionally, we report the results on a dedicated study to shed light on the resonant states production in the energy region around 2.2 GeV, which is presently rather unclear. We measure the reaction $e^+e^-\to K_SK_L$ with data collected with the $BABAR$ detector and analyse these data in conjunction with published BESIII data on $e^+e^-\to K^+K^-$ and $BABAR$ data on $e^+e^-\to K^+K^-$, $\pi^+\pi^-$, $\pi^+\pi^-\eta$, $\pi^+\pi^-\omega$. This study supports the existence of an isovector resonance $\rho(2230)$ consistent with the resonance observed by BESIII., Comment: Presented at 55th Rencontres de Moriond on QCD and High Energy Interactions (Moriond QCD 2021); On behalf of the BaBar Collaboration

Very recently, the Muon $g-2$ experiment at Fermilab has confirmed the E821 Brookhaven result, which hinted at a deviation of the muon anomalous magnetic moment from the Standard Model (SM) expectation. The combined results from Brookhaven and Fermilab show a difference with the SM prediction $\delta a_\mu = (251 \pm 59) \times 10^{-11}$ at a significance of $4.2\sigma$, strongly indicating the presence of new physics. Motivated by this new result we reexamine the contributions to the muon anomalous magnetic moment from both: (i)~the ubiquitous $U(1)$ gauge bosons of D-brane string theory constructions and (ii)~the Regge excitations of the string. We show that, for a string scale ${\cal O} ({\rm PeV})$, the contribution from anomalous $U(1)$ gauge bosons which couple to hadrons could help to reduce (though not fully eliminate) the discrepancy reported by the Muon $g-2$ Collaboration. Consistency with null results from LHC searches of new heavy vector bosons imparts the dominant constraint. We demonstrate that the contribution from Regge excitations is strongly suppressed as it was previously conjectured. We also comment on contributions from Kaluza-Klein (KK) modes, which could help resolve the $\delta a_\mu$ discrepancy. In particular, we argue that for 4-stack intersecting D-brane models, the KK excitations of the $U(1)$ boson living on the lepton brane would not couple to hadrons and therefore can evade the LHC bounds while fully bridging the $\delta a_\mu$ gap observed at Brookhaven and Fermilab., Comment: Matching version to be published in Fortsch. Phys

We study the potential impact on the electroweak (EW) fits due to the tensions between the current determinations of the hadronic vacuum polarisation (HVP) contributions to the anomalous magnetic moment of the muon ($a_\mu$), based on either phenomenological dispersion integrals using measured hadronic spectra or on Lattice QCD calculations. The impact of the current tension between the experimental measurement of $a_\mu$ and the total theoretical prediction based on the phenomenological calculations of the HVP are also studied. The correlations between the uncertainties of the theoretical predictions of $a_\mu$ and of the running of $\alpha_{QED}$ are taken into account in the studies. We conclude that the impact on the EW fit can be large in improbable scenarios involving global shifts of the full HVP contribution, while it is much smaller if the shift is restricted to a lower mass range and/or if the shift in $\alpha_{QED}$ is obtained from that in $a_\mu$ through appropriate use of the correlations. Indeed, the latter scenarios only imply at most a 2.6/16 increase in the $\chi^2/n.d.f.$ of the EW fits and relatively small changes for the resulting fit parameter values., Comment: Added 4 references and some more detailed discussions. The results and conclusions are unchanged. Version matching the published paper. 10 pages, 3 figures

Very recently, we proposed an explanation of the discrepancy between the measured anomalous magnetic moment of the muon and the Standard Model (SM) prediction in which the dominant contribution to $(g-2)_\mu$ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. In this addendum we reexamine the bounds on 4-fermion contact interactions from precise electroweak measurements and show that the constraints on KK masses and couplings are more severe than earlier thought. However, we demonstrate that our explanation remains plausible if a few KK modes are lighter than LEP energy, because if this were the case the contribution to the 4-fermion scattering from the internal propagator would be dominated by the energy and not by the mass. To accommodate the $(g-2)_\mu$ discrepancy we assume that the lepton number $L$ does not partake in the hypercharge and propagates in one extra dimension (transverse to the SM branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP energy), the string scale is roughly 10 TeV while the $L$ gauge coupling is of order $\sim 10^{-1}$., Comment: 3 pages. Addendum to arXiv:2105.02630. Published version

The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant α is of particular importance because it sets the strength of the electromagnetic interaction between light and charged elementary particles, such as the electron and the muon. Here we use matter-wave interferometry to measure the recoil velocity of a rubidium atom that absorbs a photon, and determine the fine-structure constant α−1 = 137.035999206(11) with a relative accuracy of 81 parts per trillion. The accuracy of eleven digits in α leads to an electron g factor1,2—the most precise prediction of the standard model—that has a greatly reduced uncertainty. Our value of the fine-structure constant differs by more than 5 standard deviations from the best available result from caesium recoil measurements3. Our result modifies the constraints on possible candidate dark-matter particles proposed to explain the anomalous decays of excited states of 8Be nuclei4 and paves the way for testing the discrepancy observed in the magnetic moment anomaly of the muon5 in the electron sector6. The fine-structure constant is determined with an accuracy of 81 parts per trillion using matter-wave interferometry to measure the rubidium atom recoil velocity.

The three-loop QED mass-dependent contributions to the $g-2$ of each of the charged leptons with two internal closed fermion loops, sometimes called $A^{(6)}_3\left(\frac{m_1}{m_2}, \frac{m_1}{m_3}\right)$ in the $g-2$ literature, is revisited using the Mellin-Barnes (MB) representation technique. Results for the muon and $\tau$ lepton anomalous magnetic moments $A^{(6)}_{3,\mu}$ and $A^{(6)}_{3,\tau}$, which were known as series expansions in the lepton mass ratios up to the first few terms only, are extended to their exact expressions. The contribution to the anomalous magnetic moment of the electron $A^{(6)}_{3,e}$ is also explicitly given in closed form. In addition to this, we show that the different series representations derived from the MB representation collectively converge for all possible values of the masses. Such unexpected behavior is related to the fact that these series bring into play double hypergeometric series that belong to a class of Kamp\'e de F\'eriet series which we prove to have the same simple convergence and analytic continuation properties as the Appell $F_1$ double hypergeometric series., Comment: 31 pages, 7 figures, uncertainties in Eq.(20) and some other typos corrected

We compute the leading order hadronic vacuum polarization (LO-HVP) contribution to the anomalous magnetic moment of the muon, $(g_\mu-2)$, using lattice QCD. Calculations are performed with four flavors of 4-stout-improved staggered quarks, at physical quark masses and at six values of the lattice spacing down to 0.064~fm. All strong isospin breaking and electromagnetic effects are accounted for to leading order. The infinite-volume limit is taken thanks to simulations performed in volumes of sizes up to 11~fm. Our result for the LO-HVP contribution to $(g_\mu-2)$ has a total uncertainty of 0.6\%. Surprisingly, our result eliminates the need to invoke new physics to explain the measurement of $(g_\mu-2)$.

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., 25 pages, 12 figures. One figure added, minor corrections implemented. Main results unchanged. References added and updated. Version accepted for publication on JHEP

The European physical journal / C 80(2), 81 (1-55) (2020). doi:10.1140/epjc/s10052-020-7611-9, Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) able to encompass a large number of processes within a unified framework. This allowed one to design a global fit procedure which provides a fair simultaneous description of the $e^+ e^-$ annihilation into six final states ($\pi ^+\pi ^-$, $\pi ^0\gamma $, $\eta \gamma $, $\pi ^+\pi ^-\pi ^0$, $K^+K^-$, $K_L K_S$), the dipion spectrum in the $\tau $ decay and some more light meson decay partial widths. In this paper, additional breaking schemes are defined which improve the BHLS working and extend its scope so as to absorb spacelike processes within a new framework (${\hbox {BHLS}}_2$). The phenomenology previously explored with BHLS is fully revisited in the ${\hbox {BHLS}}_2$ context with special emphasis on the $\phi $ mass region using all available data samples. It is shown that ${\hbox {BHLS}}_2$ addresses perfectly the close spacelike region covered by NA7 and Fermilab data; it is also shown that the recent lattice QCD (LQCD) information on the pion form factor are accurately predicted by the ${\hbox {BHLS}}_2$ fit functions derived from fits to only annihilation data. The contribution to the muon anomalous magnetic moment $a_\mu ^{\mathrm{th}}$ of these annihilation channels over the range of validity of ${\hbox {BHLS}}_2$ (up to $\simeq $ 1.05 GeV) is updated within the new ${\hbox {BHLS}}_2$ framework and shown to strongly reduce the former BHLS systematics. The uncertainty on $a_\mu ^{\mathrm{th}}(\sqrt{s}< 1.05 \, \hbox {GeV}$) is much improved compared to standard approaches relying on direct integration methods of measured spectra. Using the ${\hbox {BHLS}}_2$ results, the leading-order HVP contribution to the muon anomalous moment is $a_\mu ^{\mathrm{HVP-LO}}= 686.65 \pm 3.01 +(+1.16,-0.75)_{\mathrm{syst}}$ in units of $10^{-10}$. Using a conservative estimate for the light-by-light contribution, our evaluation for the muon anomalous magnetic moment is $a_\mu ^{\mathrm{th}}=\left[ 11\,659\,175.96 \pm 4.17 +(+1.16,-0.75)_{\mathrm{syst}}\right] \times 10^{-10}$. The relationship between the dispersive and LQCD approaches to the $\rho ^0$–$\gamma $ mixing is also discussed which may amount to a shift of $\delta a_\mu [\pi \pi ]_{\rho \gamma }=+(3.10\pm 0.31) \times 10^{-10}$ at LO+NLO, presently treated as additional systematics. Taking also this shift into account, the difference $a_\mu ^{\mathrm{th}}-a_\mu ^{\mathrm{BNL}}$ exhibits a significance not smaller than $3.8 \sigma $., Published by Springer, Heidelberg

International audience; 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.

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon (g−2) which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-Nc limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the Melnikov-Vainshtein constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.

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 $\Delta\alpha_{\rm had}^{(5)}(M_Z^2)$., Comment: Version to appear as Rapid Communication in Physical Review D

The European physical journal / C 80(3), 244 (1) (2020). doi:10.1140/epjc/s10052-020-7724-1, Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) able to encompass a large number of processes within a unified framework. This allowed one to design a global fit procedure which provides a fair simultaneous description of the $e^+ e^-$ annihilation into six final states ($\pi ^+\pi ^-$, $\pi ^0\gamma $, $\eta \gamma $, $\pi ^+\pi ^-\pi ^0$, $K^+K^-$, $K_L K_S$), the dipion spectrum in the $\tau $ decay and some more light meson decay partial widths. In this paper, additional breaking schemes are defined which improve the BHLS working and extend its scope so as to absorb spacelike processes within a new framework (${\hbox {BHLS}}_2$). The phenomenology previously explored with BHLS is fully revisited in the ${\hbox {BHLS}}_2$ context with special emphasis on the $\phi $ mass region using all available data samples. It is shown that ${\hbox {BHLS}}_2$ addresses perfectly the close spacelike region covered by NA7 and Fermilab data; it is also shown that the recent lattice QCD (LQCD) information on the pion form factor are accurately predicted by the ${\hbox {BHLS}}_2$ fit functions derived from fits to only annihilation data. The contribution to the muon anomalous magnetic moment $a_\mu ^{\mathrm{th}}$ of these annihilation channels over the range of validity of ${\hbox {BHLS}}_2$ (up to $\simeq $ 1.05 GeV) is updated within the new ${\hbox {BHLS}}_2$ framework and shown to strongly reduce the former BHLS systematics. The uncertainty on $a_\mu ^{\mathrm{th}}(\sqrt{s}< 1.05 \, \hbox {GeV}$) is much improved compared to standard approaches relying on direct integration methods of measured spectra. Using the ${\hbox {BHLS}}_2$ results, the leading-order HVP contribution to the muon anomalous moment is $a_\mu ^{\mathrm{HVP-LO}}= 686.65 \pm 3.01 +(+1.16,-0.75)_{\mathrm{syst}}$ in units of $10^{-10}$. Using a conservative estimate for the light-by-light contribution, our evaluation for the muon anomalous magnetic moment is $a_\mu ^{\mathrm{th}}=\left[ 11\,659\,175.96 \pm 4.17 +(+1.16,-0.75)_{\mathrm{syst}}\right] \times 10^{-10}$. The relationship between the dispersive and LQCD approaches to the $\rho ^0$–$\gamma $ mixing is also discussed which may amount to a shift of $\delta a_\mu [\pi \pi ]_{\rho \gamma }=+(3.10\pm 0.31) \times 10^{-10}$ at LO+NLO, presently treated as additional systematics. Taking also this shift into account, the difference $a_\mu ^{\mathrm{th}}-a_\mu ^{\mathrm{BNL}}$ exhibits a significance not smaller than $3.8 \sigma $., Published by Springer, Heidelberg

In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about $3.5~\sigma$ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of $0.14~$ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years., Comment: Contribution to the EPJA special issue "Lattice Field Theory during the COVID-19 pandemic" in replacement of a plenary talk at the 38th International Symposium on Lattice Field Theory (Lattice 2020). v2: minor corrections to match the published version. Some references have been added

The European physical journal / C 79(7), 586 (2019). doi:10.1140/epjc/s10052-019-7049-0, Single-propagator traces are the most elementary fermion Wick contractions which occur in numerical lattice QCD, and are usually computed by introducing random-noise estimators to profit from volume averaging. The additional contribution to the variance induced by the random noise is typically orders of magnitude larger than the one due to the gauge field. We propose a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending on the fermion bilinear considered, the cost of computing these diagrams is reduced by one to two orders of magnitude or more with respect to standard random-noise estimators. As two concrete examples of physics applications, we compute the disconnected contributions to correlation functions of two vector currents in the isosinglet ω channel and to the hadronic vacuum polarization relevant for the muon anomalous magnetic moment. In both cases, estimators with variances dominated by the gauge noise are computed with a modest numerical effort. Theory suggests large gains for disconnected three and higher point correlation functions as well. The frequency-splitting estimators and their split-even components are directly applicable to the newly proposed multi-level integration in the presence of fermions., Published by Springer, Heidelberg

7th Workshop on Theory, Phenomenology and Experiments in Flavour Physics : The Future of BSM Physics., FPCapri 2018, Anacapri, Capri, Italy, 8 Jun 2018 - 10 Jun 2018; Nuclear and particle physics proceedings 303-305, 14 - 19 (2018). doi:10.1016/j.nuclphysbps.2019.03.004, The observed deviations from the Standard Model in several $b \to s\mu\mu$ processes can be explained in terms of a new vector boson produced on-shell in B meson decays. A mass of 2.5-3 GeV and a total width of 10-20% allow to hide the associated dimuon bump in the poorly known charmonium region, and the large invisible decay width can be interpreted in terms of Dark Matter. This proposal predicts a contribution to the muon anomalous magnetic moment, that could explain the long-standing tension with the Standard Model. It also predicts sizeable invisible $B$ decays and a peculiar $q^2$-dependence of the lepton flavor universality ratios $R_K$ and $R_{K^{*}}$ , that could be tested at the LHCb and Belle-II. This proceeding is based on arXiv:1704.06188, and slightly extends it with comments about Dark Matter., Published by Elsevier, Amsterdam [u.a.]

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints., 22 pages, 10 figures. One added figure (Fig. 10) and improvements in Figs. 7,8 and 9. This version matches the published one

International audience; The BABAR Collaboration pursues an intensive program studying hadronic cross sections in low-energy electron-positron annihilations, accessible via initial-state radiation. Our measurements allow significant improvements in the precision of the predicted value of the muon anomalous magnetic moment. These improvements are necessary for shedding light on the current 3 σ difference between the predicted and the experimental values. We have published results on a number of processes with from two to six hadrons in the final state and other final states are currently under investigation. We report here on the most recent results obtained by analysing the entire BABAR dataset. We present in particular the measurement of the mode with two charged pions and two neutral pions and the measurement of the full set of final states with two kaons and one or two pions.

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 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 $(694.0 \pm 4.0)\cdot10^{-10}$. The full Standard Model prediction differs by $3.3\sigma$ from the experimental value. The five-quark hadronic contribution to $\alpha(m_Z^2)$ is evaluated to be $(276.0\pm1.0)\cdot10^{-4}$., Comment: 13 pages, 9 figures and 2 tables, published version in EPJ-C. arXiv admin note: substantial text overlap with arXiv:1706.09436

The anomalous magnetic moment of the muon is one of the most precisely measured quantities in physics. Its experimental value exhibits a $4.2 \, \sigma$ discrepancy $\delta a_\mu=(251 \pm 59) \times 10^{-11}$ with its theoretical value calculated in the standard model framework, while they agree for the electron. The muon theoretical calculation involves a mass-dependent contribution which comes from two-loop vacuum polarization insertions due to electron-positron pairs and depends on the electron to muon mass ratio $x=m_e/m_\mu$. In standard quantum mechanics, mass ratios and inverse Compton length ratios are identical. This is no longer the case in the special scale-relativity framework, in which the Planck length-scale is invariant under dilations. Using the renormalization group approach, we differentiate between the origin of $ \ln x$ logarithmic contributions which depend on mass, and $x$ linear contributions which we assume to actually depend on inverse Compton lengths. By defining the muon constant $\mathbb{C}_\mu=\ln(m_\mathbb{P}/m_\mu)$ in terms of the Planck mass $m_\mathbb{P}$, the resulting scale-relativistic correction writes $\delta a_\mu= -\alpha^2 \, (x \:\ln^3 x)/(8 \; \mathbb{C}_\mu^2)$, where $\alpha$ is the fine structure constant. Its numerical value, $(230 \pm 16) \times 10^{-11}$, is in excellent agreement with the observed theory-experiment difference., Comment: 8 pages, 1 figure, Improved and updated version, account of new experimental results

This paper introduces a new approach to measure the muon magnetic moment anomaly $a_{\mu} = (g-2)/2$, and the muon electric dipole moment (EDM) $d_{\mu}$ at the J-PARC muon facility. The goal of our experiment is to measure $a_{\mu}$ and $d_{\mu}$ using an independent method with a factor of 10 lower muon momentum, and a factor of 20 smaller diameter storage-ring solenoid compared with previous and ongoing muon $g-2$ experiments with unprecedented quality of the storage magnetic field. Additional significant differences from the present experimental method include a factor of 1,000 smaller transverse emittance of the muon beam (reaccelerated thermal muon beam), its efficient vertical injection into the solenoid, and tracking each decay positron from muon decay to obtain its momentum vector. The precision goal for $a_{\mu}$ is statistical uncertainty of 450 part per billion (ppb), similar to the present experimental uncertainty, and a systematic uncertainty less than 70 ppb. The goal for EDM is a sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$., Comment: 24 pages, 14 figures