Search

We discuss constraints on soft CP-violating couplings of axion-like particles with photon and fermions by using data on electric dipole moments of standard model particles. In particular, for the axion-like particle (ALP) leptophilic scenario, we derive bounds on CP-odd ALP-photon-photon coupling from data of the ACME collaboration on electron EDM. We also discuss prospects of the storage ring experiment to constrain the ALP&ndash, photon&ndash, photon coupling from data on proton EDM for the simplified hadrophilic interactions of ALP. The resulting constraints from experimental bounds on the muon and neutron EDMs are weak. We set constraint on the CP-odd ALP coupling with electron and derive bounds on combinations of coupling constants, which involve soft CP-violating terms.

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

We propose an extension of the Standard Model (SM) with a $U_{A'}(1)$ gauge invariant dark dector connected to the SM via a new portal -- the Stueckelberg portal, arising in the framework of dark photon $A'$ mass generation via Stueckelberg mechanism. This portal opens through the effective dim=5 operators constructed from the covariant term of the auxiliary Stueckelberg scalar field $\sigma$ providing flavor non-diagonal renormalizable couplings of both $\sigma$ and $A'$ to the SM fermions $\psi$. The Stueckelberg scalar plays a role of Goldstone boson in the generation of mass of the Dark Photon. Contrary to the conventional kinetic mixing portal, in our scenario flavor diagonal $A'$-$\psi$ couplings are not proportional to the fermion charges and are, in general, flavor nondiagonal. These features drastically change the phenomenology of dark photon $A'$ relaxing or avoiding some previously established experimental constraints. We focus on the phenomenology of the described scenario of the Stueckelberg portal in the lepton sector and analyze the contribution of the dark sector fields $A'$ to the anomalous magnetic moment of muon $(g-2)_{\mu}$, lepton flavor violating decays $l_{i}\to l_{k}\gamma$ and $\mu-e$ conversion in nuclei. We obtain limits on the model parameters from the existing data on the corresponding observables., Comment: 15 pages, 8 figures (journal version)

We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple presentation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order $\epsilon$-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators., Comment: 134 pages, 8 figures

We discuss new physics phenomenology of hidden scalar ($S$), pseudoscalar ($P$), vector ($V$) and axial-vector ($A$) particles coupled to nucleons and leptons, which could give contributions to proton charge radius, $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, $^{8}\mathrm{Be}\text{\ensuremath{-}}^{4}\mathrm{He}$ anomaly and electric dipole moment (EDM) of Standard Model (SM) particles. In particular, we estimate sensitivity of $\mathrm{NA}64\ensuremath{\mu}$ experiment to observe muon missing energy events involving hidden scalar and vector particles. That analysis is based on geant4 Monte Carlo simulation of the signal process of muon scattering off target nuclei $\ensuremath{\mu}N\ensuremath{\rightarrow}\ensuremath{\mu}NS(V)$ followed by invisible boson decay into dark matter (DM) particles, $S(V)\ensuremath{\rightarrow}\ensuremath{\chi}\ensuremath{\chi}$. The existence of light sub-GeV bosons could possibly explain the muon ($g\ensuremath{-}2$) anomaly observed. We also summarize existing bounds on ATOMKI $X17({J}^{P}={0}^{\ensuremath{-}},{1}^{\ifmmode\pm\else\textpm\fi{}})$ boson coupling with neutron, proton, and electron. We implement these constraints to estimate the contribution of $P$, $V$. and $A$ particles to proton charge radius via direct 1-loop calculation of Sachs form factors. The analysis reveals the corresponding contribution is negligible. We also calculate bounds on dark axion portal couplings of dimension-five operators, which contribute to the EDMs of leptons and neutron.

We analyze contributions to the electric dipole moment (EDM) and Schiff moment of deuteron induced by the CP-violating three-pseudoscalar meson couplings using phenomenological Lagrangian approach involving nucleons and pseudoscalar mesons P=π,K,η,η′. Deuteron is considered as a proton-neutron bound state and its properties are defined by one- and two-body forces. One-body forces correspond to a picture there; proton and neutron are quasifree constituents of deuteron and their contribution to the deuteron EDM (dEDM) is simply the sum of proton and neutron EDMs. Two-body forces in deuteron are induced by one-meson exchange between nucleons. They produce a contribution to the dEDM, which is estimated using corresponding potential approach. From numerical analysis of nucleon and deuteron EDMs, we derive stringent limits on CP-violating hadronic couplings and θ¯ parameter. We showed that proposed measurements of proton and deuteron EDMs at level of ∼10−29 by the Store Ring EDM and JEDI Collaborations will provide more stringent upper limits on the CP-violating parameters.

Results of calculation of the light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons and the dynamical quark loop to the muon anomalous magnetic moment are discussed in the framework of the nonlocal SU(3) × SU(3) chiral quark model. The model is based on four-quark interaction of the Nambu–Jona–Lasinio type and Kobayashi–Maskawa–‘t Hooft six-quark interaction. The full kinematic dependence of vertices with off-shell mesons and photons in intermediate states in the light-by-light scattering amplitude is taken into account. All calculations are elaborated in explicitly gauge-invariant manner. These results complete calculations of all hadronic light-by-light scattering contributions to aμ in the leading order in the 1/Nc expansion. The final result does not allow the discrepancy between the experiment and the Standard Model to be explained.

We complete our derivation of upper limits on the $CP$ violating $\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}$ couplings from an analysis of their two-loop contributions to the neutron electric dipole moment (nEDM). We use a phenomenological Lagrangian approach which is formulated in terms of hadronic degrees of freedom---nucleons and pseudoscalar mesons. The essential part of the Lagrangian contains the $CP$ violating couplings between $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})$ and pions. Previously, we included photons using minimal substitution in case of the proton and charged pions. Now we extend our Lagrangian by adding the nonminimal couplings, i.e., anomalous magnetic couplings of nucleons with the photon. The obtained numerical upper limits for the $\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}$ couplings $|{f}_{\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}}({M}_{\ensuremath{\eta}}^{2})|l4.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $|{f}_{{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}\ensuremath{\pi}}({M}_{{\ensuremath{\eta}}^{\ensuremath{'}}}^{2})|l3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ can be useful for the related, planned experiments at the JLab Eta Factory. Using present experimental limits on the nEDM, we derive upper limits on the $CP$ violating $\overline{\ensuremath{\theta}}$ parameter of $\overline{\ensuremath{\theta}}l4.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$.

We provide model-independent bounds on the rates of rare decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings, the nEDM arises at the two-loop level. The leading-order relativistic chiral perturbation theory calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counterterm-free result. This is an improvement upon previous estimates which used approximations in evaluating the two-loop contribution and were plagued by divergences. While constraints on the $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\ensuremath{\theta}$ term, our calculation means that whatever the origin of these couplings, the decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}2\ensuremath{\pi}$ will remain unobservable in the near future.

Chiral anomaly of gamma transition into three pions are studied in a framework of nonlocal chiral quark model. In the local limit the result is in agreement with chiral perturbative theory and reproducesWess-Zumino-Witten anomaly. Transition form factor of gamma into three pions in nonlocal quark model has a correction which vanishes in local limit.

We complete our derivation of upper limits on the CP violating ηππ and η‘ππ couplings from an analysis of their two-loop contribution to the neutron electric dipole moment (nEDM). As a result we obtain numerical upper limits for the ηππ and η‘ππ branchings and couplings which are important for planned experiments at JLab. We also derive upper limits on the CP violating θ̅parameter of QCD θ̅< 2.8 × 10−10

In the first part of the review we discuss the effective nonlocal approach in the quantum field theory. It concerns primary the historical retrospective of this approach, and than we concentrate on the interaction of matter particles (fermions and bosons) with the (abelian and nonabelian) gauge fields. In the second part of the review we consider the hadronic corrections (vacuum polarization) to the anomalous magnetic moment of the muon g - 2 factor discussed within the SUf(2) nonlocal chiral quark model. This is considered in the leading and, partially, in the next-to-leading orders (the effect of the fermion propagator dressing due to pion field) of expansion in small parameter 1/N c (N c is the number of colors in QCD).

We study the lepton flavor violating (LFV) $e(\ensuremath{\mu})\ensuremath{-}\ensuremath{\tau}$ conversion in deep inelastic scattering (DIS) of electrons (muons) on fixed-target nuclei. Our model-independent analysis is based on the set of low-energy effective four-fermion LFV operators composed of leptons and quarks with the corresponding mass scales ${\mathrm{\ensuremath{\Lambda}}}_{k}$ for each operator. Using the estimated sensitivity of the search for this LFV process in events with large missing energy in the NA64 experiment at the CERN SPS, we derive lower limits for ${\mathrm{\ensuremath{\Lambda}}}_{k}$ and compared them with the corresponding limits existing in the literature. We show that the DIS $e(\ensuremath{\mu})\ensuremath{-}\ensuremath{\tau}$ conversion is able to provide a plenty of new limits as yet nonexisting in the literature. We also analyzed the energy spectrum of the final-state $\ensuremath{\tau}$ and discussed the viability of the observation of this process in the NA64 experiment and ones akin to it. The case of polarized beams and targets is also discussed.

The transition form factor of a gamma into three pions ${F}_{3\ensuremath{\pi}}$ is studied in a framework of nonlocal chiral quark model. In the local limit the result is in agreement with chiral perturbative theory and reproduce Wess-Zumino-Witten anomaly. Nonlocality does not change the value of transition form factor in chiral limit. On the physical threshold of reaction the form factor ${F}_{3\ensuremath{\pi}}$ obtained is in a good agreement with experimental data if the current quark mass is taken into account in the model.

Using the present upper bound on the neutron electric dipole moment, we give an estimate for the upper limit of the $CP$-violating couplings of the $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})$ to the nucleon. Using this result, we then derive constraints on the $CP$-violating $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings, which define the two-pion $CP$-violating decays of the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons. Our results are relevant for the running and planned measurements of rare decays of the $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons by the GlueX Collaboration at JLab and the LHCb Collaboration at CERN.

The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model. The preliminary answer for contributions from a1 and f1 mesons to (g-2)_mu is 0.34 x 10^(-11) and does not support the Melnikov-Vainshtein estimate 2.2 x 10^(-11)., Comment: 5 pages, talk at e+e- Collisions From Phi to Psi 2019

Soon, new experiments at FNAL and J-PARC will measure the muon anomalous magnetic moments with better accuracy than before. From theoretical side, the uncertainty of the standard model prediction is dominated by the hadronic contributions. Current status of the experimental data and theoretical calculations are briefly discussed., 9 pages. Contribution to QUARKS-2016, 19th International Seminar on High Energy Physics, Pushkin, Russia, 29 May - 4 June, 2016

The current status of the muon g-2 problem is briefly discussed. We briefly discuss the latest results on the muon g-2 measured in experiment and obtained theoretically within the standard model. Special attention is for the hadronic corrections and in particular the corrections due to the light by light scattering mechanism. For latter we present the results found in the leading in 1=N c approximation with the nonlocal chiral quark model.

The correction to anomalous magnetic momentum muon from the light by light scattering diagram with intermediate pion is calculated in framework nonlocal chiral quark model. To fix the model parameters it is suggested to use the values of mass and two photon width of the neutral pion. The value of the correction is in region \(a_\mu ^{\pi ^0 , LbL} = (5.05 \pm 0.03) \times 10^{ - 10}\) for different set of model parameters.

The muon contribution to the anomalous magnetic moment from light-by-light scattering diagrams with pion participation is calculated for a nonlocal chiral quark model. For various nonlocal model parameterizations, the contribution makes a μ Had,LbL = 5.1(0.2) 10−10. Later on, we plan to calculate contributions from diagrams with an intermediate scalar meson and quark boxing.

The data for the upper limit on the electric dipole moment of the neutron (nEDM) can be explained by using different mechanisms beyond the Standard Model (SM). The nEDM can be generated by a CP-violating transition of η and η′ mesons into pion pairs. We derive the upper limits for the rates of the CP-violating decays η(η′) → 2π are by orders of magnitude more stringent than those from existing experiments so far.

The hadronic corrections to the muon anomalous magnetic moment a_mu, due to the gauge-invariant set of diagrams with dynamical quark loop light-by-light scattering insertions, are calculated in the framework of the nonlocal chiral quark model. These results complete calculations of all hadronic light-by-light scattering contributions to a_mu in the leading order in the 1/Nc expansion. The result for the quark loop contribution is a_mu^{HLbL,Loop}=(11.0+-0.9)*10^(-10), and the total result is a_mu^{HLbL,NxQM}=(16.8+-1.2)*10^(-10)., 11 pages, 5 figures, 1 table

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM., Comment: 10 pages, 5 figures

The light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons to the anomalous magnetic moment of muon is calculated in the framework of the nonlocal SU(3)x SU(3) quark model. The model is based on chirally symmetric four-quark interaction of the Nambu-Jona-Lasinio type and Kobayashi-Maskawa-t`Hooft U_A(1) breaking six-quark interaction. Full kinematic dependence of vertices with off-shell mesons and photons in intermediate states in the light-by-light scattering amplitude is taken into account. The small positive contributions from the scalar mesons stabilize the total result with respect to change of model parameters and reduces to a_\mu^{LbL,PS+S}=(6.25\pm 0.83)x10^{-10}., Comment: 11 pages, 6 figures

The light-by-light contribution to the anomalous magnetic moment of muon (g-2)_{\mu} from the hadronic exchanges in the neutral pseudoscalar meson channel is calculated in the nonlocal chiral quark model. The full kinematic dependence of the meson-two-photon vertices on the virtualities of the mesons and photons is taken into account. The status of various phenomenological and QCD short-distance constraints is discussed and the comparison with the predictions of other models is performed. It is demonstrated that the effect of the full kinematic dependence in the meson-photon vertices is to reduce the contribution of pseudoscalar exchages to a_\mu ^{PS,LbL} by approximately factor 1.5 in comparison with the most of previous estimates., Comment: 11 pages, 7 figures; version for journal, minor corrections are made

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM.

The light-by-light contribution to the anomalous magnetic moment of muon is estimated in the framework of nonlocal quark model. The partial contribution from contact diagrams and mesonic exchanges is discussed.