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We present an update of our study of high temperature QCD with three flavors of quarks, using a Symanzik improved gauge action and the Asqtad staggered quark action. Simulations are being carried out on lattices with Nt=4, 6 and 8 for the case of three degenerate quarks with masses less than or equal to the strange quark mass, $m_s$, and on lattices with Nt=6 and 8 for degenerate up and down quarks with masses in the range 0.2 m_s \leq m_{u,d} \leq 0.6 m_s, and the strange quark fixed near its physical value. We also report on first computations of quark number susceptibilities with the Asqtad action. These susceptibilities are of interest because they can be related to event-by-event fluctuations in heavy ion collision experiments. Use of the improved quark action leads to a substantial reduction in lattice artifacts. This can be seen already for free fermions and carries over into our results for QCD., Comment: Lattice2002(Non-zero temperature and density)

We describe the current status of the MILC collaboration computation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios. Progress over the past year includes: better statistics and plateaus at $\beta=6.52$ (quenched), $\beta=5.6$ ($N_F=2$) and $\beta=5.445$ ($N_F=2$), new runs with a wide range of dynamical quark masses at $\beta=5.5$ ($N_F=2$), an estimate of the systematic errors due to the chiral extrapolation, and an improved analysis which consistently takes into account both the correlations in the data at every stage and the systematic effects due to changing fitting ranges., Comment: Poster presented by C. Bernard at LATTICE96(heavy quarks); 4 pages of LaTeX, uses espcrc2 and epsf, four postscript figures included

During the past year the MILC Collaboration has continued its study of heavy-light meson decay constants with three dynamical quarks. Calculations have been extended to a second lattice spacing of about 0.09 fm. At this lattice spacing, there are results in the quenched approximation and for three sets of dynamical quark mass: m_l=m_s; m_l=0.4 m_s and m_l=0.2 m_s, where m_l is the light mass for the u and d quarks and m_s is the strange quark mass. At the coarser lattice spacing, for which results were presented at Lattice 2001, statistics have been increased for two sets of quark masses and three additional sets of quark masses have been studied, giving a total of eight combinations used to interpolate between the quenched and chiral limits. When these calculations are completed, we can study the decay constants taking into account both chiral and continuum extrapolations., Comment: Lattice2002(heavyquark), 3 pages, 3 color figures, to appear in the proceedings of Lattice 2002

We made an extensive study of the light hadron spectrum using the Wilson gauge action and Kogut-Susskind quarks. Using both dynamical quarks and the quenched approximation, we determine hadron masses for five and four gauge couplings respectively, with at least five quark masses at each coupling. In the continuum limit, we find a significant difference between two flavors of dynamical quarks and the quenched approximation for a range of quark masses., Comment: 3 pages, 3 figures, LaTeX, uses espcrc2.sty. LATTICE98(spectrum)

We report on the results of a MILC collaboration calculation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios. We discuss the most important errors in more detail than we have elsewhere., Comment: LATTICE98(heavyqk) 3 latex pages and 3 postscript figures. The perturbative correction calculated by Kuramashi has been adjusted to take into account the fact that we match to the continuum at the kinetic mass of the heavy meson, not the pole mass. This produces a 2 to 4 MeV change in final results for decay constants, and has negligible effect on decay constant ratios

We present an update on the MILC Collaboration's light hadron spectrum calculation with two flavors of dynamical, staggered quarks. We present extrapolations of the nucleon to rho mass ratio to the continuum limit for fixed values of the pi to rho mass ratio including the physical one., 3 pages, LaTex with espcrc2 and epsf, 5 postscript figures included, Lattice '97 Proceedings

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