We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision.

The SPASCHARM experiment is aimed at a systematic study of the nucleon spin structure and the spin dependence of the strong interaction of antimatter and matter with matter at energies up to 45 GeV. As part of the first stage of the experiment, the study of the spin properties of hadrons will take place in a beam of negatively charged hadrons on existing beamline 14 at the operating SPASCHARM setup at the U70 facility. At the second stage, the production of polarized beams of protons and antiprotons is envisaged in beamline 24A of the U-70 accelerator facility. A polarized antiproton beam will certainly become a unique beam in the world. It is planned to measure single-spin asymmetries in dozens of reactions, both on hydrogen and on various nuclei. At the SPASCHARM facility, it is also possible to measure the transverse polarization of hyperons and elements of the spin density matrix of vector mesons. The spin structure of the nucleon will be investigated in the study of quarkonium production to determine the contribution of gluons to the proton spin. The presence of two types of polarized beams and eight types of nonpolarized beams (π ± , K ± , p , p̅ , d , C ), in combination with a polarized target, expands the range of studies of polarization phenomena and enhances the uniqueness of the project.

The yield of gamma-quanta from nuclear fusion reactions proceeding from various spin states of muonic molecules ptμ and pdμ has been measured. The work was performed on the “Triton” facility at DLNP JINR using a specially designed liquid-tritium target. For the first time, channels of the fusion reaction with the yield of double γ-quanta were observed: ptμ → 4Heμ + γ + γ, pdμ → 3Heμ + γ + γ. The data obtained for the yield of single γ-quanta in the channel of the fusion reaction ptμ → 4Heμ + γ is consistent with earlier research. The partial coefficient of sticking of a muon to a helium nucleus was determined experimentally in a channel of pt- and pd-fusion reactions with the yield of single γ-quantum.

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

With few open channels and uncomplicated theoretical description, charged pion decays are uniquely sensitive to certain standard model (SM) symmetries, the universality of weak fermion couplings, and to aspects of pion structure and chiral dynamics. We review the current knowledge of the pion electronic decay π^+ → e^+ ν_e(γ), or π_e2(γ), and the resulting limits on non-SM processes. Focusing on the PEN experiment at the Paul Scherrer Institute (PSI), Switzerland, we examine the prospects for further improvement in the near term.

Allowed charged $\pi$ meson decays are characterized by simple dynamics, few available decay channels, mainly into leptons, and extremely well controlled radiative and loop corrections. In that sense, pion decays represent a veritable triumph of the standard model (SM) of elementary particles and interactions. This relative theoretical simplicity makes charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for studying pion structure and chiral dynamics. Even after considerable recent improvements, experimental precision is lagging far behind that of the theoretical description for pion decays. We review the current state of experimental study of the pion electronic decay $\pi^+ \to e^+\nu_e(\gamma)$, or $\pi_{e2(\gamma)}$, where the $(\gamma)$ indicates inclusion and explicit treatment of radiative decay events. We briefly review the limits on non-SM processes arising from the present level of experimental precision in $\pi_{e2(\gamma)}$ decays. Focusing on the PEN experiment at the Paul Scherrer Institute (PSI), Switzerland, we examine the prospects for further improvement in the near term.

The anomalous magnetic moment of the muon is one of the most precisely measured quantities in experimental particle physics. Its latest measurement at Brookhaven National Laboratory deviates from the Standard Model expectation by approximately 3.5 standard deviations. The goal of the new experiment, E989, now under construction at Fermilab, is a fourfold improvement in precision. Here, we discuss the details of the future measurement and its current status.

The Muon (g-2) Experiment, E989 at Fermilab, will measure the muon anomalous magnetic moment a factor-of-four more precisely than was done in E821 at the Brookhaven National Laboratory AGS. The E821 result appears to be greater than the Standard-Model prediction by more than three standard deviations. When combined with expected improvement in the Standard-Model hadronic contributions, E989 should be able to determine definitively whether or not the E821 result is evidence for physics beyond the Standard Model. After a review of the physics motivation and the basic technique, which will use the muon storage ring built at BNL and now relocated to Fermilab, the design of the new experiment is presented. This document was created in partial fulfillment of the requirements necessary to obtain DOE CD-2/3 approval.

Simple dynamics, few available decay channels, and highly controlled radiative and loop corrections, make pion and muon decays a sensitive means of exploring details of the underlying symmetries. We review the current status of the rare decays: π + → e + ν (π e2 ), π + → e + νγ (π e2γ ), π + → π 0 e + ν (π e3 ), and [Formula: see text]. For the latter we report new preliminary values for the branching ratio B(E γ > 10 MeV , θ eγ > 30°) = 4.365 (9) stat (42) syst × 10 -3 , and the decay parameter [Formula: see text], both in excellent agreement with standard model predictions. We review recent measurements, particularly by the PIBETA and PEN experiments, and near-term prospects for improvement. These and other similar precise low energy studies complement modern collider results materially.

Building on the rare pion and muon decay results of the PIBETA experiment, the PEN collaboration has undertaken a precise measurement of B_{\pi e2} = R^\pi_{e/\mu}, the \pi^+ -> e^+\nu(\gamma) decay branching ratio, at the Paul Scherrer Institute, to reduce the present 40\times experimental precision lag behind theory to ~ 6-7\times. Because of large helicity suppression, R^\pi_{e/\mu} is uniquely sensitive to contributions from non-(V-A) physics, making this decay a particularly suitable subject of study. Even at current precision, the experimental value of B_{\pi e2} provides the most accurate test of lepton universality available. During runs in 2008-10, PEN has accumulated over 2\times 10^7 \pi_{e2} events; a comprehensive maximum-likelihood analysis is currently under way. The new data will also lead to improved precision of the earlier PIBETA results on radiative \pi and \mu decays.

A search for the muon-catalyzed fusion reaction d + d -> He-4 + gamma in the dd mu muonic molecule was performed using the experimental installation TRITON with BGO detectors for gamma-quanta. A high-pressure target filled with deuterium was exposed to the negative muon beam of the JINR Phasotron to detect gamma-quanta with the energy 23.8 MeV. An experimental estimation for the yield of radiative deuteron capture from the dd mu state J = 1 was obtained at the level of eta(gamma) <= 8 x 10(-7) per fusion.

A search for the muon-catalyzed fusion reaction d + d → 4He + γ in the ddμ muonic molecule was performed using the experimental installation TRITON with BGO detectors for γ-quanta. A high-pressure target filled with deuterium was exposed to the negative muon beam of the JINR Phasotron to detect γ-quanta with the energy 23.8 MeV. An experimental estimation for the yield of radiative deuteron capture from the ddμ state J = 1 was obtained at the level of η γ ≤ 8 × 10−7 per fusion.

We have measured the pi+-->e+ nugamma branching ratio over a wide region of phase space, based on a total of 65 460 events acquired using the PIBETA detector. Minimum-chi2 fits to the measured (E(e+), E(gamma) energy distributions result in the weak form factor value of F(A)=0.0119(1) with a fixed value of F(V)=0.0259. An unconstrained fit yields F(V)=0.0258(17) and F(A)=0.0117(17). In addition, we have measured a=0.10(6) for the dependence of F(V) on q2, the e+ nu pair invariant mass squared, parametrized as F(V)(q2)=F(V)(0)(1+aq(2)). The branching ratio for the kinematic region E(gamma)>10 MeV and theta(e(+)gamma)>40 degrees is measured to be B(expt)=73.86(54)x10(-8). Earlier deviations we reported in the high-E(gamma)-low-E(e+) kinematic region are resolved without a tensor term. We also derive new values for the pion polarizability alpha(E)=2.78(10)x10(-4) fm3 and neutral pion lifetime tau(pi0)=(8.5+/-1.1)x10(-17) s.

The PEN Collaboration is conducting a new measurement of the π+ → e + vL branching ratio at the Paul Scherrer Institute, with the goal uncertainty of δB/B πe2 = 5 × 10−4 or lower. At present, the combined accuracy of all published πe2 decay measurements lags behind the theoretical calculation by a factor of 40. In this contribution we report on the PEN detector configuration and its performance during two development runs done in 2007 and 2008.

A new measurement of Be 2, the + ! e + ( ) decay branching ratio, is currently under way at the Paul Scherrer Institute. The present experimental result on Be 2 constitutes the most accurate test of lepton universality available. The accuracy, however, still lags behind the theoretical precision by over an order of magnitude. Thanks to the large helicity suppression of e2 decay, the branching ratio is susceptible to significant contributions from new physics, making this decay a particularly suitable subject of study.

A new measurement of Bπe2, the π+→e+ν(γ) decay branching ratio, is currently under way at the Paul Scherrer Institute. The present experimental result on Bπe2 constitutes the most accurate test of lepton universality available. The accuracy, however, still lags behind the theoretical precision by over an order of magnitude. Because of the large helicity suppression of the πe2 decay, its branching ratio is susceptible to significant contributions from new physics, making this decay a particularly suitable subject of study.

We review recent measurements of the rare decays: π + → π 0 e + ν (pion beta decay), π + → e + νγ (radiative pion decay), µ + → e + ν ¯ νγ (radiative muon decay), and their theoretical implications. The PIBETA experiment, with measurements recently completed at PSI, has brought about an order of magnitude improvement, or better, in the branching ratio precision for these processes. The successor PEN experiment, currently under way at PSI, aims to improve the precision of the π + → e + ν (π e2) decay branching ratio by about an order of magnitude. Each of these results contributes toward a better understanding of the limits on certain particles and interactions not included in the standard model, or toward improving the precision of chiral lagrangian and pion structure parameters. We finally review the near-term prospects for their further improvement. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

We have measured the (cid:1) þ ! e þ (cid:2)(cid:3) branching ratio over a wide region of phase space, based on a total of 65 460 events acquired using the PIBETA detector. Minimum- (cid:4) 2 fits to the measured ( E e þ , E (cid:3) ) energy distributions result in the weak form factor value of F A ¼ 0 : 0119 ð 1 Þ with a fixed value of F V ¼ 0 : 0259 . An unconstrained fit yields F V ¼ 0 : 0258 ð 17 Þ and F A ¼ 0 : 0117 ð 17 Þ . In addition, we have measured a ¼ 0 : 10 ð 6 Þ for the dependence of F V on q 2 , the e þ (cid:2) pair invariant mass squared, parametrized as F V ð q 2 Þ ¼ F V ð 0 Þð 1 þ aq 2 Þ . The branching ratio for the kinematic region E (cid:3) > 10 MeV and (cid:5) e þ (cid:3) > 40 (cid:1) is measured to be B expt ¼ 73 : 86 ð 54 Þ (cid:2) 10 (cid:3) 8 . Earlier deviations we reported in the high- E (cid:3) –low- E e þ kinematic region are resolved without a tensor term. We also derive new values for the pion polarizability (cid:6) E ¼ 2 : 78 ð 10 Þ (cid:2) 10 (cid:3) 4 fm 3 and neutral pion lifetime (cid:7) (cid:1) 0 ¼ ð 8 : 5 (cid:4) 1 : 1 Þ (cid:2) 10 (cid:3) 17 s .

M. Bychkov, ∗ D. Počanić, † B. A. VanDevender, ‡ V. A. Baranov, W. Bertl, Yu. M. Bystritsky, E. Frlež, V. A. Kalinnikov, N. V. Khomutov, A. S. Korenchenko, S. M. Korenchenko, M. Korolija, T. Kozlowski, N. P. Kravchuk, N. A. Kuchinsky, W. Li, § D. Mekterović, D. Mzhavia, 6 S. Ritt, P. Robmann, O. A. Rondon-Aramayo, A. M. Rozhdestvensky, T. Sakhelashvili, S. Scheu, U. Straumann, I. Supek, Z. Tsamalaidze, 6 A. van der Schaaf, E. P. Velicheva, V. P. Volnykh, Y. Wang, ¶ and H.-P. Wirtz ∗∗ Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA Joint Institute for Nuclear Research, RU-141980 Dubna, Russia Paul Scherrer Institute, Villigen PSI, CH-5232, Switzerland Rudjer Bošković Institute, HR-10000 Zagreb, Croatia Institute for Nuclear Studies, PL-05-400 Swierk, Poland Institute for High Energy Physics, Tbilisi State University, GUS-380086 Tbilisi, Georgia Physik Institut der Universität Zürich, CH-8057 Zürich, Switzerland (Dated: 9 Apr 2008)