Measurement of the negative muon anomalous magnetic moment to 0.7 ppm

Improved Measurements of Muonic Helium Ground-State Hyperfine Structure at a Near-Zero Magnetic Field

Muonic helium atom hyperfine structure (HFS) measurements are a sensitive tool to test the three-body atomic system and bound-state quantum electrodynamics theory, and determine fundamental constants of the negative muon magnetic moment and mass. The world's most intense pulsed negative muon beam at the Muon Science Facility of the Japan Proton Accelerator Research Complex allows improvement of previous measurements and testing further CPT invariance by comparing the magnetic moments and masses of positive and negative muons (second-generation leptons). We report new ground-state HFS measurements of muonic helium-4 atoms at a near-zero magnetic field, performed for the first time using a small admixture of CH_{4} as an electron donor to form neutral muonic helium atoms efficiently. Our analysis gives Δν=4464.980(20)  MHz (4.5 ppm), which is more precise than both previous measurements at weak and high fields. The muonium ground-state HFS was also measured under the same conditions to investigate the isotopic effect on the frequency shift due to the gas density dependence in He with CH_{4} admixture and compared with previous studies. Muonium and muonic helium can be regarded as light and heavy hydrogen isotopes with an isotopic mass ratio of 36. No isotopic effect was observed within the current experimental precision.

Two-Loop Four-Fermion Scattering Amplitude in QED

We present the first fully analytic evaluation of the transition amplitude for the scattering of a massless into a massive pair of fermions at the two-loop level in quantum electrodynamics. Our result is an essential ingredient for the determination of the electromagnetic coupling within scattering reactions, beyond the currently known accuracy, which has a crucial impact on the evaluation of the anomalous magnetic moment of the muon. It will allow, in particular, for a precise determination of the leading hadronic contribution to the (g-2)_{μ} in the MUonE experiment at CERN, and therefore can be used to shed light on the current discrepancy between the standard model prediction and the experimental measurement for this important physical observable.

Probing the explanation of the muon (g-2) anomaly and thermal light dark matter with the semi-visible dark photon channel

We report the results of a search for a new vector boson ( A ' ) decaying into two dark matter particles χ 1 χ 2 of different mass. The heavier χ 2 particle subsequently decays to χ 1 and an off-shell Dark Photon A ' ∗ → e + e - . For a sufficiently large mass splitting, this model can explain in terms of new physics the recently confirmed discrepancy observed in the muon anomalous magnetic moment at Fermilab. Remarkably, it also predicts the observed yield of thermal dark matter relic abundance. A detailed Monte-Carlo simulation was used to determine the signal yield and detection efficiency for this channel in the NA64 setup. The results were obtained re-analyzing the previous NA64 searches for an invisible decay A ' → χ χ ¯ and axion-like or pseudo-scalar particles a → γ γ . With this method, we exclude a significant portion of the parameter space justifying the muon g-2 anomaly and being compatible with the observed dark matter relic density for A ' masses from 2 m e up to 390 MeV and mixing parameter ε between 3 × 10 - 5 and 2 × 10 - 2 .

Absolute Magnetometry with ^{3}He

We report development of a highly accurate (parts per billion) absolute magnetometer based on ^{3}He NMR. Optical pumping polarizes the spins, long coherence times provide high sensitivity, and the ^{3}He electron shell effectively isolates the nuclear spin providing accuracy limited only by corrections including materials, sample shape, and magnetization. Our magnetometer was used to confirm calibration, to 32 ppb, of the magnetic-field sensors used in recent measurements of the muon magnetic moment anomaly (g_{μ}-2), which differs from the standard model by 2.4 ppm. With independent determination of the magnetic moment of ^{3}He, this work will lead the way to a new absolute magnetometry standard.

Finite-Volume Effects in (g-2)_{μ}^{HVP,LO}

An analytic expression is derived for the leading-order finite-volume effects arising in lattice QCD calculations of the hadronic-vacuum-polarization contribution to the muon's magnetic moment a_{μ}^{HVP,LO}≡(g-2)_{μ}^{HVP,LO}/2. For calculations in a finite spatial volume with periodicity L, a_{μ}^{HVP,LO}(L) admits a transseries expansion with exponentially suppressed L scaling. Using a Hamiltonian approach, we show that the leading finite-volume correction scales as exp[-M_{π}L] with a prefactor given by the (infinite-volume) Compton amplitude of the pion, integrated with the muon-mass-dependent kernel. To give a complete quantitative expression, we decompose the Compton amplitude into the spacelike pion form factor F_{π}(Q^{2}) and a multiparticle piece. We determine the latter through next-to leading order in chiral perturbation theory and find that it contributes negligibly and through a universal term that depends only on the pion decay constant, with all additional low-energy constants dropping out of the integral.

Variations on Photon Vacuum Polarization

I provide updates for the theoretical predictions of the muon and electron anomalous magnetic moments, for the shift in the fine structure constant α(MZ )and for the weak mixing parameter $ \mathop {\sin }\nolimits^2 \mathop \Theta \nolimits_w (\mathop M\nolimits_Z ) $. Phenomenological results for Euclidean time correlators, the key objects in the lattice QCD approach to hadronic vacuum polarization, are briefly considered. Furthermore,I present a list of isospin breaking and electromagnetic corrections for the lepton moments, which may be used to supplement lattice QCD results obtained in the isospin limit and without the e.m. corrections.

Lattice study of finite volume effect in HVP for muon g-2

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, [see formula in PDF],in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a−1 = 2.33 GeV. We compare two integrals of [see formula in PDF], momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of [see formula in PDF] with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in [see formula in PDF].

A storage ring experiment to detect a proton electric dipole moment

A new experiment is described to detect a permanent electric dipole moment of the proton with a sensitivity of 10^-29 e ⋅ cm by using polarized "magic" momentum 0.7 GeV/c protons in an all-electric storage ring. Systematic errors relevant to the experiment are discussed and techniques to address them are presented. The measurement is sensitive to new physics beyond the standard model at the scale of 3000 TeV.

Beyond the CMSSM without an accelerator: proton decay and direct dark matter detection

We consider two potential non-accelerator signatures of generalizations of the well-studied constrained minimal supersymmetric standard model (CMSSM). In one generalization, the universality constraints on soft supersymmetry-breaking parameters are applied at some input scale [Formula: see text]below the grand unification (GUT) scale [Formula: see text], a scenario referred to as 'sub-GUT'. The other generalization we consider is to retain GUT-scale universality for the squark and slepton masses, but to relax universality for the soft supersymmetry-breaking contributions to the masses of the Higgs doublets. As with other CMSSM-like models, the measured Higgs mass requires supersymmetric particle masses near or beyond the TeV scale. Because of these rather heavy sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5) model of grand unification can yield a proton lifetime consistent with current experimental limits, and may be accessible in existing and future proton decay experiments. Another possible signature of these CMSSM-like models is direct detection of supersymmetric dark matter. The direct dark matter scattering rate is typically below the reach of the LUX-ZEPLIN (LZ) experiment if [Formula: see text] is close to [Formula: see text], but it may lie within its reach if [Formula: see text] GeV. Likewise, generalizing the CMSSM to allow non-universal supersymmetry-breaking contributions to the Higgs offers extensive possibilities for models within reach of the LZ experiment that have long proton lifetimes.

Supersymmetric dark matter after LHC run 1

Different mechanisms operate in various regions of the MSSM parameter space to bring the relic density of the lightest neutralino, [Formula: see text], assumed here to be the lightest SUSY particle (LSP) and thus the dark matter (DM) particle, into the range allowed by astrophysics and cosmology. These mechanisms include coannihilation with some nearly degenerate next-to-lightest supersymmetric particle such as the lighter stau [Formula: see text], stop [Formula: see text] or chargino [Formula: see text], resonant annihilation via direct-channel heavy Higgs bosons H / A, the light Higgs boson h or the Z boson, and enhanced annihilation via a larger Higgsino component of the LSP in the focus-point region. These mechanisms typically select lower-dimensional subspaces in MSSM scenarios such as the CMSSM, NUHM1, NUHM2, and pMSSM10. We analyze how future LHC and direct DM searches can complement each other in the exploration of the different DM mechanisms within these scenarios. We find that the [Formula: see text] coannihilation regions of the CMSSM, NUHM1, NUHM2 can largely be explored at the LHC via searches for [Formula: see text] events and long-lived charged particles, whereas their H / A funnel, focus-point and [Formula: see text] coannihilation regions can largely be explored by the LZ and Darwin DM direct detection experiments. We find that the dominant DM mechanism in our pMSSM10 analysis is [Formula: see text] coannihilation: parts of its parameter space can be explored by the LHC, and a larger portion by future direct DM searches.

The pMSSM10 after LHC run 1

We present a frequentist analysis of the parameter space of the pMSSM10, in which the following ten soft SUSY-breaking parameters are specified independently at the mean scalar top mass scale [Formula: see text]: the gaugino masses [Formula: see text], the first-and second-generation squark masses [Formula: see text], the third-generation squark mass [Formula: see text], a common slepton mass [Formula: see text] and a common trilinear mixing parameter A, as well as the Higgs mixing parameter [Formula: see text], the pseudoscalar Higgs mass [Formula: see text] and [Formula: see text], the ratio of the two Higgs vacuum expectation values. We use the MultiNest sampling algorithm with [Formula: see text]1.2 [Formula: see text] points to sample the pMSSM10 parameter space. A dedicated study shows that the sensitivities to strongly interacting sparticle masses of ATLAS and CMS searches for jets, leptons [Formula: see text][Formula: see text] signals depend only weakly on many of the other pMSSM10 parameters. With the aid of the Atom and Scorpion codes, we also implement the LHC searches for electroweakly interacting sparticles and light stops, so as to confront the pMSSM10 parameter space with all relevant SUSY searches. In addition, our analysis includes Higgs mass and rate measurements using the HiggsSignals code, SUSY Higgs exclusion bounds, the measurements of [Formula: see text] by LHCb and CMS, other B-physics observables, electroweak precision observables, the cold dark matter density and the XENON100 and LUX searches for spin-independent dark matter scattering, assuming that the cold dark matter is mainly provided by the lightest neutralino [Formula: see text]. We show that the pMSSM10 is able to provide a supersymmetric interpretation of [Formula: see text], unlike the CMSSM, NUHM1 and NUHM2. As a result, we find (omitting Higgs rates) that the minimum [Formula: see text] with 18 degrees of freedom (d.o.f.) in the pMSSM10, corresponding to a [Formula: see text] probability of 30.8 %, to be compared with [Formula: see text] in the CMSSM (NUHM1) (NUHM2). We display the one-dimensional likelihood functions for sparticle masses, and we show that they may be significantly lighter in the pMSSM10 than in the other models, e.g., the gluino may be as light as [Formula: see text]1250 [Formula: see text] at the 68 % CL, and squarks, stops, electroweak gauginos and sleptons may be much lighter than in the CMSSM, NUHM1 and NUHM2. We discuss the discovery potential of future LHC runs, [Formula: see text] colliders and direct detection experiments.

Lepton flavor violation in flavored gauge mediation

We study the anatomy and phenomenology of lepton flavor violation (LFV) in the context of flavored gauge mediation (FGM). Within FGM, the messenger sector couples directly to the MSSM matter fields with couplings controlled by the same dynamics that explains the hierarchies in the SM Yukawas. Although the pattern of flavor violation depends on the particular underlying flavor model, FGM provides a built-in flavor suppression similar to wave function renormalization or SUSY partial compositeness. Moreover, in contrast to these models, there is an additional suppression of left-right flavor transitions by third-generation Yukawas that in particular provides an extra protection against flavor-blind phases. We exploit the consequences of this setup for lepton flavor phenomenology, assuming that the new couplings are controlled by simple [Formula: see text] flavor models that have been proposed to accommodate large neutrino mixing angles. Remarkably, it turns out that in the context of FGM these models can pass the impressive constraints from LFV processes and leptonic electric dipole moments (EDMs) even for light superpartners, therefore offering the possibility of resolving the longstanding muon [Formula: see text] anomaly.

Complete tenth-order QED contribution to the muon g-2

We report the result of our calculation of the complete tenth-order QED terms of the muon g-2. Our result is a(μ)((10))=753.29 (1.04) in units of (α/π)(5), which is about 4.5 s.d. larger than the leading-logarithmic estimate 663(20). We also improve the precision of the eighth-order QED term of a(μ), obtaining a(μ)((8))=130.8794 (63) in units of (α/π)(4). The new QED contribution is a(μ)(QED)=116,584,718,951 (80)×10(-14), which does not resolve the existing discrepancy between the standard-model prediction and measurement of a(μ).

Determining the dark matter relic density in the minimal supergravity stau-neutralino coannihilation region at the Large Hadron Collider

We examine the stau-neutralino coannihilation (CA) mechanism of the early Universe. We use the minimal supergravity (mSUGRA) model and show that from measurements at the CERN Large Hadron Collider one can predict the dark matter relic density with an uncertainty of 6% with 30 fb(-1) of data, which is comparable to the direct measurement by the Wilkinson Microwave Anisotropy Probe. This is done by measuring four mSUGRA parameters m(0), m(1/2), A(0), and tanbeta without requiring direct measurements of the top squark and bottom squark masses. We also provide precision measurements of the gaugino, squark, and lighter stau masses in this CA region without assuming gaugino universality.

Search for Lorentz and CPT violation effects in Muon spin precession

The spin precession frequency of muons stored in the (g-2) storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for a nonzero delta omega a(=omega a mu+ - omega a mu-) and a sidereal variation of omega a mu+/-). No significant effect is found, and the following limits on the standard-model extension parameters are obtained: bZ = -(1.0+/-1.1) x 10(-23) GeV; (m mu dZ0 + HXY)=(1.8+/-6.0) x 10(-23) GeV; and the 95% confidence level limits b perpendicular mu+ <1.4 x 10(-24) GeV and b perpendicular mu- <2.6 x 10(-24) GeV.

Muon (g- 2): experiment and theory

A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined bya= (g- 2)/2, where the Landég-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomalyadiffers slightly from zero (of the order 10^-3) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual 'loops' containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly fore, μ and τ. If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be ∼ (m_μ/m_e)²≈ 43 × 10³larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory, are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard-deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study.

Supersymmetry facing experiment: much ado (already) about nothing (yet)

This report emphasizes the comparison between supersymmetric models and experiments. A minimal theoretical introduction is included as a guide to the interpretation of results. The existing constraints from low energy measurements, accelerator searches (LEP, Tevatron and HERA) and non-accelerator searches for neutralinos are presented. Prospects for upgrades of these facilities and for the LHC and linear collider are summarized. Most discussions are made in the framework of the minimal supersymmetric standard model inspired by supergravity (MSUGRA). But alternatives such as gauge mediated supersymmetry breaking (GMSB), anomaly mediated supersymmetry breaking (AMSB), models with R-parity violation and even alternatives to supersymmetry are also briefly considered.

Upper bound on the hadronic light-by-light contribution to the muon g - 2

There are indications that hadronic loops in some electroweak observables are almost saturated by parton level effects. Taking this as the hypothesis for this work, we propose a genuine parton level estimate of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon, a(LBL)/(mu)(had). Our quark mass definitions and values are motivated in detail, and the simplicity of our approach allows for a transparent error estimate. For infinitely heavy quarks our treatment is exact, while for asymptotically small quark masses a(LBL)/(mu)(had) is overestimated. Interpolating, this suggests quoting an upper bound. We obtain a(LBL)/(mu)(had)<1.59x10;{-9} (95% C.L.).