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Muon G-2
Muon −2 (pronounced "gee minus two") was a particle physics experiment at Fermilab to measure the anomalous magnetic dipole moment of a muon to a precision of 0.14 Parts per million, ppm, which is a sensitive test of the Standard Model. It might also provide evidence of the existence of new particles. The muon, like its lighter sibling the electron, acts like a tiny magnet. The parameter known as the "g-factor (physics),  factor" indicates how strong the magnet is and the rate of its gyration in an externally applied magnetic field. It is this rate of gyration that is indirectly measured in the Muon ''g''−2 experiment. The value of is slightly larger than 2, hence the name of the experiment. This difference from 2 (the "anomalous" part) is caused by higher-order contributions from quantum field theory. In measuring −2 with high precision and comparing its value to the theoretical prediction, physicists will discover whether the experiment agrees wi ...
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Fermilab G-2 (E989) Ring
Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy United States Department of Energy National Labs, national laboratory specializing in high-energy particle physics. Fermilab's Main Injector, two miles (3.3 km) in circumference, is the laboratory's most powerful particle accelerator. The accelerator complex that feeds the Main Injector is under upgrade, and construction of the first building for the new PIP-II linear accelerator began in 2020. Until 2011, Fermilab was the home of the 6.28 km (3.90 mi) circumference Tevatron accelerator. The ring-shaped tunnels of the Tevatron and the Main Injector are visible from the air and by satellite. Fermilab aims to become a world center in neutrino physics. It is the host of the multi-billion dollar Deep Underground Neutrino Experiment (DUNE) now under construction. The project has suffered delays and, in 2022, the journals ''Science'' and ''Sc ...
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Brookhaven National Laboratory
Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratories, United States Department of Energy national laboratory located in Upton, New York, a hamlet of the Brookhaven, New York, Town of Brookhaven. It was formally established in 1947 at the site of Camp Upton, a former List of United States Army installations, U.S. Army base on Long Island. Located approximately 60 miles east of New York City, it is managed by Stony Brook University and Battelle Memorial Institute. Research at BNL includes nuclear and high energy physics, energy science and technology, environmental and bioscience, nanoscience, and national security. The 5,300 acre campus contains several large research facilities, including the Relativistic Heavy Ion Collider and National Synchrotron Light Source II. Seven Nobel Prizes have been awarded for work conducted at Brookhaven Lab. Overview BNL operations are overseen by a Department of Energy Site office, is staffed by approx ...
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Vacuum Polarization
In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the self-energy of the gauge boson (photon). It is analogous to the electric polarization of dielectric materials, but in vacuum without the need of a medium. The effects of vacuum polarization have been routinely observed experimentally since then as very well-understood background effects. Vacuum polarization, referred to below as the one loop contribution, occurs with leptons (electron–positron pairs) or quarks. History Vacuum polarization was first discussed in papers by Paul Dirac and Werner Heisenberg in 1934. After developments in radar equipment for World War II resulted in higher accuracy for measuring the energy levels of the h ...
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QCD Vacuum
The QCD vacuum is the quantum vacuum state of quantum chromodynamics (QCD). It is an example of a ''non-perturbative'' vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter. Symmetries and symmetry breaking Symmetries of the QCD Lagrangian Like any relativistic quantum field theory, QCD enjoys Poincaré symmetry including the discrete symmetries CPT (each of which is realized). Apart from these space-time symmetries, it also has internal symmetries. Since QCD is an SU(3) gauge theory, it has local SU(3) gauge symmetry. Since it has many flavours of quarks, it has approximate flavour and chiral symmetry. This approximation is said to involve the chiral limit of QCD. Of these chiral symmetries, the baryon number symmetry is exact. Some of the broken symmetries include the axial U(1) ...
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R (cross Section Ratio)
''R'' is the ratio of the hadronic cross section to the muon cross section in electron–positron collisions: : R = \frac, where the superscript (0) indicates that the cross section has been corrected for initial state radiation. ''R'' is an important input in the calculation of the anomalous magnetic dipole moment. Experimental values have been measured for center-of-mass energies from 400 MeV to 150 GeV. ''R'' also provides experimental confirmation of the electric charge of quarks, in particular the charm quark and bottom quark, and the existence of three quark colors. A simplified calculation of ''R'' yields : R = 3\sum_q e_q^2/e^2, where the sum is over all quark flavors with mass less than the beam energy. ''eq'' is the electric charge of the quark, and the factor of 3 accounts for the three colors of the quarks. QCD In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and ...
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Lattice QCD
Lattice QCD is a well-established non- perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/''a'', where ''a'' is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by mean ...
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Hadron
In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong nuclear force. Pronounced , the name is derived . They are analogous to molecules, which are held together by the electric force. Most of the mass of ordinary matter comes from two hadrons: the proton and the neutron, while most of the mass of the protons and neutrons is in turn due to the binding energy of their constituent quarks, due to the strong force. Hadrons are categorized into two broad families: baryons, made of an odd number of quarks (usually three) and mesons, made of an even number of quarks (usually two: one quark and one antiquark). Protons and neutrons (which make the majority of the mass of an atom) are examples of baryons; pions are an example of a meson. A tetraquark state (an exotic meson), named the Z(4430), was discovered in 2007 by the Belle Collaboration and confirmed as a resonance in 2014 by the LHCb collaboration. Two pe ...
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Virtual Particle
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle, which allows the virtual particles to spontaneously emerge from vacuum at short time and space ranges. The concept of virtual particles arises in the perturbation theory (quantum mechanics), perturbation theory of quantum field theory (QFT) where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines. Virtual particles do not necessarily carry the same mass as the corresponding ordinary particle, although they always conserve energy and momentum. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists. They are important in the ph ...
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Standard Model Of Particle Physics
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated some success in providing experimental predictions, it leaves some physical phenomena unexplained and so falls short of being a ...
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Tau (particle)
The tau (), also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin-1/2, spin of . Like the electron, the muon, and the three neutrinos, the tau is a lepton, and like all elementary particles with half-integer spin, the tau has a corresponding antiparticle of opposite charge but equal mass and spin. In the tau's case, this is the "antitau" (also called the ''positive tau''). Tau particles are denoted by the symbol and the antitaus by . Tau leptons have a lifetime of and a mass of /''c''2 (compared to /''c''2 for muons and /''c''2 for electrons). Since their interactions are very similar to those of the electron, a tau can be thought of as a ''much'' heavier version of the electron. Because of their greater mass, tau particles do not emit as much bremsstrahlung, bremsstrahlung (braking radiation) as electrons; consequently they are potentially much more highly penetrating than electrons. Bec ...
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Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up quark, up and down quark, down quarks. Electrons are extremely lightweight particles that orbit the positively charged atomic nucleus, nucleus of atoms. Their negative charge is balanced by the positive charge of protons in the nucleus, giving atoms their overall electric charge#Charge neutrality, neutral charge. Ordinary matter is composed of atoms, each consisting of a positively charged nucleus surrounded by a number of orbiting electrons equal to the number of protons. The configuration and energy levels of these orbiting electrons determine the chemical properties of an atom. Electrons are bound to the nucleus to different degrees. The outermost or valence electron, valence electrons are the least tightly bound and are responsible for th ...
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Shim (magnetism)
A shim is a device used to adjust the homogeneity of a magnetic field. Shims received their name from the purely mechanical shims used to adjust position and parallelity of the pole faces of an electromagnet. Coils used to adjust the homogeneity of a magnetic field by changing the current flowing through it were called "electrical current shims" because of their similar function. Usage in magnetic resonance spectroscopy In NMR and MRI, shimming is used prior to the operation of the magnet to eliminate inhomogeneities in its field. Initially, the magnetic field inside an NMR spectrometer or MRI scanner will be far from homogeneous compared with an "ideal" field of the device. This is a result of production tolerances and of the magnetic field of the environment. Iron constructions in walls and floor of the examination room become magnetized and disturb the field of the scanner. The probe and the sample or the patient become slightly magnetized when brought into the strong ma ...
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