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Peskin–Takeuchi Parameter
In particle physics, the Peskin–Takeuchi parameters are a set of three measurable quantities, called ''S'', ''T'', and ''U'', that parameterize potential new physics contributions to electroweak radiative corrections. They are named after physicists Michael Peskin and Tatsu Takeuchi, who proposed the parameterization in 1990; proposals from two other groups (see References below) came almost simultaneously. The Peskin–Takeuchi parameters are defined so that they are all equal to zero at a ''reference point'' in the Standard Model, with a particular value chosen for the (then unmeasured) Higgs boson mass. The parameters are then extracted from a global fit to the high-precision electroweak data from particle collider experiments (mostly the Z pole data from the CERN LEP collider) and atomic parity violation. The measured values of the Peskin–Takeuchi parameters agree with the Standard Model. They can then be used to constrain models of new physics beyond the Stan ...
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Particle Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, but ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredt ...
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Photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, (or about ). The photon belongs to the class of bosons. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric ef ...
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Momentum Transfer
In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the simplest example of scattering of two colliding particles with initial momenta \vec_,\vec_, resulting in final momenta \vec_,\vec_, the momentum transfer is given by : \vec q = \vec_ - \vec_ = \vec_ - \vec_ where the last identity expresses momentum conservation. Momentum transfer is an important quantity because \Delta x = \hbar / , q, is a better measure for the typical distance resolution of the reaction than the momenta themselves. Wave mechanics and optics A wave has a momentum p = \hbar k and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called ''momentum transfer''. The wave number k is the absolute of the wave vector k = p / \hbar and is related to the wavelength k = 2\ ...
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Muon Decay
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As with other leptons, the muon is not thought to be composed of any simpler particles; that is, it is a fundamental particle. The muon is an unstable subatomic particle with a mean lifetime of , much longer than many other subatomic particles. As with the decay of the non-elementary neutron (with a lifetime around 15 minutes), muon decay is slow (by subatomic standards) because the decay is mediated only by the weak interaction (rather than the more powerful strong interaction or electromagnetic interaction), and because the mass difference between the muon and the set of its decay products is small, providing few kinetic degrees of freedom for decay. Muon decay almost always produces at least three particles, which must include an electron of ...
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Fermi Coupling Constant
In particle physics, Fermi's interaction (also the Fermi theory of beta decay or the Fermi four-fermion interaction) is an explanation of the beta decay, proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting with one another (at one vertex of the associated Feynman diagram). This interaction explains beta decay of a neutron by direct coupling of a neutron with an electron, a neutrino (later determined to be an antineutrino) and a proton. Fermi first introduced this coupling in his description of beta decay in 1933. The Fermi interaction was the precursor to the theory for the weak interaction where the interaction between the proton–neutron and electron–antineutrino is mediated by a virtual W− boson, of which the Fermi theory is the low-energy effective field theory. History of initial rejection and later publication Fermi first submitted his "tentative" theory of beta decay to the prestigious science journal ''Nature'', which reje ...
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Quantum Electrodynamic
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen. History The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who (du ...
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Fine Structure Constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge ''e'' with the electromagnetic field, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by Arnold Sommerfeld, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the Bohr model of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887. Definition In terms of other fundamental physical constants, may be defined as: \alpha = \frac = \frac , where * is the elementary charge ...
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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). After developments in radar equipment for World War II resulted in higher accuracy for measuring the energy levels of the hydrogen atom, I.I. Rabi made measurements of the Lamb shift and the anomalous magnetic dipole moment of the electron. These effects corresponded to the deviation from the value −2 for the spectroscopic electron ''g''-factor that are predicted by the Dirac equation. Later, Hans Bethe theoretically calculated those shifts in the hydrogen energy levels due to vacuum polarization on his return train ride from the Shelter Island Conference to Cornell. The effects of vacuum polariza ...
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Electroweak Scale
In particle physics, the electroweak scale, also known as the Fermi scale, is the energy scale around 246 GeV, a typical energy of processes described by the electroweak theory. The particular number 246 GeV is taken to be the vacuum expectation value v = (G_F \sqrt)^ of the Higgs field (where G_F is the Fermi coupling constant). In some cases the term ''electroweak scale'' is used to refer to the temperature of electroweak symmetry breaking, 159.5±1.5 GeV . In other cases, the term is used more loosely to refer to energies in a broad range around 102 - 103 GeV. This is within reach of the Large Hadron Collider (LHC), which is designed for about 104 GeV in proton–proton collisions. Interactions may have been above this scale during the electroweak epoch. In the unextended Standard Model, the transition from the electroweak epoch was not a first or a second order phase transition but a continuous crossover, preventing any baryogenesis In physical cosmology, baryogen ...
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Vertex Function
In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion \psi, the antifermion \bar, and the vector potential A. Definition The vertex function \Gamma^\mu can be defined in terms of a functional derivative of the effective action Seff as :\Gamma^\mu = - The dominant (and classical) contribution to \Gamma^\mu is the gamma matrix \gamma^\mu, which explains the choice of the letter. The vertex function is constrained by the symmetries of quantum electrodynamics — Lorentz invariance; gauge invariance or the transversality of the photon, as expressed by the Ward identity; and invariance under parity — to take the following form: : \Gamma^\mu = \gamma^\mu F_1(q^2) + \frac F_2(q^2) where \sigma^ = (i/2) gamma^, \gamma^, q_ is the incoming four-momentum of the external photon (on the ...
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Nonoblique Correction
In four-fermion scattering processes of particle physics, a nonoblique correction, also called a direct correction, refers to a radiative correction of type  +  →  +  in the electroweak sector of the Standard Model. These corrections are being studied at the CERN LEP collider. Together with the oblique corrections, ''nonoblique corrections'' can be used to constrain models of physics beyond the Standard Model. Classes There are three classes of radiative corrections to these processes: * vacuum polarization corrections, * vertex corrections, and * box corrections. The vertex and box corrections, which depend on the identity of the initial and final state fermions, are referred to as the non-oblique corrections. The vacuum polarization corrections are referred to as oblique corrections, since they only affect the mixing and propagation of the gauge bosons and they do not depend on which type of fermions appear in the initial or final states. Ex ...
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