Bhabha Scattering
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Bhabha Scattering
In quantum electrodynamics, Bhabha scattering is the electron-positron scattering process: ::e^+ e^- \rightarrow e^+ e^- There are two leading-order Feynman diagrams contributing to this interaction: an annihilation process and a scattering process. Bhabha scattering is named after the Indian physicist Homi J. Bhabha. The Bhabha scattering rate is used as a luminosity monitor in electron-positron colliders. Differential cross section To leading order, the spin-averaged differential cross section for this process is ::\frac = \frac \left( u^2 \left( \frac + \frac \right)^2 + \left( \frac \right)^2 + \left( \frac \right)^2 \right) \, where ''s'',''t'', and ''u'' are the Mandelstam variables, \alpha is the fine-structure constant, and \theta is the scattering angle. This cross section is calculated neglecting the electron mass relative to the collision energy and including only the contribution from photon exchange. This is a valid approximation at collision energies small com ...
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Feynman Diagrams
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagram ...
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Bhabha S Channel Label
Bhabha may refer to: *Bhabha (surname) *Bhabha (crater), on the moon *Bhabha scattering, in quantum electrodynamics *Bhabha Atomic Research Centre See also *Homi Bhabha National Institute, an Indian deemed university *Homi Bhabha Centre for Science Education, Mumbai, India *Jamshed Bhabha Theater (NCPA), Mumbai, India *Baba (other) Baba and similar words may refer to: Places * Baba mountain range, also known as ''Koh-i-Baba'', in the Hindu Kush of Afghanistan * Baba Canton, a canton in Los Ríos Province, Ecuador * Baba, Iran, a village in Kurdistan Province * Baba, K ...
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Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in th ...
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BaBar Experiment
The BaBar experiment, or simply BaBar, is an international collaboration of more than 500 physicists and engineers studying the subatomic world at energies of approximately ten times the rest mass of a proton (~10 GeV). Its design was motivated by the investigation of charge-parity violation. BaBar is located at the SLAC National Accelerator Laboratory, which is operated by Stanford University for the Department of Energy in California. Physics BaBar was set up to understand the disparity between the matter and antimatter content of the universe by measuring Charge Parity violation. CP symmetry is a combination of Charge-conjugation symmetry (C symmetry) and Parity symmetry (P symmetry), each of which are conserved separately except in weak interactions. BaBar focuses on the study of CP violation in the B meson system. The name of the experiment is derived from the nomenclature for the B meson (symbol ) and its antiparticle (symbol , pronounced B bar). The experiment's ...
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Belle Experiment
The Belle experiment was a particle physics experiment conducted by the Belle Collaboration, an international collaboration of more than 400 physicists and engineers, at the High Energy Accelerator Research Organisation (KEK) in Tsukuba, Ibaraki Prefecture, Japan. The experiment ran from 1999 to 2010. The Belle detector was located at the collision point of the asymmetric-energy electron– positron collider, KEKB. Belle at KEKB together with the BaBar experiment at the PEP-II accelerator at SLAC were known as the B-factories as they collided electrons with positrons at the center-of-momentum energy equal to the mass of the (4S) resonance which decays to pairs of B mesons. The Belle detector was a hermetic multilayer particle detector with large solid angle coverage, vertex location with precision on the order of tens of micrometres (provided by a silicon vertex detector), good distinction between pions and kaons in the momenta range from 100 MeV/c to few GeV/c (provided by ...
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Beijing Electron Synchrotron
} Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 million residents. It has an administrative area of , the third in the country after Guangzhou and Shanghai. It is located in Northern China, and is governed as a municipality under the direct administration of the State Council with 16 urban, suburban, and rural districts.Figures based on 2006 statistics published in 2007 National Statistical Yearbook of China and available online at archive. Retrieved 21 April 2009. Beijing is mostly surrounded by Hebei Province with the exception of neighboring Tianjin to the southeast; together, the three divisions form the Jingjinji megalopolis and the national capital region of China. Beijing is a global city and one of the world's leading centres for culture, diplomacy, politics, finance, bus ...
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Stanford Large Detector
SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a United States Department of Energy National Laboratory operated by Stanford University under the programmatic direction of the U.S. Department of Energy Office of Science and located in Menlo Park, California. It is the site of the Stanford Linear Accelerator, a 3.2 kilometer (2-mile) linear accelerator constructed in 1966 and shut down in the 2000s, that could accelerate electrons to energies of 50 GeV. Today SLAC research centers on a broad program in atomic and solid-state physics, chemistry, biology, and medicine using X-rays from synchrotron radiation and a free-electron laser as well as experimental and theoretical research in elementary particle physics, astroparticle physics, and cosmology. History Founded in 1962 as the Stanford Linear Accelerator Center, the facility is located on of Stanford University-owned land on Sand Hill Road in Menlo Park, Californ ...
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Luminosity (scattering Theory)
In scattering theory and accelerator physics, luminosity (''L'') is the ratio of the number of events detected (''dN'') in a certain period of time (''dt'') to the cross-section (''σ''): : L = \frac\frac. It has the dimensions of events per time per area, and is usually expressed in the cgs units of cm−2· s−1 or the non-SI units of b−1·s−1. In practice, ''L'' is dependent on the particle beam parameters, such as beam width and particle flow rate, as well as the target properties, such as target size and density. A related quantity is integrated luminosity (''L''int), which is the integral of the luminosity with respect to time: : L_\mathrm = \int L \ dt. The luminosity and integrated luminosity are useful values to characterize the performance of a particle accelerator. In particular, all collider experiments aim to maximize their integrated luminosities, as the higher the integrated luminosity, the more data is available to analyze. Examples of collider lu ...
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Feynman Slash Notation
In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If ''A'' is a covariant vector (i.e., a 1-form), : \ \stackrel\ \gamma^1 A_1 + \gamma^2 A_2 + \gamma^3 A_3 + \gamma^4 A_4 where ''γ'' are the gamma matrices. Using the Einstein summation notation, the expression is simply : \ \stackrel\ \gamma^\mu A_\mu. Identities Using the anticommutators of the gamma matrices, one can show that for any a_\mu and b_\mu, :\begin &\equiv a^\mu a_\mu \cdot I_4 = a^2 \cdot I_4 \\ + &\equiv 2 a \cdot b \cdot I_4. \end where I_4 is the identity matrix in four dimensions. In particular, :^2 \equiv \partial^2 \cdot I_4. Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example, :\begin \operatorname() &\equiv 4 a \cdot b \\ ...
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Dirac Spinor
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group. Dirac spinors are important and interesting in numerous ways. Foremost, they are important as they do describe all of the known fundamental particle fermions in nature; this includes the electron and the quarks. Algebraically they behave, in a certain sense, as the "square root" of a vector. This is not readily apparent from direct examination, but it has slowly become clear over the last 60 years that spinorial representations are fundamental to geometry. For example, effectively all Riemannian manifolds can have spinors and spin connections built upon them, via the Clifford algebra. The Dirac spinor is specific to that ...
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Crossing Symmetry
In quantum field theory, a branch of theoretical physics, crossing is the property of scattering amplitudes that allows antiparticles to be interpreted as particles going backwards in time. Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle \mathrm to scatter with \mathrm and produce particle \mathrm and \mathrm will also give the scattering amplitude for \scriptstyle \mathrm+\bar+\mathrm to go into \mathrm, or for \scriptstyle \bar to scatter with \scriptstyle \mathrm to produce \scriptstyle \mathrm+\bar. The only difference is that the value of the energy is negative for the antiparticle. The formal way to state this property is that the antiparticle scattering amplitudes are the analytic continuation of particle scattering amplitudes to negative energies. The interpretation of this statement is that the antiparticle is in every way a particle going backwards in time. History Murray Gell-Mann and Marvin Leonard Gol ...
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Bhabha Scattering
In quantum electrodynamics, Bhabha scattering is the electron-positron scattering process: ::e^+ e^- \rightarrow e^+ e^- There are two leading-order Feynman diagrams contributing to this interaction: an annihilation process and a scattering process. Bhabha scattering is named after the Indian physicist Homi J. Bhabha. The Bhabha scattering rate is used as a luminosity monitor in electron-positron colliders. Differential cross section To leading order, the spin-averaged differential cross section for this process is ::\frac = \frac \left( u^2 \left( \frac + \frac \right)^2 + \left( \frac \right)^2 + \left( \frac \right)^2 \right) \, where ''s'',''t'', and ''u'' are the Mandelstam variables, \alpha is the fine-structure constant, and \theta is the scattering angle. This cross section is calculated neglecting the electron mass relative to the collision energy and including only the contribution from photon exchange. This is a valid approximation at collision energies small com ...
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