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Pion Decay Constant
In particle physics, the pion decay constant is the square root of the coefficient in front of the kinetic term for the pion in the low-energy effective action. It is dimensionally an energy scale and it determines the strength of the chiral symmetry breaking. The values are: :f_ = 130.41 \pm 0.03 \pm 0.20~\mbox :f_ = 130 \pm 5~\mbox Beware: There are several conventions which differ by factors of \scriptstyle \sqrt. The textbook by Weinberg uses the value 184 MeV. The textbook by Peskin and Schroeder uses the value 93 MeV. According to Brown–Rho scaling, the masses of nucleons and most light mesons decrease at finite density as the ratio of the in-medium pion decay rate to the free-space pion decay constant. The pion mass is an exception to Brown-Rho scaling because the pion's mass is protected by its Goldstone boson In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 hundredths of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the ''radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sqrt. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Term
In physics, a kinetic term is the part of the Lagrangian that is bilinear in the fields (and for nonlinear sigma models, they are not even bilinear), and usually contains two derivatives with respect to time (or space); in the case of fermions, the kinetic term usually has one derivative only. The equation of motion derived from such a Lagrangian contains differential operators which are generated by the kinetic term. Unitarity requires kinetic terms to be positive. In mechanics, the kinetic term is : T = \frac\dot x^2 = \frac\left( \frac\right)^2 . In quantum field theory, the kinetic terms for real scalar fields, electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ... and Dirac field are : T = \frac\partial_\mu \Phi \partial^\mu \Phi + \fracF_F^ + i \bar \ps ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pion
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more generally, the lightest hadrons. They are unstable, with the charged pions and decaying after a mean lifetime of 26.033 nanoseconds ( seconds), and the neutral pion decaying after a much shorter lifetime of 85 attoseconds ( seconds). Charged pions most often decay into muons and muon neutrinos, while neutral pions generally decay into gamma rays. The exchange of virtual pions, along with vector, rho and omega mesons, provides an explanation for the residual strong force between nucleons. Pions are not produced in radioactive decay, but commonly are in high-energy collisions between hadrons. Pions also result from some matter–antimatter annihilation events. All types of pions are also produced in natural processes wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Perturbation Theory
Chiral perturbation theory (ChPT) is an effective field theory constructed with a Lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics (QCD), as well as the other symmetries of parity and charge conjugation.Heinrich Leutwyler (2012), Chiral perturbation theory Scholarpedia, 7(10):8708. ChPT is a theory which allows one to study the low-energy dynamics of QCD on the basis of this underlying chiral symmetry. Goals In the theory of the strong interaction of the standard model, we describe the interactions between quarks and gluons. Due to the running of the strong coupling constant, we can apply perturbation theory in the coupling constant only at high energies. But in the low-energy regime of QCD, the degrees of freedom are no l ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Scale
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group. In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength \ell = \hbar/p where \hbar is the reduced Planck's constant and p is the momentum that is being probed. In relativistic mechanics time an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry Breaking
In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awarded the 2008 Nobel prize in physics for describing this phenomenon ("for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"). Overview Quantum chromodynamics Experimentally, it is observed that the masses of the octet of pseudoscalar mesons (such as the pion) are much lighter than the next heavier states such as the octet of vector mesons, such as rho meson. This is a consequence of spontaneous symmetry breaking of chiral symmetry in a fermion sector of QCD with 3 flavors of light quarks, , , and . Such a theory, for idealized massless quarks, has global chiral flavor symmetry. Under SSB, this is spontaneously broken to the diagonal flavor ''SU''(3) subgroup, generating eight Nambu–Goldstone bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brown–Rho Scaling
In quantum chromodynamics (QCD), Brown–Rho (BR) scaling is an approximate scaling law for hadrons in an ultra-hot, ultra-dense medium, such as hadrons in the quark epoch during the first microsecond of the Big Bang or within neutron stars. According to Gerald E. Brown and Mannque Rho in their 1991 publication in ''Physical Review Letters'': refers to the pole mass of the ρ meson, whereas refers to the in-medium mass (or running mass in the medium) of the ρ meson according to QCD sum rules. The omega meson, sigma meson, and neutron are denoted by ω, σ, and N, respectively. The symbol denotes the free-space pion decay constant. (Decay constants have a "running time" and a "pole time" similar to the "running mass" and "pole mass" concepts, according to special relativity.) The symbol is also used to denote the pion decay constant. The hypothesis of Brown–Rho scaling is supported by experimental evidence on beta decay of 14C to the 14N ground state. See also *Qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nucleon
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were thought to be elementary particles, not made up of smaller parts. Now they are known to be composite particles, made of three quarks bound together by the strong interaction. The interaction between two or more nucleons is called internucleon interaction or nuclear force, which is also ultimately caused by the strong interaction. (Before the discovery of quarks, the term "strong interaction" referred to just internucleon interactions.) Nucleons sit at the boundary where particle physics and nuclear physics overlap. Particle physics, particularly quantum chromodynamics, provides the fundamental equations that describe the properties of quarks and of the strong interaction. These equations describe quantitatively how quarks can bind toget ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly one femtometre (10 m), which is about 0.6 times the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Heavier mesons decay to lighter mesons and ultimately to stable electrons, neutrinos and photons. Outside the nucleus, mesons appear in nature only as short-lived products of very high-energy collisions between particles made of quarks, such as cosmic rays (high-energy protons and neutrons) and baryonic matter. Mesons are routinely produced artificially in cyclotrons or other particle accelerators in the collisions of protons, antiprotons, or other particles. Higher-energy (more massive) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldstone Boson
In particle and condensed matter physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu in particle physics within the context of the BCS superconductivity mechanism, and subsequently elucidated by Jeffrey Goldstone, and systematically generalized in the context of quantum field theory. In condensed matter physics such bosons are quasiparticles and are known as Anderson–Bogoliubov modes. These spinless bosons correspond to the spontaneously broken internal symmetry generators, and are characterized by the quantum numbers of these. They transform nonlinearly (shift) under the action of these generators, and can thus be excited out of the asymmetric vacuum by these generators. Thus, they can be thought of as the excitations of the field in the broken symmetry directions in group space—and are massless if the spontaneously brok ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
