Rho meson

In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as
. Along with pions and omega mesons, the rho meson carries the nuclear force within the atomic nucleus. After the pions and kaons, the rho mesons are the lightest strongly interacting particle, with a mass of 775.45±0.04 MeV (roughly 770 MeV) for all three states.[a]

The rho mesons have a very short lifetime and their decay width is about 145 MeV with the peculiar feature that the decay widths are not described by a Breit–Wigner form. The principal decay route of the rho mesons is to a pair of pions with a branching rate of 99.9%.[b]


In the De Rujula–Georgi–Glashow description of hadrons,[1] the rho mesons can be interpreted as a bound state of a quark and an anti-quark and is an excited version of the pion. Unlike the pion, the rho meson has spin j = 1 (a vector meson) and a much higher value of the mass. This mass difference between the pions and rho mesons is attributed to a large hyperfine interaction between the quark and anti-quark. The main objection with the De Rujula–Georgi–Glashow description is that it attributes the lightness of the pions as an accident rather than a result of chiral symmetry breaking.

The rho mesons can be thought of as the gauge bosons of a spontaneously broken gauge symmetry whose local character is emergent (arising from QCD); Note that this broken gauge symmetry (sometimes called hidden local symmetry) is distinct from the global chiral symmetry acting on the flavors. This was described by Howard Georgi in a paper titled "The Vector Limit of Chiral Symmetry" where he ascribed much of the literature of hidden local symmetry to a non-linear sigma model.[2]

Rho mesons
Particle name Particle
Rest mass (MeV/c2) IG JPC S C B' Mean lifetime (s)[c] Commonly decays to

(>5% of decays)

Charged rho meson[4]



775.4±0.4 1+ 1 0 0 0 ~4.5×10−24[d]
Neutral rho meson[4]
Self 775.49±0.34 1+ 1−− 0 0 0 ~4.5×10−24[d]


  1. ^ There should be a small mass difference between the
    and the
    that can be attributed to the electromagnetic self-energy of the particle as well as a small effect due to isospin breaking arising from the light quark masses; however, the current experimental limit is that this mass difference is less than 0.7 MeV.
  2. ^ Neutral rho mesons can decay to a pair of electrons or muons which occurs with a branching ratio of 5×10−5. This decay of the neutral rho to leptons can be interpreted as a mixing between the photon and rho. In principle the charged rho mesons mix with the weak vector bosons and can lead to decay to an electron or muon plus a neutrino; however, this has never been observed.
  3. ^ The exact value depends on the method used. See the given reference for detail.
  4. ^ a b PDG reports the resonance width (Γ). Here the conversion τ = ​ħΓ is given instead.


  1. ^ Rujula, Georgi, Glashow (1975) "Hadron Masses in Gauge Theory." Physical Review D12, p.147
  2. ^ H. Georgi. (1990) "Vector Realization of Chiral Symmetry." inSPIRE Record
  3. ^ C. Amsler et al. (2008): Quark Model
  4. ^ a b C. Amsler et al. (2008): Particle listings –
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:

By using effective chiral Lagrangians with a suitable incorporation of the scaling property of QCD, we establish the approximate in-medium scaling law, m*σ/mσ ≈ m*N/mN ≈ m*ρ/mρ ≈ m*ω/mω ≈ f*π/fπ. This has a highly nontrivial implication for nuclear processes at or above nuclear-matter density.

In the preceding equation, mρ refers to the pole mass of the ρ meson, whereas m*ρ 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 fπ 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 Fπ is also used to denote the pion decay constant.

For hadrons, a large part of their masses are generated by the chiral condensate. Since the chiral condensate may vary significantly in hot and/or dense matter, hadron masses would also be modified. ... Brown-Rho scaling ... suggests that the partial restoration of the chiral symmetry can be experimentally accessible by measuring in-medium hadron masses, and triggered many later theoretical and experimental works. Theoretically, a similar behavior is also found in the NJL model ... and the QCD sum rule ...

The hypothesis of Brown-Rho scaling is supported by experimental evidence on beta decay of 14C to the 14N ground state.

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").

Gauge boson

In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature, commonly called forces. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles.

All known gauge bosons have a spin of 1. Therefore, all known gauge bosons are vector bosons.

Gauge bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made of quarks; third, larger composite, non-force-carrying bosons, such as certain atoms.

Index of physics articles (R)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Length scale

In physics, length scale is a particular length or distance determined with the precision of one order of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other[citation needed][clarification needed] 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 where is the reduced Planck's constant and is the momentum that is being probed. In relativistic mechanics time and length scales are related by the speed of light. In relativistic quantum mechanics or relativistic quantum field theory, length scales are related to momentum, time and energy scales through Planck's constant and the speed of light. Often in high energy physics natural units are used where length, time, energy and momentum scales are described in the same units (usually with units of energy such as GeV).

Length scales are usually the operative scale (or at least one of the scales) in dimensional analysis. For instance, in scattering theory, the most common quantity to calculate is a cross section which has units of length squared and is measured in barns. The cross section of a given process is usually the square of the length scale.

List of mesons

This list is of all known and predicted scalar, pseudoscalar and vector mesons. See list of particles for a more detailed list of particles found in particle physics.This article contains a list of mesons, unstable subatomic particles composed of one quark and one antiquark. They are part of the hadron particle family – particles made of quarks. The other members of the hadron family are the baryons – subatomic particles composed of three quarks. The main difference between mesons and baryons is that mesons have integer spin (thus are bosons) while baryons are fermions (half-integer spin). Because mesons are bosons, the Pauli exclusion principle does not apply to them. Because of this, they can act as force mediating particles on short distances, and thus play a part in processes such as the nuclear interaction.

Since mesons are composed of quarks, they participate in both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. They are classified according to their quark content, total angular momentum, parity, and various other properties such as C-parity and G-parity. While no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and will exhibit higher-energy phenomena sooner than baryons would. For example, the charm quark was first seen in the J/Psi meson (J/ψ) in 1974, and the bottom quark in the upsilon meson (ϒ) in 1977.Each meson has a corresponding antiparticle (antimeson) where quarks are replaced by their corresponding antiquarks and vice versa. For example, a positive pion (π+) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark. Some experiments show the evidence of tetraquarks – "exotic" mesons made of two quarks and two antiquarks, but the particle physics community as a whole does not view their existence as likely, although still possible.The symbols encountered in these lists are: I (isospin), J (total angular momentum), P (parity), C (C-parity), G (G-parity), u (up quark), d (down quark), s (strange quark), c (charm quark), b (bottom quark), Q (charge), B (baryon number), S (strangeness), C (charm), and B′ (bottomness), as well as a wide array of subatomic particles (hover for name).


In particle physics, mesons ( or ) are hadronic subatomic particles composed of one quark and one antiquark, bound together by strong interactions. Because mesons are composed of quark subparticles, they have physical size, notably a diameter of roughly one femtometer, which is about 1.2 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. Charged mesons decay (sometimes through mediating particles) to form electrons and neutrinos. Uncharged mesons may decay to photons. Both of these decays imply that color is no longer a property of the byproducts.

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 ordinary matter. Mesons are also frequently produced artificially in cyclotron in the collisions of protons, antiprotons, or other particles.

Higher energy (more massive) mesons were created momentarily in the Big Bang, but are not thought to play a role in nature today. However, such heavy mesons are regularly created in particle accelerator experiments, in order to understand the nature of the heavier types of quark that compose the heavier mesons.

Mesons are part of the hadron particle family, and are defined simply as particles composed of an even number of quarks. The other members of the hadron family are the baryons: subatomic particles composed of odd numbers of valence quarks (at least 3), and some experiments show evidence of exotic mesons, which do not have the conventional valence quark content of two quarks (one quark and one antiquark), but 4 or more.

Because quarks have a spin of ​1⁄2, the difference in quark number between mesons and baryons results in conventional two-quark mesons being bosons, whereas baryons are fermions.

Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice versa. For example, a positive pion (π+) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark.

Because mesons are composed of quarks, they participate in both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. Mesons are classified according to their quark content, total angular momentum, parity and various other properties, such as C-parity and G-parity. Although no meson is stable, those of lower mass are nonetheless more stable than the more massive, and hence are easier to observe and study in particle accelerators or in cosmic ray experiments. Mesons are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher-energy phenomena more readily than do baryons. For example, the charm quark was first seen in the J/Psi meson (J/ψ) in 1974, and the bottom quark in the upsilon meson (ϒ) in 1977.

Parity (physics)

In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection):

It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.

A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180°-rotation.

In quantum mechanics, wave functions which are unchanged by a parity transformation are described as even functions, while those which change sign under a parity transformation are odd functions.

Paul Dirac

Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". He also made significant contributions to the reconciliation of general relativity with quantum mechanics.

Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "This balancing on the dizzying path between genius and madness is awful".He was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.

QCD vacuum

The Quantum Chromodynamic Vacuum or QCD vacuum is the 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.

Relativistic Breit–Wigner distribution

The relativistic Breit–Wigner distribution (after the 1936 nuclear resonance formula of Gregory Breit and Eugene Wigner) is a continuous probability distribution with the following probability density function,

where k is a constant of proportionality, equal to


(This equation is written using natural units, ħ = c = 1.)

It is most often used to model resonances (unstable particles) in high-energy physics. In this case, E is the center-of-mass energy that produces the resonance, M is the mass of the resonance, and Γ is the resonance width (or decay width), related to its mean lifetime according to τ = 1/Γ. (With units included, the formula is τ = ħ/Γ.)

The probability of producing the resonance at a given energy E is proportional to f (E), so that a plot of the production rate of the unstable particle as a function of energy traces out the shape of the relativistic Breit–Wigner distribution. Note that for values of E off the maximum at M such that |E2M2| = , (hence |EM| = Γ/2 for M≫Γ), the distribution f has attenuated to half its maximum value, which justifies the name for Γ, width at half-maximum.

In the limit of vanishing width, Γ→0, the particle becomes stable as the Lorentzian distribution f sharpens infinitely to 2M δ(E2M2).

In general, Γ can also be a function of E; this dependence is typically only important when Γ is not small compared to M and the phase space-dependence of the width needs to be taken into account. (For example, in the decay of the rho meson into a pair of pions.) The factor of M 2 that multiplies Γ2 should also be replaced with E 2 (or E 4/M 2, etc.) when the resonance is wide.

The form of the relativistic Breit–Wigner distribution arises from the propagator of an unstable particle, which has a denominator of the form p2M2 + iMΓ. (Here, p2 is the square of the four-momentum carried by that particle in the tree Feynman diagram involved.) The propagator in its rest frame then is proportional to the quantum-mechanical amplitude for the decay utilized to reconstruct that resonance,

The resulting probability distribution is proportional to the absolute square of the amplitude, so then the above relativistic Breit–Wigner distribution for the probability density function.

The form of this distribution is similar to the amplitude of the solution to the classical equation of motion for a driven harmonic oscillator damped and driven by a sinusoidal external force. It has the standard resonance form of the Lorentz, or Cauchy distribution, but involves relativistic variables s=p ², here =E 2. The distribution is the solution of the differential equation for the amplitude squared w.r.t. the energy energy (frequency), in such a classical forced oscillator,

with .

Resonance (particle physics)

In particle physics, a resonance is the peak located around a certain energy found in differential cross sections of scattering experiments. These peaks are associated with subatomic particles, which include a variety of bosons, quarks and hadrons (such as nucleons, delta baryons or upsilon mesons) and their excitations. In common usage, "resonance" only describes particles with very short lifetimes, mostly high-energy hadrons existing for 10−23 seconds or less.

The width of the resonance (Γ) is related to the mean lifetime (τ) of the particle (or its excited state) by the relation

where h is the Planck constant and .

Thus, the lifetime of a particle is the direct inverse of the particle's resonance width. For example, the charged pion has the second-longest lifetime of any meson, at 2.6033×10−8 s. Therefore, its resonance width is very small, about 2.528×10−8 eV or about 6.11 MHz. Pions are generally not considered as "resonances". The charged rho meson has a very short lifetime, about 4.41×10−24 s. Correspondingly, its resonance width is very large, at 149.1 MeV or about 36 ZHz. This amounts to nearly one-fifth of the particle's rest mass.


Rho (; uppercase Ρ, lowercase ρ or ϱ; Greek: ῥῶ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.

Samuel C. C. Ting

Samuel Chao Chung Ting (Chinese: 丁肇中; pinyin: Dīng Zhàozhōng, born January 27, 1936) is an American physicist who received the Nobel Prize in 1976, with Burton Richter, for discovering the subatomic J/ψ particle. He is the founder and principal investigator for the international $2 billion Alpha Magnetic Spectrometer experiment which was installed on the International Space Station on 19 May 2011.


In particle theory, the skyrmion () is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by Tony Skyrme in 1962. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid state physics, as well as having ties to certain areas of string theory.

Skyrmions as topological objects are important in solid state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is mapped onto a far-off edge circle of a 2D-disk, while the negative south-pole spin is mapped onto the center of the disk. In a spinor field such as for example photonic or polariton fluids the skyrmion topology corresponds to a full Poincaré beam (which is, a quantum vortex of spin comprising all the states of polarization).Skyrmions have been reported, but not conclusively proven, to be in Bose-Einstein condensates, superconductors, thin magnetic films and in chiral nematic liquid crystals.As a model of the nucleon, the topological stability of the Skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the proton does not decay. The Skyrme Lagrangian is essentially a one-parameter model of the nucleon. Fixing the parameter fixes the proton radius, and also fixes all other low-energy properties, which appear to be correct to about 30%. It is this predictive power of the model that makes it so appealing as a model of the nucleon.

Hollowed-out skyrmions form the basis for the chiral bag model (Chesire cat model) of the nucleon. Exact results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by Dan Freed. This can be interpreted as a foundation for the duality between a QCD description of the nucleon (but consisting only of quarks, and without gluons) and the Skyrme model for the nucleon.

The skyrmion can be quantized to form a quantum superposition of baryons and resonance states. It could be predicted from some nuclear matter properties.

Vector meson

In high energy physics, a vector meson is a meson with total spin 1 and odd parity (usually noted as JP = 1). Compare to a pseudovector meson, which has a total spin 1 and even parity.

Vector mesons have been seen in experiments since the 1960s, and are well known for their spectroscopic pattern of masses. Since the development of the quark model by Murray Gell-Mann (and independently by George Zweig as well), the vector mesons have demonstrated the spectroscopy of pure states. The fact that the I = 1 rho meson (ρ) and I = 0 omega meson (ω) have nearly equal mass centered on 770–780 MeV/c2, while the phi meson (φ) has a higher mass around 1020 MeV/c2, indicates that the light-quark vector mesons appear in nearly pure states with the φ meson having a nearly 100 percent amplitude of hidden strangeness.

This characteristic of the vector mesons is not at all evident in the pseudoscalar meson or scalar meson multiplets, and may be only slightly realized among the tensor meson and pseudovector meson multiplets. This fact makes the vector mesons an excellent probe of the quark flavor content of other types of mesons, measured through the respective decay rates of non-vector mesons into the different types of vector mesons. Such experiments are very revealing for theorists who seek to determine the flavor content of mixed state mesons.

At higher masses, the vector mesons include charm and bottom quarks in their structure. In this realm, the radiative processes tend to stand out, with heavy tensor and scalar mesons decaying dominantly into vector mesons by photon emission. Pseudovector mesons transition by a similar process into pseudoscalar mesons. Because much of the spectrum of heavy mesons is tied by radiative processes to the vector mesons, one may think of vector mesons as forming a sort of backbone to the spectroscopy of mesons in general.

Some vector mesons can, compared to other mesons, be measured to a very high precision. This stems from the fact that they have the same quantum numbers as the photon, JPC = 1−−. Therefore they appear in electron-positron collisions in the process , which provides experimentally a clear signal compared to other measurement, which have to use hadronic processes.

Vector meson dominance

In physics, vector meson dominance (VMD) was a model developed by J. J. Sakurai in the 1960s before the introduction of quantum chromodynamics to describe interactions between energetic photons and hadronic matter.

In particular, the hadronic components of the physical photon consist of the lightest vector mesons, ρ {\displaystyle \rho } , ω {\displaystyle \omega } and ϕ {\displaystyle \phi } . Therefore, interactions between photons and hadronic matter occur by the exchange of a hadron between the dressed photon and the hadronic target.

Virtual particle

In physics, a virtual particle is a transient quantum fluctuation that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in perturbation theory of quantum field theory 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 real particle, although they always conserve energy and momentum. The longer the virtual particle exists, the closer its characteristics come to those of ordinary particles. They are important in the physics of many processes, including particle scattering and Casimir forces. In quantum field theory, even classical forces—such as the electromagnetic repulsion or attraction between two charges—can be thought of as due to the exchange of many virtual photons between the charges. Virtual photons are the exchange particle for the electromagnetic interaction.

The term is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles": it is not; rather, "real particles" are better understood to be excitations of the underlying quantum fields. Virtual particles are also excitations of the underlying fields, but are "temporary" in the sense that they appear in calculations of interactions, but never as asymptotic states or indices to the scattering matrix. The accuracy and use of virtual particles in calculations is firmly established, but as they cannot be detected in experiments, deciding how to precisely describe them is a topic of debate.

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