User:Marshallsumter/Radiation astronomy1/Mesons

Astronomy that benefits from the detection of mesons, directly or indirectly, is meson astronomy.

For antiproton-proton annihilation at rest, a meson result is, for example,


 * $$p^+ + \bar{p}^- \rightarrow \pi^+ + \pi^-,$$


 * $${\pi}^+ \rightarrow {\mu}^+ + {\nu}_{\mu} \rightarrow e^+ + {\nu}_e + {\bar{\nu}}_{\mu} + {\nu}_{\mu},$$ and


 * $$D_S \rightarrow \tau + \bar{\nu}_{\tau} \rightarrow \nu_{\tau} + \bar{\nu}_{\tau}.$$

Radiation
A meson is a subatomic particle that is intermediate in mass between an electron and a proton and transmits the strong interaction that binds nucleons together in the atomic nucleus.

Mesons travel at speeds slower than the speed of light.

Mesons are hadronic subatomic particles, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometre, which is about $2/3$ the size of a proton or neutron.

Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons.

Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles.

In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force.

Each type of meson has a corresponding antiparticle (antimeson) in which by theory quarks are replaced by their corresponding antiquarks and vice-versa.

Mesons are subject to both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction.

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 thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would.

Potential mesons to be detected astronomically include: π, ρ, η, η′, φ, ω, J/ψ, ϒ, θ, K, B, D, and T.

Hadrons
Hadrons are subatomic particles of a type including baryons and mesons that can take part in the strong interaction and may be useful in radiation astronomy.

At right a person works lower center left in front of the huge ATLAS detector, one of six detectors attached to the Large Hadron Collider at CERN. A hadron, like an atomic nucleus, is a composite particle held together by the strong force. Hadrons are categorized into two families: baryons (such as protons and neutrons) and mesons.

Def. a "composite particle [...] held together by the strong force and (consequently) can interact with other particles via said force; a meson or a baryon" is called a hadron.

The "fact that the regime of (star-relevant) high densities and low temperatures cannot be accessed by lattice or perturbative calculations makes the quark matter EoS even less constrained than the hadronic one, where at least there is some information on ground state matter properties."

"Hybrid stars have been applied to investigate a broad range of topics regarding compact stars, such as nucleation in hadronic matter [24, 41, 42], color superconductivity in quark matter [22–26], stability [22, 43, 44], rotation of neutron stars [43, 45–51], magnetic neutrons stars [52–55], thermal evolution [56–59], proto-neutron stars [60–62], supernovae [27, 63], radial oscillations [44, 64, 65], etc. The deconfinement phase transition has been extensively studied with different models such as Nambu-Jona-Lasinio [28, 61, 66–72], MIT bag model [23, 44, 55, 73–76], quark-meson coupling models [9, 72, 77, 78], and other approaches [58, 79–84], showing that the features of the models used to describe both phases have implications for the determination of the macroscopic properties and composition of stars."

"The hadronic phase (with nucleons, hyperons and leptons) is described by the many-body forces model (MBF model), which simulates the effects of many-body forces via non-linear scalar fields contributions in the effective coupling [2]."

"The many-body forces (MBF) model [2] is a relativistic mean field model in which meson field dependences are introduced in the couplings of baryons to mesons."

The "introduction of hyperons in a hadronic model softens drastically the EoS of hadronic matter, generating a sequence of stars with much smaller maximum mass, as discussed several times on literature. For the same reason, as hyperons start to populate the core of stars, for masses above 1.5M⊙, the stars become more compact, i.e., present a smaller radius. Similarly, comparting hadronic stars [...] to all hybrid ones (all others), one can see a reduction in radius of 14.44 km to 12.32 km (Set 6) for the 1.4 M⊙ star, for example."

"For the corresponding stars modeled in a Maxwell construction [...], the phase transition takes place for chemical potentials higher than the ones in a Gibbs construction, and consequently the gap between critical and maximum masses is smaller. For this case, stars are mostly hadronic, containing only a small quark core. In particular, the critical and maximum masses are the same [...], indicating that all stars in this family are hadronic [...], as the phase transition never takes place for stable stars."

"For the 1.4M⊙ star, [...] one can see that the difference in radius can vary by more than 2 km when comparing hadronic and hybrid stars."

Hyperons
A hyperon is any baryonic form of matter that may exist in a stable form within the core of some neutron stars.

"The impact of exotic compositions on the structure of isolated neutron stars has been studied in the past for stars composed of hyperons [1–9], Delta baryon resonances [10–14], meson condensates [15–21], quarks or even color superconducting quark matter [22–26]. Such degrees of freedom are usually associated with a softening of the equation of state (EoS), impacting the maximum mass and stability of stars [27, 28]."

"When hyperons are taken into account in relativistic mean field models, especial attention must be given to the hyperon-hyperon interaction modeling due to their internal strangeness degree of freedom. This is done through the introduction of φ and σ∗ mesons, which mediate the interaction among these particles by describing repulsion and attraction features, respectively [29]. The competition between softness and stiffness of the EoS due to the presence of hyperons has been widely discussed in the literature under the name of hyperon puzzle [2–4, 7, 8, 30– 36]."

"The MBF model reproduces both nuclear matter prop- erties at saturation and the observational properties of neutron stars with hyperons [2] and magnetic hybrid stars [55, 131].""

Here's a theoretical definition:

Def. any hadron that can decompose into another hadron or baryons is called a hyperon.

Mesons
Def. a composite subatomic particle bound together by the strong interaction "intermediate between electrons and protons" is called a meson.

Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometre, which is about 2/3 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 intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons.

Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles.

In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force.

Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa.

Mesons are subject to both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction.

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 thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would.

B mesons
"The K0-K0 bar, D0-D0 bar, and B0-B0 bar oscillations are extremely sensitive to the K0 and K0 bar energy at rest. The energy is determined by the values mc2 with the related mass as well as the energy of the gravitational interaction. Assuming the CPT theorem for the inertial masses and estimating the gravitational potential through the dominant contribution of the gravitational potential of our Galaxy center, we obtain from the experimental data on the K0-K0 bar oscillations the following constraint: |(mg/mi)K0 - (mg/mi)K0 bar| ≤ 8·10-13, CL=90%. This estimation is model dependent and in particular it depends on a way we estimate the gravitational potential. Examining the K0-K0 bar, B0-B0 bar, and D0-D0 bar oscillations provides us also with weaker, but model independent constraints, which in particular rule out the very possibility of antigravity for antimatter."

"In spite of the apparent parity non-invariance of the ordinary particles, the universe could still be left-right symmetric if [charge conjugation parity] CP were an exact symmetry[11]. But this option is [...] ruled out by experiments on kaons and B-mesons!)."

In the graphs on the right, the Large Hadron Collider beauty (LHCb) detector data for the production of B0 mesons, both for central and for forward rapidities, by pp collisions is compared with the theoretical predictions from the Positive Weight Hardest Emission Generator (POWHEG) and the automation of Monte Carlo (MC) at next-to-leading order (NLO) (aMC@NLO).

"The indicated theory uncertainty band includes only the scale uncertainties, and we have verified that parton distribution function (PDF) uncertainties are not so relevant in this case. As in the case of charm, satisfactory agreement between theory and data for B meson production in the forward region is found."

Psions
On the right is a graph of the production of psi mesons (psions) at Fermilab.

The "discovery of the psi meson in 1974, independently by Samuel C.C. Ting and Burton Richter [22, 23] [pointed out] its lifetime, which was about a thousand times longer than any other similar particle’s lifetime."

The "SLAC-LBL group looked between a pair of 100-MeV "milestones" and discovered the extremely narrow psi resonance that sent the counting rate up by more than a factor of 100, within the space of 1 MeV and within an observing time interval of 2 hours."

D mesons
In the graphs on the right are comparisons of general-mass variable-flavor-number scheme (GM-VFNS) predictions with experimental data on open D0 and  production in pp collisions collected by the A Large Ion Collider Experiment (ALICE) Collaboration at the Large Hadron Collider at CERN at √S = 7 TeV. These data represent likely fluxes arising from the decay of pp collisions produced by the interactions of high-energy cosmic rays in the Earth’s atmosphere.


 * $$D_S \rightarrow \tau + \bar{\nu}_{\tau} \rightarrow \nu_{\tau} + \bar{\nu}_{\tau}.$$

[a] PDG reports the resonance width (Γ). Here the conversion τ = $1/2$ is given instead.

Xis
Ξ0 has a rest mass of 1314.86 ± 0.20 MeV/c2.

Ξ− has a rest mass of 1321.71 ± 0.07 MeV/c2.

Ξ$1/2$ has a rest mass of 5787.8 ± 5.0 ± 1.3 MeV/c2.

Sigmas
Σ+ has a rest mass of 1189.37 ± 0.07 MeV/c2.

Σ0 has a rest mass of 1192.642 ± 0.024 MeV/c2.

Σ$1,968.47$ has a rest mass of 5815.5 +0.6 −0.5 ± 1.7 MeV/c2.

The symbols encountered in these lists are: I (isospin), J (total angular momentum), P (parity (physics)|parity), u (up quark), d (down quark), s (strange quark), c (charm quark), t (top quark), b (bottom quark), Q (electric charge), S (strangeness), C (charmness), B′ (bottomness), T (topness), as well as other subatomic particles (hover for name).

Antiparticles are not listed in the table; however, they simply would have all quarks changed to antiquarks (and vice versa), and Q, B, S, C, B′, T, would be of opposite signs. I, J, and P values in red have not been firmly established by experiments, but are predicted by the quark model and are consistent with the measurements.

JP = $1/2$+ Sigma baryons
† The standard model predicts that this particle cannot exist due to the short lifetime of the top quark. [a] PDG reports the resonance width (Γ). Here the conversion τ = $1/2$ is given instead. [b] The specific values of the name has not been decided yet, but will likely be close to (5810).

JP = $ħ/&Gamma;$+ Sigma baryons
† The standard model predicts that this particle cannot exist due to the short lifetime of the top quark. [c] PDG reports the resonance width (Γ). Here the conversion τ = $0 b$ is given instead.

Lambdas
Λ0 has a rest mass of 1115.683 ± 0.006 MeV/c2.

Λ$1,314.86$ has a rest mass of 2286.46 ± 0.146 MeV/c2.

On 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states in the decay of bottom Lambda baryons (Λ$1⁄2$).

Rest mass = 5619.4 ± 0.6 MeV/c2.

Phi mesons
The phi meson $$ \Phi^0 $$(1020) has a mass of 1019.445 MeV. It decays per
 * 1) $$ \Phi^0 \rightarrow \Kappa^+ + \Kappa^- or $$
 * 2) $$ \Phi^0 \rightarrow \Kappa^0_S + \Kappa^0_L. $$

"The scalar mesons σ and δ account for the description of attraction among baryons, while repulsion is described by the vector mesons ω, $$ \rho $$ and $$ \phi $$."

"The many-body forces (MBF) model [2] is a relativistic mean field model in which meson field dependences are introduced in the couplings of baryons to mesons."

The "$$ \phi $$ mesons mediates interaction among hyperons, providing extra repulsion, which plays an important role in the description of massive stars with hyperon content [29]."

The "whole fundamental baryon octet (n, p, Σ−, Σ0, Σ+, Λ, Ξ−, Ξ0) [is exhausted] and simulates n‐order corrections to the minimal Yukawa couplings by considering many‐body nonlinear self‐couplings and meson–meson interaction terms involving scalar–isoscalar (σ, σ*), vector–isoscalar (ω, ϕ), vector–isovector (ϱ), and scalar–isovector (δ) sectors."

"The hidden mesons do not couple with nucleons, so g𝛔*N = g𝚽N = 0. [...] the following value for the delta meson-nucleon coupling constant (Bednarek 2003): gδN = 3.1 [is chosen]."

Advanced "Laser Interferometer Gravitational‐Wave Observatory (aLIGO) and Gravitational Wave Interferomenter of the European Gravitational Observatory (VIRGO) detectors measured a value of [the tidal deformability parameter] in the event GW170817 (Abbott 2017), and it has been noticed that the values of [the tidal deformability parameter] ≤ 800 in the low‐spin case and [the tidal deformability parameter] ≤ 700 in the high‐spin case are within the 90% credible interval."

Results suggest each baryon-meson coupling can by "predictions of the tidal parameter represent a useful constraint of the EoS of neutron stars."

Omega mesons
"The detection of GW170817 and its electromagnetic counterparts allows us to constrain the equation of state of dense matter [... The] couplings [for equation of state (EoS) were set] with the omega and the rho meson to xωΔ = xρΔ = 1. [This choice is] motivated by several analyses of scattering data (electron and pion scattering off nuclei), suggesting a coupling with the sigma meson [is] stronger than the coupling with the omega meson [...]."

Omega meson production:
 * 1) $$p + d \rightarrow He^3 + \omega, $$
 * 2) $$\bar{p} + p \rightarrow \omega + \eta + \pi_0, $$
 * 3) $$\pi^- + p \rightarrow \omega + n, $$
 * 4) $$p + \bar{p} \rightarrow \Kappa^+ + \Kappa^- + \omega, $$
 * 5) $$p + \bar{p} \rightarrow \Kappa 1 + \Kappa 1 + \omega, $$

Omega meson ω(782) decay modes:
 * Γ1: $$ \omega \rightarrow \pi^+ + \pi^- + \pi^0, $$
 * Γ2: $$ \omega \rightarrow \pi^0 + \gamma, $$
 * Γ3: $$ \omega \rightarrow \pi^+ + \pi^-, $$
 * Γ4: $$ \omega \rightarrow neutrals (excluding: \pi^0 + \gamma), $$
 * Γ5: $$ \omega \rightarrow \eta + \gamma, $$
 * Γ6: $$ \omega \rightarrow \pi^0 + e^+ + e^-, $$
 * Γ7: $$ \omega \rightarrow \pi^0 + \mu^+ + \mu^-, $$
 * Γ8: $$ \omega \rightarrow \eta + e^+ + e^-, $$
 * Γ9: $$ \omega \rightarrow e^+ + e^-, $$
 * 1) Γ10: $$ \omega \rightarrow \pi^+ + \pi^- + \pi^0 + \pi^0, $$
 * 2) Γ11: $$ \omega \rightarrow \pi^+ + \pi^- + \gamma, $$
 * 3) Γ12: $$ \omega \rightarrow \pi^+ + \pi^- + \pi^+ + \pi^-, $$
 * 4) Γ13: $$ \omega \rightarrow \pi^0 + \pi^0 + \gamma, $$
 * 5) Γ14: $$ \omega \rightarrow \eta + \pi^0 + \gamma, $$
 * 6) Γ15: $$ \omega \rightarrow \mu^+ + \mu^-, $$
 * 7) Γ16: $$ \omega \rightarrow 3\gamma, $$
 * 8) Γ17: $$ \omega \rightarrow \eta + \pi^0, $$
 * 9) Γ18: $$ \omega \rightarrow 2\pi^0, and$$
 * 10) Γ19: $$ \omega \rightarrow 3\pi^0. $$

Rho mesons
Rho mesons occur in three states: ρ+, ρ-, and ρ0. The rest masses are apparently the same at 775.4±0.4 and 775.49±0.34. Decay products are π± + π0 or π+ + π-, respectively.

Def. a "short-lived hadronic isospin triplet" is called a rho meson.

With "a standard relativistic equation of state (GM3) [...] rho-meson condensates can appear in the core of the neutron star as the rho mass decreases with density and magnetic field. For reasonable values of the parameters, the rho condensate can appear in a neutron star at 4.4 times the normal nuclear matter density. This number guarantees a sizeable portion of the star to have a ρ-condensed phase."

Kaons
"The muons created through decays of secondary pions and kaons are fully polarized, which results in electron/positron decay asymmetry, which in turn causes a difference in their production spectra."

The "highest energy neutrinos from GRBs mainly come from kaons."

Sigma mesons
Two "parameterizations corresponding to two different values for the coupling of the delta resonances [are considered] with the sigma meson: xσΔ = 1.15 (SFHO+HD [(Drago et al. 2014b)]) and xσΔ = 1 (SFHO+HD2)[...] motivated by several analyses of scattering data (electron and pion scattering off nuclei) [...]."

Pions
Single π0 production occurs "in neutral current neutrino interactions with water by a 1.3 GeV wide band neutrino beam."

"The Gamma-Ray Spectrometer (GRS) on [Solar Maximum Mission] SMM has detected [...] at least two of the flares have spectral properties >40 MeV that require gamma rays from the decay of neutral pions. [Pion] production can occur early in the impulsive phase as defined by hard X-rays near 100 keV."

Gamma-ray "emission matches remarkably well both the position and shape of the inner [supernova remnant] SNR shocked plasma. Furthermore, the gamma-ray spectrum shows a prominent peak near 1 GeV with a clear decrement at energies below a few hundreds of MeV as expected from neutral pion decay."

"If protons are accelerated by the shock wave of a supernova remnant, they could interact with the surrounding interstellar gas to produce short-lived particles called π0 mesons, which in turn would decay to produce γ-rays at very high, TeV, energies (1 TeV = 1012 electron volts)."

Tauons
"For ultrahigh energies the neutrino spectrum at the detector is influenced by neutrino-nucleon interactions and tauon decays during the passage through the interior of the earth."

Strong forces
If there was no nuclear force, all nuclei with two or more protons would fly apart because of the electromagnetic repulsion.

Emissions
There is a "tight overlapping of the MeV photon flow [prompt MeV γ-ray emission] with the shocked regions [containing GeV photons produced in the shocks] [from supernovae ...] These high energy photons are absorbed by the MeV photon flow and generate relativistic e± pairs. [...] Overlapping also influence neutrino emission. Besides the [3 x] 1015 ~ [3 x] 1017 eV neutrino emission [from photomeson interaction] powered by the interaction of the shock accelerated protons with the synchrotron photons [...] there comes another 1014 neutrino emission component powered by protons interacting with the MeV photon flow."

Cosmic rays
Notation: let the symbol GZK represent Greisen-Zatsepin-Kuzmin.

Single π0 production occurs "in neutral current neutrino interactions with water by a 1.3 GeV wide band neutrino beam."

"The Gamma-Ray Spectrometer (GRS) on [Solar Maximum Mission] SMM has detected [...] at least two of the flares have spectral properties >40 MeV that require gamma rays from the decay of neutral pions. [Pion] production can occur early in the impulsive phase as defined by hard X-rays near 100 keV."

Gamma-ray "emission matches remarkably well both the position and shape of the inner [supernova remnant] SNR shocked plasma. Furthermore, the gamma-ray spectrum shows a prominent peak near 1 GeV with a clear decrement at energies below a few hundreds of MeV as expected from neutral pion decay."

"Neutral current single π0 production induced by neutrinos with a mean energy of 1.3GeV is measured at a 1000 ton water Cherenkov detector as a near detector of the K2K long baseline neutrino experiment."

"The single π0 production rate by atmospheric neutrinos could be usable to distinguish between the νµ ↔ ντ and νµ ↔ νs oscillation hypotheses. The NC rate is attenuated in the case of transitions of νµ’s into sterile neutrinos, while it does not change in the νµ ↔ ντ scenario."

Based on interactions between cosmic rays and the photons of the cosmic microwave background radiation (CMB) cosmic rays with energies over the threshold energy of 5x1019 eV interact with cosmic microwave background photons $$\gamma_{\rm CMB}$$ to produce pions via the $$\Delta$$ resonance,


 * $$\gamma_{\rm CMB}+p\rightarrow\Delta^+\rightarrow p + \pi^0,$$

or


 * $$\gamma_{\rm CMB}+p\rightarrow\Delta^+\rightarrow n + \pi^+.$$

Pions produced in this manner proceed to decay in the standard pion channels—ultimately to photons for neutral pions, and photons, positrons, and various neutrinos for positive pions. Neutrons decay also to similar products, so that ultimately the energy of any cosmic ray proton is drained off by production of high energy photons plus (in some cases) high energy electron/positron pairs and neutrino pairs.

The pion production process continues until the cosmic ray energy falls below the pion production threshold. Due to the mean path associated with this interaction, extragalactic cosmic rays traveling over distances larger than 50 Mpc (163 Mly) and with energies greater than this threshold should never be observed on Earth. This distance is also known as GZK horizon.

Subatomics
An "analysis of the energy-loss distributions in the GRS HEM during the impulsive phase of this event indicates that γ-rays from the decay of π0 mesons were detected [...] The production of pions, which is accompanied (on average) by neutrons, has an energy threshold of ~290 MeV for p-p and ~180 MeV for p-α interactions, giving, therefore, a lower limit to the maximum energy of the particles accelerated at the Sun."

Protons
For antiproton-proton annihilation at rest, a meson result is, for example,


 * $$p^+ + \bar{p}^- \rightarrow \pi^+ + \pi^-$$ and


 * $${\pi}^+ \rightarrow {\mu}^+ + {\nu}_{\mu} \rightarrow e^+ + {\nu}_e + {\bar{\nu}}_{\mu} + {\nu}_{\mu}.$$

Positrons
The creation of only one photon can occur for tightly bound atomic electrons. In the most common case, two photons are created, each with energy equal to the rest energy of the electron or positron (511 keV). It is also common for three to be created, since in some angular momentum states, this is necessary to conserve C parity. Any larger number of photons [can be created], but the probability becomes lower with each additional photon. When either the electron or positron, or both, have appreciable kinetic energies, other heavier particles can also be produced (such as D mesons), since there is enough kinetic energy in the relative velocities to provide the rest energies of those particles. Photons and other light particles may be produced, but they will emerge with higher energies.

Annihilations
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron. When a low-energy positron collides with a low-energy electron, annihilation occurs, resulting in the production of two or more gamma ray photons.

Def. the process of a particle and its corresponding antiparticle combining to produce energy is called annihilation.

The figure at right shows a positron (e+) emitted from an atomic nucleus together with a neutrino (v). Subsequently, the positron moves randomly through the surrounding matter where it hits several different electrons (e-) until it finally loses enough energy that it interacts with a single electron. This process is called an "annihilation" and results in two diametrically emitted photons with a typical energy of 511 keV each. Under normal circumstances the photons are not emitted exactly diametrically (180 degrees). This is due to the remaining energy of the positron having conservation of momentum.

Electron–positron annihilation occurs when an electron and a positron (, the electron's antiparticle) collide. The result of the collision is the annihilation of the electron and positron, and the creation of gamma ray photons or, at higher energies, other particles:


 * + &rarr;  +

The process [does] satisfy a number of conservation laws, including:


 * Conservation of electric charge. The net charge before and after is zero.
 * Conservation of linear momentum and total energy. This forbids the creation of a single gamma ray. However, in quantum field theory this process is [described]; see examples of annihilation.
 * Conservation of angular momentum.

As with any two charged objects, electrons and positrons may also interact with each other without annihilating, in general by elastic scattering.

At energies near and beyond the mass of the carriers of the weak force, the W and Z bosons, the strength of the weak force becomes comparable with electromagnetism. It becomes much easier to produce particles such as neutrinos that interact only weakly.

The heaviest particle pairs yet produced by electron–positron annihilation are – pairs. The heaviest single particle is the Z boson.

Annihilation radiation is not monoenergetic, unlike gamma rays produced by radioactive decay. The production mechanism of annihilation radiation introduces Doppler broadening. The annihilation peak produced in a gamma spectrum by annihilation radiation therefore has a higher full width at half maximum (FWHM) than other gamma rays in [the] spectrum. The difference is more apparent with high resolution detectors, such as Germanium detectors, than with low resolution detectors such as Sodium iodide. Because of their well-defined energy (511 keV) and characteristic, Doppler-broadened shape, annihilation radiation can often be useful in defining the energy calibration of a gamma ray spectrum.

Muons
A "measurement of the ratio of positive to negative muon fluxes from cosmic ray interactions in the atmosphere [has been made], using data collected by the CMS detector both at ground level and in the underground experimental cavern at the CERN LHC. Muons were detected in the momentum range from 5 GeV/c to 1 TeV/c. The surface flux ratio is measured to be 1.2766±0.0032 (stat.) ±0.0032 (syst.), independent of the muon momentum, below 100 GeV/c."

"The muon charge ratio R is defined as the ratio of the number of positive- to negative-charge atmospheric muons arriving at the Earth’s surface."

"These muons arise from showers produced in interactions of high-energy cosmic ray particles with air nuclei in the upper layers of the atmosphere. The magnitude and the momentum dependence of R are determined by the production and interaction cross sections of mesons (mainly pions and kaons), and by their decay lengths. As most cosmic rays and the nuclei with which they interact are positively charged, positive meson production is favoured, hence more positive muons are expected. Previous measurements from various experiments [1–8] showed the muon charge ratio to be constant up to a momentum of about 200 GeV/c, and then to increase at higher momenta, in agreement with the predicted rise in the fraction of muons from kaon decays. Measurements of the charge ratio can be used to constrain hadronic interaction models and to predict better the atmospheric neutrino flux."

"The Compact Muon Solenoid (CMS) [9] is one of the detectors installed at the Large Hadron Collider (LHC) [10] at CERN. The main goal of the CMS experiment is to search for signals of new physics in proton-proton collisions at centre-of-mass energies from 7 to 14 TeV [11]."

"Cosmic rays were used extensively to commission the CMS detector [12, 13]. These data can also be used to performmeasurements of physical quantities related to cosmic ray muons."

"About 25 million cosmic-muon events were recorded [on the Earth's surface] during the first phase of the MTCC with the magnet at a number of field values ranging from 3.67 to 4.00 T."

"The CRAFT08 campaign was a sustained data-taking exercise in October and November 2008 with the CMS detector fully assembled in its final underground position. The full detector, ready for collecting data from LHC, participated in the run, with the magnet at the nominal field of 3.8 T. Approximately 270 million cosmic-muon events were recorded."

"Single cosmic muons are simulated using the Monte Carlo event generator CMSCGEN [18, 19], which makes use of parameterizations of the distributions of the muon energy and incidence angle based on the air shower program CORSIKA [20]. The CMS detector response is simulated using the GEANT4 program [21], which takes into account the effects of energy loss, multiple scattering, and showering in the detector. A map [19] describing the various materials between the Earth’s surface and the CMS detector is used to obtain the average expected energy loss of simulated muons as a function of their energy, impact point, and incidence direction at the surface."

"Muon tracking in CMS can be performed with the all-silicon tracker at the heart of the detector, and with either three or four stations of muon chambers installed outside the solenoid, sandwiched between steel layers serving both as hadron absorbers and as a return yoke for the magnetic field."

"Three types of muon-track reconstruction were designed for cosmic muons not originating from an LHC proton-proton collision [22]: a standalone-muon track includes only hits from the muon detectors; a tracker track includes only hits from the silicon tracker; and a global muon track combines hits from the muon system and the silicon tracker in a combined track fit. For a cosmic muon that crosses the whole CMS detector, illustrated in Fig. 1 (top), each of the above types of tracks can be fitted separately in the top and bottom halves of CMS. Alternatively, a single track fit can be made including hits from the top and bottom halves of CMS. The direction of the muon is assumed to be downwards, and the muon charge is defined accordingly."

"The analysis based on 2006 MTCC data uses standalone muons."

"Since the muons were measured only in one half of the detector, the momentum resolution is poorer than in the standalone-muon analysis using the complete detector. Having the detector on the surface, however, permitted the collection of a large number of low-momentum muons, down to a momentum of 5 GeV/c, allowing for a precise measurement of the charge ratio in the low-momentum range."

Neutrinos
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest since observation of the phenomenon implies that the neutrino has a non-zero mass.

Plasma objects
When analyzing the outcome of some experiments with muons incident on a hydrogen bubble chamber in 1956, muon-catalysis of exothermic p-d, proton and deuteron, nuclear fusion was observed, which results in a helion, a gamma ray, and a release of about 5.5 MeV of energy.

In muon-catalyzed fusion there are more fusions because the presence of the muon causes deuterium nuclei to be 207 times closer than in ordinary deuterium gas.

Earth
A "measurement of the ratio of positive to negative muon fluxes from cosmic ray interactions in the atmosphere [has been made], using data collected by the CMS detector both at ground level and in the underground experimental cavern at the CERN LHC. Muons were detected in the momentum range from 5 GeV/c to 1 TeV/c. The surface flux ratio is measured to be 1.2766±0.0032 (stat.) ±0.0032 (syst.), independent of the muon momentum, below 100 GeV/c."

"The muon charge ratio R is defined as the ratio of the number of positive- to negative-charge atmospheric muons arriving at the Earth’s surface."

"These muons arise from showers produced in interactions of high-energy cosmic ray particles with air nuclei in the upper layers of the atmosphere. The magnitude and the momentum dependence of R are determined by the production and interaction cross sections of mesons (mainly pions and kaons), and by their decay lengths. As most cosmic rays and the nuclei with which they interact are positively charged, positive meson production is favoured, hence more positive muons are expected. Previous measurements from various experiments [1–8] showed the muon charge ratio to be constant up to a momentum of about 200 GeV/c, and then to increase at higher momenta, in agreement with the predicted rise in the fraction of muons from kaon decays. Measurements of the charge ratio can be used to constrain hadronic interaction models and to predict better the atmospheric neutrino flux."

Omegas
Ω$1⁄2$ has a rest mass of 2695.2 ± 1.7 MeV/c2.

Ω$2.9$ has a rest mass of 6071 ± 40 MeV/c2.

† Particle (or quantity, i.e. spin) has neither been observed nor indicated.

Deltas
Δ++ has a rest mass of 1,232 ± 2 MeV/c2.

Δ+ has a rest mass of 1,232 ± 2 MeV/c2.

Δ0 has a rest mass of 1,232 ± 2 MeV/c2.

Δ− has a rest mass of 1,232 ± 2 MeV/c2.

Upsilon mesons
The plot on the right shows a peak at about 9.5 GeV due to the Upsilon meson.

Eta mesons
Eta mesons (547.863 ± 0.018 MeV) have the decay schemes:
 * η : $$ \eta \rightarrow \gamma + \gamma, $$
 * η : $$ \eta \rightarrow \pi^0 + \pi^0 + \pi^0, or $$
 * η : $$ \eta \rightarrow \pi^+ + \pi^0 + \pi^-, $$

Eta prime mesons (957.78 ± 0.06 MeV) have the decay schemes:
 * 1) η' : $$ \eta^' \rightarrow \pi^+ + \pi^- + \eta or $$
 * 2) η' : $$ \eta^' \rightarrow \pi^0 + \pi^0 + \gamma, $$

The charmed eta meson ηC(1S) has a rest mass of 2983.6 ± 0.7 MeV.

Hypotheses

 * 1) Although subluminal mesons are short-lived, they can be accelerated to near-luminal speeds so that they are detectable either directly or by their decay products.