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Compilation is shown of the measurements of the total extragalactic gamma-ray intensity between 1 keV and 820 GeV, with different components from current models. Credit: The e-ASTROGAM Collaboration.{{free media}}

"Previously, it was suggested that the [dark matter] DM consists of [weakly interacting massive particles] WIMPs that naturally emerge from the super-symmetric extension of the Standard model. Such a WIMP particle was predicted to have a mass of the order of 100 GeV. However, no such particle has been experimentally found and the search for DM candidates is now being broadened into other directions. Recently, the idea of involving a complete hidden sector of new particles was revitalized."[1]


Theoretical tauon astronomyEdit

Def. "an elementary particle, a lepton, having a mass almost twice that of a proton and a negative charge"[2] is called a tauon.

Def. "the antiparticle of the tauon"[3] is called an antitauon.

Koide formulaEdit

The Koide formula is


where the masses of the electron, muon, and tau are measured respectively as me = 0.510998946(3) MeV/c2, mμ = 105.6583745(24) MeV/c2, and mτ = 1,776.86(12) MeV/c2, and the digits in parentheses are the uncertainties in the last figures.[4] This gives Q = 0.666661(7).

Since the uncertainties in me and mμ are much smaller than that in mτ, the uncertainty in Q was calculated as  .

It is clear that no matter what particles are chosen to stand in place of the electron, muon, and tau, 13 ≤ Q < 1. The upper bound follows from the fact that the square roots are necessarily positive. The lower bound follows from the Cauchy–Schwarz inequality, and also from the fact that the value   can be interpreted as the squared cosine of the angle between the vector   and the vector   (see dot product).

The mystery is in the physical value. Not only is this result odd in that three apparently arbitrary numbers should give a simple fraction, but also that Q (in the case of electron, muon, and tau) is exactly halfway between the two extremes of other particle combinations: ​13 (should the three masses be equal) and 1 (should one mass dominate). The value of Q = ​23 corresponds to mτ = 1,776.969 MeV/c2.

While the original formula appeared in the context of preon models, other ways have been found to produce it (both by Sumino and by Koide, see references below). As a whole, however, understanding remains incomplete. Similar matches have been found for triplets of quarks depending on running masses.[5][6][7] With alternating quarks, chaining Koide equations for consecutive triplets, it is possible to reach a result of 173.263947(6) GeV for the mass of the top quark.[8]

There are similar empirical formulae which relate other masses. Quark masses depend on the energy scale used to measure them, which makes an analysis more complicated.

Taking the heaviest three quarks, charm (1.275 ± 0.03 GeV), bottom (4.180 ± 0.04 GeV) and top (173.0 ± 0.40 GeV), and without using their uncertainties gives the value cited,[9]


This was noticed by Rodejohann and Zhang in the first version of their 2011 article[10] but the observation was removed in the published version,[5] so the first published mention is in 2012.[9]

Similarly, the masses of the lightest quarks, up (2.2 ± 0.4 MeV), down (4.7 ± 0.3 MeV), and strange (95.0 ± 4.0 MeV), without using their experimental uncertainties yield,


In quantum field theory, quantities like coupling constant and mass "run" with the energy scale. That is, their value depends on the energy scale at which the observation occurs, in a way described by a renormalization group equation (RGE).[11] One usually expects relationships between such quantities to be simple at high energies (where some symmetry is unbroken) but not at low energies, where the RG flow will have produced complicated deviations from the high-energy relation. The Koide relation is exact (within experimental error) for the pole masses, which are low-energy quantities defined at different energy scales. For this reason, many physicists regard the relation as "numerology" (e.g.[12]). Mechanisms may explain origins of the charged lepton spectrum as well as the Koide formula, e.g., by constructing an effective field theory in which a new gauge symmetry causes the pole masses to exactly satisfy the relation.[13] A discussion on pole masses shows how the Koide formula can be reformulated without taking the square roots of masses.[14]

Electromagnetic loopsEdit

"The particle known as the muon has the same negative charge as the electron and the same spin (intrinsic angular momentum) but is considerably heavier than the electron. It may well be that the muon is a single wavelength photon twisted into a tight 4-loop helix. The pattern of magnetic and electric vectors would still be the same as for the electron. This argument may also be extended to the tauon — a super heavy version of the electron."[15]

"There is also a way to model the property of spin. Every elementary particle must possess, in addition to a characteristic mass, a certain spin (its intrinsic angular momentum). The looping and twisting motion of the confined photon is ideal for establishing a correspondence with a particle’s spin property."[15]

"According to the new paradigm, all particles consist of electromagnetic loops (or loops of loops) — all particles are essentially confined photons. When these loops are complete, resonant, and harmonic they represent independent particles, such as the electron, muon, and tauon (and their antiparticle versions)."[15]

Revised Quantum ElectrodynamicsEdit

"In all particle models of [the Revised Quantum Electrodynamic theory] RQED the source terms due to broken symmetry give rise to steady states having a nonzero rest mass and an associated nonzero spin [which] applies to particles with net charge such as the electron, muon, and tauon where the product m0M0 [...] of rest mass and magnetic moment is given a nonzero quantity. Such particles are prevented by the included magnetic field from “exploding” under the action of their electrostatic eigenforce."[16]

"Particles with net integrated electric charge, such as the electron, muon, and tauon, are given by divergent corresponding generating functions and point-charge-like geometries".[16]


"In realistic unified models involving so-called SO(10)-inspired patterns of Dirac and heavy right-handed (RH) neutrino masses, the lightest right-handed neutrino N1 is too light to yield successful thermal leptogenesis, barring highly fine tuned solutions, while the second heaviest right-handed neutrino N2 is typically in the correct mass range."[17]

Flavour "coupling effects in the Boltzmann equations may be crucial to the success of such N2 dominated leptogenesis, by helping to ensure that the flavour asymmetries produced at the N2 scale survive N1 washout."[17]

The "only relevant asymmetry is that one produced at the N2 scale in the tauon flavour".[17]

"This implies that, at least at lower order, the observed asymmetry can only be produced in the tauon flavour".[17]

The "asymmetry is mainly produced by the next-to-lightest RH neutrinos in the tauon flavour but this asymmetry is fully washed-out by the lightest RH neutrinos since the condition K ≲􏰗 1 is not compatible with the measured values of the mixing parameters."[17]

One "has also to consider that part of the asymmetry in the tauon flavour is transferred to the electron and muon flavours by flavour coupling effects due primarily to the fact that N2-decays produce in addition to an asymmetry in the tauon lepton doublets also an (hyper charge) asymmetry in the Higgs bosons. This Higgs asymmetry unavoidably induces, through the inverse decays, also an asymmetry in the lepton doublets that at the production are a coherent admixture of electron and muon components. Therefore, in this case, inverse decays actually produce an asymmetry instead of wash it out as in a traditional picture."[17]

"It should be noticed how the source of the electron and muon asymmetries is in any case the tauon asymmetry, but part of this induces a muon and an electron asymmetry thanks to flavour coupling."[17]

"The A to Z model can not only provide a satisfactory fit to all parameters in the leptonic mixing matrix but can also reproduce the correct value of the matter-antimatter asymmetry with N2-dominated leptogenesis. In this respect it is crucial to account for flavour coupling effects due to the redistribution of the asymmetry in particles that do not participate directly to the generation of the asymmetry, in primis the Higgs asymmetry. In particular a “flavour swap” scenario is realised whereby the asymmetry generated in the tauon flavour emerges as a surviving asymmetry dominantly in the muon flavour. The solution works even in the simplest case where the neutrino Dirac mass matrix is equal to the up quark mass matrix."[17]

"The muon and the tauon are unstable and after a while they decay into electrons."[18]

Dark matter particlesEdit

The “continuum” and “line” positron spectra from LKP annihilations for mB(1) = 1000 GeV. Credit: Satoshi Tsuchida and Masaki Mori.{{fairuse}}

"The fact that most of the matter in the Universe consists of non–baryonic dark matter1 is supported further by the Planck observational data,2 and dark matter should be made of particles which do not exist in the standard model of particle physics. Recent observations of cosmic positron excess3–5 could be explained by secondarily produced positrons in annihilation of dark matter particles in the Galactic halo, as is discussed by many authors (see, e.g. Refs.6–8). Among various candidates of dark matter, the lightest Kaluza–Klein particle (LKP), predicted in the theory of universal extra dimensions (UED),9–11 is unique since there would be a characteristic edge structure in the cosmic electron plus positron spectrum near the LKP mass as Cheng et al.12 predicted. The edge structure was calculated by Moiseev et al.13 for Fermi–LAT detection, but, at least in the energy range below 1000 GeV, such structure has not established so far (see, e.g. Refs.4, 14, 15). On the other hand, above 1000 GeV, the observational data are still limited, so the characteristic structure could be observed in near–future missions. For example, the Calorimetric Electron Telescope (CALET), which is a Japanese–led detector and is a fine resolution calorimeter for cosmic–ray observation installed on the International Space Station in August 2015, started exploring the energy range up to 20 TeV for electrons and positrons.16"[19]

"When LKP pairs annihilate, there are some modes which produce electrons and positrons as final products, and we categorize them into two components. One of them is a “line” component, which consists of electron–positron pairs directly produced by annihilation, and gives rise to edge structure near the LKP mass after propagating in the Galactic halo to Earth. Another is a “continuum” component, which consists of secondarily produced electrons and positrons via muon pairs, tauon pairs, quark pairs, and gauge bosons produced by LKP annihilation. The branching ratios are given as follows: 20% for charged leptons, 11% for up–type quarks, 0.7% for down–type quarks, 1% for charged gauge bosons, and 0.5% for neutral gauge bosons, respectively.11,20 We use the spectra for line and continuum components given by Cirelli et al.21 and Ciafaloni et al.,22 which are shown in [the graphs on the right] assuming 100% branching ratios for each component, where the solid line indicates the line spectrum and patterned lines show the continuum spectra from muon pairs, tauon pairs, quark pairs (b, t, c), and gauge bosons, respectively. Note that the line spectra shows a tail toward lower energies due to final state interactions. For comparison, the positron spectra without electroweak corrections are shown in thin lines for the line spectrum and the continuum spectrum for muon pairs. One can see the electroweak correction affects the spectra in the lower energy region.21, 22"[19]

"Even though neither the nature of the DM particle(s) (χ) nor the mechanism that generates it are known, there are indirect experimental evidences suggesting that χ is indeed a weakly interacting particle. Given that, it is natural to assume that the annihilation, and/or its decay, will involve leptons [...] These can be electrons and positrons, but also muons, which can be generated via annihilation χ + χ → μ+ + μ and/or decay χ → μ+ + μ. It should be noted, however, that a similar scenario is not forbidden for the τ particles either, but the cross-section for formation of a two-tauon bound state is negligible, and hence, the observation of a signature of true taonium is considered to be less likely [460]. The advantage of using muonium annihilation lines for the search of DM particles is that the muon mass is much larger than the e± and, hence, the expected signal will be cleaner."[1]


"High energy neutrinos may interact to produce a large cascade of particles. In this case, the production of Cherenkov light remains localized and the photons propagation radially outward (well, almost). The effective volume of AMANDA is much smaller for cascades than muons and the angular resolution is very poor, but there are several interesting features of cascades that make them useful to study. First, the energy resolution of the cascade event can be measured with much better precision relative to the muon signature if the vertex of the interaction is contained. Second, the backgrounds from atmospheric electron neutrinos is much smaller than muon neutrinos at these energies because the decay of atmospheric muons is suppressed by time dilation. Third, cascades are produced by electron neutrinos and tau neutrinos so the ratio of cascades to muon neutrino events provides insight on the properties of neutrino oscillation. Fourth, even downgoing neutrinos can be observed if the energy is larger than ~10 TeV. Thus, the cascade technique is sensitive to neutrinos from any direction."[20]

"Like with accelerator physics, most of the interest [in] neutrino astrophysics is at the extreme energy frontier, which we label "extreme high energy" or EHE. Perhaps the most reliable flux predictions (after atmospheric neutrinos) involve the GZK mechanism. Neutrinos are produced by the inevitable collisions between cosmic rays and the cosmic microwave background. Although the physics required by GZK mechanism is straightforward, the GZK mechanism is still in doubt because one of its predictions has not yet been confirmed. The GZK mechanism predicts are rather strong upper limit on the energy of the cosmic ray, but this upper limit has not yet been clearly identified."[20]

"Experimentally, neutrinos at EHE energies are difficult to detect. As the neutrino energies increase to 1 PeV (1015 eV), the earth becomes opaque except near the horizon. We have developed a new technique to search for "downgoing" nearly horizontal muons. They can be distinguished from the blizzard of downgoing muons from cosmic ray collisions because the energies are much higher than muons generated by cosmic ray collisions. Consequently, the topologies of the events [...] are quite different from the typical event. [A] large number of OMs [...] observe Cherenkov light. The effective detection area for muons at these energies is very large, typically 0.2 km2 for AMANDA-B10!"[20]

"The effective detection area of AMANDA-II is even larger than B10. In addition, we upgraded the data acquisition system of AMANDA-II. The new system records the complete waveform from all (usable) OMs in the array. This should dramatically improve the dynamic range of the photon measurement and allow far better energy reconstruction for these high energy events."[20]

"The EHE analysis relies on training a neural net (NN2) to separate background from signal."[20]


The tau lepton is predicted to form exotic atoms like other charged subatomic particles. One of such, called tauonium by the analogy to muonium, consists of an antitauon and an electron: τ+

Def. "a subatomic particle formed by the bound state of a matter tauon with its antimatter partner antitauon"[22] is called tauonium.

Another one is an onium atom τ+
called true tauonium and is difficult to detect due to tau's extremely short lifetime at low (non-relativistic) energies needed to form this atom. Its detection is important for quantum electrodynamics.[21]

"An interesting possibility is the formation of the analogous leptonic atoms, true muonium μ −μ+ and true tauonium τ − τ+. Initial considerations[74] were dismissed due to the short decay times of the constituent particles[75,76]. Recently however, we have revisited the question of leptonium in astrophysical environments[77]."[23]

"Because of the intrinsic instability of the particles to decay, leptonium atoms will only form for a small fraction, ∼ 10−6 – 10−7, of pairs produced with energies less than the ionisation energy of the atoms. Of these pairs, most will form leptonium, the cross-section for annihilation being much smaller under astrophysical conditions. After formation, it is possible to again produce recombination lines before annihilation, though this is complicated by the fact that the constituent particles may decay."[23]

"Nevertheless, there are significant branching ratios for both two photon annihilation and recombination lines for true muonium and small probabilities for true tauonium. Furthermore, even improbable transitions may give rise to significant signatures if the lepton pairs are produced in sufficient quantity - a situation which is common in high energy astrophysical environments. [...] In practice, leptonium formation within micro-quasar jet-star interactions, or within the accretion discs of both AGN and micro-quasars could yield signatures brighter than current detection limits, with those from micro-quasars offering the brightest estimates due to their proximity."[23]

"Analogously to the formation of positronium, it is possible to form atoms of true muonium and true tauonium. Since muons and tauons are intrinsically unstable, the formation of such leptonium atoms will be localised to their places of origin. Thus observations of true muonium or true tauonium can provide another way to distinguish between truly diffuse sources such as dark matter decay, and an unresolved distribution of point sources."[23]


This "neutrino image" of the Sun is produced by using the Super-Kamiokande to detect the neutrinos from nuclear fusion coming from the Sun. Credit: R. Svoboda and K. Gordan (LSU), and NASA.

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,

 [25] and

"All other sources of ντ are estimated to have contributed an additional 15%."[26]


for two neutrinos.[26]


where   is a hadron, for two neutrinos.[26]

B mesonsEdit

Comparison of the LHCb data on B0 meson production, both for central and for forward rapidities, with the theoretical predictions from POWHEG and aMC@NLO. Credit: Rhorry Gauld, Juan Rojo, Luca Rottoli and Jim Talbert.{{fairuse}}

"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."[27]

"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!)."[28]

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."[29]

B mesons
Particle Symbol Anti-particle Quark
Charge Isospin
Spin and parity
Rest mass
strangeness (S charm (C) bottomness (B') Mean lifetime
Commonly decays to
B meson B+ B- u  +1 1/2 0 5,279.29±0.15 0 0 +1 1.638±0.004×10−12
See   decay modes
B meson B0     0 1/2 0 5,279.61±0.16 0 0 +1 1.520±0.004×10−12
See B0 decay modes
Strange B meson     s  0 0 0 5,366.79±0.23 −1 0 +1 1.510±0.005×10−12
See Strange B0 decay modes
Charmed B meson     c  +1 0 0 6,275.1±1.0 0 +1 +1 0.507±0.009×10−12
See   decay modes


J/Ψ production is graphed. Credit: Fermilab.

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."[30]

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."[31]

Hadronic decay modes of J/ψ are strongly suppressed because of the OZI Rule, Susumu Okubo, George Zweig and Jugoro Iizuka in the 1960s[32][33][34] which strongly increases the lifetime of the particle and thereby gives it a very narrow decay width of just 93.2±2.1 keV, electromagnetic decays begin to compete with hadronic decays, and the J/ψ has a significant branching fraction to leptons:[35]

cc → ggg (64.1 ± 1.0)%
cc → γgg (8.8 ± 0.5)%
cc → γ (~25.4)%
γ→ hadrons (13.5 ± 0.3)%
γ→ e+e- (5.94 ± 0.06)%
γ→ μ+μ- (5.93 ± 0.06)%


has a rest mass of 2695.2 ± 1.7 MeV/c2.[36]

has a rest mass of 6071 ± 40 MeV/c2.[36]

class=unsortable Particle Symbol Quark
Rest mass
(electron volt MeV/speed of light c2)
Spin (physics) JParity (physics) P charge (physics) Q
(elementary charge e)
strangeness S charm (quantum number) C bottomness Mean lifetime
(second s)
class=unsortable Decays to
Charmed omega[37] Ω0
ssc 2,697.5±2.6 1/2+ 0 −2 +1 0 6.9±1.2×10−14
See Ω0
Decay Modes
Bottom omega[38] Ω
ssb 6,054.4±6.8 1/2+ −1 −2 0 −1 1.13±0.53×10−12
+ J/ψ
Double charmed omega† Ω+
scc 1/2+ +1 −1 +2 0
Charmed bottom omega† Ω0
scb 1/2+ 0 −1 +1 −1
Double bottom omega† Ω
sbb 1/2+ −1 −1 0 −2
Triple charmed omega† Ω++
ccc 3/2+ +2 0 +3 0
Double charmed bottom omega† Ω+
ccb 1/2+ +1 0 +2 −1
Charmed double bottom omega† Ω0
cbb 1/2+ 0 0 +1 −2
Triple bottom omega† Ω
bbb 3/2+ −1 0 0 −3

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


has a rest mass of 5787.8 ± 5.0 ± 1.3 MeV/c2.[36]

Xi baryons[39][40][41][42]
class=unsortable Particle Symbol Makeup Rest mass
electron volt MeV/speed of light c2
Isospin I
Spin (physics) Spin (Parity (physics) parity)
Spin (physics) JParity (physics) P
charge (physics) Q strangeness S charm (quantum number) C bottomness B Mean lifetime
second s
class=unsortable Decays to
charmed Xi[43] Ξ+
usc 2,467.9±0.4 1/2 1/2* +* +1 −1 +1 0 4.42±0.26×10−13
See Ξ+
Decay Modes
charmed Xi[43] Ξ0
dsc 2,471.0±0.4 1/2 1/2* +* 0 −1 +1 0 1.12+0.13
See Ξ0
Decay Modes
charmed Xi resonance [43] Ξ′+
usc 2,575.7±3.1 1/2 1/2+[a] +1 −1 +1 0 Ξ+
+ γ (Seen)
charmed Xi resonance [43] Ξ′0
dsc 2,578.0±2.9 1/2 1/2+[a] 0 −1 +1 0 1.1×10−13
+ γ (Seen)
Ξcc++ double charmed Xi[44] Ξ++
ucc 3621.40 ± 0.72 ± 0.27 ± 0.14 1/2* 1/2* +* +2 0 +2 0  ±0.014×10−12 [45] Λ+
+ K
+ π+
+ π+
double charmed Xi[b] [46] Ξ+
dcc 3,518.9±0.9[b] 1/2* 1/2* +* +1 0 +2 0 <3.3×10−14
+ K
+ π+
[e] or
+ D+
+ K
bottom Xi [47] Ξ0
usb 5,792±3 1/2* 1/2* +* 0 −1 0 −1 1.42+0.28
See Ξ
Decay Modes
bottom Xi or
Cascade B[39][42][47][48]
dsb 5,792.9±3.0 1/2* 1/2* +* −1 −1 0 −1 1.42×10−12
See Ξ
Decay Modes

+ J/ψ
was also seen)
dsb 5935.02 ± 0.02 ± 0.01± 0.50 1/2+ −1 −1 0 −1
dsb 5955.33 ± 0.12 ± 0.06 ± 0.50 3/2+ −1 −1 0 −1
dsb 6226.9 ± 2.0 ± 0.3 ± 0.2 −1 −1 0 −1 Λ
+ K

+ π
double bottom Xi[a] Ξ0
ubb 1/2* 1/2* +* 0 0 0 −2
double bottom Xi[a] Ξ
dbb 1/2* 1/2* +* −1 0 0 −2
charmed bottom Xi[a] Ξ+
ucb 1/2* 1/2* + +1 0 +1 −1
charmed bottom Xi[a] Ξ0
dcb 1/2* 1/2* +* 0 0 +1 −1
  1. 1.0 1.1 1.2 1.3 1.4 1.5 Particle (or quantity, i.e. spin) has neither been observed nor indicated
  2. 2.0 2.1 2.2 Some controversy exists about this data. See references
  3. This is actually a measurement of the average lifetime of b-baryons that decay to a jet containing a same-sign Ξ± l± pair. Presumably the mix is mainly Ξ
    , with some Λ


has a rest mass of 5815.5 +0.6 −0.5 ± 1.7 MeV/c2.[36]

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.[51][52]

JP = 1/2+ Sigma baryonsEdit

JP = 1/2+ Sigma baryons
Particle name Symbol Quark
MeV/speed of light|c2) Isospin|I Total angular momentum|JParity (physics)|P charge (physics)|Q (elementary charge|e) strangeness|S charm (quantum number)|C bottomness|B' topness|T s) Commonly decays to
charmed Sigma[53] Σ++
uuc 2,454.02 ± 0.18 1 1/2 + +2 0 +1 0 0 3.0 ± 0.4 × 10−22[a] Λ+
+ π+
charmed Sigma[53] Σ+
udc 2,452.9 ± 0.4 1 1/2 + +1 0 +1 0 0 >1.4 × 10−22[a] Λ+
+ π0
charmed Sigma[53] Σ0
ddc 2,453.76 ± 0.18 1 1/2 + 0 0 +1 0 0 3.0 ± 0.5 × 10−22[a] Λ+
+ π
bottom Sigma[54] Σ+
uub 5,807.7 ± 3.8 1 1/2 + +1 0 0 −1 0 Unknown Λ0
+ π+
bottom Sigma Σ0
udb Unknown 1 1/2 + 0 0 0 −1 0 Unknown Unknown
bottom Sigma[54] Σ
ddb 5,815.2 ± 2.7 1 1/2 + −1 0 0 −1 0 Unknown Λ0
+ π
Top Sigma Σ++
uut 1 1/2 + +2 0 0 0 +1
Top Sigma Σ+
udt 1 1/2 + +1 0 0 0 +1
Top Sigma Σ0
ddt 1 1/2 + 0 0 0 0 +1

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 = ħ/Γ is given instead.
[b] The specific values of the name has not been decided yet, but will likely be close to Σ

JP = 3/2+ Sigma baryonsEdit

JP = 3/2+ Sigma baryons
Particle name Symbol Quark
MeV/speed of light|c2) Isospin|I Total angular momentum|JParity (physics)|P charge (physics)|Q (elementary charge|e) strangeness|S charm (quantum number)|C bottomness|B' topness|T s) Commonly decays to
charmed Sigma[55] Σ∗++
uuc 2,518.4 ± 0.6 1 3/2 + +2 0 +1 0 0 4.4 ± 0.6 × 10−23[c] Λ+
+ π+
charmed Sigma[55] Σ∗+
udc 2,517.5 ± 2.3 1 3/2 + +1 0 +1 0 0 >3.9 × 10−23[c] Λ+
+ π0
charmed Sigma[55] Σ∗0
ddc 2,518.0 ± 0.5 1 3/2 + 0 0 +1 0 0 4.1 ± 0.5 × 10−23[c] Λ+
+ π
bottom Sigma Σ∗+
uub Unknown 1 3/2 + +1 0 0 −1 0 Unknown Unknown
bottom Sigma Σ∗0
udb Unknown 1 3/2 + 0 0 0 −1 0 Unknown Unknown
bottom Sigma Σ∗−
ddb Unknown 1 3/2 + −1 0 0 −1 0 Unknown Unknown
Top Sigma Σ∗++
uut 1 3/2 + +2 0 0 0 +1
Top Sigma Σ∗+
udt 1 3/2 + +1 0 0 0 +1
Top Sigma Σ∗0
ddt 1 3/2 + 0 0 0 0 +1

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 = ħ/Γ is given instead.


has a rest mass of 2286.46 ± 0.146 MeV/c2.[56]

On 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states in the decay of bottom Lambda baryons (Λ0

Rest mass = 5619.4 ± 0.6 MeV/c2.

D mesonsEdit

Comparison of GM-VFNS predictions with experimental data on open D0 (D0
) and D±
production in pp collisions collected by the ALICE Collaboration at √S = 7 TeV. Credit: Michael Benzke, Maria V. Garzelli and Bernd A. Kniehl.{{fairuse}}

In the graphs on the right are comparisons of general-mass variable-flavor-number scheme (GM-VFNS) predictions with experimental data on open D0 (D0
) and D±
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 mesons
Particle name Particle
Rest mass (MeV/speed of light|c2) IG JPC S C B' Mean lifetime (s) Commonly decays to

(>5% of decays)

D meson[58]

1,869.62 ± 0.20 12 0 0 +1 0 1.040 ± 0.007 × 10−12 See
decay modes
D meson[59]

1,864.84 ± 0.17 12 0 0 +1 0 4.101 ± 0.015 × 10−13 See
decay modes
Strange D meson[60]

1,968.47±0.33 0 0 +1 +1 0 (5.00±0.07) x 10-13 See
decay modes
D meson[61]

2,010.27.62 ± 0.17 12 1 0 +1 0 6.9 ± 1.9 × 10−21[a]
+ π+ or

+ π0
D meson[62]

2,006.97 ± 0.19 12 1 0 +1 0 >3.1 × 10−22[a]
+ π0 or

+ γ

[a] PDG reports the resonance width (Γ). Here the conversion τ = ​ħΓ is given instead.

Pair productionEdit

The reverse reaction, electron–positron creation, is a form of pair production governed by two-photon physics.

Two-photon physics, also called gamma-gamma physics, [studies] the interactions between two photons. If the energy in the center of mass system of the two photons is large enough, matter can be created.[63]

γ → e
 + e+

In nuclear physics, [the above reaction] occurs when a high-energy photon interacts with a nucleus. The photon must have enough energy [> 2*511 keV, or 1.022 MeV] to create an electron plus a positron. Without a nucleus to absorb momentum, a photon decaying into electron-positron pair (or other pairs for that matter [such as a muon and anti-muon or a tau and anti-tau] can never conserve energy and momentum simultaneously. [64]

These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber. In 2008 the Titan laser aimed at a 1-millimeter-thick gold target was used to generate positron–electron pairs in large numbers.[65] "The LLNL scientists created the positrons by shooting the lab's high-powered Titan laser onto a one-millimeter-thick piece of gold."[65]


Feynman diagram shows the common decays of the tau by emission of an off-shell W boson. Credit: JabberWok and Time3000.
The arrival direction of the anomalous CR event and air shower are described. Credit: P. W. Gorham, B. Rotter, P. Allison, O. Banerjee, L. Batten, J. J. Beatty, K. Bechtol, K. Belov, D. Z. Besson, W. R. Binns, V. Bugaev, P. Cao, C. C. Chen, C. H. Chen, P. Chen, J. M. Clem, A. Connolly, L. Cremonesi, B. Dailey, C. Deaconu, P. F. Dowkontt, B. D. Fox, J. W. H. Gordon, C. Hast, B. Hill, K. Hughes, J. J. Huang, R. Hupe, M. H. Israel, A. Javaid, J. Lam, K. M. Liewer, S. Y. Lin, T.C. Liu, A. Ludwig, L. Macchiarulo, S. Matsuno, C. Miki, K. Mulrey, J. Nam, C. J. Naudet, R. J. Nichol, A. Novikov, E. Oberla, M. Olmedo, R. Prechelt, S. Prohira, B. F. Rauch, J. M. Roberts, A. Romero-Wolf, J. W. Russell, D. Saltzberg, D. Seckel, H. Schoorlemmer, J. Shiao, S. Stafford, J. Stockham, M. Stockham, B. Strutt, G. S. Varner, A. G. Vieregg, S. H. Wang, S. A. Wissel.{{fairuse}}
The second of three ANITA missions as part of NASA’s Antarctica Long Duration Balloon Flight Campaign was successfully launched at 8:10 a.m. EDT, Dec. 2, 2016. Credit: NASA Goddard Space Flight Center from Greenbelt, MD, USA.{{free media}}

"The other two types of electrically charged leptons in the Standard Model, which can annihilate into photons, are the muons μ and tauons τ with masses Mμ = 105.6 MeV and Mτ =1777 MeV, respectively [466]. It is worth noting that in contrast to the electrons and positrons, the muons and the tauons can not be produced in radioactive decays of atomic nuclei, owing to their superior masses. As such, the maps based on the μ+ + μ and/or τ+ + τ annihilation peaks can provide a cleaner signal and a new information about the sites of enhanced [dark matter] DM concentration which would be complementary to the data obtained from the 511-keV surveys."[1]

The tau was detected in a series of experiments between 1974 and 1977.[66][67][68]

"We have discovered 64 events of the form e+
+ e
+ μ
+ at least two undetected particles for which we have no conventional explanation."[66]

"The advantage of using unstable leptons, rather than using electrons, for tracing DM particles is in their finite lifetime. The tauons have a lifetime of 2.9 × 10−13 s, while the muons have lifetimes of 2.2 μs. Their finite lifetimes provide an unique opportunity for mapping of DM regions with an enhanced precision. Thus, for example, DM particles with masses of the order of Mχ = 100 GeV can either annihilate or decay into muons."[1]

Tau mass is 1776.86 ± 0.12 MeV/c2,[69] mean lifetime is 2.903 ±0 .005 x 10-13 s,[69] electric charge = −1 e,[69] and spin is 1/2[69].

"Since a tauon decays into a light meson (lepton) with neutrino(s), the measurements of angular distribution for tauon on   → D(∗)τ  are difficult."[70]

The tau is the only lepton that can decay into hadrons – the other leptons do not have the necessary mass. Like the other decay modes of the tau, the hadronic decay is through the weak interaction.[71]

The branching ratio of the dominant hadronic tau decays are:[69]

  • 25.49% for decay into a charged pion, a neutral pion, and a tau neutrino;
  • 10.82% for decay into a charged pion and a tau neutrino;
  • 9.26% for decay into a charged pion, two neutral pions, and a tau neutrino;
  • 8.99% for decay into three charged pions (of which two have the same electrical charge) and a tau neutrino;
  • 2.74% for decay into three charged pions (of which two have the same electrical charge), a neutral pion, and a tau neutrino;
  • 1.04% for decay into three neutral pions, a charged pion, and a tau neutrino.

In total, the tau lepton will decay hadronically approximately 64.79% of the time.

Since the tauonic lepton number is conserved in weak decays, a tau neutrino is always created when a tau decays.[71]

The branching ratio of the common purely leptonic tau decays are:[69]

  • 17.82% for decay into a tau neutrino, electron and electron antineutrino;
  • 17.39% for decay into a tau neutrino, muon and muon antineutrino.

The similarity of values of the two branching ratios is a consequence of lepton universality.

The tau was anticipated.[72]

An "upward traveling, radio-detected cosmic-ray-like impulsive event [has] characteristics closely matching an extensive air shower. This event, observed in the third flight of the Antarctic Impulsive Transient Antenna (ANITA), a NASA-sponsored long-duration balloon payload, is consistent with a similar event reported in a previous flight. These events may be produced by the atmospheric decay of an upward-propagating τ-lepton produced by a ντ interaction, although their relatively steep arrival angles create tension with the standard model (SM) neutrino cross section. Each of the two events have a posteriori background estimates of ≲10−2 events. If these are generated by τ-lepton decay, then either the charged-current ντ cross section is suppressed at EeV energies, or the events arise at moments when the peak flux of a transient neutrino source was much larger than the typical expected cosmogenic background neutrinos."[73]

The upward traveling event is detected and described in the image and graph on the lower right. "Top: Interferometric map of the arrival direction of the anomalous CR event 15717147. Bottom: ANITA combined amplitude spectral density (ASD) for the event, from 50-800 MHz, including data from the ANITA Low Frequency Antenna (ALFA). A simulated upward-propagating extensive air shower spectral-density curve is overlain."[73]


This lepton box provides information about muons. Credit: MissMJ.
This is a Feynman Diagram of the most common of Muon Decays. Credit: Richard Feynman.

"TeV muons from γ ray primaries ... are rare because they are only produced by higher energy γ rays whose flux is suppressed by the decreasing flux at the source and by absorption on interstellar light."[74]

The muon from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with unitary negative electric charge (−1) and a spin of ​12. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton. As is the case with other leptons, the muon is not believed to have any sub-structure at all (i.e., is not thought to be composed of any simpler particles).

The muon is an unstable subatomic particle with a mean lifetime of 2.2 us. This comparatively long decay lifetime (the second longest known) is due to being mediated by the weak interaction. The only longer lifetime for an unstable subatomic particle is that for the free neutron, a baryon particle composed of quarks, which also decays via the weak force. Muon decay produces three particles, an electron plus two neutrinos of different types.

Like all elementary particles, the muon has a corresponding antiparticle of opposite charge (+1) but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ
and antimuons by μ+


The diagram plots the measured and expected fluxes of natural and reactor neutrinos. Credit: Christian Spiering.
This is the first neutrino sky map. Credit: Christian Spiering and Krishnaswamy.
One of the first upward moving muons from a neutrino interaction is illustrated. Credit: Christian Spiering.
The figure shows the muon reconstructed zenith. Credit: Christian Spiering.
Equatorial skymap of neutrino-induced muon events from 295 days of ANTARES data in 2007/2008. Credit: Christian Spiering.

Neutrino oscillation is predicted a quantum mechanical phenomenon[75] 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.

A great deal of evidence for neutrino oscillation has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies.[76]

A neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor.

The image at right shows the measured "and expected fluxes of natural and reactor neutrinos [...] The energy range from keV to several GeV is the domain of underground detectors. The region from tens of GeV to about 100 PeV, with its much smaller fluxes, is addressed by Cherenkov light detectors underwater and in ice. The highest energies are only accessible with huge detector volumes".[77]

The second image at right is the "first neutrino sky map with the celestial coordinates of 18 KGF neutrino events [...] Due to uncertainties in the azimuth, the coordinates for some events are arcs rather than points. The labels reflect the numbers and registration mode of the events (e.g. "S" for spectrograph). Only for the ringed events the sense of the direction of the registered muon is known."[77]

"Sufficiently energetic muons produced in [...] interactions [in the Earth atmosphere are called] "atmospheric muons [...] Upward-going muons must have been produced in neutrino interactions."[77]

The third image at right illustrates the "Baikal Neutrino Telescope NT200. [...] One of the first upward moving muons from a neutrino interaction recorded with the 4-string stage of the detector in 1996 [...] The Cherenkov light from the muon is recorded by 19 channels."[77]

The fourth image at right contains the number "of reconstructed muons in the 2008 ANTARES data, as a function of the reconstructed zenith angle (black error bars). Also indicated are the simulation results for atmospheric muons (red dashed), and muons induced by atmospheric neutrinos (blue). The shaded band indicates the systematic uncertainties."[77]

The image at left shows an equatorial "skymap of neutrino-induced muon events from 295 days of ANTARES data in 2007/2008. The background color scale indicates the sky visibility in percent of the time. The most significant accumulation of events, marked with a red circle, is fully compatible with the background expectation"[77]

"Atmospheric neutrinos can interact with the detector producing also hadrons. The most probable of these reactions is the single pion production [20][21]:"[78]


"There is also a small loss due to inelastic hadronic interactions of the decay particles before they are stopped."[78]

The "optical properties of mixtures of PXE [phenyl-o-xylylethane] and derivatives of mineral oils are under investigation [3]."[78]

"Neutrino detection includes four remarkable reactions:"[79]

  1. Muon production νμ + N → μ + all gives an excellent tool to search for the discrete sources, since directions of UHE muon and neutrino coincide.
  2. Resonant production of W-boson, νe + e → W → hadrons results in production of monoenergetic showers with energy E0 =  /2me = 6.3 × 106 GeV. This reaction has a large cross-section.
  3. Tau production in a detector, ντ + N → τ + hadrons, is characterised by time sequence of three signals: a shower from prompt hadrons, the Cherenkov light from τ and hadron shower from τ-decay. SuperGZK ντ are absorbed less in the Earth due to regeneration: absorbed ντ is converted into τ, which decays producing ντ again.
  4. Z-bursts provide a signal from the space, caused by the resonant Z0 production on DM neutrinos, ν + νDM → Z0 → hadrons. The energy of the detected neutrino must be tremendous: E0 =  

Non-accelerator neutrino sources "include objects with annihilation of DM (the Sun, Earth, cores of the galaxies), objects with the decays of superheavy DM particles (galactic halos) and topological defects. In the last two cases neutrinos are produced in the decays of superheavy particles with the masses up to MGUT ∼ 1016 GeV. A particle decays to virtual particles, partons, which are cascading due to QCD interaction, and at the confinement radius cascade partons are converted to hadrons, most of which are pions. Neutrinos are produced in pion decays with spectrum which can be approximately described at highest energies as dE/E2.[79]

Gamma raysEdit

The "leptons can be created not only via processes involving DM particles such as χ + χ → l+ + l, but in high energy astrophysical environments a significant number of them can also be produced via the γ + γ → l + l+ and e + e+ → l + l+ reactions. However, the muons created in these high-energy environments have energies much higher than the ionization energy (Eion ≈ 1.4 keV) of the true muonium [460] and, hence, only a small fraction of pairs with energies less then Eion will form a bound system. The muonium has two states, depending on the particles spin orientation. These are para- and orto-muonium. The para-muonioum predominantly decays via two-photon annihilation, while the orto-muonium – via electron-positron annihilation. The energy released in the two-photon annihilation is E=105.66 MeV [460]."[1]


"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."[80]

The "incoming neutrino flux [is disentangled] from the consequent τ air-shower physics. [To] establish the τ production rate we introduce an effective volume and mass for Earth-skimming τ’s, which is independent on any incoming neutrino flux [...]. This volume describes a strip within the Earth where neutrino/antineutrino-nucleon, ντ ( ) − N, interactions may produce emerging τ+ leptons which then shower in air. [General] τ upward-going showers [can be compared] to detectors such as the ongoing photo-fluorescence ground-based observatory Auger".[81]

Tau penetrating power appears only at ultra-high velocity and energy (above petaelectronvolt energies), when time dilation extends their path-length.[81]


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