Primordial Black Holes and Cosmological Phase Transitions Report ...

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$Kawasaki dynamic in continuum Math. Encounters XXXV ... - CCM$

PBHs and Cosmological Phase Transitions 40 Table 7: The fundamental mesons and their most common excited states. For each meson and antimeson it is indicated the symbol, the quark content, the electric charge e, the spin s, the mean lifetime t and, whenever possible, the two most probable decaying reactions with corresponding probabilities (for more data on these and other mesons consult the PDG – http://pdg.lbl.gov/2007/listings/contents listings.html, Yao et al., 2006). Name Meson Antimeson quark content e s m(MeV) t(s) Most probable decaying Second most probable symbol symbol reaction decaying reaction pion π + π− u ¯ d ūd ±1 0 139.57 2.6 × 10−8 π ± → µ ± + νµ 99.99% neutral pion π0 √ (self) uū − dd¯ −17 / 2 – 0 0 134.98 8.4 × 10 π0 → γ + γ 98.80% d¯s − s ¯ d / √ 2 – 0 0 497.648 8.953 × 10 −11 K 0 S → π+ + π − 69.2% K 0 S → π0 + π 0 30.7% charged kaon K + K− u¯s ūs ±1 0 493.68 1.24 × 10−8 K ± → µ ± + νµ 63.4% K ± → π ± + π0 21% neutral kaon K0 ¯ K0 d¯s ds ¯ 0 0 497.648 – – – – K–Short K0 S (self) K–Long K0 √ L (self) d¯s + sd¯ −8 / 2 – 0 0 497.648 5.116 × 10 K0 L → π± + e∓ + νe 40.6% K0 L → π± + µ ∓ + νµ 27% charged rho ρ + ρ− u ¯ d ūd ±1 1 775.4 – ρ ± → π ± + π0 ≈ 100% neutral rho ρ0 √ (self) uū − dd¯ 0 + − 0 0 / 2 – 0 1 775.49 – ρ → π + π + γ – ρ → π + γ – uū + d ¯ d / √ 2 – 0 1 782.65 – ω → π + + π − + π 0 89.1% ω → π 0 + γ 8.9% omega ω (self) phi ϕ (self) s¯s – 0 1 1019.46 – ϕ → K + + K− 49.3% ϕ → K0 S + K0 √ L 34.0% eta η (self) uū + dd¯ 0 0 0 − 2s¯s / 6 – 0 0 547.51 – η → γ + γ 39.4% η → π + π + π 32.5% eta prime η ′ √ (self) uū + dd ¯ ′ + + ′ 0 + − + s¯s / 6 – 0 0 957.78 – η → π + π + η 44.5% η → ρ + γ +(π + π + γ) 29.4% charged D D + D− c ¯ d ¯cd ±1 0 1869.62 1.04 × 10−12 D ± → K0 + ... + ¯ K0 + ... 61% D ± → K ± + ... 27% neutral D D0 ¯ D0 cū ¯cu 0 0 1864.84 4.1 × 10−13 strange D D + s D− s c¯s ¯cs ±1 0 1968.2 5.0 × 10−13 D ± s → K0 + ... + ¯ K0 + ... 39% D ± s → K± + ... 13% J/Psi J/ψ (self) c¯c – 0 1 396.92 – J/ψ → hadrons 88% J/ψ → e + + e− 6% charged B B + B − u ¯ b ūb ±1 0 5297.0 1.638 × 10 −12 B ± → l ± + νl + ... 10.9% strange B B0 s charmed B B + c B− c c¯b ¯cb ±1 0 6286 4.6 × 10−11 B ± c → J/ψ + l ± + νl – B ± c → J/ψ + π ± – neutral B B0 ¯ B0 d¯b db ¯ −12 0 0 5279.5 1.530 × 10 B0 → l + + νl + ... 10.4% ¯B 0 s s¯b ¯sb 0 0 5367.5 1.466 × 10−12 B0 s → D− s + ... 94% Upsilon Υ (self) b ¯ b – 0 1 9460.3 – Υ → τ + + τ − 2.6% Υ → µ + + µ − 2.5%
PBHs and Cosmological Phase Transitions 41 A baryon consists of a triplet of quarks. This means that we have 35 different possible combinations13 . The most common baryons in the present universe are nucleons, i.e., protons and neutrons. The proton consists of two up quarks and one down quark (uud) and the neutron consists of one up quark and two down quarks (udd). Hyperons are baryons containing at least a strange quark, but no charm or bottom quarks (e.g. Σ− ,Σ0 ,Σ + ,Ξ− ,Ξ0 ,Λ0 ,Ω− ). Charmed baryons are baryons containing at least a charm quark, but no bottom quarks (e.g. Ξ + c ,Ξ0c , Ξ + cc ,∆+ c ,Ω0c ). Bottom baryons are baryons containing at least a bottom quark (e.g. Ξ − b ,Ξ0b ,∆0b ). Some of the 35 triplets have never been observed (e.g. ubb, sbb). However, the number of known baryons is much larger than the number of different quark triplets. That is due to the existence of many excited states for each configuration. For example, in the case of the proton (uud) there are at least 25 known excited states (e.g. N(2190) + with mass ≈ 2190 MeV, N(1710) + with mass ≈ 1710 MeV, ∆ + with mass ≈ 1232 MeV) 14 . On table 8 we show the most stable known baryons. Antibaryons are triplets made of antiquarks. For each baryon there is an antibaryon, which is an antiparticle with the same mass and opposite electric charge, obtained by replacing each quark by the corresponding antiquark15 . For example, the antiparticle of the proton (uud), is the antiproton (ūū ¯ d), an antibaryon with m ≈ 938.272 MeV and e = −1. 13 The 35 different quark triplets are: uuu, uud, uus, uuc, uub, udd, uds, udc, udb, uss, usc, usb, ucc, ucb, ubb, ddd, dds, ddc, ddb, dss, dsc, dsb, dcc, dcb, dbb, sss, ssc, ssb, scc, scb, sbb, ccc, ccb, cbb and bbb. The top quark was left outside because the probability of formation of a top baryon is negligibly small. 14 For a complete list of currently known baryons (including excited states) see http://pdg.lbl.gov/2007/tables/contents tables.html. 15 Baryons are matter (they are made of quarks) and antibaryons are antimatter (they are made of antiquarks). The same idea does not apply to mesons and antimesons. That is because a meson (or antimeson) consists of a quark–antiquark pair.
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CCM-Centro de Ciências Matemática
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Contents List of Figures vii List o
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PBHs and Cosmological Phase Transit
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Table 49 (continued). PBHs and Cosm
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Table 49 (continued). Radiation EW
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