Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

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212 19. Big-Bang cosmology These methods are all consistent with the age deduced from studies of structure formation, using the microwave background and large-scale structure: t0 =13.69 ± 0.13 Gyr [24], where the extra accuracy comes at the price of assuming the Cold Dark Matter model to be true. 19.3. The Hot Thermal Universe 19.3.1. Thermodynamics of the early Universe : Through much of the radiation-dominated period, thermal equilibrium is established by the rapid rate of particle interactions relative to the expansion rate of the Universe. In equilibrium, it is straightforward to compute the thermodynamic quantities, ρ, p, and the entropy density, s. In the Standard Model, a chemical potential is often associated with baryon number, and since the net baryon density relative to the photon density is known to be very small (of order 10−10 ), we can neglect any such chemical potential when computing total thermodynamic quantities. For photons, we have (in units where � = kB =1) ργ = π2 15 T 4 ; pγ = 1 3 ργ ; sγ = 4ργ 3T ; nγ = 2ζ(3) π2 T 3 . (19.39) Eq. (19.10) can be converted into an equation for entropy conservation, d(sR 3 )/dt =0. (19.40) For radiation, this corresponds to the relationship between expansion and cooling, T ∝ R−1 in an adiabatically expanding universe. Note also that both s and nγ scale as T 3 . 19.3.2. Radiation content of the Early Universe : At the very high temperatures associated with the early Universe, massive particles are pair produced, and are part of the thermal bath. If for a given particle species i we have T ≫ mi, then we can neglect the mass and the thermodynamic quantities are easily computed. In general, we can approximate the energy density (at high temperatures) by including only those particles with mi � ≪ T . In this case, we have � ρ = gB + B 7 � � π gF 8 F 2 30 T 4 ≡ π2 30 N(T ) T 4 , (19.41) where gB(F ) is the number of degrees of freedom of each boson (fermion) and the sum runs over all boson and fermion states with m ≪ T . Eq. (19.41) defines the effective number of degrees of freedom, N(T ), by taking into account new particle degrees of freedom as the temperature is raised. The value of N(T ) at any given temperature depends on the particle physics model. In the standard SU(3)×SU(2)×U(1) model, we can specify N(T ) up to temperatures of O(100) GeV. The change in N (ignoring mass effects) can be seen in the table below. At higher temperatures, N(T ) will be model-dependent. In the radiation-dominated epoch, Eq. (19.10) can be integrated (neglecting the T -dependence of N) giving us a relationship between the age of the Universe and its temperature � 90 t = 32π3 �1/2 T GNN(T ) −2 . (19.42) Put into a more convenient form tT 2 MeV =2.4[N(T )]−1/2 , (19.43) where t is measured in seconds and TMeV in units of MeV.
19. Big-Bang cosmology 213 Temperature New <strong>Particle</strong>s 4N(T ) T
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2 PARTICLE PHYSICS BOOKLET TABLE OF
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4 1. Physical constants Table 1.1.
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6 2. Astrophysical constants 2. AST
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Page 172 and 173: 170 9. Quantum chromodynamics The c
Page 174 and 175: 172 10. Electroweak model and const
Page 184 and 185: 182 11. The CKM quark-mixing matrix
Page 190 and 191: 188 12. CP violation in meson decay
Page 196 and 197: 194 13. Neutrino mixing (L(¯νj) =
Page 198 and 199: 196 13. Neutrino mixing between the
Page 200 and 201: 198 13. Neutrino mixing Figure 13.1
Page 202 and 203: 200 14. Quark model 14. QUARK MODEL
Page 204 and 205: 202 14. Quark model This difference
Page 206 and 207: 204 16. Structure functions 16.1.1.
Page 208 and 209: 206 16. Structure functions with i
Page 210 and 211: 208 19. Big-Bang cosmology 19. BIG-
Page 212 and 213: 210 19. Big-Bang cosmology where th
Page 216 and 217: 214 21. The Cosmological Parameters
Page 218 and 219: 216 21. The Cosmological Parameters
Page 220 and 221: 218 22. Dark matter 22. DARK MATTER
Page 222 and 223: 220 22. Dark matter 22.2. Experimen
Page 224 and 225: 222 23. Cosmic microwave background
Page 226 and 227: 224 24. Cosmic rays 24. COSMIC RAYS
Page 228 and 229: 226 26. High-energy collider parame
Page 230 and 231: 228 26. High-energy collider parame
Page 232 and 233: 230 27. Passage of particles throug
Page 246 and 247: 244 28. Detectors at accelerators 2
Page 248 and 249: 246 28. Detectors at accelerators 2
Page 250 and 251: 248 28. Detectors at accelerators W
Page 252 and 253: 250 28. Detectors at accelerators m
Page 254 and 255: 252 28. Detectors at accelerators =
Page 256 and 257: 254 28. Detectors at accelerators I
Page 258 and 259: 256 29. Detectors for non-accelerat
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262 29. Detectors for non-accelerat
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264 30. Radioactivity and radiation
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266 31. Commonly used radioactive s
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268 32. Probability � ∞ � ∞
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270 32. Probability For n Gaussian
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272 33. Statistics is an unbiased e
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274 33. Statistics 33.2. Statistica
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276 33. Statistics p-value for test
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278 33. Statistics measurement. In
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280 33. Statistics if x lies betwee
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282 33. Statistics θ i ^ θ i σi
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284 33. Statistics is based on the
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286 36. Clebsch-Gordan coefficients
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288 40. Kinematics The state normal
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290 40. Kinematics 40.4.3.1. Dalitz
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292 40. Kinematics u =(p1− p4) 2
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294 40. Kinematics 40.5.3.1. Resona
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296 41. Cross-section formulae for
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302 6. Atomic and nuclear propertie
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304 NOTES
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306 NOTES
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2011 JULY AUGUST SEPTEMBER S M T W
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