Stars as Laboratories for Fundamental Physics - MPP Theory Group

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308 Chapter 8 system (ν L e , ν L µ , ν R e , ν R µ ) and (ν L e , ν L µ, ν R e , ν R µ ). Moreover, one may have both diagonal and transition magnetic moments so that for neutrinos the r.h.s. of the equation of motion is ⎛ ⎞ ⎛ ∆ m c 2θ + V νe ∆ m s 2θ µ ee B T µ µe B T ν L ⎞ e ∆ m s 2θ −∆ m c 2θ + V νµ µ eµ B T µ µµ B T ν L µ ⎜ ⎟ ⎜ ⎝ µ ee B T µ µe B T ∆ m c 2θ ∆ m s 2θ ⎠ ⎝ ν R ⎟ e ⎠ , (8.59) µ eµ B T µ µµ B T ∆ m s 2θ −∆ m c 2θ νµ R where the right-handed neutrinos do not experience a medium-induced energy shift. For certain values of the parameters the oscillations between two states may dominate which are then described by a certain 2 × 2 submatrix. Then the general treatment is much like the flavor mixing problems studied earlier. In general, a much richer collection of solutions obtains—for a review see Pulido (1992). Electric transition moments can also play a role, and precessions in electric fields may be important. Majorana neutrinos have either electric or magnetic transition moments, but not both as long as CP remains conserved. Still, even electric transition moments would lead to spin-flavor oscillations in macroscopic magnetic fields. 8.4.4 Twisting Magnetic Fields The problem of spin oscillations is further complicated by the possibility that the magnetic field changes its direction along the neutrino trajectory, i.e. that it may be “twisting” (Aneziris and Schechter 1991). In this case the equation of motion of a two-level spin-precession problem is based on the Hamiltonian ( BL B H = µ T e −iφ ) B T e iφ , (8.60) −B L where the three parameters B L , B T , and φ vary along the neutrino trajectory. The transverse field strength B T is a physical magnetic field while the longitudinal one B L is an effective magnetic field which represents the neutrino mass difference (spin-flavor oscillations!) and refractive medium effects. As long as B T maintains its direction along the trajectory, the phase φ can be globally chosen to be zero. If φ varies along the trajectory so that the neutrino experiences it to be a function of time, it is useful to transform the equation of motion to a coordinate system which corotates with B T so that in the new frame one is back to the old situation of a fixed direction for B T (Smirnov
Neutrino Oscillations 309 1991). This transformation is achieved by ν ′ = Uν where ν represents a two-level wave function and ( e −iφ/2 ) 0 U = 0 e iφ/2 , (8.61) so that the spin-up and down states acquire opposite, time-dependent phases. However, because the transformation does not mix spin up with spin down, the transition rate between the two levels is the same in both coordinate systems. The equation of motion i∂ t ν ′ = H ′ ν ′ involves the Hamiltonian H ′ = µ ( ) BL B T B T −B L ( ) −1 0 + 1 ˙φ . (8.62) 2 0 1 Put another way, the effective longitudinal magnetic field in the rotating frame is B ′ L = B L − 1 2 ˙φ/µ while B T remains unchanged. |B ′ L| can be less or larger than |B L | so that the transition rate between the two levels can be increased or decreased by a twist. B L may even be cancelled entirely, enabling resonant oscillations. For a systematic discussion of the full four-level spin-flavor problem see, for example, Akhmedov, Petcov, and Smirnov (1993).
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Georg G. Raffelt Stars as Laborator
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Table of Contents Preface (xiv) Ack
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Table of Contents vii 4.5 Neutrino
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Table of Contents ix 8. Neutrino Os
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Table of Contents xi 12. Radiative
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Table of Contents xiii 16.3 New Int
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Preface xv Second, particles from d
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Preface xvii search for proton deca
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Preface xix cuts of higher-order gr
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Preface xxi quoted “astrophysical
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Chapter 1 The Energy-Loss Argument
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The Energy-Loss Argument 3 example
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The Energy-Loss Argument 5 trinos,
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The Energy-Loss Argument 7 As a sim
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The Energy-Loss Argument 9 The most
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The Energy-Loss Argument 11 against
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The Energy-Loss Argument 13 ing M;
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The Energy-Loss Argument 15 M ′ (
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The Energy-Loss Argument 17 Table 1
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The Energy-Loss Argument 19 ing to
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The Energy-Loss Argument 21 scalars
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Chapter 2 Anomalous Stellar Energy
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Anomalous Stellar Energy Losses Bou
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Chapter 3 Particles Interacting wit
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Particles Interacting with Electron
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Chapter 4 Processes in a Nuclear Me
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Processes in a Nuclear Medium 119 t
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Processes in a Nuclear Medium 121 f
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Processes in a Nuclear Medium 123 F
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Processes in a Nuclear Medium 129 v
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Processes in a Nuclear Medium 131 4
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Processes in a Nuclear Medium 133 i
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Processes in a Nuclear Medium 135 H
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Processes in a Nuclear Medium 137 I
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Processes in a Nuclear Medium 143 i
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Processes in a Nuclear Medium 145 s
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Processes in a Nuclear Medium 147 E
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Processes in a Nuclear Medium 149 a
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Processes in a Nuclear Medium 151 T
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Processes in a Nuclear Medium 153 r
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Processes in a Nuclear Medium 155 4
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Processes in a Nuclear Medium 157 I
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Processes in a Nuclear Medium 159 t
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Processes in a Nuclear Medium 161 A
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Processes in a Nuclear Medium 163 R
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Chapter 5 Two-Photon Coupling of Lo
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Two-Photon Coupling of Low-Mass Bos
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Chapter 6 Particle Dispersion and D
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Particle Dispersion and Decays in M
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Chapter 7 Nonstandard Neutrinos The
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Nonstandard Neutrinos 253 (“spont
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Nonstandard Neutrinos 255 kinematic
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Page 279 and 280: Nonstandard Neutrinos 259 Fig. 7.2.
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Page 291 and 292: Nonstandard Neutrinos 271 component
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Page 297 and 298: Nonstandard Neutrinos 277 7.5.2 Spi
Page 299 and 300: Nonstandard Neutrinos 279 where m
Page 301 and 302: Neutrino Oscillations 281 and hence
Page 303 and 304: Neutrino Oscillations 283 As usual
Page 305 and 306: Neutrino Oscillations 285 two-flavo
Page 307 and 308: Neutrino Oscillations 287 Fig. 8.2.
Page 309 and 310: Neutrino Oscillations 289 8.2.4 Exp
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Page 321 and 322: Neutrino Oscillations 301 8.3.5 The
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Page 363 and 364: Solar Neutrinos 343 Fig. 10.1. Sola
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Page 367 and 368: Solar Neutrinos 347 10.2 Calculated
Page 369 and 370: Solar Neutrinos 349 Fig. 10.3. Norm
Page 371 and 372: Solar Neutrinos 351 a certain range
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Solar Neutrinos 359 Table 10.4. Spe
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Solar Neutrinos 361 Table 10.5. Pre
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Solar Neutrinos 363 rates attribute
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Solar Neutrinos 365 10.3.4 Water Ch
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Solar Neutrinos 367 Fig. 10.10. Dif
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Solar Neutrinos 369 Fig. 10.13. Mea
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Solar Neutrinos 371 Table 10.9. Cur
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Solar Neutrinos 373 of order the an
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Solar Neutrinos 375 Fig. 10.16. 37
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Solar Neutrinos 377 GALLEX, or Home
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Solar Neutrinos 379 Table 10.10. Me
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Solar Neutrinos 381 deficits in all
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Solar Neutrinos 383 The ν e surviv
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Solar Neutrinos 385 The allowed ran
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Solar Neutrinos 387 10.7 Spin and S
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Solar Neutrinos 389 10.8 Neutrino D
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Solar Neutrinos 391 The small- and
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Solar Neutrinos 393 flux above its
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Chapter 11 Supernova Neutrinos The
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Supernova Neutrinos 397 Fig. 11.1.
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Supernova Neutrinos 399 beyond the
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Supernova Neutrinos 401 ate neutrin
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Supernova Neutrinos 403 Convection
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Supernova Neutrinos 405 Hayes, and
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Supernova Neutrinos 407 11.2 Predic
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Supernova Neutrinos 409 must then b
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Supernova Neutrinos 411 Figure 11.6
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Supernova Neutrinos 413 signal (Sec
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Supernova Neutrinos 415 time) on 23
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Supernova Neutrinos 417 All of the
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Supernova Neutrinos 419 to multiple
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Supernova Neutrinos 421 the final-s
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Supernova Neutrinos 423 ter of 53 e
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Supernova Neutrinos 425 Given these
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Supernova Neutrinos 427 thorough st
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Supernova Neutrinos 429 The forward
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Supernova Neutrinos 431 Another int
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Supernova Neutrinos 433 ber of ν e
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Supernova Neutrinos 435 A “normal
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Supernova Neutrinos 437 Fig. 11.19.
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Supernova Neutrinos 439 The approxi
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Supernova Neutrinos 441 be taken to
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Supernova Neutrinos 443 sense that
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Supernova Neutrinos 445 presence of
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Supernova Neutrinos 447 An even mor
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Chapter 12 Radiative Particle Decay
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Radiative Particle Decays 451 one c
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Radiative Particle Decays 453 corre
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Radiative Particle Decays 455 is no
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Radiative Particle Decays 457 Fig.
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Radiative Particle Decays 461 12.3.
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Radiative Particle Decays 463 emiss
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Radiative Particle Decays 465 range
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Radiative Particle Decays 469 weak
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Radiative Particle Decays 471 value
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Radiative Particle Decays 473 ignor
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Radiative Particle Decays 479 Table
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Radiative Particle Decays 481 In or
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Radiative Particle Decays 485 while
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Radiative Particle Decays 487 h 100
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Radiative Particle Decays 491 still
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Chapter 13 What Have We Learned fro
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What Have We Learned from SN 1987A
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Axions 525 Table 14.1. Particle mag
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Axions 527 or axion decay constant.
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Axions 529 The Yukawa coupling h is
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Axions 531 14.2.3 Pseudoscalar vs.
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Axions 533 Notably, the Higgs field
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Axions 535 otic heavy quarks: only
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Axions 537 Various axion models dif
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Axions 539 Bounds on the Yukawa cou
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Axions 541 Fig. 14.5. Astrophysical
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Axions 543 decay into axions. This
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Chapter 15 Miscellaneous Exotica St
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Miscellaneous Exotica 547 Table 15.
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Miscellaneous Exotica 549 15.2.3 Pr
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Miscellaneous Exotica 551 Most rece
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Miscellaneous Exotica 553 Fig. 15.1
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Miscellaneous Exotica 555 A violati
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Miscellaneous Exotica 557 nuclei it
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Miscellaneous Exotica 559 mass, and
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Miscellaneous Exotica 561 backgroun
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Miscellaneous Exotica 563 SN 1987A
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Miscellaneous Exotica 565 which led
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Miscellaneous Exotica 567 For a nar
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Neutrinos: The Bottom Line 569 the
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Neutrinos: The Bottom Line 571 Neut
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Neutrinos: The Bottom Line 573 Apar
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Neutrinos: The Bottom Line 575 is d
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Neutrinos: The Bottom Line 577 of t
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Neutrinos: The Bottom Line 579 siti
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Units and Dimensions 581 In the ast
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Appendix B Neutrino Coupling Consta
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Appendix C Numerical Neutrino Energ
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Numerical Neutrino Energy-Loss Rate
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Numerical Neutrino Energy-Loss Rate
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Appendix D Characteristics of Stell
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Characteristics of Stellar Plasmas
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References 607 Akhmedov, E. Kh., an
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References 609 Bahcall, J. N., Kras
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References 611 Bilenky, S. M., and
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References 613 Cannon, R. D. 1970,
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References 615 Cooper-Sarkar, A. M.
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References 617 Dodelson, S., Friema
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References 619 Fukuda, Y., et al. 1
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References 621 Goyal, A., Dutta, S.
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References 623 Hoogeveen, F., and S
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References 625 Kawakami, H., et al.
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References 627 Landau, L. D., and P
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References 629 Mayle, R. W., and Wi
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References 631 Nieves, J. F., and P
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References 633 Pochoda, P., and Sch
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References 635 Ross, J. E., and All
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References 637 Shlyakhter, A. I. 19
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References 639 Totsuka, Y. 1993, Ne
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References 641 Wiezorek, C., et al.
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Acronyms 643 L l.h. l.h.s. ly LMC L
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Symbols 645 dp differential in phas
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Symbols 647 X j Peccei-Quinn charge
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Subject Index A α-Ori 189 A665, A1
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Subject Index 651 Coulomb gauge 204
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Subject Index 653 H Hayashi line 32
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Subject Index 655 multiple scatteri
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Subject Index 657 neutrino radiativ
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Subject Index 659 Primakoff process
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Subject Index 661 SN 1987A bounds (
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Subject Index 663 supernova core bi
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