Errata 28/01/2013. Chapter 1. Chapter 2

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1 Errata 8/01/013 Fundamentals of Neutrino Physics and Astrophysics C. Giunti and C.W. Kim Oxford University Press (publication date: 15 March 007; 78 pages) ± Lines are calculated before ( ) or after (+) the Anchor. If the Anchor is a page, t and b indicate, respectively, top and bottom. page iii t + 5 Universita Università Chapter 1 page 4 b eqn (.189) (/p P m)γ 0 u ( h) (p P ) 0 (/p m)γ 0 u ( h) (p P ) 0 eqn (.76) +1 following eqn (.76) following eqn (.78) eqn (.361) 1 transform as transform as (normal ordering is implicitly assumed) eqn (.378) 1 a parity transformation a passive parity transformation eqn (.385) 1 he transformation he active transformation eqn (.404) 1 he transformation he active transformation eqn (.408) 1 transform as transform as (normal ordering is implicitly assumed) eqn (.414) V A V A eqn (.414) V A V A eqn (.416) 1 a time reversal a passive time reversal eqn (.416) x ( x0, x) x x ( x0, x) x eqn (.44) the transformation the active transformation 1

2 eqn (.434) eqn (.435) (V ) (S ) ξ a ξψ b b ψ a (S ) ξξ a b ψ a ψ b ξ a ξs b ξξ a b S ξ b V eqn (.436) ( ν ) ξ a eqn (.437) eqn (.438) eqn (.439) eqn (.440) ξ a ξ b ν ξ b ψ b γ ψ a ξ b ψ b σ ν ψ a (A ) ξ a ξψ b b γ γ 5 ψ a ξ a ξa b (V ) ξ a ξ b ξ a ξ b V ( ν ) ξ a ξ b ξ a ξ b ν ψ a γ ψ b ψ a σ ν ψ b (A ) ξξ a b ψ a γ γ 5 ψ b ξξ a b A (P ) ξ a ξψ b b γ 5 ψ a (P ) ξξ a b ψ a γ 5 ψ b ξ a ξp b ξξ a b P W ξ W W W ξ W ( ) ( ξ a ξξ b W V A + ξξ a b ξ W ( ξ ) ξ a b ξ W V ( V A ξ a ξξ b W V W A A ) W + ) W

3 eqn (.454) 1 transform as transform as (normal ordering is implicitly assumed) eqn (.454) (S ) CP CP ξb CP ψ aψ b CP ξb CP S eqn (.455) (V )CP ξcp a ξb CP ψ aγ ψ b ξcp a ξb CP V eqn (.456) ( ν )CP CP ξb CP ψ aσ ν ψ b CP ξb CP ν eqn (.457) (A )CP ξ a CP ξb CP ψ aγ γ 5 ψ b ξ a CP ξb CP A eqn (.458) (P ) CP CP ξb CP ψ aγ 5 ψ b CP ξb CP P eqn (.458) +1 Since all the covariant bilinears are left invariant by a CP transformation, apart for a possible irrelevant phase (which is the same for the vector and axial currents), any possible interaction Lagrangian is invariant under CP, in agreement with the CP theorem, which says that CP is a symmetry of any relativistic local field theory. (S ) CP ξ a CP ξb CP ψ bψ a ξ a CP ξb CP S (V )CP ξcp a ξb CP ψ bγ ψ a ξcp a ξb CP V ( ν )CP ξcp a ξb CP ψ bσ ν ψ a ξ a CP ξb CP ν (A )CP ξcp a ξb ξcp a ξb CP A (P ) CP ξ a CP ξb CP ψ bγ γ 5 ψ a CP ψ bγ 5 ψ a ξcp a ξb CP P Choosing ξ a CP ξb CP, CP transforms each covariant bilinear into its Hermitian conjugate, with a minus sign for V,A and P. Since an interaction Lagrangian containing a covariant bilinear must contain also its Hermitian conjugate (the Lagrangian is Hermitian), it is invariant under CP. he minus sign in the transformation of V, A and P is compensated by a corresponding minus sign in the transformation of the fields to which they are coupled. he invariance under CP of any interaction Lagrangian containing a covariant bilinear is in agreement with the CP theorem, which says that CP is a symmetry of any relativistic local field theory. 3

4 eqn (.487) f(p,h) 1 f(p,h) 1 EV a(h) (p) 0, EV b(h) (p) 0 f(p,h) 1 EV a (h) (p) 0, f(p,h) 1 EV b (h) (p) 0 Chapter 3 eqn (3.1) [ ( I I +1 ) ( )] I3 v ( ) I 3 v eqn (3.199) +1 ε (0) (p) p ω ε (0) (p) p ω [ I ( I +1 ) ( ) ] I3 v ( I 3 ) v eqn (3.199) + ε (1) (p) p ε () (p) p 0 ε (1) (p) p ε () (p) p 0 eqn (3.199) + ε (3) (p) p ω ε (3) (p) p ω Chapter 4 ( ) ( cosϑe eqn (4.) iω 1 sinϑe i(ω +η) cosϑe iω 1 sinϑe i(ω 1 η) cosϑe iω ω1 0 e iω 1 0 eqn (4.3) 0 ω 0 e ω eqn (4.6) W 13 W 13 (ϑ 13,η 13 ) D 1 (η 13 )R 13 D 1 (η 13 ) sinϑe i(ω 1 +η) sinϑe i(ω η) cosϑe iω W 13 W 13 (ϑ 13,η 13 η 1 η 3 ) eqn (4.78) 1 η 13 η 13 η 1 η 3 eqn (4.108) +1 One can parameterize the mixing matrix as a product of the type in eqn (4.65) with W (ϑ π/,η ) on the extreme left or the extreme right. Using IfW (ϑ π/,η ) is on the extreme left or on the extreme right of the product in eqn (4.45) which parameterizes the mixing matrix, using eqn (4.78) 13 η η 13 +η 1 +η 3 eqn (4.117) +1 eqn (4.115) eqn (4.116) ) 4

5 Chapter 5 eqn (5.0) eqn (5.1) eqn (5.14) g (νe) 1 g ( νe) g (νe) 1 1+g ( νe) g (νe) g ( νe) 1 g (νe) g ( νe) Q 6 (rn i ) G N i (0) Q 6 (rn i ) Chapter 6 eqn (6.1) L αl L αl page 08 t + 5 [53,79,79,408] [53,79,N1,408] New Reference: [N1] P. Langacer, M.-X. Luo, Phys. Rev. D44, 817, eqn (6.06) ν L ML Cν L ν L ML Cν L eqn (6.10) ν L W L ML W L Cν L ν L W L ML W L Cν L eqn (6.) +5 M l. M l 0. page 7 t + 11 [53,79,79,408] [53,79,N1,408] page 8 b [814] [N,N3] New References: [N] G. Lazarides, Q. Shafi, C. Wetterich, Nucl. Phys. B181, 87, [N3] R.N. Mohapatra and G. Senjanovic, Phys. Rev. D3 165, eqn (6.345) n (i ) ( M 1 n i M )n eqn (6.418) l αl γ ρ U α ν L l αl γ ρ U α ν L W ρ eqn (6.418) l L γ ρ U n L l L γ ρ U n L W ρ Chapter 7 [ ] [ ] (L/E L/E ) eqn (7.95) exp σl/e exp (L/E L/E ) σl/e eqn (7.97) +6 eqn (7.70) eqn (7.93) 5

6 Chapter 8 eqn (8.9) M P α ormd α M P α andmd α eqn (8.77) +3 σt I σp I σt I σx I Chapter 10 eqn (10.70) 3 as an effectively incoherent sum as effectively incoherent sums Chapter 11 eqn (11.67) R multi-gev /e R sub-gev /e Chapter 1 eqn (1.13) Neglecting the small recoil energy of the neutron, the he Chapter 13 page 476 b 9 m ev m ev Chapter 16 eqn (16.13) +6 because γ is the monopole moment of the temperature: γ γ (θ,φ)yl m (θ,φ) dcosθ dφ. becausey0 0 1/ 4π and γ 1 γ (θ,φ) dcosθ dφ. 4π Chapter 17 eqn (17.49) 9 He H eqn (17.70) +6 an upper limit a lower limit 6

7 Appendix A eqn (A.19) ǫ ij ǫ lmn il im in jl jm in l m n ǫ ij ǫ lmn il im in jl jm jn l m n σ eqn (A.105) σd 0 iαd 0 0 σ i 0 σ σd 0 iαd i σ 0 Appendix B eqn (B.17) g αρ (Λ ) ρ g ν Λ ρ ν α ν g αρ (Λ ) ρ g ν Λ ν σ α σ Appendix C eqn (C.11) [ψ r (t, x, π s (t, y] ± i rs 3 ( x y) eqn (C.1) [ψ r (t, x, ψ s (t, y] ± [π r (t, x, π s (t, y] ± 0 [ψ r (t, x), π s (t, y)] ± i rs 3 ( x y) [ψ r (t, x), ψ s (t, y)] ± [π r (t, x), π s (t, y)] ± 0 Bibliography Ref. [806] J. Phys. Conf. Ser., 53, 44-8, 006 page 693 [731] and [73] are the same Ann. Rev. Nucl. Part. Sci., 56, , 006 7