Heavy sterile neutrinos - MPP Theory Group

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A.D. Dolgov et al. / Nuclear Physics B 590 (2000) 562–574 569 Fig. 2. Maximum lifetime of <strong>sterile</strong> neutrino, allowed by BBN, as a function of the heavy neutrino mass, both for an optimistic bound, N = 0.2, and for a conservative bound, N = 1.0. The upper panel corresponds to ν µ ↔ ν s or ν τ ↔ ν s mixings, while the lower one to ν e ↔ ν s mixing. Table 1 Fitting parameters for minimum allowed mixing (sin 2 θ) min fitted by Eq. (18) and maximum allowed life-time τ max fitted by Eq. (19) Mixing N (sin 2 θ) min fitting parameters τ max fitting parameters s 1 s 2 α t 1 t 2 β ν s −ν µ,τ 0.2 1423 −4.99 × 10 −6 −3.727 100.1 0.04788 −1.901 ν s −ν µ,τ 1 568.4 −5.17 × 10 −6 −3.549 128.7 0.04179 −1.828 ν s −ν e 0.2 140.4 −9.9 × 10 −6 −3.222 1218 0.0513 −2.658 ν s −ν e 1 66.33 −1.05 × 10 −5 −3.070 1699 0.0544 −2.652
570 A.D. Dolgov et al. / Nuclear Physics B 590 (2000) 562–574 which is possible for M s > 105 MeV is suppressed if M s < 140 MeV. However, for M s > 135 MeV the decay channel ν 2 → π 0 + ν a , (20) becomes open and strongly dominating. The life-time of π 0 → ν ¯ν was calculated in Refs. [26,27]. We can translate their results for the decay (20) and find for the life-time [ G 2 τ = F M s (Ms 2 − m2 π )f π 2 ] sin2 θ −1 16π [ = 5.8 × 10 −9 s sin 2 θ M s(Ms 2 − m2 π ) ] −1 m 3 , (21) π where m π = 135 MeV is the π 0 -mass and f π = 131 MeV is the coupling constant for the decay π + → µ + ν µ . Immediately after M s becomes bigger than m π the two-body decay becomes the main one and all other channels can be neglected. We cannot directly apply our numerical program (that was made for a 33.9-MeV neutrino) to this case, so we will instead make some simple order of magnitude estimates for the impact of very heavy ν 2 on BBN. One can roughly conclude that for the life-time of ν 2 smaller than 0.1 s, and corresponding cosmological temperature higher than 3 MeV, the decay products would quickly thermalize and their impact on BBN would be small. For a life-time larger than 0.1 s, and T
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Heavy sterile neutrinos - MPP Theory Group

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