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7
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84927870926
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A preliminary account of this work is given in P. Herczeg and R. N. Mohapatra, in The Vancouver Meeting, Particles and Fields '91, edited by D. Axen, D. Bryman, and M. Comyn (World Scientific, Singapore, 1992), Vol. 1, p. 572. The lower bounds on GM M bar and Gμ(e) we gave there are larger by about a factor of 3 than those given here. They were obtained by constraining m++ and m+ not only by the experimental value of the ρ1 parameter [see the text after Eq. (10)], but also by the vR-dependent theoretical bounds which follow from assuming B / R <= 104 in m02/ m++ 2= 1 / ( 1 + BR-1κ2vR-2) and m02/ m+2= 1 / ( 1 + 1/2 BR-1κ2vR-2). Although the latter bounds are reasonable theoretical constraints, we use now only the limits from the ρ1 parameter which are free from theoretical assumptions.
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8
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84927870925
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We note that if from the matrices U and V [defined after Eq. (4)] one is hierarchical, so will be the other, since the matrix K = U+V is known to be hierarchical.
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17
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84927870924
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For Ω h2 we have taken the upper bound in Ω h2<= 0.38 [Bludman (Ref. [6])]. For Ω h2= 1 our lower bounds for M ->M¯ and $μ+-> e+ν bareνmu would become smaller only by a factor of app 2. The cosmological bound holds in the form (3) provided that at the time of the decay the neutrinos are nonrelativistic and the Universe is matter dominated;
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18
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84927870923
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for mνμ apeq 1 keV this is still satisfied for τ νμ >wig 106 sec [E. W. Kolb (private communication)], while the lifetime of νμ-> νeνeν bare via ΔL0 exchange (see the text further on) is longer than the age of the Universe for mνμ
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(1983)
Nucl. Phys
, vol.227 B
, pp. 337
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Pal, P.B.1
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29
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4244089509
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Inspection shows that the νμ-> νegamma lifetime from the contribution of the ΔL+- φ2+ loop (Babu and Mohapatra) can be short (possibly as short as app 4 times 104 sec for mνμ apeq 270 keV). However, radiative lifetimes short enough to satisfy the cosmological bound are excluded from mνμ >wig 100 eV by limits on radiative decays of neutrinos emitted by SN 1987A see
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(1989)
Phys. Rev. Lett.
, vol.62
, pp. 509
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Kolb, E.W.1
Turner, M.2
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31
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84927870922
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Bludman (Ref. [6])], and for 35 eV
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32
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84927870921
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Roncadelli and Senjanović (Ref. [10]);
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33
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84927870920
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Pal (Ref. [8]);
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36
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84927870919
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The experimental limit B ( μ -> 3 e ) < 1 times 10-12 implies | fee sprime star fe μ sprime|
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38
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84927870918
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we allowed λeffapeq 1 for the effective Higgs boson self-coupling λeff]. For | fμμ | we use | fμμ | <= 0.16. This bound is obtained as follows: Inspection shows that for the ranges of fee and vR for which the bound (6) can hold, the experimental limit on mνe requires γ
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39
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33744773154
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for mνμ the first term in Eq. (2) can therefore be neglected. An analysis of pertinent data yields vR>wig 1 TeV [, ] and, as we find [see Eq. (8)], mνμ >wig 35 keV. For values of m++ corresponding to our lower bounds on M ->M¯ for given $mνμ 's, the direct phenomenological bounds on | fee| and | fμμ | are not better than the above bounds.
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(1989)
P. Langacker and S. U. Shankar, Phys. Rev. D
, vol.40
, pp. 1569
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43
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84927870917
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Particle Data Group, Phys. Lett. B 239 (1990). We neglect the small difference between | Ke μ | and | Kμ e |.
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44
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84927870916
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Mohapatra and Pal (Ref. [12]).
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50
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84927870914
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As noted by Halprin, M ->M¯ can arise in the model also via two-neutrino exchange. However, the strength of the effective interaction due to this mechanism is below $10-5GF.
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52
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84927870913
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Gunion et al. (Ref. [14]).
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56
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84927870912
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P. Herczeg and R. N. Mohapatra (unpublished); reported in P. Herczeg, in Rare Decay Symposium, edited by D. Bryman et al. (World Scientific, Singapore, 1989), p. 24.
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60
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0010128658
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Concerning indirect empirical limits on GM M bar see Gunion et al. (Ref. [14]), Chang and Keung (Ref. [14]), and Schwartz (Ref. [14]). For Gμ(e) we have evaluated constraints from data on mu decay and inverse mu decay
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(1990)
Phys. Lett. B
, vol.252
, pp. 170
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Mishra, S.R.1
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61
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0001715272
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from the W mass, and from charged current universality [see D. H. Wilkinson, TRIUMF Report No. TRI-PP-91-9 (unpublished)]. We find at 90% C.L., | Gμ(e)| < 0.28 GF, | Gμ(e)| < 0.24 GF, and | Gμ(e)| < 0.052 GF, respectively. The last bound may be affected by theoretical uncertainties.
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(1989)
Phys. Rev. D
, vol.39
, pp. 266
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Langacker, P.1
London, D.2
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62
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84927870911
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K. Jungman and W. Bertl et al., PSI Experiment No. R-89-06.1.
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63
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84927870910
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X.-Q. Lu et al., LAMPF Proposal No. LA-11842-P, 1990.
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64
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84927870909
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See Schwartz (Ref. [14]); the constraint from ρ1 gives m++ < 568 GeV.
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65
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84927870908
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Note that the term Ue μ fee2 in fμμ sprime cannot cancel fμμ , since the experimental limit on the μ -> 3 e branching ratio requires (for the range of fee and fμμ we are dealing with here) | Ue μ fee2| << fμμ (see Refs. [13] and [14]).
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66
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84927870907
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If the mixing term is small relative to m̃φ2-&mtilde02, one has for Rφ- R apeq 1 (where Rphi is the Higgs potential parameter in m̃φ2apeq RφvR2) m02= R vR2- ( β prime )2κ2. In this case even for β prime = 1, ( vR)max would increase for mνμ = 270 keV and mνμ = 35 keV only by a factor of app 1.3 and app 4, respectively.
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67
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84927870906
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Deshpande et al. (Ref. [22]).
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