Limits on the neutron-antineutron oscillation time from the stability of nuclei

Abstract

We refute a recent claim by Nazaruk that the limits placed on the freespace neutron-antineutron oscillation time τ nn can be improved by many orders of magnitude with respect to the estimate τ nn > 2(T 0 /Γ) 1/2 , where T 0 is a measured limit on the annihilation lifetime of a nucleus and Γ ∼ 100 MeV is a typical antineutron-nucleus annihilation width.In a recent letter [1], Nazaruk claims to have increased the limit obtained from the stability of nuclei on the free-space n →n oscillation time [2][3][4] by 31 orders of magnitude. In view of the startling nature of this claim, it is important to carefully inspect the derivation of this result. In this note, we point out a specific error in Nazaruk's derivation. Correcting it, one obtains a limit of the same order of magnitude as given by previous authors [2-4] who used potential models for the n-nuclear andn-nuclear dynamics. We also explain in very simple terms the origin of the standard limit.Nazaruk's framework is that of the S matrix in the diagrammatic approach. For neutron-antineutron oscillations in the nucleus, he writes down (Eq. (17) of Ref.[1]) the probability W (t) for the transition at time t aswherenn characterizes the free-space oscillation, and Wn is given by Eq. (12) of Ref.[1] (after noting that Wn = −2iTn ii by comparing Eqs. (16) and (17)):We will follow Ref.[1] in demonstrating the result for the oversimplified case where then-nuclear dynamics is reduced to just a width factor, H = −iΓ/2, with Γ ∼ 100 MeV being a typical value. The introduction of real potentials for the n andn does not change the order of magnitude of the result [3,4]. The r.h.s. of Eq. (2) is easily evaluated, resulting in Wn(t α , t β ) = 2(1 − exp[−Γ(t α − t β )/2]),which replaces Nazaruk's Eq. (18) Wn(t α , t β ) = 1 − exp[−Γ(t α − t β )].1

Restriction on the neutron-antineutron oscillations from the SNO data on the deuteron stability

“…Restrictions on the n-transition time in vacuum which follow from data on nuclei stability have been obtained previously in a number of papers by different methods, beginning with the potential approach of [4][5][6], see [15][16][17][18][19][20][21].…”

“…Presence of the second order pole in the energy variable of intermediate nucleon is a characteristic feature of diagrams describing the n-transition in 2 Later the author of [17] tried to develop a field theory motivated approach to this problem which was criticized by scientific com munity [15,16,20,14]. nuclei, as discussed in [14].…”

“…Taking this into account, we obtain from Eq. (13) for the deuteron life time (15) v 0 is the antiproton velocity in the laboratory frame where proton is at rest.…”

Limits onnn̄oscillations from nuclear stability

“…Thus, in the first paper [9] he obtained T d ∼ τ nn , resulting in the limit τ nn > 10 31 yr which advances the lower limit (1) by about 30 orders of magnitude! Dover, Gal, Richard [11] and Krivoruchenko [12] subsequently pinpointed errors in that paper and reestablished the generally accepted lower limit (1). In the second, more recent paper [10], Nazaruk 'rederived' the T d ∼ τ nn result, but argued that since the nuclear decay is non exponential, a more careful consideration of the nuclear stability limit translates into τ nn > 10 16 yr, which advances the lower limit (1) by 'only' 15 orders of magnitude.…”

“…In this note I wish to expand the arguments outlined by Dover et al [11], in order to show in detail how Eq. (1) for τ nn is obtained.…”