On the experimental search for neutron mirror neutron → oscillations Yu.N.Pokotilovski1 Joint Institute for Nuclear Research 141980 Dubna, Moscow region, Russia 6 Abstract 0 0 2 ′ Fast neutron mirrorneutron (n n ) oscillationswere pro- n → → posed recently as the explanation of the GZK puzzle. We a J discuss possible laboratory experiments to search for such os- 1 1 cillations and to improve the present very weak constraints ′ 1 on the value of the n n oscillation probability. v → 7 1 PACS: 11.30.Er; 95.35.+d; 14.20.Dh; 28.20.-v 0 1 Keywords: reflection symmetry, mirror world, neutron oscillations, neu- 0 6 tron lifetime, ultracold neutrons 0 / x e - 1 Introduction. l c u n Mirror asymmetry [1] of our world is a well established fact. The idea that the : v i Nature, if not P-symmetric, is CP-symmetric [2] has not been supported by X experiment. But in the seminal paper [1], where the parity non-conservation r a hypothesis was first proposed, the existence was suggested of new particles with the reversed asymmetry: ”If such asymmetry is indeed found, the ques- tion still could be raised whether there could not exist corresponding ele- mentary particles exhibiting opposite asymmetry such that in the broader sense there will be over-all right-left symmetry”. According to [1] the transformation in the particle space responsible for the space inversion is not a simple reflection P : ~r ~r, but a more complicated PR transformation, → − where R is the transition of the particle into the reflected state in the mirror particle space. From this point of view the Nature is PR-symmetric, the equivalence between left and right is restored. 1e-mail: [email protected]; tel: 7-49621-62790;fax: 7-49621-65429 1 This idea has been revived [3] after the observation of CP-violation. In this paper it was shown that mirror particles, if they exist, can not interact with usual particles through strong or electromagnetic interaction, but only through some weak and predominantly through gravitational interactions. They proposed also that mirror particles and massive objects can be present in our Universe. Many new ideas appeared during the last forty years on this subject. There were found strong arguments that the dark matter in the Universe may be the mirror matter. Serious implications of the experimental search for the dark matter were discussed recently. For example the results of DAMA [4] and CRESST [5] experiments were interpreted [6] as the evidence of scattering of mirror particles in the detectors. Mirror matter concept has found also development from superstring theories. The recent reviews of the state of art of theoretical and experimental investigations in the field of mirror particles may be found in [6, 7]. ′ The idea was put forward recently [8] (see also [9]) that fast n n → oscillations could provide a very effective mechanism for transport of ultra high energy cosmic protons, with the energy exceeding the Greisen-Zatsepin- Kuzmin cutoff 5 1019eV , over very large cosmological distances. × Irrespective of this particular mechanism it turned out that existing exper- ′ imental constraints on n n oscillations are very weak. The experimental → limit on the neutron antineutron oscillation time is strong enough [10] due → to the high energy release of the antineutron annihilation 2 GeV. There ′ ∼ is no such signal in the case of n n transition. Real constraints on the → characteristic time of this process are much smaller than the neutron lifetime ′ [8]. Indeed, the only signal for n n transformation is the disappearance → of neutrons from the beam. No special experiment with the aim to search for such a disappearance has been performed before. Very rough estimate of the loss of the neutron beam from the experimental search for the n n˜ - ′ → oscillations [10, 8] gives a constraint for the time of n n oscillation at the → level of 1 s. The neutron balance in reactors gives not better precision. Since ′ there is no firm predictions for the probability of the n n oscillations, an → experimental search for this transition has to be performed with the highest possible precision. The present limit on the oscillationtime of the o–positronium to the mirror o–positronium is 1 ms (see experiment [11] with reinterpretation in [12]). ≈ There are plans to improve this limit on one-two orders of magnitude [12]. 2 The phenomenology of the neutron mirror neutron oscillations is similar → to that of neutral kaon, muon antimuon and n n˜ oscillation. Starting ′ → → from n n mass matrix − ¯ L = ψMψ, (1) where spinor n ψ = , (2) n′   and M δm M = (3) ′  δm M    we have standard solution for evolution of the mirror neutron component with the initial number of ordinary neutrons n : 0 δm2 n′(t) = n(0) sin2(√∆E2 + δm2 t). (4) δm2 + ∆E2 · Here δm is the transition mass and 2∆E = M M is the mass difference ′ − of the neutron and mirror neutron states. When oscillations take place in free space the only contribution to ∆E comes from the neutron interaction with external magnetic field B: 2∆E = µB, where µ = 6 10 12 eV/G is − · the neutron magnetic moment. Introducing τ = h¯/δm and ω = ∆E/h¯ we osc obtain n(0) n′(t) = sin2( 1 + (ωτ )2 t/τ ), (5) osc osc 1 + (ωτ )2 · osc q ω 4.8 103 s 1 in the field B = 1 G. − ≈ × Since experimentally we have always ωτ 1, two limiting cases are osc ≫ possible: ωt 1 and ωt 1. In the first case the average of oscillating term ≫ ≪ is equal to 1/2, and 1 ′ n (t) = . (6) 2(ωτ )2 osc The second case gives ′ 2 n (t) = (t/τ ) . (7) osc The second, more experimentally sensitive situation, is realized when coher- ent evolution of the wave function ψ takes place in the well magnetically shielded conditions (from external and the Earth magnetic fields). 3 Now let us consider possible experimental approaches to the search of ′ n n oscillations. There are two such approaches: the neutron beam → experiments and the storage of ultracold neutrons [14]. Two kinds of the beam experiments are possible: the first one – based on the measurement of disappearance of neutrons from the beam due to ′ n n transformation and the second one, when after such hypothetical → transformationthe incident neutronbeam is stopped by the neutronabsorber, and the mirror component then again can be re-transformed to the ordinary neutron component according to Eq. (6). Let us estimate possible sensitivity. 2 Disappearance of the neutrons from the beam. Let the neutron beam with the flux φ and the average velocity v enters 0 the magnetically shielded neutron flight path of the length L. The flux of mirror neutrons at the end of the flight path is φ (t) = φ (L/vτ )2. It n′ 0 osc is just the number of neutrons disappeared from the beam. To forbid the ′ n n transformation the magnetic field B such that ω t 1 should be B → ≫ ′ switched on along the flight path. Since the change in counts due to n n → transformation is expected to be small, in the limit of one standard error during the time T for each of the measurements – with permitting and exp forbidding of oscillations, we get L φ ( )2T < (2φ T )1/2, (8) 0 exp 0 exp vτ osc and L τ > (φ T /2)1/4. (9) osc 0 exp v With φ 3 107 s 1[13], v 100 m/s, L =5 m, and the experimental time 0 − ≈ × ≈ T =1 month 2.5 106 s, we get τ >125 s. exp osc ≈ · 3 Process n n′ n. → → In this approach the flight path consists of two magnetically shielded sections with the length of L/2 each, with the perfect absorber of neutrons in the middle. In the first section the neutrons transform to the mirror state with the probability w = (L/2vτ )2, then the incident neutrons are absorbed, osc 4 ′ and, in the second section the transformation n n should take place with → the same probability. The neutron intensity at the end of the flight path is L 4 φ (t) = φ ( ) , (10) n′ 0 2vτ osc The magnetic field in any of the sections will forbid the oscillations. If the neutron detector count rate with stopped beam is φ the same considera- bgr tions give: L φ ( )4T < (2φ T )1/2, (11) 0 exp bgr exp 2vτ osc with the result L T τ > (φ )1/4( exp )1/8. (12) osc 0 2v 2φ bgr With the same parameters of the experiment and assuming φ = 0.01 s 1, bgr − we get τ > 20 s. osc 4 The storage of ultracold neutrons. The above calculation is not applicable to the ultracold (UCN) storage exper- iments [14], where the neutrons are confined in the closed chambers. In this case the neutron-wall collisions at the rate f < v > / < d >, where v is the ≈ neutron velocity and d is the distance between collisions, cause decoherence, disrupting the oscillation, the mirror component being lost, penetrating into the wall with the rate λ 1/fτ2 in the case of degaussed storage chamber, osc ≈ and with the rate λ f/2(ω τ)2 in the magnetic field B, (ω = ω B(G)), B B ≈ · when the transition to the mirror state is suppressed. If the neutron life- time storage measurements are performed in degaussed and non-degaussed conditions with the precision 1 s, what corresponds to the uncertainty of α 10 6 s 1 in the decay constant, we get the precision for the oscillation − − ∼ time τ > 1/(fα)1/2. At the typical f (5 10) we get τ > 300 500 s. osc osc ∼ − − No previous neutron lifetime measurements in UCN storage mode were performed in degaussed conditions. The interesting observation exists, how- ever, that the measurements of the neutron lifetime by two different methods: the first one – the measurement of the neutron density in the decay volume and counting the β-decay products (electrons or protons), and the second one – the storage of ultracold neutrons, give slightly different results. The table contains the results of all the measurements, which display the errors 5 not exceeding 10 s. The first method is insensitive to any invisible decay or disappearance of neutrons from the decay volume, the second method, to the contrary, is sensitive. The difference in the results of these methods, if correct, gives a hint at some invisible channel of disappearance of neutrons from storage chambers. Without the result [27] the difference in decay con- stants is (5.47 2.85) 10 6 s 1, with taking into account [27] this difference is − − ± · (9.7 2.8) 10 6 s 1. The predicted neutron decay constant into a hydrogen − − ± · atom: n H+ν˜ [28] is as low as 4 10 9 s 1, (branching ratio 3.8 10 6) e − − − → ∼ · ∼ · and can not explain the observed difference (see also [29] where the estimate of the neutron decay constant to the atomic mode has been performed, based on the earlier neutron lifetime measurements). The UCN storage measurements were performed in the Earth magnetic field 0.5 G, and using the above expression for the rate of the neu- ∼ tron loss from the chamber with the neutron-wall collision frequency f, λ = f/2(ω τ )2, we get the oscillation time τ = (f/2λ)1/2/ω . With B osc osc B f (5 10) s 1, ω 2.4 103 s 1, and λ = 5 10 6 s 1, we get τ = 0.3 0.4 − B − − − osc ≈ − ∼ · · − s - the figure close to the necessary one for the mechanism [8]! It is difficult to say at this moment how seriously this should be taken. But it is clear that high precision neutron lifetime experiments of both classes are important. On the other hand, we should not ignore the obvious trend of beam experiment lifetime data to the lesser values, in the direction of better agreement with the neutron storage results. 5 UCN flow experiment. This approach seems somewhat simpler than the precise UCN storage mea- surements. Consider UCN constant flow through the storage chamber with entrance and exit windows (it is assumed isotropic angular distribution). The neutron balance equation has the view: dN Sv (s + s )v N in out = φ s ρ µ ρ = 0. (13) 0 in dt − 4 − 4 − τ n Here N is the equilibrium number of neutrons in the chamber, φ is the 0 neutron flux density at the entrance to the chamber, s and s are the in out areas of entrance and exit windows, ρ is the neutron density in the chamber, v is the mean neutron velocity, V and S are the volume and the area of the internal surface of the chamber, µ is the neutron loss probability per 6 bounce, τ is the neutron β-decay lifetime. The first term at the right side n is the neutron influx to the chamber, the second one is the neutron loss due to collisions with the internal surface, the third one is the neutron efflux to both holes, and the last one is the neutron β-decay. If φ = const, the equilibrium neutron density 0 4φ s 0 in ρ = , (14) v(Sµ + s + s + δ) in out where δ = 4V/vτ . n We can estimate the sensitivity of equilibrium neutron density to the change of neutron loss coefficient dρ 4φ Ss 0 in = . (15) dµ −v(Sµ + s + s + δ)2 in out The detector count rate is φ s s v 0 in out I = ρs v/4 = . (16) det out Sµ + s + s + δ in out Its variations because of variation ∆µ of the neutron loss probability is φ Ss s ∆µ 0 in out ∆I = . (17) − Sµ + s + s + δ)2 in out (cid:18) At the effect of oscillationsin the limitof one error during the measurement times T with and without the magnetic field we have: exp 1 φ Ss s T 2φ Ss s T 1/2 0 in out exp 0 in out exp < . (18) (fτ )2(Sµ + s + s + δ)2 Sµ + s + s + δ! osc in out in out Finally, we have 1 (T φ s s )1/4S1/2 exp 0 in out τ > . (19) osc 21/4f (Sµ + s + s + δ)3/4 in out At µ 10 5 achieved with the Fomblin oil or grease cover of the wall surface − ∼ (see Fig. 1 in the recent review [15]), reasonably Sµ s ,s . With the in out ≪ f < v > / < d >, < d > 4V/S, taking s = s = s, demanding that in out ≈ ∼ the neutron decay does not decrease essentially the neutron density in the chamber: s 4V/(τ v), and assuming that the storage chamber is a cylinder n ≫ with the diameter and the height l we get: T φ 1/4l2 exp 0 τ 0.13 . (20) osc ≈ s v (cid:18) (cid:19) 7 During one month measurements with and without the magnetic field (T 2.5 106 s), with φ = 103 cm 2 s 1, l=100 cm, s=10 cm2, and v=400 exp 0 − − ≈ · cm/s, we get τ 420 s. osc ≈ We neglected the gravity in this estimate. More detailed optimization of the experiment in respect to all parameters taking into account the effect of gravity may increase the sensitivity considerably. In all described types of experiments the switching on weak magnetic ′ field to forbid n n oscillations, and increasing the detector’s count rate, → can, in principle, produce the opposite effect due to neutron reflection from small magnetic potential U = µB. 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