# Neutron – Mirror Neutron Oscillations: How Fast Might They Be?

###### Abstract

We discuss the phenomenological implications of the neutron () oscillation into the mirror neutron (), a hypothetical particle exactly degenerate in mass with the neutron but sterile to normal matter. We show that the present experimental data allow a maximal oscillation in vacuum with a characteristic time much shorter than the neutron lifetime, in fact as small as sec. This phenomenon may manifest in neutron disappearance and regeneration experiments perfectly accessible to present experimental capabilities and may also have interesting astrophysical consequences, in particular for the propagation of ultra high energy cosmic rays.

###### pacs:

14.20.Dh, 11.30.Fs, 12.60-i, 98.70.SaThe idea that there may exist a mirror world, a hidden parallel sector of particles that is an exact duplicate of our observable world, has attracted a significant interest over the years LY ; Holdom ; FV ; ortho ; BDM ; PLB98 ; BB-PRL ; BCV (for reviews, see IJMPA-B ; IJMPA-F ). Such a theory is based on the product of two identical gauge factors with identical particle contents, where ordinary (O) particles belonging to are singlets of , and mirror (M) particles belonging to are singlets of . Mirror parity under the proper interchange of and the respective matter fields makes the Lagrangians of both sectors identical to each other. Such a situation can emerge e.g. in the context of superstring theory.

Under this hypothesis, the Universe should contain along with the ordinary photons, electrons, nucleons etc., also their mirror partners with exactly the same masses. Invisible M-matter, interacting with O-matter via gravity, could be a viable dark matter candidate BB-PRL ; BCV ; IJMPA-B ; IJMPA-F .

Besides gravity, the two sectors could communicate by other means. In particular, any neutral O-particle, elementary or composite, can have a mixing with its M-twin. For example, kinetic mixing between ordinary and mirror photons Holdom can be revealed in the ortho-positronium oscillation ortho and can be tested also with dark matter detectors IJMPA-F . Ordinary neutrinos can mix with mirror neutrinos and thus oscillate into these sterile species FV , as well as neutral pions and Kaons into their mirror partners. Such mixings may be induced by interactions between the O- and M-fields mediated by messengers like pure gauge singlets or extra gauge bosons acting with both sectors PLB98 ; IJMPA-B .

In this letter we explore the mixing between the ordinary neutron and mirror neutron due to a small mass term . We show that the existing experimental data do not exclude a rather fast oscillation, with a timescale s. Such an intriguing possibility can be tested in small scale ”table-top” experiments, and it can have strong astrophysical implications, in particular for ultra high energy cosmic rays.

Let us take the minimal gauge symmetry for the O-sector that contains the Higgs doublet , and quarks and leptons: left , , and right footnote1 . As usual, we assign a global lepton charge to leptons and a baryon charge to quarks. If and were exactly conserved then the Majorana masses of neutrinos would be forbidden and the proton would be stable.

However, and are not perfect quantum numbers. They are related to accidental global symmetries possessed by the Standard Model Lagrangian at the level of renormalizable couplings, which can be however explicitly broken by higher order operators cutoff by large mass scales . In particular, the well-known D=5 operator (), yields, after inserting the Higgs vacuum expectation value (VEV) , small Majorana masses for neutrinos, Weinberg , while the D=9 operators or () lead to neutron - antineutron () oscillation phenomenon nnbar .

Suppose now that there exists a hidden M-sector with a gauge symmetry , a mirror Higgs doublet , and mirror quarks and leptons: , and , where one assigns a lepton charge to mirror leptons and a baryon charge to mirror quarks. Mirror parity tells that all coupling constants (gauge, Yukawa, Higgs) are identical for both sectors, the O- and M-Higgses have equal VEVs, , and hence the mass spectrum of mirror particles is exactly the same as that of ordinary ones. In addition, if the O-sector contains and violating operators like and , then analogous and violating operators and should be included in the M-sector.

Moreover, there can exist higher order operators that couple gauge singlet combinations of O- and M-particles. In particular, the D=5 operator

(1) |

induces the mixing between the ordinary and mirror neutrinos FV , and the D=9 operators coupling three ordinary and three mirror quarks,

(2) |

result in ordinary neutron - mirror neutron mixing. On the other hand, if one postulates conservation of the combined quantum number , the operators are forbidden while the operator is allowed. Hence, the exact conservation would suppress the oscillation but not the oscillation footnote2 . Taking into account that the matrix elements of the operators (2) between the neutron states are typically GeV, one estimates the mass mixing term between and states as:

(3) |

One could naively think that the bound on mixing is nearly as strong as the one on mixing: eV, or s, which follows from the direct experimental search of free neutron oscillation into antineutron () Grenoble , as well as from the limits on nuclear stability: a stable nucleus would decay into states or due to the conversion followed by or annihilation into pions with a total energy of nearly two nucleon masses Chetyrkin . However, we show below that the bound on oscillation is many orders of magnitude weaker, s. This indeed is quite surprising! The oscillation time can be much smaller than the neutron lifetime s.

As far as mirror neutrons are invisible, the oscillation can manifest experimentally only as a neutron disappearance. If , strictly free neutrons would oscillate many times with a maximal mixing angle () before they decay. Thus, instead of the exponential law for the neutron survival probability, one would observe the oscillating behaviour . Is not this immediately excluded by the experiments measuring the neutron lifetime with great accuracy? The answer is no! Simply because in these experiments neutrons and mirror neutrons are subject to very different conditions.

The evolution of free non-relativistic neutrons is described by the effective Hamiltonian in space,

(4) |

where is the neutron mass and its decay width, which, due to exact mirror parity, are precisely the same for mirror neutrons. However, the potentials and felt by and are not quite the same. Namely, since the experiments are done on Earth, the terrestrial magnetic field, G, induces an effective contribution eV, where is the neutron magnetic moment. On the other hand, as far as no mirror magnetic fields exist on Earth. Thus, for , the effective mixing angle between and states is while the oscillation time is s, and hence the average transition probability becomes . For example, for eV one has , and such a small disappearance effect could hardly be observed in the experiments. Thus, to improve the experimental sensitivity the magnetic field should be suppressed.

In the ILL-Grenoble experiment designed to search for neutron - antineutron oscillation, the magnetic field was reduced to G Grenoble . Cold neutrons propagated in vacuum with an average speed of m/s and effective time of flight s, in a -metal vessel shielding the magnetic field. No antineutrons were detected and the limit s was reported. Clearly, the search for oscillation was not the aim of this experiment, but it can be used to set a crude limit on the timescale . For larger than the neutron propagation time s, the oscillation probability is . By monitoring the neutron beam intensity it was observed that about 5 of neutrons disappeared Grenoble . If this deficit could be entirely due to oscillation, this would imply s. However, as far as most of the losses can be attributed to scatterings with the walls in the drift vessel, one can assume rather conservatively that no more than 1 of losses were due to oscillation, and thus obtain a bound s, or eV.

Let us discuss whether the bounds from nuclear stability, which give the strongest limit on , are applicable also to the case of oscillation. One may naively think that it could destabilize nuclei as follows: in a stable nucleus (e.g. O) oscillates into . Then , or its -decay products, can escape from the nucleus thus producing an unstable isotope (O) whose characteristic signals could be seen in large volume detectors as e.g. Superkamiokande.

This kind of reasoning certainly applies to neutron invisible decay channels, e.g. . However, it is invalid for the oscillation channel as far as the mirror particles , , are exactly degenerate in mass with their ordinary partners , , . Indeed, energy conservation allows the decay (or ) only if the mass difference between the isotopes and is larger than (or ). But then also the decay with neutron emission ( emission) would be kinematically allowed and such a nucleus could not be stable. One confirms by inspection that all nuclear ground states satisfying such conditions have short lifetimes rendering the extremely rare mirror channels invisible in practice footnote3 .

Thus, the oscillation cannot destabilize nuclei and so the only realistic limit remains s imposed by the data from the Grenoble experiment Grenoble .

We discuss now the possible theoretical models for the operators (2) and their phenomenological implications. The contact terms of the form with TeV, if valid at TeV energies, could have interesting consequences for future high energy colliders as the LHC. Namely, the mirror baryons could be produced in proton collisions, which would be seen as processes with baryon number violation and large missing energy.

For example, in theories with large extra dimensions ADD , the ordinary and mirror worlds can be conceived as parallel 3-dimensional branes embedded in a higher dimensional space, where O-particles with a gauge group are localized on one brane and M-particles with a gauge group on another brane, while gravity propagates in the bulk. In the context of such a theory, operators with a cutoff TeV could be induced as effects of the TeV scale quantum gravity. In addition, the baryon number can be related to a gauge symmetry in the bulk ADD , in our case , , that forbids the operators , leading to oscillations.

It is also possible that at TeV energies the terms (2) do not exist literally in the contact form, but are rather induced in the context of some renormalizable theory. Let us give a simple example of such a model. Assuming again conservation, consider the Yukawa terms

(5) |

where () is a color-triplet scalar with mass , having precisely the same gauge quantum numbers as the right down-quark , and () is its mirror partner with the same mass , whereas and are additional gauge singlet fermions, with a large mass term (for simplicity, the Yukawa constants are assumed to be of order 1). Then, at energies , the operators are induced with a cutoff scale (see Fig. 1) footnote4 .

If e.g. both and are TeV, then at TeV energies the operators (2) act in a contact form. The scale TeV can be effectively obtained on other extremes, by taking e.g. GeV and GeV, or GeV and GeV. In this case, while the detection of the scalar is within the reach of LHC, the mirror quarks cannot be produced as the messengers , are far too heavy.

Let us address now the cosmological limits. The most serious constraints come from the requirement that the O- and M-worlds should have different temperatures and at the Big Bang Nucleosynthesis (BBN) epoch. The mirror sector would contribute to the universe expansion rate as an effective number of extra neutrinos BDM , and thus the bounds on demand that or so. This can be achieved by adopting the following paradigm IJMPA-B : at the end of inflation the O- and M-worlds are (re)heated in a non symmetric way, , which can naturally occur in the context of certain inflationary models; after (re)heating, , the processes between O- and M-particles are too slow to bring the two sectors in equilibrium, so that both systems expand adiabatically, maintaining the temperature asymmetry in all subsequent epochs.

The operators (2) induce collision processes as , etc. that cause entropy transfer between the ordinary and mirror sectors. Their effective rate scales as , where the coefficient accounts for phase space factors, and for TeV they would be in equilibrium at temperatures above TeV or so. Thus, in order to fulfill the BBN request on the asymmetry, the (re)heat temperature should be smaller than TeV footnote5 .

This applies only if at temperatures the operators (2) act in the contact form. In the context of the model presented above, that is true if the scalar is heavy enough, TeV or so. For smaller , however, the dominant process at temperatures would be rather . Comparing its rate with the Hubble parameter (), one obtains that these processes would bring the two sectors in equilibrium only at temperatures above , i.e., .

Hence, the output of the limit strongly depends on . For TeV it is milder: e.g. for GeV ( GeV) it turns GeV. But it sharply strengthens with increasing , and for TeV becomes roughly TeV. This restricts the possible inflation scenarios and excludes many popular scenarios for primordial baryogenesis.

But on the other hand, the same particle exchange processes between O- and M-sectors, or , once they are out of equilibrium, violate , and possibly also , could provide a plausible low-temperature baryogenesis mechanism for both observable matter (O-baryons) and dark matter (M-baryons), along the lines of the leptogenesis scheme via the scatterings suggested in BB-PRL ; IJMPA-B .

The fast oscillation could have intriguing implications for ultra high energy (UHE) cosmic rays. Namely, when a UHE proton scatters a relic photon, it produces a neutron that promptly oscillates into a mirror neutron which then decays into a mirror proton . The latter undergoes a symmetric process, scattering a mirror relic photon and producing back an ordinary nucleon. However, as the M-sector is cooler, , the mean free path of is larger by a factor of than that of ordinary protons ( Mpc). In this way, the UHE protons could propagate at large cosmological distances without significant energy losses. This may relax the Greisen-Zatsepin-Kuzmin cutoff in the cosmic ray spectrum GZK and also explain the correlation between the observed UHE protons and far distant sources as BL Lacertae TT .

Concluding, we observed an intriguing loophole in the physics of such a familiar and long studied particle as the neutron: the existing experimental data do not exclude that its oscillation time into a mirror partner may be as small as 1 s. This oscillation, however, is impossible for neutrons bound in nuclei, while for free neutrons it is suppressed by matter and magnetic field effects footnote6 .

Our suggestion is falsifiable at small costs. ”Table-top” experiments searching for neutron disappearance () and regeneration (), performed in proper ”background-free” conditions, may discover the neutron - mirror neutron oscillation and thus reveal the existence of sterile partners of nucleons, opening up a window to the mirror world with a number of serious implications in astrophysics and cosmology.

We are grateful to V. Berezinsky, S.L. Glashow, S. Gninenko, Y. Kamyshkov, V. Kuzmin, R.N. Mohapatra, V. Nesvizhevsky, T. Soldner and I. Tkachev for useful discussions. The work of Z.B. is partially supported by the MIUR biennal Grant No. PRIN/2004024710/002, and that of L.B. by the Grant POCTI/FNU/43666/2002.

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