Search for mirror dark matter in a laboratory experiment with ultracold neutrons
ABSTRACT Mirror matter is considered as a candidate for dark matter. To investigate this possibility an experimental search for neutron - mirror neutron transitions has been carried out using storage of ultracold neutrons in a trap with different magnetic fields. As a result, a new limit for the neutron - mirror neutron oscillation time tau_osc has been obtained, tau_osc >= 448 s (90% C.L.). As a side result, some restriction of the presence of a mirror magnetic field in the range 0 - 1200 nT has been obtained.
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ABSTRACT: Physical processes involving weak interactions have mirror images which can be mimicked in the natural universe only by exchanging matter and antimatter. This experimental observation is easily explained by the hypothesis that spatial inversion exchanges matter and antimatter. Yet according to conventional theory, the parity operator P does not exchange matter and antimatter but instead yields phenomena which have never been observed. We examine the conventional derivation of the Dirac parity operator and find that it incorrectly identifies the matrices associated with probability density (γ 0 rather than the identity matrix I) and current (γ i rather than γ 5 σ i ). This illusory functional dependence incorrectly requires that γ 0 preserve its sign under spatial inversion. This requirement results in a mixed-parity vector space defined relative to velocity, which is otherwise isomorphic to the spatial axes. We derive a new spatial inversion operator M (for mirroring) by introducing a pseudoscalar unit imaginary and requiring that for any set of orthogonal basis vectors, all three must have the same parity. The M operator is a symmetry of the Dirac equation. It exchanges positive and negative energy eigenfunctions, consistent with all experimental evidence of mirror symmetry between matter and antimatter. This result provides a simple reason for the apparent absence in nature of mirror-like phenomena, such as right-handed neutrinos, which do not exchange matter and antimatter. A new time reversal operator B (for backward) is also derived to be consistent with the geometry of the polar vectors inverted by the M operator. Mathematics Subject Classification (2010)14.J33–35Q41–81R50Advances in Applied Clifford Algebras 01/2011; 21(2):283-295. · 0.53 Impact Factor
Search for neutron – mirror neutron oscillations
in a laboratory experiment with ultracold neutrons
A.P. Serebrov1*, E.B. Aleksandrov2, N.A. Dovator2, S.P. Dmitriev2, A.K. Fomin1,
P. Geltenbort3, A.G. Kharitonov1, I.A. Krasnoschekova1, M.S. Lasakov1,
A.N. Murashkin1, G.E. Shmelev1, V.E. Varlamov1, A.V. Vassiljev1,
O.M. Zherebtsov1, O. Zimmer3,4
1 Petersburg Nuclear Physics Institute, RAS, 188300 Gatchina, Leningrad District,
2 Ioffe Physico-Technical Institute, RAS, 194021 St. Petersburg, Russia
3 Institut Laue-Langevin, BP 156, 38042 Grenoble cedex 9, France
4 Physik-Department E18, TU München, 85748 Garching, Germany
* Corresponding author
Petersburg Nuclear Physics Institute
Gatchina, Leningrad district
Telephone: +7 81371 46001
Fax: +7 81371 30072
Mirror matter is considered as a candidate for dark matter. In connection with this an
experimental search for neutron – mirror neutron (nn) transitions has been carried out
using storage of ultracold neutrons in a trap with different magnetic fields. As a result, a
new limit for the neutron – mirror neutron oscillation time
has been obtained,
≥ 448 s (90% C.L.), assuming that there is no mirror magnetic field larger than
100 nT. Besides a first attempt to obtain some restriction for mirror magnetic field has
Keywords: mirror world; neutron oscillations; ultracold neutrons
There are at least three motivations for the experimental search of mirror matter. First,
in our world the weak interaction violates the P-parity and the presence of a mirror
world would restore it . Second, mirror matter can be considered as a natural
candidate for the dark matter in the Universe [2,3]. And in third place, neutral
elementary particles, e.g. photon or neutrino, could oscillate into their mirror partners
. In particular, it was pointed out recently  that a neutron – mirror neutron
oscillation (nn) could be considerably faster than neutron decay, which would have
interesting experimental and astrophysical implications.
Experiments to search for nn transitions were carried out recently [6,7], which
provided new limits on the nn oscillation time. Our collaboration published the best
limit so far,
> 414 s (90% C.L.) . This article presents results of an additional
series of experiments carried out in autumn 2007, which somewhat improve the limit.
Further experiments have been performed with a wider range of magnetic fields whose
implications shall be discussed as well.
The experimental setup is shown in Fig. 1. Ultracold neutrons (UCN) are trapped
in a storage vessel inside a magnetic shielding which allows us to screen the Earth’s
magnetic field to a level below 20 nT. A solenoid within the shield can produce a
homogeneous magnetic field up to a few hundred microtesla. The magnetic field
settings were controlled by Cs-magnetometers.
Fig. 1. Experimental setup (top view). 1: UCN input guide; 2: UCN storage chamber; 3:
magnetic shielding; 4: solenoid; 5-6: UCN detectors; 7-9: valves; 10: Cs-
magnetometers, 11: monitor detector, 12: entrance valve.
The experimental task is to study the dependence of the UCN storage time
constant on the magnetic field. If neutron and mirror neutron have exactly the same
mass and if there is an interaction mixing these states, transitions will be possible if
there are no magnetic field and mirror magnetic field or if interaction with magnetic and
mirror magnetic fields compensate each other. Mirror neutrons then leave the trap
because they practically do not interact with ordinary matter. In the following we
assume, if not stated differently and as supposed in references [6,7], the absence of a
mirror magnetic field at the site of the experiment (see discussion below). A magnetic
field created by the solenoid will then suppress transitions and may therefore lead to an
increase of the UCN storage time constant. By measuring the numbers of neutrons in
N t and
for a short holding time t1 and a long one, t2, both for
magnetic field switched off, N0, and switched on, NB, the storage time constant is
obtained. For sensitivity reasons, the long holding time t2 is chosen to be close to the
storage time constant of the trap itself. The searched effect will manifest as a deviation
of the ratio
NN from unity at t2. Fig. 2 shows schematically the typical dependence
of the number of neutrons after different holding times in the trap with magnetic field
on or off. The effect on neutron count rates may be 10-3 or even smaller. Therefore,
measurements with short holding time t1 are obligatory to check for any systematic
effect. For instance, the initial number of neutrons after filling the trap could depend on
the magnetic field due to a small polarization of the UCN beam combined with a Stern-
Gerlach effect . Besides, switching on the current of the solenoid for producing the
magnetic field might influence the electronic counting system. Such an effect was
observed on the monitor detector used in this experiment. Although it could be
suppressed by properly choosing the discriminator threshold, the monitor detector data
were not used in the final data analysis. Instead, we took advantage of the high count
rates in the main detectors in a continuous-flow mode, operation compared to storage
mode. In the flow mode the entrance and the exit valves of the UCN trap were kept
open, such that the dwell time of UCN in the trap is on average only about 20 s
(calculated in a MC simulation) compared to a typical holding time of about 300 s.
These measurements showed that related systematic effects are smaller than 6×10-5.
number of neutrons (log. scale)
holding time, s
Fig. 2. Schematic representation of the exponential decrease of neutron counts in UCN
storage in the trap for a holding time
ht . Measurements for short time
1t serve for
control, and the measurements with the long time 2t are used to search for the effect.
The ratio of the neutron numbers N0/NB measured at the holding time t2 is related
to the probability for a nn transition as
t n T
t n T
0B nnh nnh
is the average probability for such a transition during the flight time
ft of a
neutron in-between collisions with the trap walls, and
is the average number of
collisions during the holding time
hT . For
the probability for a nn transition
is then [5,8]
P t b
is the oscillation time, the magnetic moment of the neutron, and b the
magnetic field. As shown in ref. , an exact solution of the transition probability in
material traps does not add significant corrections to eq. (2), which is derived for free
space without boundaries. After numerical integration over the UCN spectrum for
different neutron flight times
ft one obtains the final numerical dependence which can
be approximated as
P T bTb b
denotes the mean square time of the neutron free flight, the average
frequency of neutron collisions with the trap walls,
hT the total holding time of neutrons
in the trap (i.e. the sum of the holding time
ht with the trap valves closed, the average
, and the average emptying time
b is a device specific
parameter of this approximation. For the used trap – a horizontal cylinder with a
diameter of 45 cm and a length of 120 cm – it is 700 nT,
=0.012 s2 and =11 s-1.
Hence, a magnetic field of 700 nT will suppress the transition possibility to 1/e. More
details of the setup can be found in ref. .
Unfortunately, there is not much information available about presence and size of
mirror magnetic fields. A geophysical analysis constrains the Earth’s mirror matter to
below 3.8×10-3 . Model-dependent considerations of gravitational capture of dark
matter bound to the Solar System estimate its total amount to 1.78×10-5 Earth masses
, of which only three-tenth of a percent is enclosed by the orbit of the Earth.
Although there is no direct relation between mass of dark matter and mirror magnetic
field, but taking the average magnetic field in our Galaxy of about 1 nT also as a
“representative guess” for the mirror magnetic field, our analysis of the previous
experiment  was performed under the assumption of a negligible mirror magnetic
field. It should be noted that, however, an interaction of mirror dark matter and ordinary
matter due to photon – mirror photon kinetic mixing  could provide an efficient
mechanism to capture mirror matter in the Earth, as put forward in  to explain the
result of the DAMA experiment to search for dark matter . In this connection the
papers [15,16] discuss the possible existence of mirror magnetic fields of the order of
microtesla or larger. Therefore, we decided to extend our experiment to a few more
magnetic field settings around zero, scanning from 20 nT up to 1200 nT, and also to
increase the “strong field” setting by one order of magnitude to 20 µT. Moreover, the
direction of this field was periodically changed. On one hand one achieves more
statistics to improve the experimental limit for the nn oscillation time, adopting again
the assumption that no mirror magnetic field exists and observing that this weak-field
range is still sensitive to nn oscillation (see eq. (3)). On the other hand the presence of a
mirror magnetic field in the range 0 to 1200 nT (in corresponding “mirror” units) could
be verified in case an increase of the probability for nn oscillations will be observed
due to the compensation of the mirror neutron interaction energy with the mirror
magnetic field by the neutron’s one with the ordinary magnetic field. No statistically
significant deviation was observed. Therefore, the results of these measurements were
analyzed using eq. (3) and assuming the absence of a mirror magnetic field. Fig. 3
shows the results of measurements for the dependence
in eq. (3) as a
function of the magnetic field: b < 20 nT, b = 70 nT, 300 nT, 560 nT, and 1200 nT.
From this data a new limit for nn oscillations can be extracted by fitting eq. (3). The
=(2.84 ± 2.03)×10-6 s-2 with
=1.98, from which we derive
Turning the argument around and supposing the existence of a nn mixing
sufficiently large to result in a nn oscillation time of
200 s (90% C.L.) for
degenerate states (the weaker limit is due to the lower statistical accuracy of individual
measurements), the absence of any statistically significant dependence of magnetic
fields in the range 0 – 1200 nT can be interpreted as a restriction for mirror magnetic
field in the same range. It should be noted that this experiment has been carried out with
a horizontal direction of the magnetic field (in laboratory co-ordinates), such that the
time averaged effect of the mirror magnetic field in Universe and the Solar System may
be reduced by the Earth rotation. In order to obtain definite conclusions for Earth mirror
magnetic field, these measurements should be carried out not only covering a much
wider range of magnetic field in steps of about 400 nT, but also for three different field
directions, which was not feasible within the available beam time.
Fig. 3. Results of measurements with scanning the “zero” magnetic field. The results for
We obtained some additional experimental information from measurements with
the “strong” magnetic field only, but in opposite directions, B = ±20 µT, in order to
investigate a possible dependence on the direction of this field. The data were analyzed
in terms of the ratio R, defined as
, which is given in Fig. 4.
The result r= (–0.06 ± 1.01)×10-4 with
=1.64 indicates that there is no such
dependence within the quoted accuracy. An additional series of measurements was
carried out for opposite vertical magnetic fields with strength ±20 µT. The measured
r-ratios are shown in Fig. 5. The mean value is r= (7.5 ± 2.4)×10-4 with
To study the non-statistical dispersion of the individual results the influence of
switching the current on the electronic counting system was studied using continuous-
flow mode with high statistics. No effect was found on the accuracy level 10-4 (as
indicated by the fourth data point before the end of the series in Fig. 5). As such control
measurements were not carried out close to those points with maximum deviation 3.6
the reason of these deviations remains unclear.
28 Aug 11 Sep25 Sep 9 Oct23 Oct 6 Nov20 Nov
Fig. 4. Study of the effect
with horizontal magnetic field.
To summarize, under the simplest assumption that there exists no mirror magnetic
fields, we obtain
=(2.84 ± 2.03)×10-6 s-2, which corresponds to a lower limit
403 s (90% C.L.) on the nn oscillation time. Combining this result with our
=(1.29 ± 2.76)×10-6 s-2 (
414 s (90% C.L.)) , an improved
=(2.29 ± 1.64)×10-6 s-2 is obtained. Hence, our improved new limit on the
nn oscillation time is
≥ 448 s (90% C.L.).
If one supposes the existence of a nn mixing sufficiently large, i.e. resulting in a
nn oscillation time of
200 s (90% C.L.) for degenerate states, a possible Earth
mirror magnetic fields at the place of our experimental installation can be restricted in
horizontal direction to 0 – 1200 nT.
0 20004000 6000 800010000 12000 14000
26 Nov 28 Nov 30 Nov 2 Dec 4 Dec 6 Dec
Fig. 5. Study of the effect
with vertical magnetic field.
Acknowledgements: we would like to thank Z. Berezhiani and B. Kerbikov for
useful discussions. This work has been carried out with support of the PFBR grant 07-
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