# 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. · 0.58 Impact Factor

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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,

Russia

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

A.P. Serebrov

Petersburg Nuclear Physics Institute

Gatchina, Leningrad district

188300 Russia

Telephone: +7 81371 46001

Fax: +7 81371 30072

E-mail: serebrov@pnpi.spb.ru

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Abstract

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

osc

has been obtained,

osc

≥ 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

been done.

Keywords: mirror world; neutron oscillations; ultracold neutrons

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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 [1]. 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

[4]. In particular, it was pointed out recently [5] 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,

osc

> 414 s (90% C.L.) [7]. 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.

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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

1

N t and

2

N t

for a short holding time t1 and a long one, t2, both for

the trap

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

0B

/

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 [8]. 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.

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number of neutrons (log. scale)

NB(t1)

N0(t1)

0

B

R(t2) =

R(t1) =

t2

t1

holding time, s

N0(t1)

NB(t1)

N0(t2)

NB(t2)

searched

effect

control

measurement

NB(t2)

N0(t2)

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

f

t n T

f

t n T

0B nnh nnh

/ exp1

RNNPP

. (1)

f

t

nn

P

is the average probability for such a transition during the flight time

ft of a

neutron in-between collisions with the trap walls, and

h

n T

is the average number of

collisions during the holding time

hT . For

osc

1

b

the probability for a nn transition

is then [5,8]

2

2

f

2

osc

f

osc

nnf

22

2

oscosc

sin1

sin

2

2

,

1

22

tb

b

t

P t b

bb

, (2)

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where

osc

is the oscillation time, the magnetic moment of the neutron, and b the

magnetic field. As shown in ref. [9], 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

2

f

2

osc

*

nnhh

,exp(/)

t

P T bTb b

. (3)

Here

2

ft

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

filling time

fill

, and the average emptying time

emp

) and

*

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,

2

ft

=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. [7].

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 [10]. 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

[11], 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 [7] 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 [12] could provide an efficient

mechanism to capture mirror matter in the Earth, as put forward in [13] to explain the

result of the DAMA experiment to search for dark matter [14]. In this connection the

papers [15,16] discuss the possible existence of mirror magnetic fields of the order of

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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

2*

oscexp(

/)

b b

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

result is

2

osc

=(2.84 ± 2.03)×10-6 s-2 with

2

=1.98, from which we derive

osc

403 s

(90% C.L.).

Turning the argument around and supposing the existence of a nn mixing

sufficiently large to result in a nn oscillation time of

osc

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.

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0 200400600

b, nT

8001000 1200

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

-2

osc·exp(-b/b

*)·10

6

Fig. 3. Results of measurements with scanning the “zero” magnetic field. The results for

++

bB

1/

rNN

and

bB

1/

rNN

are combined.

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

BB

/1

RNNr

, which is given in Fig. 4.

The result r= (–0.06 ± 1.01)×10-4 with

2

=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

2

=1.89.

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

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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

-30

-25

-20

-15

-10

-5

0

5

10

15

20

r

±-effect·10

4

2007

Fig. 4. Study of the effect

+

BB

1/

rNN

with horizontal magnetic field.

To summarize, under the simplest assumption that there exists no mirror magnetic

fields, we obtain

2

osc

=(2.84 ± 2.03)×10-6 s-2, which corresponds to a lower limit

of

osc

403 s (90% C.L.) on the nn oscillation time. Combining this result with our

previous limit,

2

osc

=(1.29 ± 2.76)×10-6 s-2 (

osc

414 s (90% C.L.)) [7], an improved

limit of

2

osc

=(2.29 ± 1.64)×10-6 s-2 is obtained. Hence, our improved new limit on the

nn oscillation time is

osc

≥ 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

osc

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.

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0 20004000 6000 800010000 12000 14000

-6

-4

-2

0

2

4

6

r

±-effect·10

3

26 Nov 28 Nov 30 Nov 2 Dec 4 Dec 6 Dec

time, min

2007

Fig. 5. Study of the effect

+

BB

1/

rNN

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-

02-00859.

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