Eur. Phys. J. C (2020) 80:107
https://doi.org/10.1140/epjc/s10052-020-7664-9
Regular Article - Experimental Physics
Statistical sensitivity estimates for oscillating electric dipole
moment measurements in storage rings
J. Pretz
1,2,3,a
, S. P. Chang
4,5
, V. Hejny
1
, S. Karanth
6
, S. Park
4
, Y. Semertzidis
4,5
, E. Stephenson
7
, H. Ströher
1,8
1
Institut für Kernphysik, Forschungszentrum Jülich, 52425 Jülich, Germany
2
III. Physikalisches Institut B, RWTH Aachen University, 52056 Aachen, Germany
3
JARA-FAME, Forschungszentrum Jülich, RWTH Aachen University, Aachen, Germany
4
Center for Axion and Precision Physics Research, IBS, Daejeon 34051, Republic of Korea
5
Department of Physics, KAIST, Daejeon 34141, Republic of Korea
6
Marian Smoluchowski Institute of Physics, Jagiellionian Univsersity, Cracow, Poland
7
Indiana Univ., Bloomington, IN 47408, USA
8
JARA–FAME (Forces and Matter Experiments), Forschungszentrum Jülich, RWTH Aachen University, Aachen, Germany
Received: 4 December 2019 / Accepted: 19 January 2020
© The Author(s) 2020
Abstract In this paper analytical expressions are derived to
describe the spin motion of a particle in magnetic and electric
fields in the presence of an axion field causing an oscillat-
ing electric dipole moment (EDM). These equations are used
to estimate statistical sensitivities for axion searches at stor-
age rings. The estimates obtained from the analytic expres-
sions are compared to numerical estimates from simulations
in Chang et al. (Phys Rev D 99(8):083002, 2019). A good
agreement is found.
1 Introduction and motivation
Axions and axion like particles (ALPs) are candidates for
dark matter. There is thus a huge experimental effort for the
search of these kind of particles. For a detailed review, we
refer the reader to references [2,3]. Axions and ALPs can
interact with ordinary matter in various ways. Reference [4]
identifies three terms:
a
f
0
F
μν
˜
F
μν
,
a
f
a
G
μν
˜
G
μν
,
∂
μ
a
f
a
¯
Ψ
f
γ
μ
γ
5
Ψ (1)
describing the coupling to photons, gluons and to the spin
of fermions, respectively. The vast majority of experi-
ments makes use of the first term [e.g. Cavity experiments
(ADMX), helioscopes (CAST), light-through-wall experi-
ments (ALPS)]. In addition, astrophysical observations also
provide sensitive limits to the axion-photon coupling. In gen-
eral, it is rather difficult for these experiments to reach masses
below 10
−6
eV, one reason being that the axion wave length
a
e-mail: pretz@physik.rwth-aachen.de
becomes too large. Furthermore, these experiments are mea-
suring rates proportional to at least a small amplitude squared.
For the second (and third) term in the list (1)thisisdiffer-
ent. It turns out that the second term has the same structure
as the QCD-θ term which is also responsible for an electric
dipole moment (EDM) of nucleons. The axion field gives
rise to an effective time-dependent θ -term and oscillates at
a frequency proportional to the mass of the axion m
a
.This
gives rise to an oscillating EDM. New opportunities to search
for axions/ALPs with much higher sensitivity arise, because
the signal is proportional to an amplitude A and not to its
square. To date, NMR based methods are being used to look
at oscillating EDMs [5].
Another possibility is to search for axions/ALPs in stor-
age rings. Storage ring experiments have been proposed to
search for electric dipole moments of charge particles [6,7].
These experiments allow also, with small modifications, to
search for oscillating EDMs. This possibility is discussed
in this paper. Section 2 explains the principle of the exper-
iment, how the (oscillating) EDM alters the spin motion in
electromagnetic fields and leads to a polarization observable.
In Sect. 3 statistical sensitivities for oscillating EDMs based
on these polarization observables are presented.
2 Spin motion in storage rings
The spin motion relative to the momentum vector in elec-
tric and magnetic fields is governed by the Thomas-BMT
equation [8–10]:
dS
dt
= (
MDM
+
EDM
) × S, (2)
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