Reply to Comment on “An Improved Experimental Limit on the Electric Dipole
Moment of the Neutron”
C.A. Baker,1 D.D. Doyle,2 P. Geltenbort,3 K. Green,1, 2 M.G.D. van der Grinten,1, 2 P.G. Harris,2 P.
Iaydjiev∗,1 S.N. Ivanov†,1 D.J.R. May,2 J.M. Pendlebury,2 J.D. Richardson,2 D. Shiers,2 and K.F. Smith2
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK
Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, UK
Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
(Dated: December 11, 2018)
PACS numbers: 13.40.Em, 07.55.Ge, 11.30.Er, 14.20.Dh
Our Letter [1] places a new experimental limit on the
electric dipole moment (EDM) of the neutron. The Com-
ment [2] points out that we did not explicitly include
in our analysis the effect of the Earth’s rotation, which
shifts all of the frequency ratio measurements Ra to lower
(higher) values by 1.3 ppm when the B0 field is upwards
(downwards). However, this effect is essentially indis-
tinguishable from other effects that can shift Ra, and
all such shifts were compensated for in [1] by using ex-
perimentally determined values of Ra0 (which we call
Ra0↓ and Ra0↑, respectively, for the two polarities of B0),
where 〈∂Bz/∂z〉V = 0.
We turn now to the details. Naively, one would ex-
pect that the crossing point of the lines in Fig. 2 of [1]
(which lies at Ra − 1 = 5.9 ± 0.8 ppm) would have
〈∂Bz/∂z〉V = 0, with its ordinate yielding the true
EDM. However, what were referred to in [1] as horizon-
tal quadrupole fields (involving ∂Bx/∂y etc.) shift these
lines towards the right. A difference in the strengths
of these quadrupolar fields upon B0 reversal leads to a
differential shift in Ra, and thus to a vertical displace-
ment of the crossing point. The Earth’s rotation mim-
ics this behavior precisely, by moving the B0-down (-
up) line leftwards (rightwards). Thus, where quadrupole
fields are mentioned in [1], one might better read this as
“quadrupole fields and Earth-rotation effects combined”.
The “quadrupole shift” listed in Table 1 of [1] simply rep-
resents the move from the crossing point to the average
of the EDM values determined (independently) by the
measured Ra0↓ and Ra0↑ values.
The shift measurements are described (rather than just
“mentioned”) in [1]. First, the strongest constraint arises
from a study of the depolarization of the neutrons as a
function of Ra, and thus, effectively, as a function of
〈∂Bz/∂z〉V . Neutrons of different energies have different
heights of their centers of mass, and thus the T2 spin re-
laxation is maximized when〈(∂Bz/∂z)
2〉V is minimized.
The values of Ra−1 at which the polarization product α
was found to peak were (5.7± 0.2, 5.9± 0.2) ppm for B0
∗On leave from Institute of Nuclear Research and Nuclear Energy,
Sofia, Bulgaria
†On leave from Petersburg Nuclear Physics Institute, Russia
up, down respectively. In the presence of the dipole in the
region of the door of the storage chamber [1], the point
for B0 down (up) at which 〈(∂Bz/∂z)
2〉V is minimized
is 0.2 ppm higher (lower) than the point Ra0↓ (Ra0↑).
These data provide direct, independent measurements
for each B0 polarity of the actual values Ra0 at which
〈∂Bz/∂z〉V = 0, taking into account any and all shift
mechanisms, known or unknown, acting on Ra. Since
these depolarization results are drawn from the EDM
data themselves, they cannot be described as “ex post
facto”. We conclude from our data that the differen-
tial quadrupole shift and Earth rotation effect cancel to
within 15% in our apparatus. The fact that the resulting
dn values ((−0.6 ± 2.3,−0.9 ± 2.3) × 10
−26 e cm for B0
up, down respectively) agree so well with each other gives
added confidence in the experimental results overall.
Second, after about 60% of the data had been taken, a
bottle of variable height was used to measure the profile
of the magnetic field within the storage volume. Ex-
trapolation of these data to the EDM bottle (which does
include a small correction due to Earth’s rotation) yields
Ra0↑ −Ra0↓ = (1.5± 1.0) ppm.
Our data show no evidence for changes in the relevant
long-term B-field properties from the periodic disassem-
bly of the magnetic shields.
Since the publication of [1], we have improved our fit-
ting procedure to take full account of correlations be-
tween the quadrupole and dipole corrections, and to in-
clude explicitly the effect of the Earth’s rotation. The
results yield new net shifts (to be compared with those
listed in Table 1 of [1]) for the dipole and combined
quadrupole/Earth rotation effects of (−0.46,+0.30) ×
10−26 e cm respectively, with a net uncertainty of 0.37×
10−26 e cm for both. In combination with the other ef-
fects discussed in [1] this yields an overall systematic cor-
rection to the crossing point of (0.20±0.76)×10−26 e cm
for the second analysis of [1]. The final value for the EDM
from this analysis is then (−0.4± 1.5(stat)± 0.8(syst))×
10−26 e cm, implying |dn| < 2.8× 10
−26 e cm (90% CL),
identical to the previous limit from this analysis.
The Comment asserts incorrectly that the Ra−1 values
averaged to zero in the first analysis of [1]. By choice of
the applied ∂Bz/∂z, they averaged to 8.9 ppm for both
B0 polarities. Since any net differential shifts in Ra have
been shown to be small, this analysis need not be altered.
http://arxiv.org/abs/0704.1354v1
In conclusion, the overall limit of |dn| < 2.9 × 10
−26 e cm (90% CL) remains unchanged.
[1] C. Baker et al., Phys. Rev. Lett. 97, 131801 (2006).
[2] S.K. Lamoreaux and R. Golub, Phys. Rev. Lett., 98,
149101, (2007).

  The Authors reply to the Comment of Golub and Lamoreaux. The experimental
limit on the neutron electric dipole moment remains unchanged from that
previously announced.

Reply to Comment on “An Improved Experimental Limit on the Electric Dipole
Moment of the Neutron”
C.A. Baker,1 D.D. Doyle,2 P. Geltenbort,3 K. Green,1, 2 M.G.D. van der Grinten,1, 2 P.G. Harris,2 P.
Iaydjiev∗,1 S.N. Ivanov†,1 D.J.R. May,2 J.M. Pendlebury,2 J.D. Richardson,2 D. Shiers,2 and K.F. Smith2
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK
Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, UK
Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
(Dated: December 11, 2018)
PACS numbers: 13.40.Em, 07.55.Ge, 11.30.Er, 14.20.Dh
Our Letter [1] places a new experimental limit on the
electric dipole moment (EDM) of the neutron. The Com-
ment [2] points out that we did not explicitly include
in our analysis the effect of the Earth’s rotation, which
shifts all of the frequency ratio measurements Ra to lower
(higher) values by 1.3 ppm when the B0 field is upwards
(downwards). However, this effect is essentially indis-
tinguishable from other effects that can shift Ra, and
all such shifts were compensated for in [1] by using ex-
perimentally determined values of Ra0 (which we call
Ra0↓ and Ra0↑, respectively, for the two polarities of B0),
where 〈∂Bz/∂z〉V = 0.
We turn now to the details. Naively, one would ex-
pect that the crossing point of the lines in Fig. 2 of [1]
(which lies at Ra − 1 = 5.9 ± 0.8 ppm) would have
〈∂Bz/∂z〉V = 0, with its ordinate yielding the true
EDM. However, what were referred to in [1] as horizon-
tal quadrupole fields (involving ∂Bx/∂y etc.) shift these
lines towards the right. A difference in the strengths
of these quadrupolar fields upon B0 reversal leads to a
differential shift in Ra, and thus to a vertical displace-
ment of the crossing point. The Earth’s rotation mim-
ics this behavior precisely, by moving the B0-down (-
up) line leftwards (rightwards). Thus, where quadrupole
fields are mentioned in [1], one might better read this as
“quadrupole fields and Earth-rotation effects combined”.
The “quadrupole shift” listed in Table 1 of [1] simply rep-
resents the move from the crossing point to the average
of the EDM values determined (independently) by the
measured Ra0↓ and Ra0↑ values.
The shift measurements are described (rather than just
“mentioned”) in [1]. First, the strongest constraint arises
from a study of the depolarization of the neutrons as a
function of Ra, and thus, effectively, as a function of
〈∂Bz/∂z〉V . Neutrons of different energies have different
heights of their centers of mass, and thus the T2 spin re-
laxation is maximized when〈(∂Bz/∂z)
2〉V is minimized.
The values of Ra−1 at which the polarization product α
was found to peak were (5.7± 0.2, 5.9± 0.2) ppm for B0
∗On leave from Institute of Nuclear Research and Nuclear Energy,
Sofia, Bulgaria
†On leave from Petersburg Nuclear Physics Institute, Russia
up, down respectively. In the presence of the dipole in the
region of the door of the storage chamber [1], the point
for B0 down (up) at which 〈(∂Bz/∂z)
2〉V is minimized
is 0.2 ppm higher (lower) than the point Ra0↓ (Ra0↑).
These data provide direct, independent measurements
for each B0 polarity of the actual values Ra0 at which
〈∂Bz/∂z〉V = 0, taking into account any and all shift
mechanisms, known or unknown, acting on Ra. Since
these depolarization results are drawn from the EDM
data themselves, they cannot be described as “ex post
facto”. We conclude from our data that the differen-
tial quadrupole shift and Earth rotation effect cancel to
within 15% in our apparatus. The fact that the resulting
dn values ((−0.6 ± 2.3,−0.9 ± 2.3) × 10
−26 e cm for B0
up, down respectively) agree so well with each other gives
added confidence in the experimental results overall.
Second, after about 60% of the data had been taken, a
bottle of variable height was used to measure the profile
of the magnetic field within the storage volume. Ex-
trapolation of these data to the EDM bottle (which does
include a small correction due to Earth’s rotation) yields
Ra0↑ −Ra0↓ = (1.5± 1.0) ppm.
Our data show no evidence for changes in the relevant
long-term B-field properties from the periodic disassem-
bly of the magnetic shields.
Since the publication of [1], we have improved our fit-
ting procedure to take full account of correlations be-
tween the quadrupole and dipole corrections, and to in-
clude explicitly the effect of the Earth’s rotation. The
results yield new net shifts (to be compared with those
listed in Table 1 of [1]) for the dipole and combined
quadrupole/Earth rotation effects of (−0.46,+0.30) ×
10−26 e cm respectively, with a net uncertainty of 0.37×
10−26 e cm for both. In combination with the other ef-
fects discussed in [1] this yields an overall systematic cor-
rection to the crossing point of (0.20±0.76)×10−26 e cm
for the second analysis of [1]. The final value for the EDM
from this analysis is then (−0.4± 1.5(stat)± 0.8(syst))×
10−26 e cm, implying |dn| < 2.8× 10
−26 e cm (90% CL),
identical to the previous limit from this analysis.
The Comment asserts incorrectly that the Ra−1 values
averaged to zero in the first analysis of [1]. By choice of
the applied ∂Bz/∂z, they averaged to 8.9 ppm for both
B0 polarities. Since any net differential shifts in Ra have
been shown to be small, this analysis need not be altered.
http://arxiv.org/abs/0704.1354v1
In conclusion, the overall limit of |dn| < 2.9 × 10
−26 e cm (90% CL) remains unchanged.
[1] C. Baker et al., Phys. Rev. Lett. 97, 131801 (2006).
[2] S.K. Lamoreaux and R. Golub, Phys. Rev. Lett., 98,
149101, (2007).
