Download The electric dipole moment of elementary particles

I L NUOV0
CIMENTO
VOL. X I , ~ . 6
16 Marzo 1959
The Electric Dipole Moment of Elementary Particles.
R . L. G A a w I ~"
IBM
Watson Lab. a~d Dept. o/ Pl~ysics, Columbia U~iversity - New York
L. ]~I. LEDEI~I.~-(*)
C E R N - (leneva
(rieevuto il 12 Dicembre 1958)
- - The detection of electric dipole moments (EDM) of elem e n t a r y particles is discussed and a new limit to the size of the electron
ED3~[ is presented ( ~ e-1.5.10 -15 cm). This result is used in a discussion
of recent observations of positronium annihilation.
Summary.
1.
-
Introduction.
I t is still of c o n s i d e r a b l e i n t e r e s t in t h e t e s t i n g of t i m e - r e v e r s n l i n v a r i a n c e
and parity conservation to attempt to detect the electric dipole moment (EDM)
of a n e l e m e n t a r y p a r t i c l e . T h e e x i s t e n c e of a n E D M i m p l i e s n o n - i n v a r i a n c e
u n d e r t i m e r e v e r s a l a n d n o n - c o n s e r v a t i o n of p a r i t y (~~) a n d i t s a b s e n c e u n d e r
(*) J. S. Guggenheim Fellow, 1958-59. Permanent address: D e p a r t m e n t of Physics,
Columbia University, New York.
(1) E. M. PU~C]~LL ~nd N. F. RA~SE:~': Pl~ys. Rev., 78, 807 (1950); J. SMITH,
E. M. PUrCeLL and N. F. RA~S~Y: Phys. Rev., 10S, 120 (1957).
(2) L. LANDAU: ZU. Aksper. Teor. Fiz., 32, 405 (1957); Nucl. Phys., 3, 405 (1957).
(3) T. D. L]~E and C. 5I. YA.~(~: Elementary Particles a~d Weak I~deractio?ts, B N L 443
(T-91) (1957), p. 17.
(a) N . F . RA_MS]~:~':Phys. Rev., 109, 225 (1958).
(5) D. BERLEY, R. L. GAlCWIN, G. GIDAI, and L. M. LED~nMAN: Phys. Rev. Lett.,
1, 144 (1958).
THE
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OF
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PARTICLES
777
a severe test is a sensitive indication of invariance of tile particle under space
reflection or t i m e reversal (~).
SMITH, PURCELL and RAMSEY (1) in an atomic b e a m resonance e x p e r i m e n t
h a v e set an u p p e r limit to the electric dipole m o m e n t of the neutron. Their
result is D . < 10 -~° cm where D. multiplied by the electric charge gives the
dipole m o m e n t . Since we k n o w t h a t p a r i t y is not conserved, we m a y regard
this m e a s u r e m e n t as showing t h a t IF 12.i G [2< 3.10 - ~ , where G is the probability a m p l i t u d e for p a r i t y mixing (which m a y be large), and F is the relative
a m p l i t u d e n o n - i n v a r i a n t under t i m e reversal (*).
M o t i v a t e d b y the desire to find some difference between the m u o n and the
electron other t h a n the rest mass, a search has been m a d e for a m u o n electric
dipole m o m e n t with the following result (5):
(1)
D~ ~ 10 -1~ e r a .
A discussion (7) of the effects of a possible electron electric dipole m o m e n t
in the spectroscopy of the hydrogen a t o m led to the results (this applies equally
well to the proton):
(])
De < 10 - ~ c m .
R e c e n t reports (7) of the observation of effect proportional to ~ . E in posit r o n i u m have led us to a f u r t h e r e x a m i n a t i o n of this question. We call attention in this note to three points:
i)
moment
practice,
sequent
M a n y proposed experiments designed to detect the electric dipole
of charged particles are based on tile incorr'ect notion t h a t it is, in
possible to a p p l y an electric field to such a particle without the confree acceleration implied b y Newton's second law.
ii) There exist in the literature, d a t a on tile b e h a v i o u r of free electrons
which enable a more sensitive limit t h a n (2) to be found for the electron EDM.
This t y p e of e x p e r i m e n t m a y be i m p r o v e d b y an additional order of magnitude.
iii) The limit thus set m a k e s it e x t r e m e l y unlikely ttmt intrinsic electric
m o m e n t s are responsible for the (( ~ . E )~ effect observed in positronium.
(6) I. ZEL'DOVlCII: Journ. Exp. Theor. Phys., 6, 1148 (1958). Translation. This
illuminating paper discusses the connection between electric moments and asymmetric decay.
(*) Alternatively, IE 12< 3" 10-13, where E is that amplitude which introduces both
parity and time-reversal mixing.
(:) G. •EINBERG: Phys. Rev. (to be published).
(s) F. OBENSnAN and L. PAGE: Phys. Rev. (to be published).
50
- II Nuovo
Cimento.
778
2. -
R.L. GARWIN and L. M. LEDER.~IAN
A n a l y s i s of s o m e i n c o r r e c t e x p e r i m e n t s .
M a n y e x p e r i m e n t s h a v e been p e r f o r m e d or proposed for the m e a s u r e m e n t
of the E D M of charged particles. These generally r u n into a difficulty which
does not exist for neutral particles (1). The p r o b l e m caused b y the charge
is simply t h a t to m e a s u r e an ED~[ one m u s t a p p l y an electric field at the particle in order to generate an i n t e r a c t i o n energy for the p a r a m e t e r being observed. A charged particle c a n n o t exist unaccelerated in an electric field.
However, charged particles in m a t t e r h a v e t i m e - a v e r a g e d motions which are
either rest or uniform (drift) velocity with respect to the applied electric field.
Such a r r a n g e m e n t s h a v e essentially no sensitivity to EDM. The essential
reason is t h a t all forces acting on the particle in m a t t e r are electrical. F o r
example, the mobility of ions in liquids is well k n o w n to be of the order ~ some
cm/s per k V / c m of applied field. Charged particles, e.g. ions in the liquid,
m o v e at constant velocity in zero average field since the electric drag exerted
b y the m e d i u m exactly equals the applied field. Thus, for example, proposals
to observe ~ shift in the resonant f r e q u e n c y in nuclear m a g n e t i c resonance
carried out in the presence of a strong electric field, i.e. observing the param e t e r d in ( / ~ - H + d a . E ) , fail because the nucleus shifts to the new m i n i m u m
in the total electric p o t e n t i a l which it experiences. Quan t.um mechanical considerations do not alter the conclusion t h a t the charged particle m u s t be accelerated b y the applied field in order to detect the E D M (*).
3. - E D M of t h e free e l e c t r o n .
I t happens t h a t an e x p e r i m e n t h~s been p e r f o r m e d for quite n different
purpose which has considerable sensitivity to the electron EDM. This is the
anomalous .q-factor e x p e r i m e n t of PIDD, LOUISELL and CRANE (9). I n this
e x p e r i m e n t electrons polarized n o r m a l to a uniform magnetic field are caused
to execute a large n u m b e r ( ~ 107) of orbital revolutions in a m a g n e t i c field.
The vertical plane precession induced b y the supposed E D M builds up only
for a single half-period of the anomalous m o m e n t precession before decreasing
again, since thereafter the spin points in the opposite sense in the orbit plane.
H o w e v e r , no significant reduction in polarization is observed t h e r e b y setting
(') W. PAUL however notes that a second order effect may be observed in a strong
electric field gradient. In this case the resultant electric field is proportional to the
EDM times the field gradient.
(9) R. W. PIDD: Bull. Am. Phys. Soc., 7, 364 (1958) and private communication.
See also H. R. CRANE, R. W. PIDD and W. H. LOUISELL: Phys. Rev., 91, 475 (1953).
THE
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3IOMENT
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779
a limit on the electric dipole m o m e n t equal to t h a t of the a n o m a l o u s m a g n e t i c
m o m e n t (v/c~l):
Do < 2~ - ~
,
.'. De < 3"10 -14 c m .
A quite different calculation can be m a d e using the results of this experiment.
An electric dipole m o m e n t of m a g n i t u d e e times the anomalous magnetic mom e n t would change the anomalous precession period b y ~ f a c t o r ~ 1 + ~ / 2 .
This can be seen b y t r e a t i n g the E D M precession in the electric field (v/e)× Ho
as if a rotating' m a g n e t i c field of m a g n i t u d e (~e/2z~)(v/c)Ho were applied and
E D M = 0. I n the CS r o t a t i n g with the cyclotron f r e q u e n c y we observe two
s t a t i o n a r y orthogonal fields: (ec~/2z)(v/C)Ho and H 0 - - (o)/y)-= (o:/2n)Ho. Since
this e x p e r i m e n t agrees with m e a s u r e m e n t s of the ~momalous m o m e n t of the
b o u n d electron (7) and with t h e o r y to within at least 10 -:' of the anomalous
m o m e n t , we find i m m e d i a t e l y t h a t
(3)
9o £- 1.5.10-~ (,m.
A f u r t h e r increase in sensitivity can be obtained b y a direct analysis b y M o t t
scattering of the out-of-plane polarization for electrons which h a v e been stored
in the magnetic field for ~ and ~ periods of the anomalous precession. A measur e m e n t to 1 ° would yield a sensitivity D ~ ]0 -~6 cm.
4. - a - E
e f f e c t in p o s i t r o n i u m .
I n this experiment, an effect is observed when p o s i t r o n i u m is formed b y
polarized positrons in a ]5 k V / c m electric field (s). The effect (a change in
the detected rate of 2 - q u a n t u m annihilation) has the s y m m o t r y a.E. We
only c o m m e n t here on the impossibility of this effect being due to intrinsic
E D M of the e l e m e n t a r y particles as limited b y (3) (we invoke the CPT t h e o r e m
here only to similarly restrict the E I ) M of the positron). The a r g u m e n t is
independent of the details of the e x p e r i m e n t and is m a d e t~s follows. The
m a x i m u m interaction energy produced b y the electric field is, using (3)
eDeE ~ (5-10-1°)(10-15)(50) = 3"10 .2:3 e r g .
The corresponding angular frequency of the free oscillations between eigenstates of the p e r t u r b e d s y s t e m is thus
~0~
eDeE
< 3.104 s _ l .
. . . .
780
R.
L.
GAR'WIN
and
L.
I~.
LEDER[YIAN
Since this corresponds to a period considerably longer t h a n the lifetime of
triplet positronium ( ~ 10 -7 s) the m a x i m u m amplitude of such a presumed
intrinsic E D M effect is
(10-7)(4.10 4) = 4.10-3
which is far from the 5 % effect observed. This is certainly an absolute maxi m u m , since detailed calculation of matrix elements, s y m m e t r y considerations, etc., can only reduce tile effect. Thus, if the effect should turn out
to actually have the s y m m e t r y ¢~.E (and not be a p . E effect masquerading as
u . E because of the ¢~.p correlation in weak interactions (8)) it would have
to be a t t r i b u t e d to the interactions involved in positronium formation and
decay.
One of us (LML) would like to t h a n k C E R N
ItALPERN and A. PETERlgAN for useful discussions.
RIASSUNT0
for hospitality,
and
I.
(*)
Si discnte 19 rivelazione dei mornenti di dipolo elettrico (EDM) delle p~rtieelle
elementari e si ottiene un nuovo limite della grandezza dell'EDM dell'elettrone
( ~ e.l.5.10 -15 cm). Si usa tale risult~to nella discussione di recenti osservazioni dell'annichilamento del positonio.
(*) ~ l r a d ~ z i o ~ e
a c~tra deZla R e d c ~ z i o n c .