Concerning the measurement of the gravitational acceleration of charged particles

V01ume 226, num6er 3,4

PHY51C5 L E 7 7 E R 5 8

10 Au9u5t 1989

C 0 N C E R N 1 N 6 7 H E M E A 5 U R E M E N 7 0 F 7 H E 6RAV17A710NAL ACCELERA710N 0 F C H A R 6 E D PAR71CLE5 D. HAJDUK0V1C 1 CERN, CH-1211 6eneva 23, 5w1t2er1and Rece1ved 9 May 1989

Mea5urement 0f the 9rav1tat10na1 acce1erat10n 0f ant1matter 15 0f fundamenta1 1mp0rtance a5 a te5t 0f the weak e4u1va1ence pr1nc1p1e and may a150 te5t 50me the0r1e5 0 f 4 u a n t u m 9rav1ty. A new 1dea h0w t0 perf0rm 5uch a mea5urement 15 pre5ented (at a the0ret1ca1 1eve1). 1t may 1ead t0 a mea5urement 0f 9rav1tat10na1 acce1erat10n 0f ant1pr0t0n5 and p051tr0n5 a5 we11 a5 0rd1nary part1c1e5, pr0t0n5, e1ectr0n5 and certa1n 10n5.

A5 wa5 rea112ed 6y Newt0n, there are tw0 4u1te d15t1nct c0ncept5 0f ma55 1nv01ved 1n 9rav1tat10n [ 1 ]: the 1nert1a1 ma55, m1, 0f a free1y fa111n9 60dy, wh1ch 15 a k1nemat1c 4uant1ty determ1n1n9 the pr0p0rt10na11ty 0f f0rce and acce1erat10n, and the 9rav1tat10na1 ma55, mcj, wh1ch mea5ure5 the 60dy•5 c0up11n9 t0 the 9rav1tat10na1 f1e1d. 7he weak e4u1va1ence pr1nc1p1e 5tate5 that

m1=m~

(1)

f0r a11 06ject5, w1th the re5u1t that the ma55 0fthe 06ject fact0r5 0ut 0f the 9rav1tat10na1 e4uat10n5 0f m0t10n. Up t0 n0w, the weak e4u1va1ence pr1nc1p1e ha5 0n1y 6een te5ted f0r 0rd1nary matter. 1n the E6tv65 exper1ment [2], f0r 6u1k matter 1n the Earth•5 9rav1tat10na1 f1e1d, the pr1nc1p1e ha5 6een ver1f1ed w1th a prec1510n 0f f1ve part5 1n 109 f0r a var1ety 0f mater1a15. (Let u5 n0te that F156ach et a1. [3], 1n a pre5uma61y 1nc0rrect reana1y515 0f the E~5tv65 exper1ment, c0nc1uded that E6tv65 data 1n fact ••5upp0rt the ex15tence 0f an 1ntermed1ate-ran9e c0up11n9 t0 the 6ary0n num6er 0r the hyperchar9e••.) F0r 6u1k matter 1n the 5un•5 9rav1tat10na1 f1e1d, D1cke [4] and 8ra91n5k1 [ 5 ] ach1eved much h19her prec1510n t0 5evera1 part51n 1012. F0r free part1c1e5 5uch a5 at0m5 [ 6 ], 0 n 1eave fr0m the Facu1ty 0f Natura1 5c1ence5 and Mathemat1c5, M0ntene9r0, Yu9051av1a.

352

neutr0n5 [ 7 ] and ph0t0n5 [ 8 ] the accuracy ach1eved ha5 0n1y 6een 0ne part 1n 102 0r 103. 1t 15 c1ear that 5uch a fundamenta1 pr1nc1p1e (weak e4u1va1ence) wh1ch ha5 1mp11cat10n5 6ey0nd any part1cu1ar c1a55 0f the0r1e5 ha5 t0 6e te5ted a150 f0r ant1matter. 8e51de5 the weak e4u1va1ence pr1nc1p1e, a mea5urement 0f the 9rav1tat10na1 acce1erat10n 0f ant1matter 15 1mp0rtant 1n the c0ntext 0f certa1n attempt5 t0 f0rmu1ate a the0ry 0f 4uantum 9rav1ty. 7he5e the0r1e5 pred1ct that there w111 6e 5p1n-1 (9rav1ph0t0n) and 5p1n-0 (9rav15ca1ar) partner5 0f the 5p1n-2 9rav1t0n [9]. 7he5e new partner5 are expected t0 c0up1e w1th appr0x1mate1y 9rav1tat10na1 5tren9th t0 50me c0n5erved char9e (5uch a5 6ary0n4uark and/0r 1ept0n num6er), and t0 6e ma551ve (pr0duce Yukawa p0tent1a15). Phen0men01091ca11y, under certa1n c0nd1t10n5 [ 10 ] the 5tat1c p0tent1a1 ener9y 6etween tw0 p01nt ma55e5 m1 and m2 15

V(r)=-6

m~rn2 ( 1 7 a e - ~ / ~ + 6 e -r/-~) r

(2)

where a and 6 are the m0du11 0f pr0duct5 0fthe vect0r and 5ca1ar char9e5 (1n un1t5 6m~m2) and v and 5 are the 1nver5e 9rav1ph0t0n and 9rav15ca1ar ma55e5 (ran9e5). 1n 9enera1 the ••char9e•• 15 4ue5t10n w1116e 50me 11near c0m61nat10n 0f 6ary0n and 1ept0n num6er5.7h15 f0rce w111theref0re 6e c0mp051t10n-dependent. 7he - ( + ) 519n 1n fr0nt 0 f a 1n e4. (2) 15 ch05en f0r the 1nteract10n 6etween matter and matter (ant1matter). A 9enera1 pred1ct10n 0f th15 type 0f the-

V01ume 226, num6er 3,4

PHY51C5 LE77ER5 8

0ry 15, then, that ant1matter w0u1d exper1ence a 9reater 9rav1tat10na1 acce1erat10n t0ward5 the earth than matter. 7h15 c1ear1y v101ate5 the weak e4u1va1ence pr1nc1p1e. Let u5 n0te that there are attempt5 t0 1nterpret 9e0phy51ca1 and 1a60rat0ry exper1menta1 data 0n an0ma10u5 9rav1tat10na1 effect5 6y e4. (2), 1.e. 1n term5 0f 6r0ken-5uper5ymmetry 4uantum9rav1ty m0de15 [ 1 1 ]. 1n fact, 1t may 6e that 50me exper1ment5 [ 12 ] w1th c0ntrad1ct0ry re5u1t5, when 1nterpreted w1th a 51n91e Yukawa term (a5 pe0p1e u5ua11y d0 when c0n51der1n9 a ••f1fth f0rce•• [ 3,13 ] ), are c0n515tent when 1nterpreted 6y e4. (2). 1n any ca5e, exper1menta1 te5t5 0f the weak e4u1va1ence pr1nc1p1e w1th ant1matter are 0f fundamenta1 1mp0rtance. 5uch an exper1ment, LEAR P5 200 (a mea5urement 0f the 9rav1tat10na1 acce1erat10n 0f the ant1pr0t0n) wa5 pr0p05ed and appr0ved at CERN three year5 a90 [ 14 ]. 7he f1r5t (and techn1ca11y very d1ff1cu1t) 5tep 1n the pr0p05ed exper1ment 15 t0 trap and 5t0re ant1pr0t0n5 1n a Penn1n9 trap at a temperature a5 10w a5 the temperature 0f 114u1d he11um. After that, the part1c1e5 w111 6e re1ea5ed vert1ca11y, a few at a t1me, 1nt0 a dr1ft tu6e (w1th a c0ax1a1 ma9net1c f1e1d f0r rad1a11y c0nf1n1n9 the ant1pr0t0n5) u5ed t0 5h1e1d the part1c1e 0r61t5 fr0m 5tray e1ectr1c f1e1d5. 7he part1c1e t1me-0f-f119ht 5pectrum thr0u9h the dr1ft tu6e 15 then mea5ured. 7h15 5pectrum, ref1ect1n9 the 1n1t1a1 d15tr16ut10n 0f ve10c1t1e5, w111exh161t a cut-0ff c0rre5p0nd1n9 t0 the e4ua11ty 0f the 1n1t1a1 k1net1c ener9y and the 9rav1tat10na1 p0tent1a1 ener9y chan9e 1n the dr1ft tu6e. 7h15 cut-0ff t1me 15 re1ated t0 the 9rav1tat10na1 acce1erat10n a exper1enced 6y the part1c1e 6y tc= ~ , where L 15 the dr1ft 1en9th. F0r m0re techn1ca1 deta115 and 5tudy 0f unwanted effect5 (e1ectr05tat1c effect5, ma9net05tat1c effect5, the patch effect, the e1ectr0n and the 1att1ce 5a9 effect, therma1 and vacuum effect5) 5ee ref. [141. 0 n e 0fthe ma1n tr0u61e51n th15 m0dern ver510n 0f the 6a111e0 exper1ment 15 that the 9rav1tat10na1 p0tent1a1 ener9y chan9e (f0r an accepta61e dr1ft tu6e 0f a60ut L = 1 m) 15 0r 0rder U~ 10 - 7 eV ( ~ 10 - 3 K ) wh1ch 15 5ma11, even c0mpared w1th the va1ue k87=3.45×10 -4 eV f0r 7 = 4 K (a temperature wh1ch ha5 yet t0 6e ach1eved). A5 a c0n5e4uence there are a 5ma11 num6er 0f 5uch 10w-ener9y ant1pr0t0n51n the 1n1t1a1 d15tr16ut10n and the p00r 5tat15t1c5 p05e a pr061em 1n a determ1nat10n 0f the cut-0ff t1me. 8e-

10 Au9u5t 1989

cau5e 0f th15 pr061em and 50me 0ther techn1ca1 pr061em5 there 15 9r0w1n9 d0u6t a60ut the p05516111ty 0f the pr0p05ed mea5urement w1th0ut 50me new 1dea5 [ 15 ]. 50, new 1dea5 are enc0ura9ed. We may a55ume the ava11a6111ty0fant1pr0t0n5 (0r p051tr0n5) at r00m temperature [ 15 ]. 7hu5 the 4ue5t10n 15 h0w t0 u5e the5e part1c1e51n 0rder t0 mea5ure the1r 9rav1tat10na1 acce1erat10n. 1n the pre5ent paper a 51mp1e meth0d 15 5tud1ed 6y a55um1n9 1dea1 exper1menta1 c0nd1t10n5. A deta11ed 5tudy 0f the meth0d under rea1 exper1menta1 c0nd1t10n5 w1116e a 5u6ject 0f an0ther pu611cat10n 1n c011a60rat10n w1th my exper1menta1 c011ea9ue5. 1n 0rder t0 9ra5p the 1dea, 1et u5 5tart fr0m the e4uat10n 0f m0t10n 0f a char9e 4 1n an e1ectr0ma9net1c f1e1d

dp dt =4E +4v×8

(3)

7he 501ut10n 0f th15 e4uat10n f0r a part1c1e w1th n0n-re1at1v15t1c ve10c1ty (v<< c) 1n cr055ed, c0n5tant and un1f0rm e1ectr1c and ma9net1c f1e1d5 may 6e f0und 1n any 900d 600k 0n e1ectr0dynam1c5 (5ee f0r examp1e ref. [16]). 7he cruc1a1 p01nt f0r further ana1y515 15 that 1n the d1rect10n perpend1cu1ar t0 the c0mm0n p1ane 0f f1e1d5E and 8, a part1c1e m0ve5 w1th a ve10c1ty wh1ch 15 a per10d1c funct10n 0f t1me w1th an avera9e va1ue, dr1ft ve10c1ty

E×8 /2dr1ft-- 82

(4)

1n the part1cu1ar ca5e E = 0, vdr1ft= 0 and the 0r61t 0f the part1c1e 15 a he11x, w1th 1t5 ax15 para11e1 t0 8. Let u5 c0n51der the ca5e when E = 0 , 6ut 1n5tead there 15 a c0n5tant and un1f0rm 9rav1tat10na1 f1e1d. 7hen, 1n5tead 0f 4E there 15 a term m1a 1n e4. (3), a 6e1n9 the 9rav1tat10na1 acce1erat10n. 50, 9rav1tat10n 15 e4u1va1ent t0 the ex15tence 0f an e1ectr1c f1e1d E= m~a/4 1n e4. (3). 7he c0rre5p0nd1n9 expre5510n f0r dr1ft ve10c1ty 15 m1

v~.~ = ~ - ~ a × 8 .

(5)

N0w, 1et u5 have a 100k at f19. 1.7he ma9net1c f1e1d 15 a10n9 the h0r120nta1 2 ax15 and 9rav1tat10na1 acce1erat10n a10n9 the vert1ca1 y ax15. 7he part1c1e m0ve5 1n the 2 d1rect10n w1th a un1f0rm ve10c1ty. 1n the y 353

V01ume 226, num6er 3,4

L7

PHY51C5 L E 7 7 E R 5 8

~-8

10 Au9u5t 1989

f1e1d u5ed 15 a61e t0 c0nf1ne 0n1y part1c1e5 w1th an ener9y 1e55 than E0 Part1c1e5 w1th h19her ener9y w111d1rect1y 90 t0 p1ane 8 and 6e detected, 91v1n9 a 5et 0f p01nt5 wh05e 9e0metr1ca1 centre can 6e ea511y f0und. 1n fact, 6ecau5e 0fthe 5ma11 dr1ft ve10c1ty, there 15n0t any detecta61e dr1ft a10n9 the x ax15 f0r 5uch part1c1e5. 50 the5e part1c1e5 91ve u5 1nf0rmat10n a60ut the x c00rd1nate when there 15 n0 dr1ft. Part1c1e5 w1th ener9y 5ma11er than E~ w1116e c0nf1ned f0r a t1me 2".7he e1ectr1c f1e1d c0u1d then 6e 5w1tched 0ff a110w1n9 them t0 h1t p1ane 8, and 6e detected, wh1ch w11191ve a new 5et 0f p01nt5 w1th a 9e0metr1ca1 centre at a d15tance x,~1r~ fr0m the f1r5t 0ne. 7hen, Vdr1ft ~ 1/)dr1ft1 - -

x
d1rect10n the ve10c1ty 15 a per10d1c funct10n 0f t1me w1th avera9e va1ue vv= 0.50 the part1c1e 15 n0t rea11y fa111n9. We can th1nk 0f 1t a5 c0nf1ned 1n a h0r120nta1 p1ane (a p1ane para11e1 t0 the x2 p1ane 1n f19. 1 ). 7he m0t10n 1n the x d1rect10n 15 a150 a per10d1c funct10n 0f t1me, 6ut w1th an avera9e dr1ft ve10c1ty 91ven 6y e4. (5). 7he dr1ft ve10c1ty 15 very 5ma11 (and much 5ma11er than the ve10c1ty a10n9 the 2 ax15). 50 1t 15 nece55ary t0 have the p05516111ty t0 c0nf1ne the part1c1e 1n the 5pace 6etween tw0 vert1ca1 p1ane5 (p1ane5 A and 8 1n f19. 1 ) para11e1 t0 the x y p1ane. 1t may 6e d0ne w1th an appr0pr1ate e1ectr1c f1e1d c0111near t0 the 2 ax15. 8ecau5e 0f 5uch an e1ectr1c f1e1d, 1n5tead 0f m0v1n9 w1th un1f0rm ve10c1ty, the part1c1e w11105c111ate a10n9 the 2 ax15. 7he m0t10n 1n the x and y d1rect10n5 w111rema1n unchan9ed. 7he rea1 exper1ment w0u1d 6e perf0rmed w1th many part1c1e5. 1n the 1dea1 ca5e they w0u1d 6e 1aunched 0ne 6y 0ne, 5ay, fr0m the 1eft t0 the r19ht 1n f19. 1. A detect0r at p1ane 8 w111mea5ure t1me 0f arr1va1 and p051t10n. (7h15 may 6e d0ne w1th a m1cr0channe1 p1ate detect0r [ 17 ] 0r 50me 0ther p051t10n5en51t1ve detect0r. ) 1t 15 appr0pr1ate (and rea115t1c) that the e1ectr1c 354

Xdr1f1

2"

(6)

Fr0m ( 5 ) and (6), tak1n9 1nt0 acc0unt that a and 8 are perpend1cu1ar, we can ca1cu1ate the 9rav1tat10na1 acce1erat10n: a=

[418 Xdr1n m1

2

(7)

(Let u5 n0te that m~ 15 exper1menta11y kn0wn w1th h19h accuracy t0 6e the 5ame f0r part1c1e5 and ant1part1c1e5 [ 18 ], a5 the0ret1ca11y pred1cted 6y the C P 7 the0rem. ) 1n add1t10n, f0r kn0wn 8, 4 and the mea5ured dr1ft d1rect10n (p051t1ve 0r ne9at1ve) 1t 15 ea5y t0 d15t1n9u15h 6etween expected acce1erat10n d0wn, and unexpected, 6ut f0r ant1matter perhap5 p055161e, acce1erat10n up. After d15cu5510n5 w1th a num6er 0f pe0p1e, 1 have under5t00d that a maj0r1ty are n0t fam111ar w1th the fact that a char9ed part1c1e d0e5 n0t fa11 1n cr055ed c0n5tant and un1f0rm 9rav1tat10na1 and ma9net1c f1e1d5.50, 1 have dec1ded t0 91ve here the fu11501ut10n 0f the e4uat10n 0f m0t10n 1n cr055ed 9rav1tat10na1 and ma9net1c f1e1d5 1nc1ud1n9 a150 an e1ectr1ca1 f1e1d u5ed f0r c0nf1n1n9 the part1c1e 6etween p1ane5 A and 8 1n f19. 1, and a 5ma115tray e1ectr1c f1e1d. 7he e4uat10n 0f m0t10n 1n th15 ca5e 15 dp dt = m ~ a + 4 v × 8 + 4 E

(8)

w1th the 9rav1tat10na1 acce1erat10n a, ve10c1ty v, e1ectr1c f1e1d E and ma9net1c f1e1d 8 91ven 6y

V01ume 226, n u m 6 e r 3,4

a=aj,

PHY51C5 L E 7 7 E R 5 8

v=21+jj+~k,

E=E,1+Ej+E~k,

/2V0 , ) (E.,~)c0~ -~-0~-2 c05 yc05 c~) 2 - -6.,.2,

8=8k,

(9)

where 1,j and k are un1t vect0r5 a10n9 the c0rre5p0nd1n9 rectan9u1ar axe5 (5ee a150 f19. 1 ). U51n9 (8) and (9) a very 51mp1e ca1cu1at10n 1ead5 t0 the 5y5tem 0f e4uat10n5

e= c/E:. mt

(E,,),,0,f~

(10)

1t 15 an 1dea1 51tuat10n t0 have E~=E,,= 0 1n the 5y5tem (10). H0wever, the e1ectr1c f1e1d wh1ch we u5e t0 c0nf1ne the part1c1e 15 a1way5 1n a d1rect10n 2• (w1th un1t vect0r k• ) 5119ht1y d1fferent fr0m 2. 1n add1t10n there are a1way5 5ma11 5tray f1e1d5. (1n a 5uperc0nduct1n9 dr1ft tu6e a5 dem0n5trated 6y W1tte60rn and Fa1r6ank [19], 5tray e1ectr1c f1e1d5 c0u1d 6e c0ntr011ed at the 1eve1 0f 10 - ~ V / m . ) 1n the rea1 exper1menta1 c0nd1t10n5, f0r examp1e, a c0nf1n1n9 e1ectr05tat1c p0tent1a1 0f the f0rm

(E~)~0nf ~ - ( ~

E,-=-8,-2-e,,

(11)

Can 6e pr0dUCed. Here d and V0 are kn0Wn parameter5, r 15 the rad1u5 vect0r 0f a 91ven p01nt, and k• 15 the un1t vect0r 1ntr0duced a60ve. 50 we have

0Vc0°f

(12)

Ec0nf= -- - - ,

~r

.e., d2

(Ev)c0nf=

(E•-)c0nf=

2v0

-- • d2

--

21/0

(14)

( X C05 0~ + y C05 f1+ 2 C05 y ) C 0 5 a ,

Ev=-dv2-ey, E2 = - d22 - e2. (15)

--du + k 0 u = - --4 (c~x+1~y)2- - 4- (e~+1e,.) +1a , dt m~ rn~ 5+.-Q22= -

4 e-,

(16)

m1

w1th

09= 48,

t~22=-4-4 8:,

m1

V~0nf= V 0 ( ~ )

C0527)2 = - a = 2 .

1ntr0duc1n9 ( 15 ) 1nt0 (10) 91ve5

2

2~

•(2r0 ) • d2 c057c05f1 2--8~,2,

We 5ha11 a150 1nC1ude 50me 5ma11, 6ut n0t preC15e1y kn0wn, c0n5tant 5tray f1e1d5, ex, e~, e- 50 that f0r e1ectr1c f1e1d5 1n 5y5tem (10) we have

d (2+1~,)+1 4 8 ( 2 + 1 p ) = ~ (E,-+1E~.)+1a, dt m~ m~

( E v ) c 0 n f --

10 Au9u5t 1989

u=2+11).

(17)

m1

7he 9enera1 501ut10n 0f the 5ec0nd e4uat10n 0f 5y5tem ( 16 ) 15

2=A 51n (f2t + 0) - ~ ,

( 18

)

where A and 0 depend 0n 1n1t1a1 c0nd1t10n5, 50, the part1c1e 05c111ate5 a10n9 2 and can 6e c0nf1ned 6etween p1ane5 A and 8 1n f19. 1. U51n9 (18), the f1r5t e4uat10n5 0f 5y5tem (16) can 6e tran5f0rmed 1nt0 dU --

dt + 1 0 m = - ~

51n(£2t+0) + ~ + 1 a ,

(19)

w1th (x c05 a+y c05f1+2 c05 y) c05f1,

d--7- (xc05 a+yc05f1+2c05

7)

c05 y, (13)

where c05 c~=1.k~, c05 f1=].k~, c05 y=k.k•. 8ecau5e 0f the fact that c05 y 15 much 1ar9er than c05 c~ and c05 f1, ( 13 ) can 6e 51mp11f1ed:

~4=A -4-4 (8~+1f1y), m1

,

~+1~8,,-cx-14,

).

(20)

7he 9enera1 501ut10n 0f (19) 15

355

V01ume 226, num6er 3,4

u=2+1)=

-

PHY51C5 LE77ER5 8

5¢ 0)( 1 -- ~ 2 / 0 9 2 )

× ( ~ - c05(12t+ 0) - 1 51n (£2t + 0 ) ) a .~ + -- + • + c0n5t, e - 1~,. (D

1(D

(21 )

A5 a c0n5e4uence 0f (21 ), 2 and 3• are per10d1c funct10n5 0f t1me w1th avera9e va1ue5

10 Au9u5t 1989

1 w0u1d 11ke t0 t h a n k m y exper1menta1 c011ea9ue5 J. Eade5 f r 0 m the L E A R P5 200 exper1ment a n d R. Hur5t f r 0 m the W A 8 2 exper1ment at C E R N f0r 10n9 d15cu5510n5 a 6 0 u t th15 51mp1e 1dea a n d the1r e n c 0 u r a 9 e m e n t ( very 1 m p 0 r t a n t f0r a pure the0r15t) that the 1dea 5eem5 t0 6e pr0m151n9 1n rea1 exper1menta1 c0nd1t10n5 a n d w0rth further ana1y515. 1 a m e5pec1a11y 9ratefu1 t0 J 0 h n E1115 f0r c 0 m m e n t 5 0 n the m a n u 5cr1pt a n d h05p1ta11ty 1n the C E R N 7 H D1v1510n.

Reference5 4

C-

6)

(23)

1n the 1dea1 ca5e w h e n 5tray e1ectr1c f1e1d5 are 2er0 (6=6=C,=0), we have 51mp1y fc=a/09 a n d )5=0. W1th a 900d c0ntr01 0 f 5tray f1e1d5 a5 1n ref. [ 19 ], dr1ft a10n9 the x ax15 cau5ed 6y e1ectr1c f1e1d5 15 m u c h 5ma11er t h a n that cau5ed 6y 9rav1tat10n. Dr1ft a10n9 the y ax15 15 a150 5ma11 ( a n d e v e n a 1ar9er dr1ft a10n9 y 15 n 0 t 1 m p 0 r t a n t f0r 0 u r m e a 5 u r e m e n t wh1ch 15 1n fact a m e a 5 u r e m e n t 0 f dr1ft a10n9 the x ax15). F1na11y, 1et u5 n 0 t e that the e55ent1a1 part 0 f the m e t h 0 d 15 the ex15tence 0 f cr055ed 9rav1tat10na1 a n d ma9net1c f1e1d5. 7 h e pr061em 0 f c 0 n f 1 n e m e n t 0 f the part1c1e m a y 6e 501ved 1n a way wh1ch d1ffer5 f r 0 m the c0nf1n1n9 e1ectr05tat1c p0tent1a1 ( 1 1 ). 7 h e m e a 5 u r e m e n t 0f the dr1ft ve10c1ty ( 6 ) 5eem5 t0 6e a150 a f u n d a m e n t a 1 part 0 f the m e t h 0 d , 6 u t w h 0 kn0w5• 1t m a y even e n d u p 11ke 50me 9rav1tat10na1 ver510n 0 f the Ha11 effect. 0 f c0ur5e, the p05516111ty 0 f hav1n9 a ca116rat10n w1th H - 10n5 ex15t5 here a5 we11 a5 1n the 0r191na1 pr0p05a1, L E A R P5 2 0 0 . 1 n fact, 1n pr1nc1p1e, th15 m e t h 0 d 15 appr0pr1ate f0r a1110n9-11ved char9ed part1c1e5.7he m e a 5 u r e m e n t w1th ant1pr0t0n5 a n d p051tr0n5 15 the m05t 1mp0rtant, 6 u t 6ecau5e 0 f p 0 0 r exper1menta1 1nf0rmat10n a 6 0 u t free part1c1e5, 5uch m e a 5 u r e m e n t 5 5h0u1d a150 6e p e r f 0 r m e d w1th pr0t0n5, e1ectr0n5 a n d d1fferent 10n5. H 0 w e v e r , n 0 0 n e can expect a n ea5y exper1ment w1th part1c1e5 a n d 5uch a fee61e f0rce a5 9rav1ty. A 10t 0 f w0rk ha5 t0 6e d 0 n e 6ef0re we k n 0 w f0r 5ure 1f 1t 15 p055161e w1th t0day•5 exper1menta1 fac111t1e5. We mu5t n 0 t f0r9et that f r 0 m a the0ret1ca1 p01nt 0f v1ew, the 1dea 0 f the 0r191na1 P5 200 pr0p05a115 a150 4u1te 51mp1e a n d p055161e.

356

[ 1] 1. Newt0n, Pr1nc1p1a (L0nd0n, 1686). [2] R.V. E6tv135,Math. Nat. 8er. Un9arn 8 (1890) 65; R.V. E15tv~55et a1., Ann. Phy5. (Le1p219) 68 (1922) 11. [3] E. F15h6ach et a1., Phy5. Rev. Lett. 56 (1986) 3. [4] P.6. R011, R. Kr0tk0v and R.H. D1cke, Ann. Phy5. (NY) 26 (1967) 42. [ 5 ] V.8.8ra91n5k11 and V.1. Pan0v, 50v. Phy5. JE7P 34 ( 1972 ) 463. [6] 1. E5termann et a1., Phy5. Rev. 71 (1947) 238. [7] A.W. McReyn01d5, Phy5. Rev. 83 ( 1951 ) 172, 233; J.W.7. Da665 et a1., Phy5. Rev. 8 139 (1965) 756; L. K0e5ter, Phy5. Rev. D 14 (1976) 907. [8] R.V. P0und and 6.A. Re6ka Jr., Phy5. Rev. Lett. 4 (1960) 337; R.V. P0und and J.L. 5n1der, Phy5. Rev. 8140 (1965 ) 788. [9]Y. Fuj11, Nature Phy5. 5c1. 234 (1971) 5; Phy5. Rev. D 9 (1974) 874; 5. Ferrara and P. van N1euwenhu12en, Phy5. Rev. Len. 37 (1976) 1669; C.K. 2ach05, Phy5. Lett. 8 76 (1978) 329; J. 5cherk, Phy5. Lett. 8 88 (1979) 265; 1n: Un1f1cat10n0f the fundamenta1 art1c1e 1nteract10n5,ed5.5. Ferrara, J. E1115 and P. van N1euwenhu12en ( P1enum, New Y0rk, 1981 ); 1.8ar5 and M. V155er, Phy5. Rev. Lett. 57 (1986) 25: H. 1t0yama et a1., Nuc1. Phy5. 8 279 ( 1987 ) 380. [ 10 ] 7. 601dman et a1., Phy5. Len. 8 171 ( 1986 ) 217. [11] F.D. 5tacey et a1., Phy5. Rev. D 36 (1987) 2374; M.M. N1et0 et a1., Phy5. Rev. D 28 (1988) 2937. [ 12 ] C.W. 5tu665 et a1., Phy5. Rev. Lett. 58 ( 1987 ) 1070; E.6. Ade16er9er et a1., Phy5. Rev. Lett. 59 (1987) 849; P. 7h1e6er9er, Phy5. Rev. Lett. 58 (1987) 1066. [ 131 F.D. 5tacey et a1., Rev. M0d. Phy5. 59 ( 1987 ) 157. [ 14] LEAR P5200 C011a6., CERN/P5CC/86-2; P5CC/P94. [ 15] J. Eadc5 and 6. 70re111 (LEAR P5 200 C011a6.), pr1vate c0mmun1cat10n. [ 16 ]L.D. Landau and E.M. L1f5h1t2,7he c1a551ca1the0ry 0f f1e1d5 (Per9am0n, 0xf0rd, 1975 ). [ 17] J.L. W12a, Nuc1.1n5trum. Meth. 162 (1979) 587. [ 18 ] Part1c1e Data 6r0up, C.6. W0h1 et a1., Rev1ew 0f part1c1e pr0pert1e5, Rev. M0d. Phy5. 56 (1984) 37. [19] F.C. W1tte60rn and W.M. Fa1r6ank, Rev. 5c1. 1n5t. 48 (1971) 1.