- Email: [email protected]
Colored lepton production in hadron colliders
V01ume 1648, n u m 6 e r 4,5,6
PHY51C5 L E 7 7 E R 5
12 Decem6er 1985
C 0 L 0 R E D L E P 7 0 N P R 0 D U C 7 1 0 N 1N H A D R 0 N C 0 L L 1 D E R 5 Y05ef N1R Department 0f Nuc1ear Phy51c5, We12mann 1n5t1tute 0f 5c1ence, Reh0v0t 76100, 15rae1 Rece1ved 27 Au9u5t 1985
1f ••c010red neutr1n05•• ex15t, the1r ma55 can 6e much 119hter than the 5ca1e 0f c0mp051tene55. 1f they are 5uff1c1ent1y 119ht, they c0u1d 6e pr0duced at the C E R N and Ferm11a6 pp c0111der5. We ca1cu1ate t0ta1 cr055 5ect10n5 and expected num6er 0f event5 f0r the re1evant ener91e5. 7 h e decay 0f the 51n91y pr0duced c010red neutr1n0 5h0u1d 1eave an exper1menta1 519nature 0f a m0n0jet. We f1nd the an9u1ar d15tr16ut10n 0f the5e m0n0jet5. 1f ••c010red e1ectr0n5•• ex15t, then the1r ma55 5h0u1d 6e 0f the 0rder 0f c0mp051tene55 5ca1e, and they 5h0u1d 6e pr0duced 1n future mu1t1-7eV hadr0n c0111der5. We f1nd the1r t0ta1 pr0duct10n cr055 5ect10n5 and the an9u1ar d15tr16ut10n 0f the 91u0n-m0n0jet ar151n9 fr0m the c010red e1ectr0n decay.
1n 5evera1 c0mp051te m0de15 [1 ] 1ept0n5 c0nta1n c010red pre0n5.7he5e pre50n5 are c0up1ed 50 a5 t0 f0rm a c010r 51n91et. 7he 5ame c0n5t1tuent5, h0wever, can a1way5 6e c0up1ed t0 a c010r-0ctet, ~8~ 7he ma55 0f the c010red 1ept0n 5h0u1d n0rmaUy 6e 0f the 0rder 0f the 5ca1e 0f c0mp051tene55, A, that 15 t0 5ay a60ve 1 7eV. We f1r5t c0n51der the ••c010red neutr1n0••-u 8 . 7h15 15 a c010r 0ctet ferm10n w1th a11 0ther 4uantum num6er5 51m11ar t0 th05e 0f the neutr1n0.1t wa5 5h0wn [2] that the 5ame mechan15m that wa5 5u99e5ted [3] t0 exp1a1n the appr0x1mate ma551e55ne55 0f 0rd1nary neutr1n05, can make the c010red neutr11a05 much 119hter than the 5ca1e 0f c0mp051tene55.7he ex15tence 0f c010red neutr1n05 91ve5 r15e t0 add1t10na1 5e1fener9y d1a9ram5 f0r 0rd1nary neutr1n05.70 5uppre55 the5e c0ntr16ut10n5 (0f 0rder A) 1t wa5 5u99e5ted [4] that c010red neutr1n05 are par1ty d0u61et5.1f 5uch 15 the ca5e, the d1a90na112at10n 0f the ma55 matr1x 91ve5 tw0 ma55 e19en5tate5 0f ma55 A2/M R where M R 15 the 5ca1e 0f 1eft-r19ht 5ymmetry 6reak1n9.7he5e tw0 11near c0m61nat10n5 0f ch1ra11ty 5tate5 are a1m05t pure 1eft-handed. 1f we take A = 0(1 7eV) and M R = 0(10 7eV) [5] we 9et f0r the 1eft-handed c010red neutr1n05 M(v8L ) = A2/MR = 0(100 6 e V ) .
(1)
1n 0ur pre5ent d15cu5510n we a55ume that v 8 15 1eft0370-2693/85/$ 03.30 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115111n9 D1v1510n)
handed and par1ty-d0u61et. 1n 0ur ca1cu1at10n5 we put A = 1 7eV. A re1at1ve1y 119ht v 8 c0u1d 6e pr0duced at the CERN p - f f c0111der at pre5ent ener91e5 (630 6eV) 0r 1n the Ferm11a6 7evatr0n 1n the near future (2000 6eV). v8 c0u1d 6e pr0duced [2,6] e1ther v1a p~ v8v, 0r 1n pa1r5 v1a p~ ~ v8F 8 . 1n 60th ca5e5 the c010red neutr1n0 decay5 1nt0 a 91u0n and an 0rd1nary neutr1n0.7he 51n91e v 8 c0u1d 6e pr0duced at 10wer ener91e5 6ut 1t5 pr0duct10n 15 5uppre55ed 6y the 9vv 8 vertex. 7heref0re, we expect that at ener91e5 h19h en0u9h a60ve thre5h01d, pa1r pr0duct10n w111d0m1nate. Pa1r pr0duct10n pr0ceed5 v1a tw0 5u6pr0ce55e5: (a) 4~ ~ v8v8 ;• def1n1n9 R = M(v8)2/~ , where 9 15 the 5u6pr0ce55 center-0f-ma55 ener9y, we 9et a t0ta1 cr055 5ect10n 0f 0(4~ ~ v8~8) = (161ra2/99)(1 - 4R) 1/2(1 - R ) .
(2)
(6) 99 ~ v8P8; the t0ta1 cr055 5ect10n 15 1
a(99 ~ v8~8) = (37rt~2/4~) ~(1 - 4R) 1/2(-8 + 38R)
1 + ( 1 - 4 R ) 1/2 4~]"
+ 3(2 - 5R - 4 R 2 ) 1 n 1 -- 0
(3)
F0r the 51n91e v 8 pr0duct10n, we a55ume the 9vv 8 c0up11n9 t0 6e (95/A)6a6kv0uv where k 15 the 91u0n 395
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
2 m0mentum. 7he 99vv 8 c0up11n9 15 then (95/A)~ a 6c °uv~ 7he tw0 5U6pr0ce55e5 are: (a) 4~ ~ v8v, 0(4ff ~ vv8) = (8rta2/27A2)(1 - R)2(1 + 2 R ) .
(4)
C0) 99 -+ vv8,
0(99~ vv8) = (3~ra2/8A2){(1 - R ) ( ~ + ~ R + 15R 2) + [2R/(1 + R ) ] ( 1 + 7 R + 4 R 2 + 2 R 3 ) 1 n R } .
(5)
7he 51n91e v 8 pr0duct10n cr055 5ect10n 15 rea11y an upper 60und, a5 the 9uv 8 effect1ve c0up11n9 may 1nc1ude an unkn0wn p0wer 0fM(v8)/A. When c0nv01ut1n9 0ver the ener91e5 0f the 5u6pr0ce55e5, we u5e the wave funct10n5 0f E1chten et a1. [7]. 7he ma55 dependence 0f the v 8 pr0duct10n cr055 5ect10n5 15 5h0wn f0r center-0f-ma55 ener91e5 0 f V ~ -= 630 6 e V and 2000 6 e V (f19.1). A5 c0u1d 6e expected, the ma55 dependence 15 weaker f0r h19her ener91e5. At 5uff1c1ent1y 10w ma55, pa1r pr0duct10n 15 the
12 Decem6er 1985
d0m1nant pr0ce55, 6ecau5e the 51n91e c010red neutr1n0 pr0duct10n 15 5uppre55ed 6y the 9pv 8 c0up11n9. At pre5ent (1nte9rated 1um1n051ty 0f 150 n 6 - 1 at 540 6 e V and 400 n6 - 1 at 630 6 e V ) , 0ne c0u1d have 5een 1 event 0r m0re 0f each k1nd 1f the v 8 ma55 15 1e55 than a60ut 120 6 e V . F0r a 100 6 e V v 8 we 5h0u1d have 5een 3 event5 0f pa1r pr0duct10n and 1e55 than 2 event5 0f 51n91y pr0duced v8, wh11e f0r an 85 6 e V v 8 we ant1c1pate 15 and 1e55 than 6 event5, re5pect1ve1y. F0r M(v8)= 50 6 e V , wh1ch 15 a1ready ru1ed 0ut, the expected num6er5 0 f event5 are 550 and 1e55 than 50, re5pect1ve1y. We may c0nc1ude that 1f a c010red neutr1n0 ex15ted at 5uff1c1ent1y 10w ma55 (depend1n9 0n tw0 y e t unkn0wn 5ca1e5), 1t 5h0u1d have 6een pr0duced at pre5ent c0111der5 1n detecta61e rate5.1n a 2000 6 e V c0111der w1th an 1nte9rated 1um1n051ty 0f 1037 cm - 2 , we w111 have 100 event5/y 0f pa1r pr0duct10n f0r M(v8) < 220 6eV. Exper1menta1 cut5, h0wever, w111 reduce the num6er 0f detected event5.7he decay~v8 ~ v + 4 + ~ may have a 6ranch-
45=630 6eV
~/5=2000 6eV ....
1 ....
1 ....
1 ....
F
102
10 0
101
10-4
t~ 10-8
k,
•
10 0
-
~
2
10-1
10-2
10-3 10-12 10 - 4
10-5 100
200
~00
MA55 0F u8 (6eV)
400
500
,,] . . . . 1 , ~ , 1 . . . . 1,,%,1 100 200 300 MA55 0F v 8 (6eV)
400
500
F19.1.70ta1 cr055 5ect10n5 f0r v5 pr0duct10n at ~ff-= 630 6eV and 2000 6eV. 7he 5011dcurve 91ve5the upper 60und f0r 51n91ev5 pr0duct10n. 7he da5hed curve5 91ve def•m1te pred1ef10n f0r pa1r pr0duct10n cr055 5ect10n5. Exper1menta1 cut5 and p055161e n0n1ead1n9 decay m0de5 0f v5 have 6een 19n0red 1n the5e 9raph5. 396
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
ma55 frame. 1t turn5 0ut that the 4uark 5u6pr0ce55 c0ntr16ute5 t0 90 ° peak wh11e the 5hape 0f the 91u0n c0ntr16ut10n var1e5 w1th ener9y. 7he f1na1 re5u1t 5h0w5 a very f1at max1mum at 90 ° (f19.2). 1f, h0wever, the pr0t0n ener9y 15 c105e t0 thre5h01d 50 that 0n1y hard part0n5 part1c1pate, then the 4uark c0ntr16ut10n w111d0m1nate and we w111have a m0re pr0n0unced 90 ° peak. 7 h e mu1t1-7eV c0111der, 5uch a5 55C 0r LHC, w111 pr06a61y 6r1n9 u5 t0 a ran9e 0f ener91e5 c105e t0, 0r a60ve, the 5ca1e 0f c0mp051tene55.7he pa1r pr0duct10n ca1cu1at10n5 d0 n0t depend 0n A and can 6e 5afe1y extrap01ated t0 th15 ran9e 0f ener91e5. A5 f0r the 51n91e c010red 1ept0n pr0duct10n, 51nce the 1mp0rtant c0ntr16ut10n5 c0me fr0m 5u6pr0ce55 ener91e5 c105e t0 thre5h01d, 0ur ca1cu1at10n5 5h0u1d 5erve a5 a fa1r appr0x1mat10n. 0ne 5h0u1d n0t f0r9et, h0wever, that 1f 4uark5 and 1ept0n5 have 50me pre0n5 1n c0mm0n, there 15 an apprec1a61e c0ntr16ut10n t0 the ~8 pr0duct10n fr0m an effect1ve f0ur-ferm10n c0up11n9 [9]. 7he term5 c0m1n9 fr0m th15 d1a9ram 6ec0me 1mp0rtant f0r • > a5A2 , that 15 at CM ener91e5 h19her than 300 6eV. At 9 ~ A the d1rect c0ntact term w111d0m1nate, a51t may 6e a 100 t1me51ar9er than the 5tr0n9
1n9 rat10 0f the 0rder 0f 10% and w111reduce even further the num6er 0f ea511y 1dent1f1a61e event5. 7 h e 51n91y pr0duced c010red neutr1n0 decay51nt0 a 91u0n and an ant1neutr1n0: p + ~--~v8 + v ~9 + V.
12 Decem6er 1985
(6)
7h15 91ve5 a un14ue exper1menta1 519nature 0f a 91u0n m0n0jet and m1551n9 m0mentum 1n the 0pp051te d1rect10n. F1nd1n9 the an9u1ar d15tr16ut10n 0f the 0ut901n9 91u0n 15 c0mp11cated 6y tw0 rea50n5: (a) 7he 0ut901n9 neutr1n0 and ant1-neutr1n0 cann0t 6e detected. 7heref0re the re5t frame 0f the decay1n9 c010red neutr1n0 cann0t 6e exper1menta11y determ1ned, and we have t0 f1nd the an9u1ar d15tr16ut10n 0f m0n0jet5 1n the pr0t0n-ant1pr0t0n center-0fma55 frame. (6) A1th0u9h we dea1 w1th 5tr0n9 1nteract10n5, we may n0t u5e par1ty a5 a 900d 5ymmetry, 6ecau5e we have a55umed that 1t 15 6r0ken 6y ma55 term5. We have u5ed 5p1n den51ty matr1x techn14ue5 [8] t0 f1nd the an9u1ar d15tr16ut10n 1n the u 8 re5t frame, and then tran5f0rmed the re5u1t5 t0 the center-0f0.51 .
•
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.
.
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.
1
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17
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11" 1/
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•
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0.485
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-0.5
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0.5
1
C05 • F19.2. An9u1ar d15tr16ut10n 0f m0n0jet5 (51n91y pr0duced v5 decay), at ~,~= 0.63 7eV (5011d curve), 2 7eV (d0t-da5hed curve) and 1 0 7eV (da5hed curve). 7he re5u1t5 axe n0rma112ed 50 that an 1nte9rat10n 0ver c05 0 91ve5 1. 397
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
12 Decem6er 1985
PR070N-AN71PR070N
~1 . . . .
1 ....
1 ....
PR070N-PR070N
1•••
10 3
10 3
••• • 10 2
•
1- •
10 2
•
%. 1 ~
•
101
X
••
101
0
6
100
100
•
•
•
~, ~ "~--....~ 10-1
~
-
-~
10-1
1 ....
00
200
300
400
MA55 0F v 8 (6eV)
00
1 ....
1 ....
200 300 M A 5 5 0F v 8 (6eV)
1,
•
1
J
400
F19.3.70ta1 cr055 5ect10n5 f0r u5 pr0duct10n at 10, 20 and 40 7eV. 7he 5011d curve5 91ve the upper 60und f0r 51n91e u5 p r 0 d u c t10n. 7he da5hed curve5 91ve def1n1te pred1ct10n f0r pa1r pr0duct10n cr055 5ect10n5. Center-0f-ma55 ener91e5 are den0ted (1n 7eV). Exper1menta1 cut5 and p055161e n0n4ead1n9 decay m0de5 0f u8 have 6een 19n0red 1n the5e 9raph5.
1nteract10n c0ntr16ut10n. 5t111, f0r hadr0n5 c0111d1n9 at 5evera1 ten5 0f 7eV, 501ft 91u0n5 are the 1mp0rtant c0n5t1tuent5, and the effect 0f a11 4uark d1a9ram5 may 6ec0me m1n0r a9a1n. We have d0ne ca1cu1at10n5 f0r center-0f-ma55 ener91e5 0f 10, 20 and 40 7eV, f0r 60th p r 0 t 0 n - p r 0 t 0 n and pr0t0n-ant1pr0t0n c0111der5. F0r pr0ce55e5 d05e t0 thre5h01d, where 0n1y the ••hard•• c0n5t1tuent5 take part, cr055 5ect10n5 w111 6e 1ar9er 1n a p r 0 t 0 n ant1pr0t0n c0111der (6ut 0ne ha5 t0 remem6er that 1t5 1um1n051ty 15 11ke1y t0 6e 5ma11er). 7he t0ta1 cr055 5ect10n5 0f a 0.1 7eV v 8 are 5h0wn 1n f19.3. Pa1r pr0duct10n 15 d0m1nant f0r a 5uff1c1ent1y 10w rat10 M(v8)2/L7he pha5e-5pace fact0r make5 the t0ta1 cr055 5ect10n5 1ncrea5e w1th ener9y. 7he 51n91e v 8 pr0duct10n 15 a1m05t a c0n5tant a5 a funct10n 0f ma55 and ener9y. A5 50ft 91u0n5 are d0m1nant, cr055 5ect10n5 1n p - p and p - ~ c0111der5 are 51m11ar. 7he an9u1ar d15tr16ut10n 0f m0n0jet5 f0r a 100 6 e V v 8 1n V~-= 10 7eV 15 pre5ented 1n f19.2.1t 15 398
ma1n1y determ1ned 6y the 91u0n 5u6-pr0ce55.1t 5t111 ha5 a 90 ° peak, a1th0u9h f1atter than 1n 10wer ener91e5. At 20 and 40 7eV the d15tr16ut10n 6ec0me5 even c105er t0 150tr0py. 7he e 8 ca1cu1at10n5 are 5u6ject t0 5ma11er uncerta1nt1e5, 51nce they pre5uma61y depend 0n1y 0n 0ne unkn0wn 5ca1e, A. We take e 8 t0 6e a c010r-0ctet ferm10n w1th a11 0ther 4uantum num6er5 51m11ar t0 th05e 0f an 0rd1nary e1ectr0n. We a55ume 1t5 ma55 t0 e4ua1 A, name1y we take M(e8) = 0(1 7eV). We d0 n0t take 1nt0 acc0unt a ch1ra1 de9ree 0f freed0m (wh1ch w111 1ntr0duce a fact0r 0f 2 1nt0 0ur t0ta1 cr055 5ect10n5 ca1cu1at10n5). 7he t0ta1 cr055 5ect10n5 f0r pa1r pr0duct10n are 91ven 6y 0(44- ~ e~ e8-) = (1~re2/95)(1 - 4R) 1/2(1 + 2 R ) , (7)
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
12 Decem6er 1985 PR070N-PR070N
PR070N-AN71PR070N
10 0
2 6
.... 1 ....
1 ....
1••
100
~L
10-1
10-1
10-2
10-2
10-3
10-3 10 -4
10-4
6
10-5
10-5
! 10-6 1
10-6
10-7
10-7
10-8
,
2 3 MA55 0P e8 (7eV)
4
10-8
5
1
2
3
4
5
MA55 0F e8 (7eV)
F19.4.70ta1 cr055 5ect10n5 f0r e5 pr0duct10n at 10, 20 and 40 7eV. 7he 5011d curve5 91ve cr055 5ect10n5 f0r 51n91e e 5 pr0duct10n. 7he da5hed curve5 91ve pa1r pr0duct10n cr055 5ect10n5. Center-0f-ma55 ener91e5 are den0ted (1n 7eV). Exper1menta1 cut5 and p055161e n0n-1ead1n9 decay m0de5 0f e8 have 6een 19n0red 1n the5e 9raph5. /
0(99 ~ e~ e~-) = (3rr0t2 [2~)~-(1 - 4R) 1/2 (4 + 17R) + 3(1 + 4R - 4R 2) 1n 1 + (1 - 4R) 1/2 ]
(8)
1 - (1 - 4 R ) 1 1 2 ]
R 15 n0w M(e5)2/f. F0r the 51n91e e 8 pr0duct10n the cr055 5ect10n5 are 51m11art0 th05e 0f v 8. 7he ma55 dependence 0f the t0ta1 cr055 5ect10n5 15 5h0wn 1n f19.4. 7he 51n91e e 8 pr0duct10n 15 5tr0n9er a5 the 9ee 8 vertex ha5 n0 rea50n t0 6e 5uppre55ed. F0r a p r 0 t 0 n pr0t0n c0111der w1th 1nte9rated 1um1n051ty 0f 104° c m - 2 / y , we 5h0u1d 5ee 100 event5/y 0r m0re 0f pa1r pr0duced e8, 1f the ma55 0f the c010red e1ectr0n 15 1e55 than 1.2 7eV at a 10 7eV c01hder, 2.2 7eV at a 20 7eV c0111der and 3.6 7eV at a 40 7eV c0111der. F0r a 1 03 7 c m - 2 pr0t0n-ant1pr0t0n c0111der the re5pect1ve ma55e5 are 0.6, 0.9 and 1.3 7eV. 51n91y pr0duced e 8 may 6e detected 1n th15 rate 1n the p - p c0U1der 1f 1t5 ma55 15 119hter than 2.8 7eV (x/5- = 10 7eV), 5.2 7eV (V~-= 20 7eV) and 9 7eV (V~-= 40 7eV•). F0r p - ~
c0111der5 the re5pect1ve ma55e5 are 1,1.8 and 3.6 7eV. A5 f0r the an9u1ar d15tr16ut10n 0f the m0n0jet5, we 5h0u1d remem6er that the 0ut901n9 e1ectr0n and p051tr0n 1n p + ~---> e 8 + e + +9+ e-
(9)
are detecta61e. 7hu5 1t 15 5uff1c1ent t0 f1nd the an9u1ar d15tr16ut10n 1n the c010red e1ectr0n re5t frame. M0re0ver, we may n0w u5e par1ty 1nvar1ance. C0n5e4uent1y, 1t 15 ea5y t0 5h0w that the m0n0jet5 are 150tr0p1ca11y d15tr16uted 1n the e 8 re5t frame. 70 c0nc1ude, 1eft-handed c010red neutr1n05 c0u1d 6e 5uff1c1ent1y 119ht t0 6e detected at pre5ent c0111der5. 7hu5, ex15t1n9 0r near-future exper1ment5 are a60ut t0 e1ther pr0ve the1r ex15tence 0r put 519n1f1cant 10wer 60und5 0n the1r ma55.1f the 5ca1e 0f c0mp051tene55 399
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
11e5 at a60ut 1 7eV, the p055161e ex15tence 0f c010red 1ept0n5 5h0u1d 6e dec1ded at the next 9enerat10n 0f hadr0n c0111der5.51n91y pr0duced c010red 1ept0n5 pr0duce 1n the1r decay a m0n0jet. 7he an9u1ar d15. tr16ut10n 0f the5e m0n0jet5 15 appr0x1mate1y 150tr0p1c f0r 1eft-handed c010red neutr1n05. C010red e1ectr0n5 decay 150tr0p1ca11y 1n the1r re5t frame. 1n a recent prepr1nt 6y 8aur and 5tren9 [10] wh1ch we have rece1ved after the c0mp1et10n 0 f th15 w0rk, cr055 5ect10n5 0 f u 8 pa1r pr0duct10n at 10w ener91e5 are ca1cu1ated. (We thank H. Harar1 f0r draw1n9 0ur attent10n t0 th15 prepr1nt.) We n0te that the ca1cu1at10n5 1n ref. [10] d0 n0t app1y t0 the ca5e where 0n1y the 1eft-handed c0mp0nent 0f P8 15 119ht. 1 w15h t0 thank H. Harar1 f0r many va1ua61e d15cu5510n5.1 w0u1d 11ke t0 thank C. Qu199 f0r pr0v1d1n9 me a c0mputer pr09ram that ena61ed the ca1cu1at10n 0f the wavefunct10n5.1 am 9ratefu1 t0 6 . Date, M. Leurer and M. H1r5ch6er9 f0r fru1tfu1 adv1ce5.
400
12 Decem6er 1985
Reference5 [1 ] 5ee e~9. H. Harar1 and N. 5e16er9, Phy5. Lett. 988 (1981) 269;. E.6.54u1re5, Phy5. Lett. 948 (1980) 54; H. Fr1t25eh and 6. Mande16aum, Phy5. Lett. 1028 (1981) 319. [2] H. Harar1, Phy5. Lett. 1568 (1985) 250. [3] M. 6e11-Mann, P. Ram0nd and R. 51an5ky, 1n: 5uper9rav1ty, ed5. P. van N1euwenhu12en and D.2. Freedman (N0rth-H011and, Am5terdam, 1979); 7. Yana91da, unpu6115hed; R.N. M0hapatra and 6.5enjan0v1e, Phy5. Rev. D23 (1981) 165. [4] C.8. Ch1u and Y.8. Da1, Phy5. Lett. 1088 (1982) 341. [5] H. Harar1 and M. Leurer, Nue1. Phy5. 8233 (1984) 221. [6] 5.F. K1n9 and 5.R. 5harpe, Phy5. Lett. 1438 (1984) 494. [7 ] E. E1chten, L. H1nch11ffe, K. Lane and C. Qu199, Rev. M0d. Phy5.56 (1984) 579. [8] 5ee e.9. K. 60ttfr1ed and J.D. Jack50n, Nu0v0 C1ment0 63 (1964) 309. [9] E. E1chten, K. Lane and M. Pe5hk1n, Phy5. Rev. Lett. 50 (1983) 811. [10] U. 8aur and K.H. 5tren9, Phy5. Lett. 1628 (1985)456.
PHY51C5 L E 7 7 E R 5
12 Decem6er 1985
C 0 L 0 R E D L E P 7 0 N P R 0 D U C 7 1 0 N 1N H A D R 0 N C 0 L L 1 D E R 5 Y05ef N1R Department 0f Nuc1ear Phy51c5, We12mann 1n5t1tute 0f 5c1ence, Reh0v0t 76100, 15rae1 Rece1ved 27 Au9u5t 1985
1f ••c010red neutr1n05•• ex15t, the1r ma55 can 6e much 119hter than the 5ca1e 0f c0mp051tene55. 1f they are 5uff1c1ent1y 119ht, they c0u1d 6e pr0duced at the C E R N and Ferm11a6 pp c0111der5. We ca1cu1ate t0ta1 cr055 5ect10n5 and expected num6er 0f event5 f0r the re1evant ener91e5. 7 h e decay 0f the 51n91y pr0duced c010red neutr1n0 5h0u1d 1eave an exper1menta1 519nature 0f a m0n0jet. We f1nd the an9u1ar d15tr16ut10n 0f the5e m0n0jet5. 1f ••c010red e1ectr0n5•• ex15t, then the1r ma55 5h0u1d 6e 0f the 0rder 0f c0mp051tene55 5ca1e, and they 5h0u1d 6e pr0duced 1n future mu1t1-7eV hadr0n c0111der5. We f1nd the1r t0ta1 pr0duct10n cr055 5ect10n5 and the an9u1ar d15tr16ut10n 0f the 91u0n-m0n0jet ar151n9 fr0m the c010red e1ectr0n decay.
1n 5evera1 c0mp051te m0de15 [1 ] 1ept0n5 c0nta1n c010red pre0n5.7he5e pre50n5 are c0up1ed 50 a5 t0 f0rm a c010r 51n91et. 7he 5ame c0n5t1tuent5, h0wever, can a1way5 6e c0up1ed t0 a c010r-0ctet, ~8~ 7he ma55 0f the c010red 1ept0n 5h0u1d n0rmaUy 6e 0f the 0rder 0f the 5ca1e 0f c0mp051tene55, A, that 15 t0 5ay a60ve 1 7eV. We f1r5t c0n51der the ••c010red neutr1n0••-u 8 . 7h15 15 a c010r 0ctet ferm10n w1th a11 0ther 4uantum num6er5 51m11ar t0 th05e 0f the neutr1n0.1t wa5 5h0wn [2] that the 5ame mechan15m that wa5 5u99e5ted [3] t0 exp1a1n the appr0x1mate ma551e55ne55 0f 0rd1nary neutr1n05, can make the c010red neutr11a05 much 119hter than the 5ca1e 0f c0mp051tene55.7he ex15tence 0f c010red neutr1n05 91ve5 r15e t0 add1t10na1 5e1fener9y d1a9ram5 f0r 0rd1nary neutr1n05.70 5uppre55 the5e c0ntr16ut10n5 (0f 0rder A) 1t wa5 5u99e5ted [4] that c010red neutr1n05 are par1ty d0u61et5.1f 5uch 15 the ca5e, the d1a90na112at10n 0f the ma55 matr1x 91ve5 tw0 ma55 e19en5tate5 0f ma55 A2/M R where M R 15 the 5ca1e 0f 1eft-r19ht 5ymmetry 6reak1n9.7he5e tw0 11near c0m61nat10n5 0f ch1ra11ty 5tate5 are a1m05t pure 1eft-handed. 1f we take A = 0(1 7eV) and M R = 0(10 7eV) [5] we 9et f0r the 1eft-handed c010red neutr1n05 M(v8L ) = A2/MR = 0(100 6 e V ) .
(1)
1n 0ur pre5ent d15cu5510n we a55ume that v 8 15 1eft0370-2693/85/$ 03.30 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115111n9 D1v1510n)
handed and par1ty-d0u61et. 1n 0ur ca1cu1at10n5 we put A = 1 7eV. A re1at1ve1y 119ht v 8 c0u1d 6e pr0duced at the CERN p - f f c0111der at pre5ent ener91e5 (630 6eV) 0r 1n the Ferm11a6 7evatr0n 1n the near future (2000 6eV). v8 c0u1d 6e pr0duced [2,6] e1ther v1a p~ v8v, 0r 1n pa1r5 v1a p~ ~ v8F 8 . 1n 60th ca5e5 the c010red neutr1n0 decay5 1nt0 a 91u0n and an 0rd1nary neutr1n0.7he 51n91e v 8 c0u1d 6e pr0duced at 10wer ener91e5 6ut 1t5 pr0duct10n 15 5uppre55ed 6y the 9vv 8 vertex. 7heref0re, we expect that at ener91e5 h19h en0u9h a60ve thre5h01d, pa1r pr0duct10n w111d0m1nate. Pa1r pr0duct10n pr0ceed5 v1a tw0 5u6pr0ce55e5: (a) 4~ ~ v8v8 ;• def1n1n9 R = M(v8)2/~ , where 9 15 the 5u6pr0ce55 center-0f-ma55 ener9y, we 9et a t0ta1 cr055 5ect10n 0f 0(4~ ~ v8~8) = (161ra2/99)(1 - 4R) 1/2(1 - R ) .
(2)
(6) 99 ~ v8P8; the t0ta1 cr055 5ect10n 15 1
a(99 ~ v8~8) = (37rt~2/4~) ~(1 - 4R) 1/2(-8 + 38R)
1 + ( 1 - 4 R ) 1/2 4~]"
+ 3(2 - 5R - 4 R 2 ) 1 n 1 -- 0
(3)
F0r the 51n91e v 8 pr0duct10n, we a55ume the 9vv 8 c0up11n9 t0 6e (95/A)6a6kv0uv where k 15 the 91u0n 395
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
2 m0mentum. 7he 99vv 8 c0up11n9 15 then (95/A)~ a 6c °uv~ 7he tw0 5U6pr0ce55e5 are: (a) 4~ ~ v8v, 0(4ff ~ vv8) = (8rta2/27A2)(1 - R)2(1 + 2 R ) .
(4)
C0) 99 -+ vv8,
0(99~ vv8) = (3~ra2/8A2){(1 - R ) ( ~ + ~ R + 15R 2) + [2R/(1 + R ) ] ( 1 + 7 R + 4 R 2 + 2 R 3 ) 1 n R } .
(5)
7he 51n91e v 8 pr0duct10n cr055 5ect10n 15 rea11y an upper 60und, a5 the 9uv 8 effect1ve c0up11n9 may 1nc1ude an unkn0wn p0wer 0fM(v8)/A. When c0nv01ut1n9 0ver the ener91e5 0f the 5u6pr0ce55e5, we u5e the wave funct10n5 0f E1chten et a1. [7]. 7he ma55 dependence 0f the v 8 pr0duct10n cr055 5ect10n5 15 5h0wn f0r center-0f-ma55 ener91e5 0 f V ~ -= 630 6 e V and 2000 6 e V (f19.1). A5 c0u1d 6e expected, the ma55 dependence 15 weaker f0r h19her ener91e5. At 5uff1c1ent1y 10w ma55, pa1r pr0duct10n 15 the
12 Decem6er 1985
d0m1nant pr0ce55, 6ecau5e the 51n91e c010red neutr1n0 pr0duct10n 15 5uppre55ed 6y the 9pv 8 c0up11n9. At pre5ent (1nte9rated 1um1n051ty 0f 150 n 6 - 1 at 540 6 e V and 400 n6 - 1 at 630 6 e V ) , 0ne c0u1d have 5een 1 event 0r m0re 0f each k1nd 1f the v 8 ma55 15 1e55 than a60ut 120 6 e V . F0r a 100 6 e V v 8 we 5h0u1d have 5een 3 event5 0f pa1r pr0duct10n and 1e55 than 2 event5 0f 51n91y pr0duced v8, wh11e f0r an 85 6 e V v 8 we ant1c1pate 15 and 1e55 than 6 event5, re5pect1ve1y. F0r M(v8)= 50 6 e V , wh1ch 15 a1ready ru1ed 0ut, the expected num6er5 0 f event5 are 550 and 1e55 than 50, re5pect1ve1y. We may c0nc1ude that 1f a c010red neutr1n0 ex15ted at 5uff1c1ent1y 10w ma55 (depend1n9 0n tw0 y e t unkn0wn 5ca1e5), 1t 5h0u1d have 6een pr0duced at pre5ent c0111der5 1n detecta61e rate5.1n a 2000 6 e V c0111der w1th an 1nte9rated 1um1n051ty 0f 1037 cm - 2 , we w111 have 100 event5/y 0f pa1r pr0duct10n f0r M(v8) < 220 6eV. Exper1menta1 cut5, h0wever, w111 reduce the num6er 0f detected event5.7he decay~v8 ~ v + 4 + ~ may have a 6ranch-
45=630 6eV
~/5=2000 6eV ....
1 ....
1 ....
1 ....
F
102
10 0
101
10-4
t~ 10-8
k,
•
10 0
-
~
2
10-1
10-2
10-3 10-12 10 - 4
10-5 100
200
~00
MA55 0F u8 (6eV)
400
500
,,] . . . . 1 , ~ , 1 . . . . 1,,%,1 100 200 300 MA55 0F v 8 (6eV)
400
500
F19.1.70ta1 cr055 5ect10n5 f0r v5 pr0duct10n at ~ff-= 630 6eV and 2000 6eV. 7he 5011dcurve 91ve5the upper 60und f0r 51n91ev5 pr0duct10n. 7he da5hed curve5 91ve def•m1te pred1ef10n f0r pa1r pr0duct10n cr055 5ect10n5. Exper1menta1 cut5 and p055161e n0n1ead1n9 decay m0de5 0f v5 have 6een 19n0red 1n the5e 9raph5. 396
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
ma55 frame. 1t turn5 0ut that the 4uark 5u6pr0ce55 c0ntr16ute5 t0 90 ° peak wh11e the 5hape 0f the 91u0n c0ntr16ut10n var1e5 w1th ener9y. 7he f1na1 re5u1t 5h0w5 a very f1at max1mum at 90 ° (f19.2). 1f, h0wever, the pr0t0n ener9y 15 c105e t0 thre5h01d 50 that 0n1y hard part0n5 part1c1pate, then the 4uark c0ntr16ut10n w111d0m1nate and we w111have a m0re pr0n0unced 90 ° peak. 7 h e mu1t1-7eV c0111der, 5uch a5 55C 0r LHC, w111 pr06a61y 6r1n9 u5 t0 a ran9e 0f ener91e5 c105e t0, 0r a60ve, the 5ca1e 0f c0mp051tene55.7he pa1r pr0duct10n ca1cu1at10n5 d0 n0t depend 0n A and can 6e 5afe1y extrap01ated t0 th15 ran9e 0f ener91e5. A5 f0r the 51n91e c010red 1ept0n pr0duct10n, 51nce the 1mp0rtant c0ntr16ut10n5 c0me fr0m 5u6pr0ce55 ener91e5 c105e t0 thre5h01d, 0ur ca1cu1at10n5 5h0u1d 5erve a5 a fa1r appr0x1mat10n. 0ne 5h0u1d n0t f0r9et, h0wever, that 1f 4uark5 and 1ept0n5 have 50me pre0n5 1n c0mm0n, there 15 an apprec1a61e c0ntr16ut10n t0 the ~8 pr0duct10n fr0m an effect1ve f0ur-ferm10n c0up11n9 [9]. 7he term5 c0m1n9 fr0m th15 d1a9ram 6ec0me 1mp0rtant f0r • > a5A2 , that 15 at CM ener91e5 h19her than 300 6eV. At 9 ~ A the d1rect c0ntact term w111d0m1nate, a51t may 6e a 100 t1me51ar9er than the 5tr0n9
1n9 rat10 0f the 0rder 0f 10% and w111reduce even further the num6er 0f ea511y 1dent1f1a61e event5. 7 h e 51n91y pr0duced c010red neutr1n0 decay51nt0 a 91u0n and an ant1neutr1n0: p + ~--~v8 + v ~9 + V.
12 Decem6er 1985
(6)
7h15 91ve5 a un14ue exper1menta1 519nature 0f a 91u0n m0n0jet and m1551n9 m0mentum 1n the 0pp051te d1rect10n. F1nd1n9 the an9u1ar d15tr16ut10n 0f the 0ut901n9 91u0n 15 c0mp11cated 6y tw0 rea50n5: (a) 7he 0ut901n9 neutr1n0 and ant1-neutr1n0 cann0t 6e detected. 7heref0re the re5t frame 0f the decay1n9 c010red neutr1n0 cann0t 6e exper1menta11y determ1ned, and we have t0 f1nd the an9u1ar d15tr16ut10n 0f m0n0jet5 1n the pr0t0n-ant1pr0t0n center-0fma55 frame. (6) A1th0u9h we dea1 w1th 5tr0n9 1nteract10n5, we may n0t u5e par1ty a5 a 900d 5ymmetry, 6ecau5e we have a55umed that 1t 15 6r0ken 6y ma55 term5. We have u5ed 5p1n den51ty matr1x techn14ue5 [8] t0 f1nd the an9u1ar d15tr16ut10n 1n the u 8 re5t frame, and then tran5f0rmed the re5u1t5 t0 the center-0f0.51 .
•
•
•
•
0.50 -
1
<•
0. 50 -
.
.
.
.
1
"
.
.
.
.
1
r° j
•~
/ /•
•
1
x.••
// /
17
".~
11" 1/
0.49(•
•
"•
/
•6
•
"~
1
0.485
-1
-0.5
0
0.5
1
C05 • F19.2. An9u1ar d15tr16ut10n 0f m0n0jet5 (51n91y pr0duced v5 decay), at ~,~= 0.63 7eV (5011d curve), 2 7eV (d0t-da5hed curve) and 1 0 7eV (da5hed curve). 7he re5u1t5 axe n0rma112ed 50 that an 1nte9rat10n 0ver c05 0 91ve5 1. 397
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
12 Decem6er 1985
PR070N-AN71PR070N
~1 . . . .
1 ....
1 ....
PR070N-PR070N
1•••
10 3
10 3
••• • 10 2
•
1- •
10 2
•
%. 1 ~
•
101
X
••
101
0
6
100
100
•
•
•
~, ~ "~--....~ 10-1
~
-
-~
10-1
1 ....
00
200
300
400
MA55 0F v 8 (6eV)
00
1 ....
1 ....
200 300 M A 5 5 0F v 8 (6eV)
1,
•
1
J
400
F19.3.70ta1 cr055 5ect10n5 f0r u5 pr0duct10n at 10, 20 and 40 7eV. 7he 5011d curve5 91ve the upper 60und f0r 51n91e u5 p r 0 d u c t10n. 7he da5hed curve5 91ve def1n1te pred1ct10n f0r pa1r pr0duct10n cr055 5ect10n5. Center-0f-ma55 ener91e5 are den0ted (1n 7eV). Exper1menta1 cut5 and p055161e n0n4ead1n9 decay m0de5 0f u8 have 6een 19n0red 1n the5e 9raph5.
1nteract10n c0ntr16ut10n. 5t111, f0r hadr0n5 c0111d1n9 at 5evera1 ten5 0f 7eV, 501ft 91u0n5 are the 1mp0rtant c0n5t1tuent5, and the effect 0f a11 4uark d1a9ram5 may 6ec0me m1n0r a9a1n. We have d0ne ca1cu1at10n5 f0r center-0f-ma55 ener91e5 0f 10, 20 and 40 7eV, f0r 60th p r 0 t 0 n - p r 0 t 0 n and pr0t0n-ant1pr0t0n c0111der5. F0r pr0ce55e5 d05e t0 thre5h01d, where 0n1y the ••hard•• c0n5t1tuent5 take part, cr055 5ect10n5 w111 6e 1ar9er 1n a p r 0 t 0 n ant1pr0t0n c0111der (6ut 0ne ha5 t0 remem6er that 1t5 1um1n051ty 15 11ke1y t0 6e 5ma11er). 7he t0ta1 cr055 5ect10n5 0f a 0.1 7eV v 8 are 5h0wn 1n f19.3. Pa1r pr0duct10n 15 d0m1nant f0r a 5uff1c1ent1y 10w rat10 M(v8)2/L7he pha5e-5pace fact0r make5 the t0ta1 cr055 5ect10n5 1ncrea5e w1th ener9y. 7he 51n91e v 8 pr0duct10n 15 a1m05t a c0n5tant a5 a funct10n 0f ma55 and ener9y. A5 50ft 91u0n5 are d0m1nant, cr055 5ect10n5 1n p - p and p - ~ c0111der5 are 51m11ar. 7he an9u1ar d15tr16ut10n 0f m0n0jet5 f0r a 100 6 e V v 8 1n V~-= 10 7eV 15 pre5ented 1n f19.2.1t 15 398
ma1n1y determ1ned 6y the 91u0n 5u6-pr0ce55.1t 5t111 ha5 a 90 ° peak, a1th0u9h f1atter than 1n 10wer ener91e5. At 20 and 40 7eV the d15tr16ut10n 6ec0me5 even c105er t0 150tr0py. 7he e 8 ca1cu1at10n5 are 5u6ject t0 5ma11er uncerta1nt1e5, 51nce they pre5uma61y depend 0n1y 0n 0ne unkn0wn 5ca1e, A. We take e 8 t0 6e a c010r-0ctet ferm10n w1th a11 0ther 4uantum num6er5 51m11ar t0 th05e 0f an 0rd1nary e1ectr0n. We a55ume 1t5 ma55 t0 e4ua1 A, name1y we take M(e8) = 0(1 7eV). We d0 n0t take 1nt0 acc0unt a ch1ra1 de9ree 0f freed0m (wh1ch w111 1ntr0duce a fact0r 0f 2 1nt0 0ur t0ta1 cr055 5ect10n5 ca1cu1at10n5). 7he t0ta1 cr055 5ect10n5 f0r pa1r pr0duct10n are 91ven 6y 0(44- ~ e~ e8-) = (1~re2/95)(1 - 4R) 1/2(1 + 2 R ) , (7)
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
12 Decem6er 1985 PR070N-PR070N
PR070N-AN71PR070N
10 0
2 6
.... 1 ....
1 ....
1••
100
~L
10-1
10-1
10-2
10-2
10-3
10-3 10 -4
10-4
6
10-5
10-5
! 10-6 1
10-6
10-7
10-7
10-8
,
2 3 MA55 0P e8 (7eV)
4
10-8
5
1
2
3
4
5
MA55 0F e8 (7eV)
F19.4.70ta1 cr055 5ect10n5 f0r e5 pr0duct10n at 10, 20 and 40 7eV. 7he 5011d curve5 91ve cr055 5ect10n5 f0r 51n91e e 5 pr0duct10n. 7he da5hed curve5 91ve pa1r pr0duct10n cr055 5ect10n5. Center-0f-ma55 ener91e5 are den0ted (1n 7eV). Exper1menta1 cut5 and p055161e n0n-1ead1n9 decay m0de5 0f e8 have 6een 19n0red 1n the5e 9raph5. /
0(99 ~ e~ e~-) = (3rr0t2 [2~)~-(1 - 4R) 1/2 (4 + 17R) + 3(1 + 4R - 4R 2) 1n 1 + (1 - 4R) 1/2 ]
(8)
1 - (1 - 4 R ) 1 1 2 ]
R 15 n0w M(e5)2/f. F0r the 51n91e e 8 pr0duct10n the cr055 5ect10n5 are 51m11art0 th05e 0f v 8. 7he ma55 dependence 0f the t0ta1 cr055 5ect10n5 15 5h0wn 1n f19.4. 7he 51n91e e 8 pr0duct10n 15 5tr0n9er a5 the 9ee 8 vertex ha5 n0 rea50n t0 6e 5uppre55ed. F0r a p r 0 t 0 n pr0t0n c0111der w1th 1nte9rated 1um1n051ty 0f 104° c m - 2 / y , we 5h0u1d 5ee 100 event5/y 0r m0re 0f pa1r pr0duced e8, 1f the ma55 0f the c010red e1ectr0n 15 1e55 than 1.2 7eV at a 10 7eV c01hder, 2.2 7eV at a 20 7eV c0111der and 3.6 7eV at a 40 7eV c0111der. F0r a 1 03 7 c m - 2 pr0t0n-ant1pr0t0n c0111der the re5pect1ve ma55e5 are 0.6, 0.9 and 1.3 7eV. 51n91y pr0duced e 8 may 6e detected 1n th15 rate 1n the p - p c0U1der 1f 1t5 ma55 15 119hter than 2.8 7eV (x/5- = 10 7eV), 5.2 7eV (V~-= 20 7eV) and 9 7eV (V~-= 40 7eV•). F0r p - ~
c0111der5 the re5pect1ve ma55e5 are 1,1.8 and 3.6 7eV. A5 f0r the an9u1ar d15tr16ut10n 0f the m0n0jet5, we 5h0u1d remem6er that the 0ut901n9 e1ectr0n and p051tr0n 1n p + ~---> e 8 + e + +9+ e-
(9)
are detecta61e. 7hu5 1t 15 5uff1c1ent t0 f1nd the an9u1ar d15tr16ut10n 1n the c010red e1ectr0n re5t frame. M0re0ver, we may n0w u5e par1ty 1nvar1ance. C0n5e4uent1y, 1t 15 ea5y t0 5h0w that the m0n0jet5 are 150tr0p1ca11y d15tr16uted 1n the e 8 re5t frame. 70 c0nc1ude, 1eft-handed c010red neutr1n05 c0u1d 6e 5uff1c1ent1y 119ht t0 6e detected at pre5ent c0111der5. 7hu5, ex15t1n9 0r near-future exper1ment5 are a60ut t0 e1ther pr0ve the1r ex15tence 0r put 519n1f1cant 10wer 60und5 0n the1r ma55.1f the 5ca1e 0f c0mp051tene55 399
V01ume 1648, num6er 4,5,6
PHY51C5 LE77ER5
11e5 at a60ut 1 7eV, the p055161e ex15tence 0f c010red 1ept0n5 5h0u1d 6e dec1ded at the next 9enerat10n 0f hadr0n c0111der5.51n91y pr0duced c010red 1ept0n5 pr0duce 1n the1r decay a m0n0jet. 7he an9u1ar d15. tr16ut10n 0f the5e m0n0jet5 15 appr0x1mate1y 150tr0p1c f0r 1eft-handed c010red neutr1n05. C010red e1ectr0n5 decay 150tr0p1ca11y 1n the1r re5t frame. 1n a recent prepr1nt 6y 8aur and 5tren9 [10] wh1ch we have rece1ved after the c0mp1et10n 0 f th15 w0rk, cr055 5ect10n5 0 f u 8 pa1r pr0duct10n at 10w ener91e5 are ca1cu1ated. (We thank H. Harar1 f0r draw1n9 0ur attent10n t0 th15 prepr1nt.) We n0te that the ca1cu1at10n5 1n ref. [10] d0 n0t app1y t0 the ca5e where 0n1y the 1eft-handed c0mp0nent 0f P8 15 119ht. 1 w15h t0 thank H. Harar1 f0r many va1ua61e d15cu5510n5.1 w0u1d 11ke t0 thank C. Qu199 f0r pr0v1d1n9 me a c0mputer pr09ram that ena61ed the ca1cu1at10n 0f the wavefunct10n5.1 am 9ratefu1 t0 6 . Date, M. Leurer and M. H1r5ch6er9 f0r fru1tfu1 adv1ce5.
400
12 Decem6er 1985
Reference5 [1 ] 5ee e~9. H. Harar1 and N. 5e16er9, Phy5. Lett. 988 (1981) 269;. E.6.54u1re5, Phy5. Lett. 948 (1980) 54; H. Fr1t25eh and 6. Mande16aum, Phy5. Lett. 1028 (1981) 319. [2] H. Harar1, Phy5. Lett. 1568 (1985) 250. [3] M. 6e11-Mann, P. Ram0nd and R. 51an5ky, 1n: 5uper9rav1ty, ed5. P. van N1euwenhu12en and D.2. Freedman (N0rth-H011and, Am5terdam, 1979); 7. Yana91da, unpu6115hed; R.N. M0hapatra and 6.5enjan0v1e, Phy5. Rev. D23 (1981) 165. [4] C.8. Ch1u and Y.8. Da1, Phy5. Lett. 1088 (1982) 341. [5] H. Harar1 and M. Leurer, Nue1. Phy5. 8233 (1984) 221. [6] 5.F. K1n9 and 5.R. 5harpe, Phy5. Lett. 1438 (1984) 494. [7 ] E. E1chten, L. H1nch11ffe, K. Lane and C. Qu199, Rev. M0d. Phy5.56 (1984) 579. [8] 5ee e.9. K. 60ttfr1ed and J.D. Jack50n, Nu0v0 C1ment0 63 (1964) 309. [9] E. E1chten, K. Lane and M. Pe5hk1n, Phy5. Rev. Lett. 50 (1983) 811. [10] U. 8aur and K.H. 5tren9, Phy5. Lett. 1628 (1985)456.