Asymmetries in heavy fermion production and decay

V01ume 191, num6er 3

PHY51C5 LE77ER5 8

11 June 1987

A5YMME7R1E5 1N HEAVY F E R M 1 0 N P R 0 D U C 7 1 0 N AND DECAY 5tan151aw JADACH ~ and J0hann H. K 0 H N Max-P1anck-1n5t1tutJ~r Phy51k und A5tr0phy51k - werner-He15en6er9-1n5t1tutJ~r Phy51kP.0. 80x 40 12 12, D-8000 Mun1ch, Fed. Rep. 6ermany Rece1ved 15 Decem6er 1986;rev15edmanu5cr1ptrece1ved 13 March 1987

We ca1cu1atethe f0rward-6ackward a5ymmetr1e50f heavy ferm10n5and 0f 1ept0n5 fr0m the1r 5em11ept0n1cdecay 1n e•e ann1h11at10n. 1n part1cu1arwe 5tudythe c0rrect10n5t0 the 10we5t-0rderpred1ct10nre5u1t1n9fr0m 1n1t1a1-5taterad1at10n, k1nemat1c effect51n heavy4uark decayand the r01e0f 4uark p01ar12at10n.

Prec1510n mea5urement5 0f f0rward-6ackward a5ymmetr1e5 and 0f 1eft-r19ht a5ymmetr1e5 (w1th 10n91tud1na11y p01ar12ed 6eam5) c0n5t1tute an 1mp0rtant 90a1 0f the e•e - c0111der5pre5ent1y under c0n5truct10n: KEK, 5LC and LEP. A5ymmetr1e5 w1th pure1y 1ept0n1c f1na1 5tate5 are the0ret1ca11y c1ean and may 5erve t0 te5t the 5tandard m0de1 w1th very h19h accuracy [ 1 ]. A5ymmetr1e5 w1th 4uark f1na1 5tate5 are 5u6ject t0 9reater uncerta1nt1e5.7he5e 0r191nate fr0m h19her-0rder QCD c0rrect10n5, wh1ch were ca1cu1ated 1n ref. [ 2 ] and were f0und t0 6e 5ma11, fr0m the hadr0n12at10n 0f 4uark5 and fr0m the fact that 0ne ha5 t0 deduce the a5ymmetry fr0m an ana1y515 0f the decay pr0duct5. 7he1r exper1menta1 determ1nat10n 15 neverthe1e55 1mp0rtant t0 mea5ure the e1ectr0weak c0up11n95 0f heavy 4uark5 0r t0 9et a h1nt 0n add1t10na1 c0up11n95 fr0m exten510n5 0f the 5tandard m0de1. 1n part1cu1ar f0r eventua11y d15c0vered new heavy 06ject5 11ke the t0p 4uark, a f0urth 9enerat10n 6 0r 0ther c010red ferm10n5 [ a5 5u99e5ted f0r examp1e fr0m E (6)] the5e a5ymmetr1e5 a110w an 1ndependent determ1nat10n 0f 4uark char9e5 and 0f the weak 1505p1n w1th 5y5temat1c err0r5 d1fferent fr0m th05e 0f t0ta1 cr055 5ect10n mea5urement5. 0 n t0p 0f the 2 ° 0ne expect5 1ar9e c0unt1n9 rate5, the f1na1 an5wer w1116e d0m1nated 6y 5y5temat1c uncerta1nt1e5 and a prec1510n mea5urement re4u1re5 deta11ed under5tand1n9 0f heavy ferm10n pr0duct10n and decay. 1n th15 paper we 1nve5t19ate the chan9e5 0f the a5ymmetry at the 4uark 1eve1 and 0f decay pr0duct5 wh1ch re5u1t fr0m 1n1t1a1-5tate rad1at10n, k1nemat1c effect5 1n heavy 4uark decay and the r01e 0f 4uark p01ar12at10n. 1n pr1nc1p1e there are tw0 way5 t0 mea5ure the 4uark a5ymmetry: 0 n e may e1ther attempt t0 rec0n5truct heavy me50n5 fr0m the1r decay pr0duct5 0r 0ne may d1rect1y u5e the a5ymmetry 0f decay pr0duct5 - prefera61y 0f mu0n5 0r e1ectr0n5. 1n the f0rmer ca5e 0ne re11e5 heav11y 0n the appr0pr1ate jet rec0n5truct10n a190r1thm and the re5u1t 15 pre5uma61y affected 6y uncerta1nt1e5 fr0m m0de1 dependence. 7he advanta9e 0f th15 appr0ach 15 0fc0ur5e that the mea5ured a5ymmetry w1116e d1rect1y re1ated t0 and 1n fact appr0x1mate1y e4ua1 t0 the 0r191na1 4uark a5ymmetry. Mu0n5 (0r e1ectr0n5) a5 decay pr0duct5 c0n5t1tute a rather c1ean 519na1 f0r a new heavy ferm10n and th15 ha5 a1ready 6een u5ed 4u1te 5ucce55fu11yt0 ta9 8 me50n5 and mea5ure the1r a5ymmetry :J. F0r new heavy 4uark5 the5e d15tr16ut10n5 are 5tr0n91y 1nf1uenced 6y the c105e pr0x1m1ty 0fthe1r pr0duct10n thre5h01d, the 1ar9e ener9y re1ea5e 1n the decay and the re5u1t1n9 5p111-0ver0f 4uark5 1nt0 the 0pp051te hem15phere, wh1ch 1ead5 t0 a 5tr0n9 reduct10n 0f the mu0n a5ymmetry. 7hey w111furtherm0re 6e affected 6y 5p1n effect5, a5 d15cu55ed 1n deta11 1n ref5. [ 4,5 ] f0r mu0n-ener9y d15tr16ut10n5. 0n 1eave0f a65ence fr0m 1n5t1tute0f Phy51c5,Ja9e110n1anUn1ver51ty,PL-30059Crac0w, P01and. :t F0r a recent rev1ew5ee ref. [ 3]. 0370-2693/87/$ 03.50 • E15ev1er 5c1ence Pu6115her5 8.V. (N0rth-H011and Phy51c5 Pu6115h1n9 D1v1510n)

313

V01ume 191, num6er 3

PHY51C5 LE77ER5 8

11 June 1987

At the 4uark 1eve1 the cr055 5ect10n, 1nc1ud1n9 the dependence 0n the 5p1n vect0r5 5 and 9, can 6e wr1tten 1n the f0rm

da = A ( 1 + au5 u + au9•• + cu~5~9" ) d L1P5 (p+ +p• ; Pv , P~ ).

( 1)

7he funct10n A 5tand5 f0r the 5p1n-avera9ed d1fferent1a1 cr055 5ect10n and the c0eff1c1ent5 a, d and c determ1ne the 5p1n dependence. 7hey are funct10n5 0f the m0menta 0f the 1nc0m1n9 and 0ut901n9 ferm10n5 and (1f 1n1t1a15tate rad1at10n 15 taken 1nt0 acc0unt) 0f the ph0t0n m0mentum. 7he exp11c1t f0rmu1ae f0r A, au, du, and cu~ may 6e f0und 1n ref. [ 5 ]. 7he m0d1f1cat10n5 wh1ch are nece55ary f0r 1nc1u510n 0f the 1n1t1a1-5tate 6rem55trah1un9 are d15cu55ed 1n ref5. [6,7 ]. 7he d1fferent1a1 rate f0r the decay 0f F 1nt0 1t5 150partner 1"2,a mu0n p1u5 a neutr1n0 15 91ven 6y 1 62 M4 d/" = 2m~ 2 - 128 [M2w • (Pc, +P•0 2] 2 +F2wM2w [(PF + mF5)"Pr2] (Pr, ~/~3) d L1P5(pv; pf,),

where f2 and 1•3 5tand f0r ~t- and 9, (v, and ~t+ ) 1n the decay 0 f a ferm10n w1th 73= -• 1nt0 a f0rm 51m11ar t0 e4. (1): d/•v = 8 ( 1 +6~5 u) d L1P5(pF;•,),

(2)

(+•). 1t can 6e ca5t

dare = 8 ( 1 +/~u9~) d L1P5(pr;p~,),

(3)

where the vect0r 6 (/~) 15, 6y c0n5truct10n, pure1y 5pace11ke 1n the F- (F-) re5t frame, 1.e., 6•pF= ~P~= 0. 7he d1fferent1a1 cr055 5ect10n f0r the c0m61ned pr0duct10n and decay ,pr0ce55 then read5 dtr = A 8 / ~ ( 1 - a u 6 u - d u ~ + c u ~ 6 u ~ ~) d L1P5(p+ +p•

;PF,P~) d L1P5(pF; pf,) d L1P5(pr; p•,).

(4)

7he fact0r A 8 8 1n the a60ve d1fferent1a1 cr055 5ect10n repre5ent5 the unc0rre1ated pr0duct10n and decay. 7he c0rre1at10n5 1n the decay5 and a11 0ther 5p1n effect5 are ent1re1y due t0 the acc0mpany1n9 6racket fact0r. 7he5e f0rmu1a5 are d1rect1y app11ca61e f0r pr0duct10n and decay 0f heavy 1ept0n5 - f0r heavy 4uark5 the 5p1n effect5 are weakened. 7h15 can 6e effect1ve1y acc0unted f0r 6y the 5u65t1tut10n 5u~j~,. 7he dep01ar12at10n fact0r f15 expected t0 6e ar0und • f0r t0p 4uark5 w1th ma55e5 6e10w ~2 80 6 e V [4] and 0 f0r 6 4uark5 wh05e decay rate 15 pre5uma61y 5uppre55ed 6y 5ma11 m1x1n9 an91e5. [J~ r15e5 t0 • f0r a KM 5uppre5510n fact0r 1ar9er than (13 6e7/m~)8.] 1n f19. 1 we c0mpare the f0rward-6ackward a5ymmetry 0f t0p 4uark5 A ~a and 0f 60tt0m 4uark5 A ~va w1th 1n1t1a1-5tate rad1at10n and the a5ymmetry 0f (pr0mpt) mu0n5 fr0m 4uark decay A~8 +3 t0 the a5ymmetry ca1cu1ated fr0m 80rn d1a9ram5 ~f1 Re EvA A w ( 8 0 r n ) = •Dv(3-f12) +DAf12,

(5)

where f1= (1-4m~/5)1/2,

Dv = 1 Q e Q v / d + v e v v 1 2 + a ~ , d=

DA= ( ~ + a e )2a v 2,

EvA=(2v~vv+Q~Qv/d)a~av,

5 1 v v = 2 1 ~ - 4 Q F 51n20w, aF=2~v. 5 - M 2 + 1 r 2 M 2 16 51n20w c0520w •

:2 F0r even heav1er4uark5 the weak decay rate 15c0mpara61e0r 1ar9er than the hyperf1ne5p11tt1n96etween 7and 7* and we expect a tran51t10n t0f= 1. F0r m0re deta1150n u1tra-heavy4uark5 5ee ref. [8]. :3 7he a5ymmetr1e5have 6een ca1cu1atedw1ththe M0nte Car10 Pr09ram71P-70P [ 9 ]. 7hr0u9h0ut th15paper we 5ha11u5e a5 parameter5 M2=94 6eV and 51n20w= 0.222. 314

V01ume 191, num6er 3

0.5

a

80RN

0.4

PHY51C5 LE77ER5 8

11 June 1987

~~" A;8

1

AF8

0.5

6

m••6:60 (]eV

0.2 0.t, 0.1 0.3 0.0

•

0.2 -0.1 -0.2

mt:60 6eV

0.1

20 1 60

1

70

1

[aeV]

E6eam

90

100

60

70

E6,,m [6eV]

90

100

F19. 1. F0rward-6ackward a5ymmetr1e5 f0r t0p 4uark5 (a) and 60tt0m 4uark5 (6) (a55um1n9 6 ~ c + W * ) at the 80rn 1eve1, 1nc1ud1n9 1n1t1a1-5tate rad1at10n, and f0r mu0n5 (p+ f0r t and p f0r 6) fr0m 4uark decay 1nc1ud1n9 1n1t1a1-5tate rad1at10n (m4 = 60 6eV, f , = •, J~ = 0). 81ack c1rc1e5 repre5ent the re5u1t5 0f the M0nte Car10 ca1cu1at10n5 (7 × 104 event5 per p01nt) wh1ch are j01ned w1th the 5011d 11ne t0 9u1de the eye.

7he ma9n1tude 0f the QCD c0rrect10n5 t0 the an9u1ar d15tr16ut10n can 6e character12ed 6y c0eff1c1ent5 0~4 and f14, wh1ch are re1ated t0 the f0rward-6ackward a5ymmetry thr0u9h AF8

-

/~4 1 + ~0~4 "

(6)

7hey have 6een ca1cu1ated ~+41n ref. [2] and are 5h0wn 1n f195. 2a and 26 t0 10we5t 0rder (PM) and 1nc1ud1n9 QCD c0rrect10n5 ( Q C D ) a5 a funct10n 0f the t0p 4uark ma55 f0r EcM=M2. Apart fr0m the re910n very c105e t0 thre5h01d the c0rrect10n5 are 5ma11. 1n ta61e 1 we 5tudy the re1at1ve 1mp0rtance 0f the 1n1t1a1 5tate rad1at10n 1n m0re deta11 f0r m t-~ 60 6 e V and ~x/5= 80 6eV. Quark and mu0n a5ymmetr1e5 are m0d1f1ed 0n1y 5119ht1y. 1n add1t10n 0ne m19ht c0n51der the p05516111ty t0 e11m1nate event5 w1th 512ea61e 1n1t1a1-5tate rad1at10n. (1n event5 w1th 0n1y n0n-1ept0n1c 0r w1th 0ne 5em11ept0n1c decay the ener9y 0f the ph0t0n 1n the 6eam p1pe can 6e rec0n5tructed - at 1ea5t 1n pr1nc1p1e.) F0r var10u5 1ncrea51n91Y harder cut5 0n Ev the 4uark a5ymmetry c0me5 c105er t0 the 0r191na1 va1ue.

14 We thank the auth0r5 0f ref. [2] f0r pr0v1d1n9 u5 w1th an updated ver510n 0ff19. 26. 1

0.95 / 1

1.0 . . . . . .

,

1

. . ~ a 4 (PM1

1

1

• r14(0.C01

~

134(PM)

\

,

a-

0.90

1

[34 ( 1•M)N,

0.15 0.10

0.5

0.05

/0

2•0

3•0

m0 E6ev3

L0

0

1~0

• 20

3•0

• 40

rn4 [6eV]

F19. 2. QCD c0rrect10n5 t0 the parameter5 0t4 (a) and f14 (6) 0n the 2 ° f0r t0p 4uark5 a5 a funct10n 0f the1r ma55 ( fr0m ref. [ 2 ] ).

315

V01ume 191, num6er 3

PHY51C5 LE77ER5 8

11 June 1987

7a61e 1 Dependence 0f the f0rward-6ackward a5ymmetr1e50n the 1n1t1a1-5tateQED 6rem55trah1un9.7hea5ymmetryA~8 15ca1cu1atedu51n9the m0mentum 0ft and A~8 u51n9the m0mentum 0fthe p+ fr0m t decay. 1nc1udedare a150the va1ue50f a5ymmetr1e5f0r var10u5cut-0ff5 0n the ph0t0n ener9yEy and the va1ue0fA~8 1n 80rn appr0x1mat10n.7he ma550fthe t-4uark 15taken t0 6e 60 6eV and the 6eam ener9y 80 6eV. 1n 6racket5 are the num6er5 0f event5.

A~8 A~-~

A11

Ey < 10 6eV

Ev < 5 6eV

80rn

0.465_+0.004 0.107_+0.004 (63400)

0.479_+0.004 0.123_+0.004 (55500)

0.480_+0.004 0.125-+0.005 (50400)

0.486 -

7 h e 5p111-0ver 1nt0 the 0pp051te hem15phere reduce5 the m u 0 n a5ymmetry 4u1te 5u65tant1a11y a n d 5p1n effect5 may 1ead t0 further, even m0re dramat1c chan9e, a5 15 5h0wn 1n f19. 1 and a150 1n ta61e 2. 5p1n effect5 may even 1nvert the 519n 0f the a5ymmetry c105e t0 thre5h01d, a5 15 a150 ev1dent fr0m f19. 1a. 1t 15 1n th15 ener9y ran9e where t0p 4uark5 are d0m1nant1y pr0duced w1th ne9at1ve p01ar12at10n and the mu0n5 are em1tted a9a1n5t the d1rect10n 0f f119ht. 7 h e 11m1t1n9va1ue A ~8 ~ - 0 . 2 at thre5h01d c0ntra5t5 5harp1y w1th A ~8 = 0 a n d 15 a150 ea511y under5t00d: t0p 4uark5 are pr0duced at thre5h01d w1th a p01ar12at10n a10n9 the e - 6eam d1rect10n PL--~ ( -2a¢vJDv)[vevt +Re(QeQt/d)] ~ - 0 . 9

(7)

and the an9u1ar d15tr16ut10n 0f the mu0n5 ~ (1 + PLfc05 0) then 91ve5 the 065erved a5ymmetry. 0 n e m19ht try t0 rec0ver the 0r191na1 re5u1t 6y ta991n9 fa5t 1ept0n5 w1th x c105e t0 xmax wh1ch were nece55ar11y em1tted a10n9 the 4uark d1rect10n. 1n fact th15 m e t h 0 d w0rk5 f 0 r f - - 0 a5 15 the ca5e f0r a 6 4uark 0r 1f the 4uark p01ar12at10n happen5 t0 6e 5ma11. 1n 9enera1, h0wever, th15 cut 1ntr0duce5 a 61a5 w1th re5pect t0 4uark 5p1n5. 1n the extreme c a 5 e f = 1 and xmax f0r examp1e 0ne w0u1d 5e1ect r19ht-handed p01ar12ed t0p 4uark5 0n1y. 19n0r1n9 the 5ma11 c0ntr16ut10n fr0m the ph0t0n, the cr055 5ect10n 0n t0p 0f the 2 f0r r19ht-handed (1eft-handed) t0p 4uark5 15

7a61e 2 Dependence 0f the f0rward-6ackward a5ymmetr1e5 0n the dep01ar12at10n parameter fand 0n 1n1t1a1-5tateQED 6rem55trah1un9 (n0 cut5). 1nc1udedare a150the va1ue50fA~a f0r var10u5cut-0ff5 0n x~=E~/E6.... where E, 15the ener9y 0f~t+. 7he ma55 0fthe t 4uark 15 taken t0 6e 40 6eV and the 6eam ener9y E6eam= •M2= 47 6eV. 1n 6racket5 are the num6er5 0f event5. A~n

A~8

a11

a11

x,<0.2

x,>0.2

x~>0.4

x,>0.6

f= ~, w1th1n1t1a1-5tate 0.127_+0.005 6rem55trah1un9 (47100)

0.011_+0.005 -0.037+0.008 (47100) (15200)

0.038-+0.006 0.088-+0.012 (31900) (8030)

0.040-+0.042 (565)

f= •, n0 1n1t1a1-5tate 6rem55trah1un9

0.139_+0.005 (51500)

0.010_+0.005 -0.041_+0.008 (51500) (16500)

0.034+0.006 (35000)

0.081_+0.011 (8820)

0.097_+0.040 (618)

f= 0, w1th1n1t1a1-5tate 0.127_+0.004 6rem55trah1un9 (78600)

0.048-+0.004 -0.003-+0.007 (78600) (21400)

0.067_+0.005 0.099_+0.007 (57200) (17600)

0.100_+0.026 (1460)

f= 1, w1th 1n1t1a1-5tate 0.122_+0.005 -0.017_+0.005 6rem55trah1un9 (47200) (47200)

316

-0.047_+0.008 (17600)

0.001•+0.007 (29600)

0.018+0.013 (5630)

-0.080_+0.060 (270)

V01ume 191, num6er 3

PHY51C5 LE77ER5 8

11 June 1987

d0-R,L - 0c (v,2 + at2)//2(1 +c0520) +2v~2(1 •//2) +4r~vfaf//c05 0 d c05 0

-7-2[Vrar//(1 +C052 0) + r e ( ~ +a2//2) c05 0], r~ =2veae/(~ +a 2)

(8)

and 1ead5 t0 an 1nte9rated cr055 5ect10n w1th re1at1ve we19ht 0"R•L 0C~{ [ •V2(3--//2) +a~f12 ] -7-2Vfar//}

(9)

a n d t0 f0rward--6aCkWard a5ymmetr1e5

A% L = (rJtrR,L)[2vtat//-7- ( ~ +a2//2)].

(10)

7 h e actua1 a5ymmetr1e5 f0r d1fferent cut5 0n the m u 0 n ener91e5 and f0r d1fferent a55umpt10n5 0 n f a n d 1n1t1a15tate rad1at10n are 91ven 1n ta61e 2. A rather 5tr0n9 d e p e n d e n c e 0 f A ~ a 0n x0 15 ev1dent, a n d even f0r x 0 > 0 . 6 c105e t0 xm,x=0.76 0ne d0e5 n0t rec0ver the 0r191na1 4uark a5ymmetry 0f 0. 1n fact, the 11m1t1n9 re5u1t can ea511y 6e under5t00d a5 a m1xture 0f A Ra = - 0.031 a n d A La = 0.166 w1th re1at1ve we19ht5 • (1 + f ) trR = 0.074 and • (1 - f ) 0L = 0.314 f0r f = •.

C0nC1U510n5. 7 h e determ1nat10n 0f e1eCtr0weak C0Up11n95, 1n part1CU1ar 0f new heavy 4Uark5 thr0U9h a5ymmetr1e5 w111 c0n5t1tute an 1mp0rtant a1m 0f future e+e - mach1ne5. 1n1t1a1-5tate rad1at10n affect5 the5e a5ymmetr1e5 0n1y 5119ht1y a n d 1n a we11 c0ntr011a61e manner. A5ymmetr1e5 0f decay pr0duct5 11ke p r 0 m p t mu0n5 0r e1ectr0n5 are 5tr0n91y 1nf1uenced 6y 5p111-0ver fr0m the decay a n d 6y 5p1n effect5. 7hu5 0ne need5 a m0de1 f0r the 5tren9th 0f the dep01ar12at10n thr0u9h hadr0n1c 1nteract10n5. 7 h e va11d1ty 0 f th15 m0de1 can 6e te5ted 6y a mea5urement 0f the c0m61ned ener9y and an9u1ar d15tr16ut10n. Lept0n-ant11ept0n c0rre1at10n5 1n event5 where 60th 4uark5 decay 5em11ept0n1ca11y w111 c0nta1n a term pr0p0rt10na1 t0 f2 a n d thu5 w111 pr0v1de an0ther te5t 0f th15 appr0ach. 7 h e auth0r5 W0U1d 11ke t0 thank the mem6er5 0 f the heavy 4Uark a n d 1ept0n 5U69r0Up 0f the ECFA w0rk5h0p LEP200, 1n part1CU1ar P. 2erwa5, P. 190-Kemene5 a n d R. 5ett1e5 f0r 5t1mU1at1n9 d15CU5510n5 wh1Ch 1n1t1ated th15 pre5ent W0rk.

ReferenCe5 [ 1] 6. A1tare111et a1., 1n: Phy51c5at LEP, CERN Rep0rt CERN 86-02 (1986), ed5. J. E1115and R. Pecce1. [2] J. Jer5ak, E. Laermann and P.M. 2erwa5, Phy5. Rev. D 25 (1982) 1218, and Erratum, t0 6e pu6115hed. [3] D.H. 5ax0n, prepr1nt RAL-86-073. [4] J.H. K11hn, Nuc1. Phy5. 8 237 (1984) 77, and reference5 there1n. [5] J.H. Kf1hn, A. Re1ter and P.M. 2erwa5, Nuc1. Phy5. 8 272 (1986) 360; J.H. K11hnand F. Wa9ner, Nuc1. Phy5. 8 236 (1984) 16. [6] F.A. 8erend5 and R. K1e155,Nuc1. Phy5. 8 178 (1981) 141. [7] F.A. 8erend5, R. K1e155and 5. Jadach, C0mput. Phy5. C0mmun. 29 (1983) 185, and reference5 there1n. [8] 1. 8191, Y. D0k5h1t2er, V. Kh02e, J. K11hnand P. 2erwa5, Phy5. Lett. 8 181 (1986) 157. [ 9 ] 5. Jadach and J.H. K11hn,prepr1nt MP1-PAE/P7h 64/86.

317