Dilepton signatures for B0B 0 mixing and the t-quark at pp colliders

Volume 143B, number 1, 2, 3

PHYSICS LETTERS

9 August 1984

DILEPTON S I G N A T U R E S FOR B ° - B ° MIXING A N D THE t-QUARK AT p~ COLLIDERS

V. B A R G E R Physics Department, University of Wisconsin, Madison, WI 53706, USA

and R.J.N. P H I L L I P S Rutherford Appleton Laboratory, Chilton, Oxon, England Received 1 February 1984

We quantify dilepton signals expected in p~ collider experiments from the decay of c~, b-b, tl, t-b, bt heavy quark pairs produced via parton fusion and radiative processes. The b-b signals dominate and it is feasible to measure B ° - B ° mixing from the ratio of like-sign to unlike-sign dileptons; 10% mixing doubles the unmixed ratio for back-to-back leptons with PT > 5 GeV. The tI, t-b, bI signals can be selectively extracted by azimuthal and lepton-isolation cuts.

Cascade decays of heavy quarks give characteristic multilepton final states that offer distinctive signatures for their detection in p~ collider experiments. Although these interesting possibilities have been recognized for some time [1], quantitative analyses have not been made to the same extent as for the higher-rate single-lepton and jet topology signatures [2]. D a t a taken in experiments [3] at the C E R N collider may already contain information on multilepton production that bears on important questions like B ° - B ° mixing "and t-quark production. Fig. 1 schematically indicates heavy-quark origins of multileptons in p~ collisions, for the case of no mixing. In the present work, we evaluate theoretical expectations for the largest multilepton signals, namely unlike-sign and like-sign dileptons, to estimate B°-B ° mixing effects and to determine how well the contributions from c, b and t quarks can be distinguished. The d+ d- backgrounds from electroweak Z ° and y* D r e l l - Y a n processes are not considered in this paper, since these contributions can be distinguished or avoided completely. D r e l l - Y a n leptons are characteristically isolated

from hadronic jets, unlike the leptons from c or b decay, and do not have the hadronic activity typical of t-quark decays; furthermore, there is no D r e l l - Y a n contribution to e+/~ - and ~ + e - , whose heavy quark production rates are the same as e+e - a n d / ~ + ~ - . We find that bb production and decay dominate both the like-sign (LS) and unlike-sign (US) dilepton rates and can be further enhanced by azimuthal correlation cuts. The L S / U S ratio for approximately back-to-back dileptons offers a possible measure of B°-B ° mixing, free from normalization uncertainties and trigger bias. A distinctive difference between heavy quark contributions is found in the azimuthal angle correlation between the leptons, about the beam axis, when a minimum PT cut is imposed. In b-b events there is a peak at ,#--- 180 o (back-to-back leptons where one comes from b and the other from b) and a peak at ~ = 0 o (unlike-sign leptons coming from the same b-parent). Radiative processes q~ gbb, q g - ~ qbb, gg--, gbb fill in the azimuthal region between these peaks at a substantially lower level. In tt, t-b, bI events the azimuthal distribu-

0370-2693/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

259

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m÷

~-

X

t

Fig. 1. Fish-bone diagrams, indicating principal heavy quark cascade decay origins of "multilepton final states in p~ collisions; any ( ~ ) leptonic vertex can be replaced by a (q'F:l)quark vertex. There are also suppressed contributions via g = • or q = c which we ignore here,

tions are c o m p a r a t i v e l y flat. By c o m b i n i n g a z i m u t h a l i n f o r m a t i o n with l e p t o n i s o l a t i o n criteria, it is p o s s i b l e either to p u r i f y the b b samp l e o r to distinguish the t - q u a r k signal. W e calculate the p r o d u c t i o n of h e a v y q u a r k s Q = c, b, t f r o m light q u a r k s q a n d gluons g via the following p a r t o n subprocesses q~t, gg -+ Q Q ,

(la)

q'~W

(lb)

±~Q',Q, q~I~Z°~QQ, (-) (-) _ q~l --" g Q Q , q g ---' q Q Q , gg ---' gOO. _

(lc)

M u l t i p l e soft gluon emission is i n c l u d e d in processes ( l a ) a n d ( l b ) t h r o u g h the semi-empirical Q C D transverse m o m e n t u m d i s t r i b u t i o n of the p r o d u c e d Q Q p a i r p r o p o s e d in ref. [4]. H a r d p a r t o n emission is c a l c u l a t e d explicitly t h r o u g h processes ( l c ) with a light p a r t o n cutoff PT > 5 260

9 August 1984

G e V following ref. [5], using the massless m a t r i x d e m e n t s a n d crossing factors of ref. [6]. P a r t o n d i s t r i b u t i o n s are t a k e n from Owens a n d R e y a [7], evolved up to Q2 = ~ the subprocess C M energy squared, with Q0---1.8 G e V a n d A = 0.3 GeV. P r o d u c t i o n cross sections are calculated at the overall C M energy yes- --- 540 GeV, c o r r e s p o n d ing to the initial o p e r a t i o n of the C E R N p ~ collider, with q u a r k masses m c - - 1 . 5 GeV, m b = 4.6 G e V a n d as a typical e x a m p l e m t = 35 GeV. I n calculating the cross sections for the processes ( l b ) we include a Q C D - m o t i v a t e d e n h a n c e m e n t factor K = 2, which gives W a n d Z p r o d u c t i o n in agreem e n t with e x p e r i m e n t [3]. T h e actual h a d r o p r o d u c t i o n cross section for Q Q pairs m a y exceed o u r p r e s e n t estimates because (i) we have i g n o r e d p o s s i b l e K - f a c t o r enh a n c e m e n t s f r o m higher o r d e r Q C D a n d (ii) we h a v e ignored p o s s i b l e c o n t r i b u t i o n s [8] from h e a v y q u a r k c o m p o n e n t s in the i n c i d e n t hadrons. T h e p r o d u c e d h e a v y quarks are taken to fragm e n t into h e a v y h a d r o n s of a p p r o x i m a t e l y the s a m e mass, using the m o d e l of Peterson et al. [9] in the l a b o r a t o r y frame. T h e h e a v y h a d r o n s are t a k e n to d e c a y b y t -~ b ~ c -~ s cascade, with V - A m a t r i x d e m e n t s , as in previous w o r k b y Barger et al. [1,2,4,5]. T o ensure correct p h a s e - s p a c e b o u n d s , the h e a v y q u a r k masses here are e q u a t e d to the c o r r e s p o n d i n g lowest h a d r o n masses: m b = m a = 5.2 GeV, mc = m D = 1.87 G e V with m t = m x = 35 G e V assumed. T h e b - q u a r k p r o d u c e d in T - h a d r o n d e c a y is f r a g m e n t e d to a B-hadron, using the m o d e l of ref. [9] in the T-rest frame. T h e c - q u a r k p r o d u c e d in B - h a d r o n d e c a y is given 8-function c - + D f r a g m e n t a t i o n to agree with the o b s e r v e d B - + D X s p e c t r u m [10]. F i n a l l y we assume m e a n s e m i l e p t o n i c b r a n c h i n g fractions B ( t ~ b e g ) = 0.10 b a s e d on f r e e - q u a r k d e c a y a n d B ( b --+ ceu) = 0.125, B ( c - ~ s e p ) = 0.10 b a s e d on d a t a [11]. The a b o v e i n g r e d i e n t s are c o m b i n e d in M o n t e C a r l o calculations that c o n s t r u c t h e a v y q u a r k p r o d u c t i o n a n d d e c a y events at the q u a r k - l e p t o n level, allowing us to evaluate cross sections a n d d i s t r i b u t i o n of interest. O u r results for c h a r g e d d i l e p t o n s are as follows. ( A ) Cross sections versus acceptance cut. I n p r a c tice one c a n n o t i d e n t i f y electrons or m u o n s b e l o w s o m e m i n i m u m transverse m o m e n t u m PT with re-

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spect to the beam axis. Hitherto experimental studies have concentrated on P'r(~) > 5 GeV and PT(e) > 15 GeV, but it is expected that electrons m a y soon be identifiable down to PT of 5 GeV. Fig. 2a shows results for the unlike-sign dilepton cross section o ( U S ) - o(@+@ - ) = o(@+e - ) = o(e+@ - ) = o(e+e - )

(2)

versus PT cut (assumed the same for both leptons), separating the contributions of b-b, c~, tI, t-b, b1 origin. The unlike-sign dilepton rate is dominated by the b-b contribution for any PT cutoff that gives a reasonable cross section. For pT(CUt)= 5 GeV, the bb cross section is about 200 pb. With the present integrated luminosity, &a_ 0.136 p b - 1, this corresponds to 30 /~+/~- events of b-b origin, and equal numbers of/x+e - , e+/x - and e+e - events. These leptons typically lie in or near narrow hadronic jets (associated with b-hadronization and b ~ c decay) unlike events of D r e l l - Y a n type where the leptons are not within jets or t-quark events with broader jets. Measurement of the dilepton rate is a direct test of b-b production models. The relative suppression of cE contributions is largely due to the softer fragmentation of the c-quark and the t~-contribution suffers from a high threshold. Fig. 2b shows the corresponding like-sign dilep-

103

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9 August 1984

ton cross section o ( L S ) --- a(@-/~-) + o(/t+@ +) =a(e-e-)+o(e+e

+)

= 1 [ o ( p , - e - ) + o(p,+e+)],

(3)

ignoring the possibility of neutral particle-antiparticle mixing. There is no c~ or D r e l l - Y a n contribution here, only b and t quarks contribute. Again bTa dominates for low PT cut-offs, but less decisively than before. For p T(CUt)= 5 GeV, o(LS, b b ) = 50 pb corresponding to 7 like-sign dimuon events at the existing luminosity. Henceforth we shall specialize to the acceptance cut PT > 6 GeV for both leptons, and ignore c~ relative to bb contributions. (B) Azimuthal correlation between leptons. The lepton correlation in relative azimuth A¢ about the b e a m axis is a striking property of the bb contribution that can be used either to purify the bb sample or to help in separating out t-quark signals. Parent b-quarks necessarily have high PT and are approximately back-to-back in the transverse plane, in order to meet the PT cut requirements on the decay leptons. Since there is little energy release in b-decay compared to pT(b) > 6 GeV, the b-jets are well collimated and the leptons are highly correlated, with A~. near 0 o (for both leptons from the same parent b) or A~ near 180 ° (for one

I

I LIKE-SIGN

_

,ek - \ IX,..

\\ \ _

t9

^,_ I0 I-

\~..""..

"--" , / b i F

16'0L

tb,bt

t

x ~ ~'

...... "-_ --'\ "'"~ "

"x

I

\'\",\.""

4 8 12 PT(CUt) (GeV)

_

...I "g,

I

I

4

8

I~ .

12

PT(CUt) (GeV)

Fig. 2. Cross section dependence on the lepton PT cut at V~-=540 GeV, with m t = 35 GeV: (a) unlike-sign dileptons, (b) like-sign dileptons. 261

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lepton from each of b, b). In contrast, a decaying t-quark releases enough energy that it need not have high PT and the leptons have little azimuthal correlation. Fig. 3a shows the distribution in Aq) for unlikesign dileptons, with the convention that 0 ~< Aq, ~< 180 °. The bb contributions peak near A~ = 0 ° and 180 ° as discussed above, while the radiative corrections of eq. (lc) provide a broader effect that spreads across the entire range at a level comparable with the tI and tb signals. The latter show m u c h less peaking_ as expected; the narrow enhancement in the tb signal near A@ = 0 is attributable to dileptons coming from the b - q u a r k which has a jacobian peak at high PT" It is argued in ref. [5] that the present calculation of bb radiative corrections m a y be an overestimate, but one must be cautious and it would be unsafe to assume that the t-quark signals can be separated from bb backg r o u n d by azimuthal cuts alone. Fig. 3b shows the azimuthal correlation for like-sign dileptons. Here the bb signal peaks at A~b = 180 o only (no LS dileptons from a c o m m o n parent). Both the tI and tb signals are enhanced toward 180 o, since for any given lepton there is a greater supply of fast same-sign partners in the other heavy quark jet, but the enhancement is m u c h less sharp. The etectroweak t-b, bI contributions dominate for Aft < 140 o.

I

I

I

I

I /

I

1 CD

~

-

P'r>6GeVbb~t~~ bE

,., 10-I

.<-

Invariant dilepton mass is another useful quantity. It too provides a clean separation of ¢ ' - d + pairs from a c o m m o n b-quark parent, but there is no distinctive feature comparable to the Ae? -- 180 o peak. Hence invariant mass is less helpful than A~ to discriminate between different heavy quark contributions. (C) B°-B ° mixing. One of the more interesting questions that can be answered by p~ collider experiments is that of B ° - B ° mixing [12], which would cause some decays into "wrong-sign" leptons. In the justifiable approximation of neglecting 3 F / F , the probability A for B ° ~ ~0 decay relative to B ° ~ B ° decay is

A = (3m/I')2/[2 + ( 3 m / p ) 2 ] ,

(4)

where 3m, 3F are the differences of Bs° and B°L masses and widths and F is the mean width. Of course B°(bd) and B°(b~) mesons have separate mixings A s and A d. F r o m the d o m i n a n t t-exchange box diagram and d o m i n a n t b ~ c decay, the usual result is [12,131

(3m/F)q

=

2

.2

2

KqRe( UtbUtq )/IUcbI ,

Kq = 32~r,lBaf 2qm2/( 3m 4 ) -- 5,

(5a) (5b)

where q = d, s; this numerical value of K is based

I

I

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PT• 6 GeV

io-1 -

,,,,gli

., .........

1984

I

(b) LIKESIGN

(a) UNLIKE SIGN / A

9 August

bb/ /"

"'~'"

tb,b~ ./"/Z ~

.e--"L

i5 2

f. I ./"t~

_

l o- a

10-3 _ I 0

16 3

I

I

I

00 120 A~ (deg)

I

180

I

0

I

60

I

I

120

I

180

A~ (deg)

Fig. 3. Cross sections versus the azimuthal angle Aq~between leptons, about the beam axis for V's= 540 GeV, with m t = 35 GeV: (a) unlike-sign dileptons, (b) like-sign dileptons. 262

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on a short-distance factor 71--0.8, a bag factor B B = 0.4, an optimistically large [14] decay constant f B q = 0.5 GeV, m b = 5 GeV and m t = 35 GeV. With the particle data book conventions for the parameters of the mixing matrix U and the experimental constraint that the angles 0i are all small

(Sm/r)s --- KsRe ( Uc~,)/lUcbl2 =KsCOS[2arg(O3-O2ei'~)], (Sm/F)d = g d cos 28 szs2/[Ucbl 2,

(6a) (6b)

where U~b -----03 -- 02 e i*. The experimental constraints from hyperon decays and b-decays are [13,15] 01=0.23,

IUcbl =

0.02 G 02 < 0.10,

03<0.04,

0.06.

(7)

Eq. (6a) then shows that BS mixing can range from near maximal to zero; the maximal case would be indicated by the K L - K s box-diagram analysis of CP violation. The Bd mixing again depends critically on 8 and 0z, and is bounded by A d < 0.1. Lepton measurements are sensitive only t o the average behavior of B-semileptonic decays. For a pure single B ° sample, the f r a c t i o n , that decays to "wrong-sign" leptons is simply , = A / ( 1 + A ) . However, in fact B - h a d r o n samples are mixtures of (b~), (bd), (bg) mesons and also baryons. Let us assume that the pickup of h, d, g quarks to form mesons is in the ratio l : l : h , where plausibly X = 0.3-0.5 from the observed suppression of leading kaons relative to pions in neutrino experiments. Then the mean probability of wrong-sign leptons (neglecting baryon contributions) is ,=[AJ(l+Ad)+hAs/(l+As)]/[2+h].

(8)

For the maximal case A d = 0.1, A s = 0.9, X = 0.5, we obtain c = 0.13. However, this depends critically on the B-decay constant; with the value [16] faq -- 0.1 GeV we o b t a i n , = 0.004 instead. B°-B ° mixing leads to unconventional lepton charges and hence affects the LS and US dilepton rates. It is advantageous to concentrate on backto-back pairs (i.e. those with different b, b parents) since dileptons from a common parent are always US; our subsequent remarks refer exclusively to

9 August 1984

dileptons in the Aq,= 180 ° peak. The L S / U S ratio is a good measure of mixing, and fortunately is independent of the bb production cross section and acceptance criteria; the ratio does depend on the b and c decays, on which there is independent experimental information, and on the PT spectrum of b-production which can be calibrated against the observed lepton PT spectrum. Without mixing, the LS contribution comes entirely from one primary plus one secondary lepton (e.g. b ~ cY-~, b -~ ~-~ s & u ) , whereas the US contribution is from two primary or two secondary leptons. With mixing, some of these previously US configurations becomes LS pairs, and vice versa. For these dileptons in the A ~ = 180 ° peak, the dependence of the cross sections on the mixing parameter c is o ( L S , , ) = [(1 _ , ) 2 + , 2 ] o(LS, O) + 2 , ( 1 - , ) o ( U S , 0),

o(vs, ,)= [(1

+,q o(us, 0)

(9)

+ 2,(1 - , ) o ( L S , 0), where the same pT cut must be uniformly applied. At high PT the abundance of secondary leptons is depleted relative to primary leptons and hence a(LS, 0) is much smaller than o(US, 0). For cuts in the range 4 GeV < p x(CUt) < 8 GeV we find o(LS, 0 ) / o ( U S , 0 ) = 1/4, and hence o(LS, , ) / o ( U S , ~) = (1 + 6 , ) / ( 4 - 6c).

(10)

For c = 0.1 there is a factor 2 effect, with the ratio becoming 1/2. To ensure that the bb event sample is free of D r e l l - Y a n and t-contamination, one may require that the back-to-back leptons be contained within narrow jets. The small c~ background contributes to US only, since D ° - D ° mixing is expected to be negligible; this background may also be removable by considerations of lepton PT transverse to the jet axes, but at most c~ serves only to dilute any potential B°-B ° mixing signal. Identification of leptons within narrow jets is a serious practical problem in the original C E R N detectors [3], where electrons are reliably recognized only in some isolation and muons can be faked by pion decay in a small but significant 263

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pT>6GeV

"~ "~ IO-t~ .C}

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(b) LIKE SIGN

(a) UNLIKE SIGN I ~

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/

-

ONE LEPTON / ISOLATED /.__~

pT > 6 GeV ONE LEPTON ISOLATED

10-I

l/

/' f"

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. . . . . .

=o-Z ~ b b

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f

io-3 I

I

60 Z~

I

I 120 (deg)

I

180

0

I

I

60

I X

120

180

A ~ (deg)

Fig. 4. Cross sections as in fig. 3 except now with requirement that at least one of the leptons be isolated accordingto eq. (11).

fraction of events. However, the muon backgrounds are less serious for dileptons than for single leptons and will be further reduced by the introduction of microvertex detectors in the future. (D) Lepton isolation cuts. Rejection of bb and cE events is necessary if we are to study the t-quark signal using dileptons. Techniques for removing bb and cE backgrounds to the single-lepton signal have been described previously [4,5]; the essential requirement is isolation of the lepton from accompanying hadronic Px. This preferentially rejects the well-collimated jets from b and c quarks with little cost to the t-signal. In the present context of dileptons, it is undesirable to require isolation for both leptons, since this would suppress all signals except the US tI contribution with both leptons from primary t---, b¢~, decays. In particular, the interesting LS and US tb signals would be lost. Accordingly, we require only one of the two leptons to be isolated. To illustrate, we consider the modest isolation requirement

Table 1 tt tb, bI 264

o(US)/o(¢) 0.04 0.02

o(LS)/o(g) 0.01 0.06

E ( h a d r o n i c p x in 30 o cone about lepton direction) < 4 GeV.

(11)

Fig. 4 shows the resulting q,-distributions. The t-signals stand out clearly over substantial ranges of q~. We expect that the consideration of jet topologies would differentiate the tt and tb, bI events and also permit further suppression of b-b, c6 backgrounds. It is interesting to compare dilepton to single lepton rates, especially for tI to circumvent questions about cross section normalization. To identify the t-quark single-lepton signals, a PT > 8 GeV lepton cut was found to be necessary [4]; with this cut and single-lepton isolation we obtain the ratios as shown in table 1, where o ( g ) - o(/~ +) + o(bt-) = o(e+) + o(e-). We thank D. Cline for discussion about dilepton measurements at the C E R N p~ collider. This research was supported in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation, and in part by the Department of Energy under contract DE-AC02-76ER00881.

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[2]

[3]

[4] [5] [6] [7] [8]

PHYSICS LETTERS

S. Pakvasa, M. Dechantsreiter, F. Haizen and D.M. Scott, Phys. Rev. D20 (1979) 2869; M. Cabibbo and L. Maiani, Phys. Lett. 87B (1979) 366; L.L. Chau, W.Y. Keung and S.C.C. Ting, Phys. Rev. D24 (1981) 2862; F.E. Paige, AlP Conf. Proc. No. 85 (ALP, New York, 1981) p. 168; V. Barger, A.D. Martin and R.J.N. Phillips, Phys. Rev. D28 (1983) 145. V. Barger, A.D. Martin and R.J.N. Phillips, Phys. Lett. 125B (1983) 339, 343; R.M. Godbole, S. Pakvasa and D.P. Roy, Phys. Rev. Lett. 50 (1983) 1539; R. Horgan and M. Jacob, Phys. Lett. 107B (1981) 395; CERN-TH.3682 (1983); F. Halzen and D.M. Scott, Phys. Lett. 129B (1983) 341; R. Odorico, Bologna report IFUB 83/6; G. Ballocchi and R. Odorico, Bologna report IFUB 83/11; L.M. Sehgal and P. Zerwas, Aachen report PITHA 83/10 (1983); K. Hagiwara and W.F. Long, Phys. Lett. 13"2B (1983) 202; D. DiBitonto, Proc. Moriond Workshop on ~p physics (1983). UA1 Collab., G. Arnison et al., Phys. Lett. 122B (1983) 103; 126B (1983) 398; UA2 Coltab., M. Banner et al., Phys. Lett. 122B (1983) 476; UA2 Collab., P. Bagnaia et al., Phys. Lett. 129B (1983) 130. V. Barger et at., Madison preprint PH/133 (1983). V. Barger et al., Madison preprint PH/143 (1983). F.A. Berends et al., Phys. Lett. 103B (1981) 124; F. Halzen and P. Hoyer, Phys. Lett. 130B (1983) 326. J.F. Owens and E. Reya, Phys. Rev. D17 (1978) 3003. B.L. Combridge, Nucl. Phys. B151 (1979) 429; V. Barger, F. Halzen and W.Y. Keung, Phys. Rev. D24 (1981) 1428.

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[9] C. Peterson, D. Schlatter, I. Schmitt and P.M. Zerwas, Phys. Rev. D27 (1983) 105. [10] J. Green et al., Phys. Rev. Lett. 51 (1983) 347. [11] G.H. Trilling, Phys. Rep. 75 (1981) 57; Particle Data Group, Review of Particle Proporties, Phys. Lett. l l l B (1982) 1; H. Schneider, Proc. Brighton Conf. (1983); K. Chadwick et at., Phys. Rev. D27 (1983) 475, and references therein. [12] J. Ellis, M.K. Gaillard, D.V. Nanopoulos and S. Rudaz, Nud. Phys. B131 (1977) 285; A. Ali and A. Aydin, Nucl. Phys. B148 (1979) 165; V. Barger, W.F. Long and S. Pakvasa, Phys. Rev. D21 (1980) 174; J. Hagelin, Phys. Rev. D20 (1979) 2893; B.A. Campbell and P.J. O'Donnell, Phys. Rev. D25 (1982) 1989; L.L. Chau, W.Y. Keung and M.D. Tran, Phys. Rev. D27 (1983) 2145. [13] S. Pakvasa, Phys. Rev. D28 (1983) 2915; L.L. Chau and W.Y. Keung, BNL preprint (1983); I. Bigi and A.I. Sanda, Fermilab-Pub-83/74-THY; F.J. Gilman and J. Hagelin, Phys. Lett. 133B (1983) 443; E. Paschos and U. Turke, Santa Barbara preprint NSFITP-83-168; E. Ma, W.A. Simmons and S.F. Tuan, Phys. Rev. D20 (1979) 2888; J. Hagelin and M.B. Wise, Nucl. Phys. B189 (1981) 87; J. Hagelin, Nucl. Phys. B193 (1981) 123; E. Franco, M. Lusignoh and A. Pugliese, Nucl. Phys. B194 (1982) 403. [14] V. Novikov et al., Phys. Rev. Lett. 38 (1977) 626. [15] L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945; K. Kteinknecht and B. Renk, Z. Phys. C16 (1982) 7; T. Brown and S. Pakvasa, private communication. [16] E. Golowich, Phys. Lett. 91B (1980) 271.

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