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Is a low-mass top quark ruled out?
Volume 196, number 2
PHYSICS LETTERS B
1 October 1987
IS A L O W - M A S S T O P Q U A R K R U L E D O U T ? J.R. CUDELL, F. H A L Z E N
Physics Department, Universityof Wisconsin, Madison, W153706, USA X.-G. HE and S. PAKVASA
Department of Physics and Astronomy, Universityof Hawaii, Honolulu, HI 96822, USA Received 26 June 1987
In view of the recent ARGUS measurement of B°-B° mixing, we carefully reexamine the mass limits for the top quark. The actual limit depends critically on the value of the confinement parameters for the B°-l]° and the K°-I¢° systems, as well as on the structure of the Kobayashi-Maskawa matrix which we reconsider ab initio. The large uncertainties associated with these parameters as well as with input experimental errors allow us to accomodate any top mass above the present PETRA limit of 23 GeV. We also discuss other measurements relevant to the top mass and conclude that the experimental search for small top mass at TRISTAN and SLC is still relevant.
Recently, the A R G U S collaboration a n n o u n c e d a m e a s u r e m e n t of mixing in the Bd-Ba o -o system [ 1 ]. Their value rud = 0.21 _+0.07 seems surprisingly large for the standard model with three generations ~1. Several new analyses [ 3 ] have appeared, some of which suggest that this result, along with k n o w n values of e, ... requires the top quark mass rnt to be larger than 45 GeV. The existence of such a b o u n d for rnt is crucial not only in view of speculations on the value of m, in the range 23-35 GeV b u t even more importantly for T R I S T A N and SLC where this is precisely the range of masses that can be explored. With this in m i n d , we reexamine the calculation of E a n d rud. We conclude that for a reasonable range of parameters, it iS possible to accomodate all the data for mt in the range 25-35 GeV. The m e a s u r e m e n t of rB~=-F(B°--+~+X)/F(B°-~I2-X) can be translated into 1 8 m { / F = [ 2 r u J ( 1 o -o system. This FBo)],/2 = 0.73 _+0.18, with 8 m the eigenstate mass difference and F the m e a n width of the Ba-Bd quantity has been analysed theoretically [ 4] and depends on the following parameters: the Bo-lifetime and mass, vB and roB, the top quark mass mt, a c o n f i n e m e n t factor Bu, the decay constant fB a n d the K o b a y a s h i - M a s k a w a matrix elements U,b a n d Utd. Moreover, the box-diagram factor further depends on the W mass mw and the Q C D corrections on AQcD a n d the b o t t o m quark mass rob. The K o b a y a s h i - M a s k a w a elements of interest are not experimentally k n o w n and one has to extract them from unitarity constraints a n d from the k n o w n values of the other elements. We assume 3 generations a n d no supersymmetry and use the following parametrization, in terms of mixing angles 0,, 02, 03, and CP-violating phase 6, with 0 ~<0i ~ 7c/2 a n d 0 ~<6 ~<2n by convention. We write & = s i n 0i, ci=cos 0i, so the matrix U can be written
Sud Sus Sub~ / CI Scd fcs Scb)=~SIC2 U~d fts U~.b/ \SIS2
--sic 3
--sis 3
ClC2C3--$2s3ei6 CIC2S3-}-S2c3eia I . CIS2C3-J¢-C2S3eia
cis2s3--c2c3ei'5,]
The experimental constraints ~2 on the absolute values are summarized in table 1. A recent analysis of the CLEO ~' For previous estimates see ref. [2]. ~2We use the values of I UodI and IUosl given in a recent summary by Marciano [ 5 ]. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B . V . ( N o r t h - H o l l a n d Physics Publishing Division)
227
Volume 196, number 2
PHYSICS LETTERS B
Table 1 Data and errors.
1 October 1987
Table 2 Parameters of the problem.
Quantity
Mean value
Error
Parameter
Minimum value
Maximum value
I U~al
0.9744 0.220 0.207 0.95 ~<0.20 0.11 1.16 5.2752 81.8 2.275 0.73
0.001 0.002 0.024 0.14
s, s2 s3 ~
0.21 0 0 0 0.1 1.1 4.4 20 0.4 0.01
0.23 0.15 0.1 2n 0.4 1.8 5.2 100 2.0-1.5 0.1-0.06
I U~ I I U¢~[ [ Ucsl
I U, b]/I U,,bl B~t rB (10-M-~ s) rnn (GeV) mw (GeV) (10 -3) 8mlF
-
0.01 0.14 0.0028 1.5 0.021 0.18
AQC D
m~ mb m~ BK f~ ×BB
data [6 ] gives a new b o u n d for the ratio o f moduli: [ Uuu]l[ Ucb[ ~<0.20 and we consider only this limit in the following. [ gcb] itself can be d e t e r m i n e d by the B-width F B a n d the B semileptonic branching ratio Bs~, as given by the formula 2 5 1 I vcbl 2 CFmb, {m
F B ( G e V ) --Bsl
i-92~-~
y
"J\-~b,ff "QcD'
with
f(x) = 1--Sx 2 +8X6--x s -24x41nx,
Xoc D = 1 - [ 2 a s ( m b ) / 3 x ] ( ~ 2 - - ~ )
and Bs~ the semileptonic branching fraction o f the B meson. One further constraint on the K o b a y a s h i - M a s k a w a matrix comes from the m e a s u r e m e n t o f e in the K ° - K ° SYstem. This quantity d e p e n d s [ 7 ] on I Uab l, a = c, t, b = d, s, on the W mass, on the top a n d c h a r m quark masses and through radiative corrections on AQCD a n d mb. F u r t h e r m o r e , a c o n f i n e m e n t p a r a m e t e r BK appears for the K ° - K ° system. The range considered for all p a r a m e t e r s is given in table 2. The m a i n unknowns o f the p r o b l e m are the quark masses a n d the matrix elements BK and ~ ×BB: 4~2 ~e2 O (KO i gLTl,dgLy~,d i i~d ) = 3,,,Kj K~,K ,
(BO igLTUdl~LTu75d i g0 )
~
4
" g / T / 2B j4~2 B ~i~ B
•
Lattice calculations as well as Q C D sum rules yield a value for BK o f o r d e r 1. We allow it here to vary [ 8 ] between 0,33 a n d 2. Likewise, we allow the p r o d u c t f 2 × BB to vary between 0.01 and 0.1 G e V 2. The quark masses entering most formulae are ambiguous as one does not know whether to use the current mass or the constituent mass. We allow t h e m to range from the smallest current mass to the lightest meson mass. One could in principle further constraint the p r o b l e m by calculating eve a n d 8rnK. However, the theoretical calculations predict [ 9 ] for a large range o f mt e'/e ~ ( 0 . 2 - 0 . 8 ) × 10 -2 subject to large uncertainties. The current experimental value [ 10 ] e'/e = (3.5 +_3.0 _+2.0) × 10- 3 is well within this range. The presence o f uncalculated long-range contributions to 6 i n k prohibits any reliable theoretical estimate o f that quantity. One is thus confronted with a m u l t i - p a r a m e t e r fit to the set o f d a t a given in table 1. One can define a probability density for a given set o f parameters, assuming that the errors on the d a t a are uncorrelated a n d gaussian. One then varies all the p a r a m e t e r s o f the p r o b l e m to find the m a x i m u m o f that density for a given top quark mass. This m a x i m u m probability gives a measure o f the likelihood o f a given top quark mass and is plotted in fig. 1 where 1 is the m a x i m u m possible value with all the gaussians calculated at the mean. One curve is 228
Volume 196, number 2 1.0
PHYSICS LETTERS B
,
I
,
I
'
I
I
] 40
I
I 60
I
] 80
1 October 1987
0.8 a 0.6 e~ o
I I I I ! I i i
o
0.4 E E 0.2
I !
0 20
mt
(6eV)
I 100
Fig. 1. Maximum probability density as a function of the top quark mass, leaving all otherparameters free. The plain curve is for f~×BB-~0.1 GeV2 and BK~<2.0, the dashed curve for f~ ×Bs-~ 0.06 GeV- and BK~<1.5.
for the bag p a r a m e t e r s allowed to vary in the full interval given in table 1 a n d the other is for the somewhat more restrictive ranges ~ × BB ~<0.06 G e V 2 a n d BK ~< 1.5. The m a x i m u m p r o b a b i l i t y density is realized for a given set o f values o f the p a r a m e t e r s a n d so defines a "best fit". Fixing all the p a r a m e t e r s b u t one at their value at m a x i m u m , we calculate for each top quark mass an error at the 90% confidence level. These are shown in figs. 2 a n d 3, for each considered range o f bag parameters. It is clear that i f f 2 × BB and BK are allowed to reach values as high as 0.1 GeV 2 and 2 respectively, one can adjust the other p a r a m e t e r s o f the p r o b l e m to fit all data equally welt for any top mass above the P E T R A limit o f 23 GeV. Even when one restricts the confinement factors to the smaller limits 0.06 G e V 2 a n d 1.5 respectively, the m a x i m u m probability density for masses o f order 25 (20) GeV gets reduced by a factor ~ 0.53 (0.22). This m e a n s that the experimental quantities are on the average 0.4 (0.6) s t a n d a r d d e v i a t i o n away from their m e a n value. In fact, the p r o b a b i l i t y d r o p m a i n l y comes from I Uua] = 0.9752 (0.9752) a n d 8m/F = 0.53 (0.23), which agree with the A R G U S d a t a at the l a ( 2 a ) level. Clearly, masses of order 23-40 GeV cannot be ruled
out. O u r analysis differs from the previous ones in that we used the e x p e r i m e n t a l constraints on I Uabl directly a n d allowed the bag factors to vary, along with all the other p a r a m e t e r s o f the problem. We want to p o i n t out here that the cross-hatched regions o f figs. 2 a n d 3 do not represent absolute bounds. They have been d e r i v e d by integrating the p r o b a b i l i t y density a r o u n d the m a x i m u m that we found. As the p r o b a b i l i t y density depends on 12 variables, the m a x i m u m value has several branches, as shown in fig. 1 and we have only given one o f the m a n y possibilities. The allowed range o f the phase o f the K o b a y a s h i - M a s k a w a matrix is however similar for different branches, a n d the new m e a s u r e m e n t o f rBd shows that for values o f m~ smaller than 80 GeV, cos & has been established to be negative [ 11 ]. We have also investigated the possible range for rBs--F( B ° ~ + X ) / F ( B % t ~ - X ) . We assume the same matrix element as for Bo°, except for the K o b a y a s h i - M a s k a w a mixing. Our best fit gives to rB,> 0.75 for 25 GeV ~
Volume 196, number 2
PHYSICS LETTERS B
1 October 1987
O.tC
0.06
0.02 20
60
20
60
100
100
20
60
I00
20
60
100
20
60
100
20
60
I00
20
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20
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60
100
4 S
7o
2 I
0 20
60
I00
20
60
"
I00
na t
20
,,
60
100
ol20
(GeV)
Fig. 2.90% CL regions on all the parameters as a function of the top quark mass, obtained by fixing all parameters but one at their value at maximum probability density. The cross-hatched regions correspond to the plain curve of fig. 1. ground with the background related to the production of the lighter charm and bottom quarks. For a light top the decay leptons are not sufficiently energetic to use prompt electrons as a signature. One inevitably relies on muon and multimuon data. Working at a nominal m u o n m i n i m u m transverse m o m e n t u m of 3 GeV in the inclusive rate dcr/dpT for prompt m u o n decay from a 25 GeV top is indeed a few nb/GeV inside 1.5 units of rapidity [ 12 ]. The corresponding rate from charm and bottom decay is however two orders of magnitude larger. Although cuts can be designed to increase the signal to noise one ultimately has to rely on isolation cuts to reduce the background by at least a factor o f 10. One requires the absence of hadronic activity in the direction o f the lepton thus eliminating semileptonic decays of charm and bottom quarks with large transverse momentum faking a top quark. While this might be possible for a heavy top it is a difficult procedure for a 25 GeV quark. Not only is one dealing with accompanying jet activity which is relatively weak, but the problem of fake isolation resulting from mismeasurement of the accompanying jet axis becomes more severe for the softer jets associated with the background to a top quark as light as 25 GeV. It should also be pointed out that any limits from such experiments eventually depend on the calculation of the production cross section. These calculations are still ambiguous because potentially large contributions of higher order 2-to-3 processes are not theoretically under control. A 90% CL on the existence of a top can be greatly modified by a factor o f 2 change in the calculated expected cross section. Given these problems it has been suggested [ 12 ] that dileptons are a superior signature for searching for a relatively light top. The dimuon cross section d ~ / d M is indeed o f the order of a pb/GeV for d i m u o n masses of order 10 GeV and rn~ = 25 GeV. Although this might correspond to an observable rate, the corresponding rate for dimuons from ce and bb pairs is again two orders of magnitude larger. The problem remains. It can now be solved by increasing the m i n i m u m m o m e n t u m cut on the decay leptons. The associated reduction in 230
PHYSICS LETTERS B
Volume 196, number 2
1 October 1987
0.06
0.04
0.02 20
60
I00
20
60
20
I00
o
.
60
1
3
IO0
20
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100
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20
60
lO0
60
IOO
~
o.11
20
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100
20
60
tO0
20
60
1OO
20
60
IO0
0,09 20
006r, 20
60
, 60
0, 100
20
,
m t (GeV) Fig. 3. Same as fig. 2, the cross-hatched regions corresponding to the dashed curve of fig. 1.
cross section puts the top out of reach of present experiments. Nevertheless this procedure is very promising with the increased luminosity expected at CERN and Fermilab. It also allows a search for eg events which provide in this context the ultimate signature. For a cut on the muon and electron transverse momentum of 5 and 15 GeV respectively we estimate that da/dM exceeds 0.1 pb/GeV for M(eg) = 20-30 GeV. These estimates correspond to m~= 25 GeV and x/s= 630 GeV. This cross section quickly rises with energy. In conclusion one can safely say that it will be easier either to rule out or to establish the existence of a top quark from p~) collider data in the 30-50 GeV region than to close the window just above the PETRA limit of 23 GeV. We also recall [ 13 ] here the fact that the present information on the weak boson widths extracted from the ratio of W, Z cross sections statistically favors a top quark mass below 60 GeV. We would like to acknowledge helpful discussions with V. Barger and valuable help from T. Han. 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 US Department of Energy under contracts DE-AC0276ER00881 and DE-AN03-76SF00235.
References [ 1] ARGUS Collab., H. Albrecht et al, Phys. Lett. B 192 (1987) 245. [2] E.g., F.J. Gilman and J.S. Hagelin, Phys. Lett. B 133 (1983) 443; L.L Chau and W.Y. Keung, Phys. Rev. D 29 (1983) 592; A.J. Buras, W. Slominski and H. Steger, Nucl. Phys. B 238 (1984) 529; I.I. Bigi and A.I. Sanda, Phys. Rev. D 29 (1984) 1393;
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PHYSICS LETTERS B
1 October 1987
E.A. Paschos and U. Tiirke, Nucl. Phys. B 243 (1984) 29; T. Brown and S. Pakvasa, Phys. Rev. D 31 (1985) 1661. [3] V. Barger, T. Han and D.V Nanopoulos, Phys. Lett. B 194 (1987) 312; J. Ellis, J.S. Hagelin and S. Rudaz, Phys. Lett. B 192 (1987) 201; L.L. Cau and W.-Y. Keung, UC-Davis preprint UCD-87-02 (1987); F.J. Gilman, SLAC preprint SLAC-PUB-4315 (1987); A. Datta, E.A. Paschos and U. Tfirke, Phys. Lett. B 196 (1987) 000; M. Tanimoto, Ehime preprint EHU-04-1987 (1987); D. Du and Z. Zhao, IAS preprint IAS SNS-HEP-87/23 (1987); I.I. Bigi and A.I. Sanda, Phys. Lett. B 194 (1987) 307. [4] J.S. Hagelin, Nucl. Phys. B 193 (1981) 123; T. Inami and C.S. Lim, Prog. Theor. Phys. 65 (1981) 297; E. Franco, M. Lusignoli and A. Pugliese, Nucl. Phys. B 194 (1982) 403. [ 5 ] W. Marciano, Talk Intern. Symp. for the Fourth family of quarks and leptons ( Santa Monica, CA, February 1987), to be published. [6] S. Behrends et al., CLEO preprint CLNS-87-78/CLEO-87-5 (1987). [7] T. Inami and C.S. Lim, Prog. Theor. Phys. 65 (1981) 297; F.J. Gilman and M.B. Wise, Phys. Rev. D 27 (1983) 1128; P.H. Ginsparg, S.L. Glashow and M.B. Wise, Phys. Rev. Lett. 50 (1983) 1415. [ 8 ] P. Langacker, in: Proc. 1985 Intern. Symp. on Lepton and photon interactions at high energies, eds. M. Konuma and K. Takahashi (Kyoto University, Kyoto, 1986)p. 186. [ 9 ] W.A. Bardeen, A.J. Buras and J.M. Gerard, Max Planck Institute preprint MPI-PAE/PTh 55/86 (1986 ). [ 10] G. Bock, Talk Intern. Symp. for the Fourth family of quarks and leptons (Santa Monica, CA, February 1987), to be published. [ 11 ] S. Pakvasa, Phys. Rev. D 28 (1983) 2915. [ 12 ] E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Lett. B 141 (1984) 429. [13] F. Halzen, Phys. Lett. B 182 (1986) 388; F. Halzen, C.S. Kim and S. Willenbrock, Madison Preprint MAD/PH/342.
232
PHYSICS LETTERS B
1 October 1987
IS A L O W - M A S S T O P Q U A R K R U L E D O U T ? J.R. CUDELL, F. H A L Z E N
Physics Department, Universityof Wisconsin, Madison, W153706, USA X.-G. HE and S. PAKVASA
Department of Physics and Astronomy, Universityof Hawaii, Honolulu, HI 96822, USA Received 26 June 1987
In view of the recent ARGUS measurement of B°-B° mixing, we carefully reexamine the mass limits for the top quark. The actual limit depends critically on the value of the confinement parameters for the B°-l]° and the K°-I¢° systems, as well as on the structure of the Kobayashi-Maskawa matrix which we reconsider ab initio. The large uncertainties associated with these parameters as well as with input experimental errors allow us to accomodate any top mass above the present PETRA limit of 23 GeV. We also discuss other measurements relevant to the top mass and conclude that the experimental search for small top mass at TRISTAN and SLC is still relevant.
Recently, the A R G U S collaboration a n n o u n c e d a m e a s u r e m e n t of mixing in the Bd-Ba o -o system [ 1 ]. Their value rud = 0.21 _+0.07 seems surprisingly large for the standard model with three generations ~1. Several new analyses [ 3 ] have appeared, some of which suggest that this result, along with k n o w n values of e, ... requires the top quark mass rnt to be larger than 45 GeV. The existence of such a b o u n d for rnt is crucial not only in view of speculations on the value of m, in the range 23-35 GeV b u t even more importantly for T R I S T A N and SLC where this is precisely the range of masses that can be explored. With this in m i n d , we reexamine the calculation of E a n d rud. We conclude that for a reasonable range of parameters, it iS possible to accomodate all the data for mt in the range 25-35 GeV. The m e a s u r e m e n t of rB~=-F(B°--+~+X)/F(B°-~I2-X) can be translated into 1 8 m { / F = [ 2 r u J ( 1 o -o system. This FBo)],/2 = 0.73 _+0.18, with 8 m the eigenstate mass difference and F the m e a n width of the Ba-Bd quantity has been analysed theoretically [ 4] and depends on the following parameters: the Bo-lifetime and mass, vB and roB, the top quark mass mt, a c o n f i n e m e n t factor Bu, the decay constant fB a n d the K o b a y a s h i - M a s k a w a matrix elements U,b a n d Utd. Moreover, the box-diagram factor further depends on the W mass mw and the Q C D corrections on AQcD a n d the b o t t o m quark mass rob. The K o b a y a s h i - M a s k a w a elements of interest are not experimentally k n o w n and one has to extract them from unitarity constraints a n d from the k n o w n values of the other elements. We assume 3 generations a n d no supersymmetry and use the following parametrization, in terms of mixing angles 0,, 02, 03, and CP-violating phase 6, with 0 ~<0i ~ 7c/2 a n d 0 ~<6 ~<2n by convention. We write & = s i n 0i, ci=cos 0i, so the matrix U can be written
Sud Sus Sub~ / CI Scd fcs Scb)=~SIC2 U~d fts U~.b/ \SIS2
--sic 3
--sis 3
ClC2C3--$2s3ei6 CIC2S3-}-S2c3eia I . CIS2C3-J¢-C2S3eia
cis2s3--c2c3ei'5,]
The experimental constraints ~2 on the absolute values are summarized in table 1. A recent analysis of the CLEO ~' For previous estimates see ref. [2]. ~2We use the values of I UodI and IUosl given in a recent summary by Marciano [ 5 ]. 0370-2693/87/$ 03.50 © Elsevier Science Publishers B . V . ( N o r t h - H o l l a n d Physics Publishing Division)
227
Volume 196, number 2
PHYSICS LETTERS B
Table 1 Data and errors.
1 October 1987
Table 2 Parameters of the problem.
Quantity
Mean value
Error
Parameter
Minimum value
Maximum value
I U~al
0.9744 0.220 0.207 0.95 ~<0.20 0.11 1.16 5.2752 81.8 2.275 0.73
0.001 0.002 0.024 0.14
s, s2 s3 ~
0.21 0 0 0 0.1 1.1 4.4 20 0.4 0.01
0.23 0.15 0.1 2n 0.4 1.8 5.2 100 2.0-1.5 0.1-0.06
I U~ I I U¢~[ [ Ucsl
I U, b]/I U,,bl B~t rB (10-M-~ s) rnn (GeV) mw (GeV) (10 -3) 8mlF
-
0.01 0.14 0.0028 1.5 0.021 0.18
AQC D
m~ mb m~ BK f~ ×BB
data [6 ] gives a new b o u n d for the ratio o f moduli: [ Uuu]l[ Ucb[ ~<0.20 and we consider only this limit in the following. [ gcb] itself can be d e t e r m i n e d by the B-width F B a n d the B semileptonic branching ratio Bs~, as given by the formula 2 5 1 I vcbl 2 CFmb, {m
F B ( G e V ) --Bsl
i-92~-~
y
"J\-~b,ff "QcD'
with
f(x) = 1--Sx 2 +8X6--x s -24x41nx,
Xoc D = 1 - [ 2 a s ( m b ) / 3 x ] ( ~ 2 - - ~ )
and Bs~ the semileptonic branching fraction o f the B meson. One further constraint on the K o b a y a s h i - M a s k a w a matrix comes from the m e a s u r e m e n t o f e in the K ° - K ° SYstem. This quantity d e p e n d s [ 7 ] on I Uab l, a = c, t, b = d, s, on the W mass, on the top a n d c h a r m quark masses and through radiative corrections on AQCD a n d mb. F u r t h e r m o r e , a c o n f i n e m e n t p a r a m e t e r BK appears for the K ° - K ° system. The range considered for all p a r a m e t e r s is given in table 2. The m a i n unknowns o f the p r o b l e m are the quark masses a n d the matrix elements BK and ~ ×BB: 4~2 ~e2 O (KO i gLTl,dgLy~,d i i~d ) = 3,,,Kj K~,K ,
(BO igLTUdl~LTu75d i g0 )
~
4
" g / T / 2B j4~2 B ~i~ B
•
Lattice calculations as well as Q C D sum rules yield a value for BK o f o r d e r 1. We allow it here to vary [ 8 ] between 0,33 a n d 2. Likewise, we allow the p r o d u c t f 2 × BB to vary between 0.01 and 0.1 G e V 2. The quark masses entering most formulae are ambiguous as one does not know whether to use the current mass or the constituent mass. We allow t h e m to range from the smallest current mass to the lightest meson mass. One could in principle further constraint the p r o b l e m by calculating eve a n d 8rnK. However, the theoretical calculations predict [ 9 ] for a large range o f mt e'/e ~ ( 0 . 2 - 0 . 8 ) × 10 -2 subject to large uncertainties. The current experimental value [ 10 ] e'/e = (3.5 +_3.0 _+2.0) × 10- 3 is well within this range. The presence o f uncalculated long-range contributions to 6 i n k prohibits any reliable theoretical estimate o f that quantity. One is thus confronted with a m u l t i - p a r a m e t e r fit to the set o f d a t a given in table 1. One can define a probability density for a given set o f parameters, assuming that the errors on the d a t a are uncorrelated a n d gaussian. One then varies all the p a r a m e t e r s o f the p r o b l e m to find the m a x i m u m o f that density for a given top quark mass. This m a x i m u m probability gives a measure o f the likelihood o f a given top quark mass and is plotted in fig. 1 where 1 is the m a x i m u m possible value with all the gaussians calculated at the mean. One curve is 228
Volume 196, number 2 1.0
PHYSICS LETTERS B
,
I
,
I
'
I
I
] 40
I
I 60
I
] 80
1 October 1987
0.8 a 0.6 e~ o
I I I I ! I i i
o
0.4 E E 0.2
I !
0 20
mt
(6eV)
I 100
Fig. 1. Maximum probability density as a function of the top quark mass, leaving all otherparameters free. The plain curve is for f~×BB-~0.1 GeV2 and BK~<2.0, the dashed curve for f~ ×Bs-~ 0.06 GeV- and BK~<1.5.
for the bag p a r a m e t e r s allowed to vary in the full interval given in table 1 a n d the other is for the somewhat more restrictive ranges ~ × BB ~<0.06 G e V 2 a n d BK ~< 1.5. The m a x i m u m p r o b a b i l i t y density is realized for a given set o f values o f the p a r a m e t e r s a n d so defines a "best fit". Fixing all the p a r a m e t e r s b u t one at their value at m a x i m u m , we calculate for each top quark mass an error at the 90% confidence level. These are shown in figs. 2 a n d 3, for each considered range o f bag parameters. It is clear that i f f 2 × BB and BK are allowed to reach values as high as 0.1 GeV 2 and 2 respectively, one can adjust the other p a r a m e t e r s o f the p r o b l e m to fit all data equally welt for any top mass above the P E T R A limit o f 23 GeV. Even when one restricts the confinement factors to the smaller limits 0.06 G e V 2 a n d 1.5 respectively, the m a x i m u m probability density for masses o f order 25 (20) GeV gets reduced by a factor ~ 0.53 (0.22). This m e a n s that the experimental quantities are on the average 0.4 (0.6) s t a n d a r d d e v i a t i o n away from their m e a n value. In fact, the p r o b a b i l i t y d r o p m a i n l y comes from I Uua] = 0.9752 (0.9752) a n d 8m/F = 0.53 (0.23), which agree with the A R G U S d a t a at the l a ( 2 a ) level. Clearly, masses of order 23-40 GeV cannot be ruled
out. O u r analysis differs from the previous ones in that we used the e x p e r i m e n t a l constraints on I Uabl directly a n d allowed the bag factors to vary, along with all the other p a r a m e t e r s o f the problem. We want to p o i n t out here that the cross-hatched regions o f figs. 2 a n d 3 do not represent absolute bounds. They have been d e r i v e d by integrating the p r o b a b i l i t y density a r o u n d the m a x i m u m that we found. As the p r o b a b i l i t y density depends on 12 variables, the m a x i m u m value has several branches, as shown in fig. 1 and we have only given one o f the m a n y possibilities. The allowed range o f the phase o f the K o b a y a s h i - M a s k a w a matrix is however similar for different branches, a n d the new m e a s u r e m e n t o f rBd shows that for values o f m~ smaller than 80 GeV, cos & has been established to be negative [ 11 ]. We have also investigated the possible range for rBs--F( B ° ~ + X ) / F ( B % t ~ - X ) . We assume the same matrix element as for Bo°, except for the K o b a y a s h i - M a s k a w a mixing. Our best fit gives to rB,> 0.75 for 25 GeV ~
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Fig. 2.90% CL regions on all the parameters as a function of the top quark mass, obtained by fixing all parameters but one at their value at maximum probability density. The cross-hatched regions correspond to the plain curve of fig. 1. ground with the background related to the production of the lighter charm and bottom quarks. For a light top the decay leptons are not sufficiently energetic to use prompt electrons as a signature. One inevitably relies on muon and multimuon data. Working at a nominal m u o n m i n i m u m transverse m o m e n t u m of 3 GeV in the inclusive rate dcr/dpT for prompt m u o n decay from a 25 GeV top is indeed a few nb/GeV inside 1.5 units of rapidity [ 12 ]. The corresponding rate from charm and bottom decay is however two orders of magnitude larger. Although cuts can be designed to increase the signal to noise one ultimately has to rely on isolation cuts to reduce the background by at least a factor o f 10. One requires the absence of hadronic activity in the direction o f the lepton thus eliminating semileptonic decays of charm and bottom quarks with large transverse momentum faking a top quark. While this might be possible for a heavy top it is a difficult procedure for a 25 GeV quark. Not only is one dealing with accompanying jet activity which is relatively weak, but the problem of fake isolation resulting from mismeasurement of the accompanying jet axis becomes more severe for the softer jets associated with the background to a top quark as light as 25 GeV. It should also be pointed out that any limits from such experiments eventually depend on the calculation of the production cross section. These calculations are still ambiguous because potentially large contributions of higher order 2-to-3 processes are not theoretically under control. A 90% CL on the existence of a top can be greatly modified by a factor o f 2 change in the calculated expected cross section. Given these problems it has been suggested [ 12 ] that dileptons are a superior signature for searching for a relatively light top. The dimuon cross section d ~ / d M is indeed o f the order of a pb/GeV for d i m u o n masses of order 10 GeV and rn~ = 25 GeV. Although this might correspond to an observable rate, the corresponding rate for dimuons from ce and bb pairs is again two orders of magnitude larger. The problem remains. It can now be solved by increasing the m i n i m u m m o m e n t u m cut on the decay leptons. The associated reduction in 230
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cross section puts the top out of reach of present experiments. Nevertheless this procedure is very promising with the increased luminosity expected at CERN and Fermilab. It also allows a search for eg events which provide in this context the ultimate signature. For a cut on the muon and electron transverse momentum of 5 and 15 GeV respectively we estimate that da/dM exceeds 0.1 pb/GeV for M(eg) = 20-30 GeV. These estimates correspond to m~= 25 GeV and x/s= 630 GeV. This cross section quickly rises with energy. In conclusion one can safely say that it will be easier either to rule out or to establish the existence of a top quark from p~) collider data in the 30-50 GeV region than to close the window just above the PETRA limit of 23 GeV. We also recall [ 13 ] here the fact that the present information on the weak boson widths extracted from the ratio of W, Z cross sections statistically favors a top quark mass below 60 GeV. We would like to acknowledge helpful discussions with V. Barger and valuable help from T. Han. 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 US Department of Energy under contracts DE-AC0276ER00881 and DE-AN03-76SF00235.
References [ 1] ARGUS Collab., H. Albrecht et al, Phys. Lett. B 192 (1987) 245. [2] E.g., F.J. Gilman and J.S. Hagelin, Phys. Lett. B 133 (1983) 443; L.L Chau and W.Y. Keung, Phys. Rev. D 29 (1983) 592; A.J. Buras, W. Slominski and H. Steger, Nucl. Phys. B 238 (1984) 529; I.I. Bigi and A.I. Sanda, Phys. Rev. D 29 (1984) 1393;
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E.A. Paschos and U. Tiirke, Nucl. Phys. B 243 (1984) 29; T. Brown and S. Pakvasa, Phys. Rev. D 31 (1985) 1661. [3] V. Barger, T. Han and D.V Nanopoulos, Phys. Lett. B 194 (1987) 312; J. Ellis, J.S. Hagelin and S. Rudaz, Phys. Lett. B 192 (1987) 201; L.L. Cau and W.-Y. Keung, UC-Davis preprint UCD-87-02 (1987); F.J. Gilman, SLAC preprint SLAC-PUB-4315 (1987); A. Datta, E.A. Paschos and U. Tfirke, Phys. Lett. B 196 (1987) 000; M. Tanimoto, Ehime preprint EHU-04-1987 (1987); D. Du and Z. Zhao, IAS preprint IAS SNS-HEP-87/23 (1987); I.I. Bigi and A.I. Sanda, Phys. Lett. B 194 (1987) 307. [4] J.S. Hagelin, Nucl. Phys. B 193 (1981) 123; T. Inami and C.S. Lim, Prog. Theor. Phys. 65 (1981) 297; E. Franco, M. Lusignoli and A. Pugliese, Nucl. Phys. B 194 (1982) 403. [ 5 ] W. Marciano, Talk Intern. Symp. for the Fourth family of quarks and leptons ( Santa Monica, CA, February 1987), to be published. [6] S. Behrends et al., CLEO preprint CLNS-87-78/CLEO-87-5 (1987). [7] T. Inami and C.S. Lim, Prog. Theor. Phys. 65 (1981) 297; F.J. Gilman and M.B. Wise, Phys. Rev. D 27 (1983) 1128; P.H. Ginsparg, S.L. Glashow and M.B. Wise, Phys. Rev. Lett. 50 (1983) 1415. [ 8 ] P. Langacker, in: Proc. 1985 Intern. Symp. on Lepton and photon interactions at high energies, eds. M. Konuma and K. Takahashi (Kyoto University, Kyoto, 1986)p. 186. [ 9 ] W.A. Bardeen, A.J. Buras and J.M. Gerard, Max Planck Institute preprint MPI-PAE/PTh 55/86 (1986 ). [ 10] G. Bock, Talk Intern. Symp. for the Fourth family of quarks and leptons (Santa Monica, CA, February 1987), to be published. [ 11 ] S. Pakvasa, Phys. Rev. D 28 (1983) 2915. [ 12 ] E.W.N. Glover, F. Halzen and A.D. Martin, Phys. Lett. B 141 (1984) 429. [13] F. Halzen, Phys. Lett. B 182 (1986) 388; F. Halzen, C.S. Kim and S. Willenbrock, Madison Preprint MAD/PH/342.
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