RARE B AND C DECAYS,
AND THE CKM MATRIX



Jon J. Thaler
University of Illinois
Urbana, IL 61801 USA
jjt@uiuc.edu





I report on developments in the experimental and
phenomenological understanding of the rare decays of mesons
containing b and c quarks, especially as they pertain to the
understanding of the CKM matrix and the testing of the standard
 25 Jul 1995 model. Some related measurements are also discussed.


Introduction

There have, historically, been two principal approaches to testing theories of
particle physics. One has been the use of novel accelerators to study previously
inaccessible or unknown phenomena. The other has been the increasingly precise
measurement of known processes or particles. The recent discovery of the top quark1

is an example of the former, while the precise measurement of Zo decays2 is an
example of the latter. The LHC will be the next novel accelerator to be built, so the
next decade's progress will rely on our ability to improve experimental and theoretical
precision. Fortunately, there is much activity in this direction, and I am confident that
progress will continue to be made.

In this talk, I will discuss the past year's work on rare decays of B and D mesons,
which has tended to focus on two large issues. The first is the improvement in the
measurement of the CKM matrix elements. The origin of quark mixing remains
obscure, and precise measurement may be required to reveal a pattern. The second
issue is the search for phenomena which do not fit within the standard model. The
discovery of CP violation is an archetypal example of such a phenomenon (in 1964,
K
L was a rare decay). By organizing my talk around these two issues, I will, by
necessity, mention a few topics which are somewhat outside the scope implied by the
title. I will also not mention a few topics which I ought to (but my talk is not allowed
to run overtime). I will leave most of CP violation to Kacper Zalewski3.

What's new

I list here the new developments that I will discuss:

E791 (FNAL): New limits on FCNC in D decays.4
E687 (FNAL): New limits on CP violation in D decays.5
New measurements of Cabibbo suppressed D decays.6
CDF (FNAL): New limits on FCNC in B decays.7
ALEPH (LEP): Rare hadronic B decays.8
DELPHI (LEP): Rare hadronic B decays.9
CLEO (Cornell): New limits on CP violation in D decay.10
New limits on radiative D decay.11
Observation of B .12
Improved measurements of rare hadronic B decays.13
New measurement of D e14
BES (Beijing): Measurement of Ds .15
Phenomenology: DCSD and mixing might interfere in the D system.16
Inclusive b c can be used for Vcb.17



CKM Matrix

Here is the CKM matrix, as given by the Particle Data Group18, showing
Wolfenstein's parameterization19:


1 - 2 A3 ( - i)

v
2
ud vus vub

2
V = v

cd vcs vcb - 1 - A2

2
v

td vts vtb A
3 1
( - -i) -A2 1


0
.94747 -0.94759 0.218-0.224 0.002 -0.005
=
0.218 -0.224 0.9738-0.9752 0.032 -0.048

0.004
-0.015 0.030 -0.048 0.9988 -0.9995

These are 90% confidence level intervals. Some are known very well and some
hardly at all. Also, some of the values given are calculated, in the absence of direct
experimental data, by assuming 3-generation unitarity. We desire not only to improve
the accuracy, but also to reduce the reliance on standard model assumptions. The
parameterization itself needs to be tested. For example, to what accuracy does
|Vcb| = |Vts|? Some issues related to the accuracy of the Wolfenstein parameterization
are discussed by Buras, et al.20 Figure 1 shows the usual graphical representation of
the relation between , , and the CKM matrix elements. The fact that , , and A are
all O(1) justifies the form chosen.

There has been some new experimental data in the past year, but the biggest
changes have come from improved theoretical understanding. Vcb is now known
about twice as well as before, and there are the first beginnings of measurements of
Vts and Vtb.

I will have little to say about the "Cabibbo" (2x2) part of the matrix. It is
measured to be:

Vud = 0.9744  0.0010 Beta decay,
Vus = 0.2205  0.0018 K e,
Vcs = 1.02  0.18 D Ke,
Vcd = 0.204  0.017 Charm production by neutrinos.






(,)



V* V
ub t d
||V || ||V ||
cb cb

(1 ,0 )

Figure 1: One unitarity triangle that can be formed with the CKM matrix.



The measurement of V is not improved by recent CLEO results, B(De)/ (DKe)
cd

= 0.103  0.039  0.013, because DKe background contaminates the signal. This
situation is not likely to change significantly until the CLEO-III upgrade,21 which will
have improved particle identification, is complete. It is sobering to note that the
accuracy of the 2x2 matrix is not sufficient to infer the presence of a third generation
solely from unitarity considerations. Unless there is something vastly wrong with Vtb,
it seems unlikely that a fourth generation will be discovered by studying the CKM
matrix.

At the present time, rare B decays are comparable with K meson CP violation in
their ability to determine the Wolfenstein parameters and .22 Figure 2 shows the
current situation. Modest improvement in the B system will show that _ 0 without
relying on K mesons. A comparison of K and B decays will test consistency of the
model, especially when K+ + is measured. For the next few years more progress
will be in the B system, at least partly because more effort is going into that work.

Various B processes allow direct measurements of four of the five outer CKM
matrix elements. I will discuss each of them here. Glasgow results are taken from Ali
and London.23


Vub V
=0.0750.010.01 td
V =0.240.04 K
cb Vcb





0.4

Allowed






0
-0.4 0 0.4

Figure 2: Allowed region of the - plane.


Vub

Processes such as B , , , , which have only light quarks in the final
state, are sensitive to Vub. The best measurements have come from inclusive
b u decays24 (see figure 3). The useful end point of the lepton spectrum is only a
small part of the phase space, and there are severe theoretical uncertainties in the
analysis. |V / V | = 0.075  0.02 V = (3.10.9)10-3. This spring, CLEO announced
ub cb ub

the observation of the exclusive mode,12 with a branching ratio of






-
(1.70  0 . 51  0 .31  0 . 27 ) 10 4 ( ) ( )
. They also obtained B / B < 3 .4 . Figure 4
shows the result.






CLEO determines the neutrino momentum by fully reconstructing the entire
event. The large data sets which this method requires are only now becoming
available. The result is somewhat model dependent because of acceptance
limitations. I quote the branching ratio which uses the WSB model, since ISGW is
2

incompatible with the upper limit. Theory predicts25 B( ) = (5 -12 ) Vub . So,

V ~ (4.52.3)10-3, with comparable experimental and theoretical uncertainties. This
ub

is not yet a competitive method, but its usefulness will increase with detector upgrades
(background reduction) and more theoretical work.


BB data

60 Scaled continuum

Fit to continuum
40


20


0

BB data - Fit

Predicted bc
40
Signal
region



0


2.00 2.25 2.50 2.75 3.00

Lepton momentum (GeV/c)

Figure 3: Inclusive measurement of b u .






30


Fit







,






 



















20 bc

















                     




























                






                
10                  


        







        
         
     







        
         
     







        
         
     
    





























    
    
  
 
  
Events per 7.5 MeV



    
    
  
 
  

















  
  
 
  











  
  
 
  












 
 
  



























































































































































  
0    

5.1 5.2 5.3
Beam Constrained Mass (GeV)
Figure 4: Beam constrained mass in BB events.



Vcb


Vcb controls most B decays, such as B D, D , and D , so, strictly speaking,
this quantity falls outside a rare decay talk. I will mention it briefly. There are no
new experimental results, but there is an important theoretical
development. A typical old result26 is CLEO's measurement
-1
B
( D )
= (29.9 1.9  2 .7  2.0 )ns . This yields F(1)V = 0.0351  0.0019 
cb
0.0018  0.0008, and HQET tells us F(1) = 0.910.0427. At Glasgow we had Vcb = 0.039
 0.006. Shifman and Ultrasev17 have observed that inclusive c also provides useful
information about Vcb. Neubert,27 and Ball, Benke, and Braun28 have used this to
obtain Vcb = 0.0410.003, a significant improvement.

Vtb

There has until now been no data with a direct bearing on Vtb. The PDG number
is obtained from unitarity constraints. CDF has now measured29 the probabilities for tt
BF(t Wb ) = +0.13+0.13
0 .87-0.30-0.11
events to have 0, 1, or 2 b-quark jets. They obtain BF(t Wq ) , which
>
implies Vtb 0.016 if one assumes that there are no unknown decay channels. The
limit is very weak, because Vtb is being played against Vts and Vtd. A significantly

better limit will require a measurement of qq t b after the Main Injector is
operational at Fermilab. Stelzer and Willenbrock estimate30 that 10% accuracy can be
obtained with 3 fb-1 of integrated luminosity.

Vtd

CKM matrix elements which do not have a "b" in the subscript may nevertheless
be measured in B decays which depend on loops. For example, if V = 1
tb then BB
mixing tells us20,22

0.76 0.5
- 170GeV x 1.5 ps
V = 3 200MeV
d

td 8 .7 10 B

B f B mt 0 .72 B
= 9
( .9 1.8 )10-3

For this purpose mt, xd, and B are all known quite well, 5.3%, 5.7%, and 3.8%

respectively. BB is known to 5-10% as well, so fB dominates the uncertainty. I will
d
discuss the determination of fB and fD below. A hundred thousand t-quark events
would allow LHC to measure Vtd directly. This is a difficult measurement.


50





25






0

Events / 0.1 GeV


-25


1.8 2.0 2.2 2.4 2.6 2.8

E (GeV)
Figure 5: Inclusive bs photon energy spectrum observed by CLEO.
The curve is the theoretical prediction.

Vts

The CLEO observation31 of the electromagnetic penguin, bs, (see figure 5) has
been used by Griffin, Masip, and McGuigan32 to extract Vts = 0.026  0.006  0.011.
*
The amplitude for this process is proportional to VtbVts , so they assume that Vtb = 1
(see the discussion above). They also must determine the form factors by

extrapolating from D K * . BsB s mixing is a more promising long term method,
but at this time there is only a limit, xs  9.33

fBd

The interpretation of BB mixing data is limited by the knowledge of the heavy-
light decay constant fB . There is no direct experimental measurement of this number;
d

only upper limits exist for the most promising decay mode, B.


Experiment Limit on B

ALEPH34 1.810-3
ARGUS35 10.410-3
CLEO36 2.210-3


These results are background limited. CLEO may have improved sensitivity with its
new silicon vertex detector, which will allow separation of from charm and other
backgrounds. It remains to be seen whether CLEO can achieve the factor of 100
required to detect the anticipated 410-5 branching ratio.

In the absence of a measurement, one relies on more indirect methods. Much
effort has gone into calculating fB and fD. Recent results are promising, but the
uncertainties are still large. I take some lattice results from a review talk by S.
Gsken.37



Group fD (MeV) f (MeV) f
Ds Bd (MeV)


PSI-WUI37 170  30 180  50


BLS37 208  35  12 147  6  23


MILC38 180  4  18  16 194  3  16  9 148  4  14  19


LANL39 230 to 240 260 to 270


Neubert, et al.40 281  44



In general, f is about 10% larger than f . The last result is not a lattice calculation,
Qs Qd
but the use of factorization and B(BoD+Ds) / B(BoD+-) = 4.63  1.45.

The values of fD are especially interesting, because D
s s has been measured.




Group fD (MeV)
s


WA7541 232452048

CLEO42 344375242

+150+40
BES15 430-130 -40
Only the BES result is new since last summer. They observe 3 events. CLEO has
about 80 events, but the background, mostly charm semileptonic decays, is large (see
figure 6). Improved vertex reconstruction will reduce the signal to background ratio.


60


2


40


#    






#







  
# 




































   












    


   






    








   







   

   






   













20







 
"
" " " "





 
"
" " " "





 





 

$







 
   
!
$ ! !
!
!





!
$ ! !
!
!
Events per 20 Mev/c



0
0.00 0.10 0.20 0.30
Mass difference M (GeV/c2)
* ( )
Figure 6:
CLEO data for Ds Ds  The dashed histogram is
the background, measured using electrons.

Beyond the SM:

Searches for new phenomena, even when unsuccessful, teach us much about
particle physics. Unsuccessful searches for flavor changing neutral currents (FCNC)
led to the GIM mechanism. Now, the D meson system may be the best low energy
place to look for nonstandard physics, because the standard model predicts
unmeasurably small mixing, CP violation, and FCNC.

D mixing & CP:

Mixing (or DCSD) has now been seen both by CLEO43 and E-791.44


BR Do K + -
( ) = (7.7 2.5 2.5)10-3 x
= (2.9 1.0 1. 0) tan4 c (CLEO)
BR Do K - +
( )

+ + =
BR D K - +
( ) (10. 3  2 . 4 1.3 )10 -3
= (3.9 0.9  0.5 )tan4 c (E 791)
BR D + K -+ +
( )

CLEO does not have lifetime information. That would distinguish mixing
from doubly Cabibbo suppressed decays (DCSD). The best mixing limit


remains that from Fermilab E61545 using semileptonic decays:

r < 5.610-3. Other results46 assume no interference between DCSD and mixing,
mix

which is probably incorrect.47,48 There remains some controversy about whether the
standard model predicts very small r (10-8) or quite large (~10-3). The issue is the
mix

size of long distance corrections.48,49 If the prediction is small, then mixing could be a
signal for new physics. A fourth generation, two Higgs doublets, or leptoquarks can
all cause significant mixing.48

E-687 and CLEO have new limits on CP violation in D decays.50 These are still
not very stringent: A < 5-10% in several decay modes such as DoK+K-.
CP


B mixing and CP:

Asymmetries due to the CP impurity of the mass states, as in the K system, are
expected to be very small, because /M << 1. For example, the standard model
predicts semileptonic charge asymmetries O(10-3) for B and O(10-4) for B . Direct CP
d s

violation in decay rates requires the interference between two processes leading to the
same final state In order to perform consistency tests, one wants to look at various
channels which measure different angles of the unitary triangle, One way to have two
interfering processes is to look at states (e.g., CP eigenstates) which are equally
accessible from Bo and B o . In that case mixing may produce interference. One
difficulty is identifying the initial state. Another difficulty is that the time integrated
asymmetry is zero. Asymmetric B factories will attack this problem by looking at the
time dependence and tagging one B using the decays of the other.

Comparison of B f with B f does not require a time measurement, and it can be
used with charged B's. Interference occurs when two different diagrams contribute to
the process (e.g., tree and penguin for K-o). One is not restricted to Bo decays. B
will do as well. The trick is to find decay modes which have both a significant
asymmetry and a large enough branching ratio to be observable. An asymmetry also
requires both weak and strong phases for the two diagrams.

New results on rare hadronic B decays, such as Bo+- and K+-, have
implications for future CP violation searches. Bo+- is dominated by the bu
spectator diagram. It could be used to measure +
V and CP. BoK - is primarily a
ub

hadronic penguin. The recent discussion of extracting phase angles from time
integrated rates51 is of obvious interest to CLEO, which will have high luminosity
(comparable to the B factories), but equal beam energies. The idea is that CP could
be observed in B as well as Bo decays, because direct CP is expected to be
significant. An example is: 
BK , B, BK . CP violation would


r 2 A(+o )
+ o) ) - o
-
A(K o)
2 2 A(K
. .. A(
2 2
r


A(K o-) = A(K o+)
Figure 7: Amplitude triangles for three B decay modes. CKM unitarity
and SU(3) symmetry imply the triangle relationships among
the decay amplitudes.


manifest itself as a charge asymmetry in the decay rates (see figure 7). CLEO quotes
only upper limits13 in any single exclusive channel, (1 - 5)10-5 in +-, K+-, +o, K+o,
oo, Ko+, and Koo. However, there is an unambiguous signal in the
= +5 .6 +2.2
sum +- 17 . 2
+K+-. N+KK -4.9 -2.5 events (5.2 from 0, see figure 8).
Particle identification limitations prevent a clean separation. B(+- or K+-) =
(1.80.60.2)105. ALEPH has 2 +- events (one event reported in `94 has been cut),
while DELPHI has 3 events in different modes. They both report upper limits
somewhat higher than CLEO's. New results are expected this summer. An increase of
a factor of ten in integrated luminosity, so that there are about 100 events in each
mode, along with an improvement in particle identification, may allow a 10 degree
measurement of .

FCNC:
Flavor changing neutral currents (B or D or X ) have much in common with
the radiative penguin process, b,c X. Having two charged leptons in the final state,
they are easier to detect. However, the decay rates are expected to be quite a bit
smaller, and they suffer from significant contamination from long distance effects,
especially B X. There are several new results on FCNC (see the table on the next
page). All are limits, although CLEO will approach the standard model prediction for

BoKoe+e- in the next year or two. Due to large long distance (vector dominance)
effects in radiative D decays, only D++e+e- appears to have a new physics
opportunity in the D system.


6








K+-
2 +-

   
4    





   





   





   





   





   





   





   





   





   





   





   





   





   





   





   





   





   





                   
2                    
                   





                   





                   





                   





                   





                   





                   





                   
Events per 2.5 MeV / c            



  
 
 
 
                       
 
 
 
 
 
 
 
  
 
 
 






                                                   





                                                   





                                                   





                                                   





                                                   





                                                   





                                                   





                                                   





                                                   





                                                   





5.21 5.23 5.25 5.27 5.29

Mass (GeV/c2 )

Figure 8: CLEO's evidence for B or K.




Experiment Process Upper limit SM prediction52


CLEO13 B+K+e+e- 1.210 -5 0.0610 -5


K++- 0.910 -5 0.0610 -5


BoKoe+e- 1.610 -5 0.5610 -5


Ko+- 3.110 -5 0.2910 -5


CLEO11 D(,,) (1 to 2)10 -4 10 -6 to 10 -4


CDF7 B+K++- 3.510 -5 0.0610 -5


K+*+- 5.110 -5 0.2310 -5


B o+- 0.210 -5 810 -11
d


B o+- 0.710 -5 210 -9
s


E7914 D++e+e- 6.610 -5 ~110 -8

++- 1.810 -5 "



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

CLEO

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Unitarity

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 

































































































SM

 

































































































1 
 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 

































































































0 
 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 







































































































 

































































































-1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

D0 & CDF

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

-2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 







 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 


 


 


 


 


 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 






-4 -2 0 2 4

Figure 9: 90% c.l. limits on WW anomalous couplings. The dashed
oval is the unitarity limit for W = 1.5 TeV. Adapted from
Hinchliffe.53



Anomalous gauge boson couplings:

Finally, I would like to mention a pretty result. The CLEO value31 for B(bs) =
(2.32  0.57  0.35)10-4, can be combined with CDF and D0 measurements54 of W
production to constrain anomalous WW couplings (see figure 9). The results are
consistent with the standard model (no anomalous couplings). The limits are already
better than unitarity constraints, and will continue to improve.

Acknowledgments

I would like to thank all those people who provided me with their data,
especially, Tony Liss, Tom LeCompte, Alan Litke, Wilbur Venus, Karen Lingel, Mats
Selen, Milind Purohit, Jeff Appel, and Noel Stanton. I would also like to thank Scott
Willenbrock and Aida El-Khadra for stimulating discussions. Finally, I thank Tom
Browder and Klaus Honscheid, whose "B Mesons" review paper provided valuable
guidance.

1 Observation of the Top Quark, talk at this conference by Soo-Bong Kim.
2 Precision Tests of Electroweak Interactions, talk at this conference by Wolfgang Hollik.
3 Structure and Decay of Heavy Quarks, talk at this conference by Kacper Zalewski.
4 M. V. Purohit, J. A. Appel, and Noel Stanton, private communication.
5 P. Frabetti, et al., Phys. Rev. D50,2953(1994).
6 P. Frabetti, et al., Phys. Lett . B321,295(1994) and Phys Lett B346,199(1995).
7 Carol Anway-Wiese, Fermilab-Conf-94/210-E.
8 A.M. Litke, SCIPP 94/35 (1994). in Proceedings of the XXVII International Conference on High Energy Physics
(Glasgow 1994), p. 1333, and private communication.



9 CERN-PPE/Draft2/Paper0104. Wilbur Venus, private communication.
10 J. Bartelt, et al., CLNS 95/1333.
11 M. Selen, talk at APS Meeting, April 1995.
12 L. Gibbons, talk at 30th Rencontres de Moriond (1995).
13 S. Playfer and S. Stone, HEPSY 95-01 , to appear in Intl. J. Mod. Phys. Lett.
14 F. Butler, et al., CLNS 95/1324 (1995).
15 J.Z. Dai, et al., SLAC-PUB-95-6746 (1995), to appear in Phys. Rev. Lett.
16 T. Liu, in Proceedings of the CHARM2000 Workshop, 375(1995),
G. Blaylock, A. Seiden, and Y. Nir, SCIPP-95-16 .
17 M. Shifman, in Proceedings of the XXVII International Conference on High Energy Physics (Glasgow 1994), p,
1125,
M. Shifman and N. G. Ultrasev, TPI-MINN-94/41-T .
18 Particle Data Group, Phys. Rev. D50, 1175 (1994)..
19 L. Wolfenstein, Phys. Rev. Lett 51, 1945 (1983).
20 A. J. Buras, M. E. Lautenbacher, and G. Ostermaier, Phys. Rev. D50, 3433 (1994).
21 K. Berkelman, CLNS 93/1265 (1993).
22 A. J. Buras, MPI-PhT/95-17, to appear in Acta Physica Polonica.
23 A. Ali and D. London, in Proceedings of the XXVII International Conference on High Energy Physics (Glasgow
1994), 1133 (1995),
A. Ali and D. London, CERN-TH.7398/94.
24 H. Albrecht, et al., Phys. Lett. B234, 409 (1990),
H. Albrecht, et al., Phys. Lett. B255, 297 (1991),
R. Fulton, et al., Phys. Rev. Lett. 64, 16 (1990),
J. Bartelt, et al., Phys. Rev. Lett. 71, 4111 (1993).
25 M. Wirbel, B. Stech, and M. Bauer, Z. Phys. C29, 637 (1985).
J. G. Krner and G.A. Schuler, Z. Phys. C38, 511 (1988),
P. Ball, Phys. Rev. D48, 3190 (1994),
S. Narison, CERN-TH.7237/94 (1994),
N. Isgur and D. Scora, CEBAF-TH-94-14 (1994),
R. Faustov, V.O. Galkin, and A. Yu. Mishurov, .
26 B. Barish, et al., Phys. Rev. D51, 1014(1995),
M. Athenas, et al., Phys. Rev. Lett. 73, 3503(1994),
I.J. Scott, in Proceedings of the XXVII International Conference on High Energy Physics (Glasgow 1994),
1121(1995),
H. Albrecht, et al., Z. Phys. C57, 533(1993),
H. Albrecht, et al., Phys. Lett. B318, 397(1993).
27 M. Neubert, in Proceedings of the XXVII International Conference on High Energy Physics (Glasgow 1994), 1129
(1995),
M. Neubert, CERN-TH/95-107 ,
28 P. Ball, M. Benke, and V.M. Braun, CERN-TH/95-65 ,
also see T.E. Browder and K. Honscheid, OHSTPY-HEP-E-95-010,
to appear in Progress in Nuclear and Particle Physics 35.
29 T. J. LeCompte and R. M. Roser, CDF/ANAL/TOP/CDFR/3056 (1995),
and private communication.
30 T. Stelzer and S. Willenbrock, ILL-(TH)-95-30, .
31 R. Ammar, et al., Phys. Rev. Lett. 71, 674(1993),
M.S. Alam, et al., Phys. Rev. Lett. 74, 2885(1995).
32 P.A. Griffin, M. Masip, and M. McGuigan, Phys. Rev. D 50, 5751 (1994).
33 Yi-Bin Pan, in Proceedings of the XXVII International Conference on High Energy Physics (Glasgow 1994), p. 753,
S. Komamiya, ibid., p. 757.
34 D. Buskulic, et al., Phys. Lett. B343, 444 (1994).
35 H. Albrecht, et al., DESY 94-246.
36 J. Alexander, et al., CLEO-CONF-94-5, to appear in Phys Rev Lett.
37 S. Gsken, WUB 95-08, talk at Workshop on Heavy Quarks.
38 C. Bernard, et al., FSU-SCRI-95C-28, talk at LISHEP95 .
39 T, Bhattacharya and R. Gupta, .
40 M. Neubert, V, Rieckert, B. Stech, Q.P. Xu, in Heavy Flavors (A. Buras and M. Lindner, eds.), p. 286 (1992).



41 S. Aoki, et al., Prog. Theor. Phys. 89, 131 (1993).
42 D. Acosta, et al., Phys. Rev. D49, 5690 (1994).
43 D. Cinabro, et al., Phys. Rev. Lett. 72, 1406(1994),
44 M. Purohit and J. Weiner, FERMILAB-CONF-94/408-E, to appear in the Proceedings of the Eight Meeting of the
DPF of the APS (DPF `94).
45 W.C. Louis, et al., Phys. Rev. Lett. 56, 1027(1986).
46 M.V. Purohit, et al., FERMILAB-CONF-94/186-E.
47 T. Liu, in the Proceedings of the CHARM2000 Workshop, 375(1995),
G. Blaylock, A. Seiden, and Y. Nir, SCIPP-95-16 .
48 J.L. Hewett, SLAC-PUB-95-6821 .
49 T.A. Kaeding, LBL-37224 ,
L. Wolfenstein, Phys. Lett. B164, 170(1985),
L. Wolfenstein, CMU-HEP95-04 .
50 P. Frabetti, et al., Phys. Rev. D50,2953(1994),
J. Bartelt, et al., CLNS 95/1333.
51 M. Gronau, J.l. Rosner, and D. London, Phys. Rev. Lett. 73, 21(1994),
N. G. Deshpande and X-G. He, Phys. Rev. Lett. 74, 26(1995),
M. Gronau, et al., TECHNION-PH-95-10, ,
O.F. Hernandez, UdeM-GPP-TH-95-20, .
52 A. Ali and T. Mannel, Phys. Lett. B264, 446 (1991),
A. Ali, C. Greub, and T. Mannel, DESY-93-016 (1993),
G. Burdman, E. Golowich, J. L. Hewett, and S. Pakvasa, SLAC-PUB-6692 ,
A. J. Schwartz, Mod. Phys. Lett. A8, 967 (1993).
53 I. Hinchliffe, LBL-37014 , talk at International Symposium on Vector Boson Self Interactions
(1995).
54 F. Abe, et al., Phys. Rev. Lett. 74, 1936 (1995),
S. Abachi, FERMILAB-PUB-95-101-E .



