Rare, Leptonic, and Hadronic Decays of Charmed Mesons - A Review -

6 Pages·0.21 MB·English

by  Hitoshi Yamamoto

HUTP-96/A-001
Rare, Leptonic, and Hadronic Decays of Charmed Mesons
- A Review -
Hitoshi Yamamoto
Haravard University, 42 Oxford St., Cambridge, Massachusetts 02138, U.S.A.
Abstract fDS =fDS∗)6
6
Wereviewthephysicsofrare,leptonic,andhadronic
9
decaysofcharmedmesonsbasedontheresultssubmitted 3.5%
19 to this conference (EPS 95, Brussels). fDS(∗)(MeV)=(281±39)sB(DS φπ). (3)
→

n
The uncertainty in the model-dependent value B(D
a 1 Rare and leptonic decays S →
J φπ) = 3.5 0.4%8 has been a issue for some time, but
±
5 1.1 D+ µ+ν thedifferentdependenceonB(DS →φπ)ofthetwofDS
S → measurements (2) and (3) above allows us to determine
18v1 TabnyhneihdielactaiyonDoS+f c→onslt+itνue(nltisquea,rµk,soarndτ)thoeccruartsetihsrgoiuvgehn b(Dsot(ti∗lh)lDdf∗eD)p:SenadnsdoBn(tDhSe f→actoφrπiz)atjiuosnt absysutmheptcioonnsiinsteBnc→y7
S
012 Γ=|Vcs|2G2FM8DπSfD2Sm2l(cid:16)1− MmD22lS(cid:17)2; fDS =277±25(MeV), B(DS →φπ)=3.60±0.64%.
6
9 thus, it is sensitive to the DS decay constant fDS which 1.2 Isospin violating decay DS∗+ →DS+π0
/ in turn is related to the overlapof c and s¯quarks in the
h The decay D∗+ D+π0 is prohibited by isospin. The
p meson Ψ(0) (in non-relativistic quark model) by1 amplitude ofSthe→domSinant channel D∗+ D+γ is pro-
- S → S
p portional to the total effective magnetic moment which
12
e f = Ψ(0). (1) is naively given by
h DS sMDS| |
: qc qs
v ~µ= ~s + ~s
c s
i This mode was first observed by WA752 using emul- mc ms
X
sion exposed to π− beam from CERN SPS, followed by
ar CLEO3 and BES4. For this conference, CLEO has up- wanhderse qqcu(a=rk2s/,3aen)da~nsdarqes(t=he−c1o/r3rees)paornedtihneg cshpainrsgewshoifchc
datedthemeasurementwithhigherstatistics. CLEOob- are aligned in the case of D∗. Using constituent masses
serves this decay mode in the decay chain D∗+ D+γ, S
D+ µ+ν. The hermiticity of the detectoSr w→as uSsed mc = 1.5 GeV and ms = 0.4 GeV, one can see that the
S → dominant mode is highly suppressed. Such near cancel-
to obtain the missing momentum in the hemisphere of
lation in the dominant mode makes it difficult to pre-
the decay, which was then interpreted as the momen- dict the branching fraction for D∗+ D+π0. One
tum of the neutrino. A clear peak in the mass differ- S → S
ence MDs∗−MDS isseenandthe new resultis shownin
Table 1 together with previous results. The average of
f (MeV) Method
WA75,BES,and CLEO(95)gives(using both statistical DS
WA752 232 45 20 48 π− on emulsion
and systematic errors) CLEO(93)3 344±37±52±42 e+e− (10 GeV c.m.)
BES4 4±30+15±0 4±0 e+e− (4 GeV c.m.)
f (MeV)=(273 30) B(DS →φπ). (2) CLEO(95)5 284 3−0130±30 16 e+e− (10 GeV c.m.)
DS ± 3.5% ± ± ±
r
The parameter f can also be obtained by comparing Table 1: Mesurements of the decay constant fDS from the decay
(∗) ∗ DS ∗ modeDS+→µ+ν. Thefirsterrorisstatistical,secondsystematic,
Bfac→torDizSatiDon.toThseemnielewptroensiucltdefrcoamy BCL→EODilsν(aassssuummiinngg thethirdwhengivenoirsBun(DceSrt→ainφtyπ)in(CDLSEpOro).ductionrate(WA75)
estimate9 based on η-π0 mixing (together with HQET CKMelements. It is convenientto classify the two-body
and chiral perturbation theory) gives a range of a few decays to three categories: (Class-1) The amplitude is
%. CLEO10 has searched for this mode using the de- f a ;e.g. D0 K−π+. (Class-2)Theamplitudeisf a ;
1 1 2 2
cay mode D+ φπ+, and looks at the mass difference e.g. D0 K¯0→π0 (‘color-suppressed’). (Class-3)Theam-
M(D∗+) MS(D→+). Acleansignalwith14+4.6eventswas plitude i→s (f a +f a ); e.g. D+ K¯0π+. where the
S − S −4.0 1 1 2 2 →
observed. Itisthennormalizedtothedominantradiative constantsf dependonformfactorsanddecayconstants
i
decay to give and typically well within factor of two of each other if
relatedby flavorSU(3) (apartfromisospinfactors). Fit-
Γ(DS∗+ →DS+π0)/Γ(DS∗+ →DS+γ)=0.062+−00..002108±0.022. tainndgDth+e recK¯en0tπ+m,etahseurveamlueenstosfoaf ,Da0 a→re fKou−nπd+t,oK¯b0eπ0,
The transition D∗ D π tells us that the parity of D∗ → 1 2
iDs+(−γ)JinwdihcearteesJtihsSatht→eJspSin1o.fDTS∗h.uAs,lspoo,stshibeldeescpayinD/pS∗a+ri→tSy a1 ∼1.15, a2 ∼−0.51
ofSD∗ is 1−,2+,3−...,≥with 1− being the most natural which indicates that the Class 3 decays involve destruc-
S
candidate. This is also consistent with the quark model tiveinterferences. Thecolorsuppressionandinterference
prediction for the mass splitting11 suppressioneachamountstoveryroughlyafactorof1/4
in decay rate. The parameters a and a , however, in
32πα 1 2
M(3S ) M(1S )= s Ψ(0)2. principle depend onfinal state andmay not be the same
1 0
− 9m m | |
c s for other decay modes such as D KK,ππ. Another
→
factor that can affect the rate is the phase space; in the
With α =0.5 and eq. (1), this gives 0.13 GeV which is
s
comparisons that follow, however, the phase-space fac-
quite consistent with the experimental value of 0.1416
0.0018 GeV. ± tors are mostly within 20% including P-wave decays.
0040695-001
700
10
8
600
) )
21MeV / c) 6 25 MeV/c 68 25 MeV/c 450000
nts / ( 4 s / ( s / ( 300
ve nt 4 nt
E e e
v v 200
E E
2 2
100
0 0
0 1.8 1.9 2 1.8 1.9 2
135 140 145 150 155 160
∆Mπ ( MeV / c2 ) M(K +p - p +) GeV/c2 M(K -p +p +) GeV/c2
Figure 1: Mass difference ∆Mπ ≡ M(DS∗+)−M(DS+) for the Figure2: MassdistributionfortheDCSDmodeD+→K+π−π+
isospin violating decay D∗+ → D+π0 (CLEO). The dotted line (left)andthecorrespondingCabibbo-alloweddecay(right)(E687).
isthebackground estimSatedfromS the D+ andπ0 sidebands. Theenhancement at1.97GeVisDS+→K+π−π+. Cutsareopti-
S mizedfortheD+ decay.
2 Hadronic decays 2.1 Singly and Doubly-Cabibbo-Suppressed Decays
In the factorization model of Bauer, Stech, and Wirbel Possibly three DCSD (Doubly Cabibbo Suppressed De-
(BSW)12, the hadronic two-body decays of charmed cay) modes have been observed thus far: D0 K+π−,
mesonsoccurthroughtheeffectiveHamiltoniangivenby D+ K+π−π+, and D+ φK+. The r→esults are
→ →
given in Table 2. It should be noted that the decay
GF ∗ D0 K+π− can also occur by D0 D¯0 mixing. In-
Hhad = √2VudVcs[a1(du)had(cb)had+a2(db)had(cu)had] clud→ing the interference, the time-dep−endent and time-
integrated decay rates are given by
where (..) indicates the factorized current ready to
had
forma final-statemeson. The d¯canbe changedtos¯and 1 2
Γ(D0 K+π−)(t)= a2 ρ + ρ t e−t, (4)
s may be changed to d with appropriate change in the → | | D √2 M
(cid:12) (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
R (def.) Exp. R(%) R in unit of λ4 or λ2
Γ(D0 K+π−)/Γ(D0 K−π+) CLEO13 0.77 0.25 0.25 (2.92 0.95 0.95)λ4
→ → ± ± ± ±
E68714 0.72 0.23 0.17 (2.73 0.87 0.64)λ4
Γ(D+ K+π−π+)/Γ(D+ K−π+π+) ± ± ± ±
→ → E79115 1.03 0.24 0.13 (3.9 0.9 0.5)λ4
Γ(D+ K∗0π+)/Γ(D+ K−π+π+) E68714 ±<0.02±1 ± ±
Γ(D+→ K+ρ0)/Γ(D+ →K−π+π+) E68714 <0.067
Γ(D+ →K+K−K+)/Γ→(D+ φπ+) E68716 <2.5
→ →
Γ(D+ φK+)/Γ(D+ φπ+) E68716 <2.1 <0.41λ2
Γ(D+ →φK+)/Γ(D+ →φπ+) E69117 5.8+3.2 0.7 (1.1+0.6 0.1)λ2
Γ(D+ →K+π−π+)/Γ(D→+ φπ+) E68714 28−2.66± 5 −0.5±
Γ(DS+→ K¯∗0π+)/Γ(D+S →φπ+) E68714 18±5±4 (3.5 1.0 0.8)λ2
S → S → ± ± ± ±
Γ(D+ K+ρ0)/Γ(D+ φπ+) E68714 <8
Γ(D+ S →K+K−K+)/Γ(SD→+ φπ+) E68716 <1.6
S → S →
Γ(D+ φK+)/Γ(D+ φπ+) E68716 <1.3 <0.25λ2
S → S →
Table 2: Mesurements of DCSD modes of D+ and singly-Cabibbo-suppressed modes of D+. The Cabibbo suppression factor used is
S
λ≡tanθC =0.226. AlsolistedaretwoCabibbo-suppressedmodesofDS+. E687,E691(photo-production)andE791(hadro-production)are
fixed-targetexperimentsatFermilab.
Naively, one expects that a DCSD mode to be sup-
pressed by a factor λ4 (λ tanθ ) relative to the corre-
c
sponding Cabibbo-favored≡mode. Assuming no D0 D¯0
mixing, the DCSD decay D0 K+π− is about 3 t−imes
→
larger than the naive expectation even though statisti-
cally not very significant. A straight application of the
BSW model12 predicts 1.5 λ4 where the enhancement
is almost entirely accounted for by the difference in the
decay constants: (f /f )2. The measured DCSD en-
K π
hancement for D+ K+π−π+ is slightly more signif-
→
icant. This is expected since the only resonance sub-
mode in the Cabibbo-favored mode is D+ ”K¯∗0”π+
(”K¯∗0” stands for any excited state of K¯→0) which is
Class-3 and suppressed by the destructive interference.
FDig∗u0re→3:DT0πh0e(dCeLcaEyOD).0T→heKdoStKteSdtliangegesdhobwysDth∗e+D→∗ sDid0eπb+anadn.d DIn facKt,πtπhe3-Dbo+dy→deKca−yπs+tπh+atiisstnhoetodnolmyinmaotdede baymroensg-
→
onance submodes20.
R B(D0 →K+π−) =r +√2r r cos(φ φ )+r , The decay of D+ to 3 charged kaons is a DCSD by
≡ B(D0 K−π+) D D M D− M M charge conservation. At quark diagram level, the spec-
→
where tator DCSD has a pair of dd¯quarks while the 3K± fi-
nal state has no valence dd¯quarks. Thus, the strong fi-
a δγ/2+iδm
ρD D √rDeiφD, ρM √rMeiφM, nal state interaction (FSI) should annihilate the dd¯pair
≡ a ≡ ≡ √2γ ≡
and create ss¯ pair. Another possibility is the annihila-
with a Amp(D0 K−π+), a Amp(D0 tion mode cd¯ us¯ followed by creation of a ss¯ pairs,
D
K+π−),≡γ is the aver→age D0 decay ra≡te, t is in un→it but this mode→itself is doubly-Cabibbo-suppressed and
of 1/γ, and assumed r 1. The expressions expected to be small. This leads to suppression of the
M,D
above are identical for D¯0 ≪K+π− with the redef- 3K± DCSD mode relative to the naive expectation. As
initions a Amp(D¯0 K→+π−) a Amp(D¯0 can be seen in the table, the experimental upper limit
D
K−π+). A≡ssuming CP→symmetry, valu≡es of ρ a→re for B(D+ φK+)/B(D+ φπ+) (φ K+K−) is
D,M
→ → →
the same for the charge conjugate cases. Note that less than half (E687)or about equal to (E691) the naive
the parameter r is the standard mixing parameter value. Note that the normalization mode φπ+ itself is
M
r = (D0 decays as D¯0)/(D0 decays as D0). E69119 color-suppressed (Class-2). The abnormally large value
M
gives r <0.39% neglecting the interference term. The B(D+ K+K−K+)/B(D+ K−π+π+)=(5.7 2.0
M
→ → ± ±
limit, however, increases about factor of three when no 0.7)% by WA8218 (which is about 20 times larger than
constraint is imposed on the interference phase. the naive expectation) is not consistent with these re-
Exp. D0 K+K−(%) D0 K0K¯0(%)
→ →
CLEO24 0.455 0.029 0.024 0.048 0.012 0.006
± ± ± ±
E68725 0.437 0.028 0.060 0.207 0.069 0.073
± ± ± ±
average 0.451 0.033 0.051 0.021
± ±
Table3: Cabibbo-suppresseddecays D0→K+K−,K0K¯0.
R(def.) Exp. ratio
Γ(D+→π¯0π+) CLEO26 0.028 0.006 0.006
Γ(D+→K¯−π+π+) ± ±
Γ(D+→K¯0K+) E68727 0.25 0.04 0.02
Γ(D+→K¯0π+) ± ±
Γ(DS+→K0π+) E68727 0.18 0.21
Γ(DS+→K¯0K+) ±
Γ(DS+→K0π+) MKIII28 <0.21
Γ(D+→φπ+)
S
Table 4: Cabibbo-suppressed decays of D+ and DS+ to two pseu- Figure 4: Dalitz plot of the Cabibbo-suppressed decay D+ →
doscalars. K−K+π+ by E687. The φπ+ band and the K¯∗0π+ band are
clearlyseen.
sults. Alsolistedisthesingly-Cabibbo-suppressedmodes
of DS+ which have the same final states as the DCSD which means that half the time it shows up as KSKS
modesofD+ andthuscanbemeasuredinthesameanal- and half the as K K . This is correct even with CP
L L
yses. The decay DS+ →φK+ is Class-3 and expected to violation. Thus we have
be suppressed by destructive interference (there are two
s¯ quarks in the final state) which is consistent with the B(D0 K0K¯0)=2B(D0 KSKS).
→ →
upperlimit. The decayDS+ →K¯∗0π+ is Class-1andone The decay D0 K0K¯0 cannot occur by a spectator
would expect that the naive suppression factor should →
diagram without FSI. It could occur by exchange dia-
work; the measurement, however,is on the high side. grams: cu¯ ss¯ with a dd¯pair creation from vacuum,
In the flavor SU(3) limit, the Cabibbo-suppressed or cu¯ dd¯→with a ss¯ pair creation from vacuum. The
modes D KK and D ππ are expected to be the →
→ → two exchange amplitudes, however,cancel exactly in the
same. In comparing with the data, however, one needs
limit of the flavor SU(3) in 2 generations(an example of
to take into account the FSI which rotates the phases of GIM cancellation)29. Thus, it is likely that the K0K¯0
isospin amplitudes. For D0 →KK, we have mode is dominated by the feed though from the K+K−
Amp(K+K−) = 12(A1+A0) imnoTdaebdleu3e.toToFgSeIt.hLeratweistthrDesultsπfπordDat0a→froKmKthearpeagrtivicelne
Amp(K0K¯0) = q1(A A ), data group8, we get →
2 1− 0
q B(K+K−)+B(K0K¯0)
where A (I = 0,1) is the isospin=I amplitude. Note
I =2.03 0.27
that phase rotations of A change the decay rate of each B(π+π−)+B(π0π0) ±
I
mode, but keep the sum unchanged:
which is larger than the naive value of unity. The BSW
1 model prediction is 1.3 which is still smaller than the
Γ(K+K−)+Γ(K0K¯0)= (A 2+ A 2).
2 | 0| | 1| experimental value above.
Cabibbo-suppressed 2-body decays of D+ and D+
The mode D+ K¯0K+ is purely I = 1, and thus the S
→ are shown in Table 4. As mentioned earlier, the decays
ratedoesnotchangeundertheFSI.Hereweareassuming
D+ π0π+ andK¯0K+ donotsufferfrom(elastic)FSI.
that the FSI is elastic (i.e. KK channels stay within KK →
The D+ π0π+ mode is Class-3, and thus expected to
channels), and if the FSI is inelastic the above relations →
be suppressed due to the destructive interference, while
are no longer correct. The inelastic FSI, however, is ex-
the D+ K¯0K+ mode is not. Using B(D+ K¯0π+)
pectTedhetoKb0eK¯sm0malol.dTehisedseittuecatteidonbyisKsiSmKilaSr.fSoirnDce0th→etπwπo. =the2.r7a4ti±o→0o.f2t9h%e tawnodCBa(bDib+b→o-sKup−pπre+sπse+d)d=ec9a.y1→s±is0.6%8,
neutral kaons are produced coherently in a symmetric
L=0 state, one has to take into account the quantum Γ(D+ K¯0K+)
correlationwhenconvertingtheKSKS ratetotheK0K¯0 2Γ(D+→ π0π+) =1.4±0.5,
→
rate. The state can be written as
where the factor of 2 in the denominator is the isospin
D0 K0K¯0+K¯0K0 =K K +K K factor, or equivalently due to the fact that π0 is half
S S L L
→
uu¯ and half dd¯. This factor is expected to be en- Mode Exp. Asymmetry
hanced due to the suppression of π0π+. The ratio K+K−π+ 0.031 0.068
Γ(D+ K¯0K+)/Γ(D+ K¯0π+) = 0.25 0.04 0.02 D+ K¯∗0K+ E68733 − 0.12± 0.13
→ → ± ±
itself is larger than the naive Cabibbo suppression of → φπ+ 0−.066 ±0.086
λ2 0.05. This is probably because the normalization E68733 0.024±0.084
mod∼e D+ K¯0π+ is suppressed by the destructive in- K+K− CLEO34 0.069±0.059
→
terference (Class-3). K φ CLEO34 0.007±0.090
colorF-osurpDpSr+e,sstehde(in.eo.rmCalaliszsa-t2i)o,nwmhioledDe S+DS+→→K0Kπ¯+0Kis+noist D0 → KK−SSππ+0 CCLLEEOO3344 −−00..000193±±00..001310
(Class-1). Thus,weexpecttheratiotobeenhancedwith ±
respectto the naive factor ofλ2 ∼0.05. The experimen- Table 5: CP asymmetries of D0,+ decays. The asymmetries by
tal data is not yet conclusive at this point. It should E687 are normalized to D+ → K−π+π+ and D0 → K−π+.
be noted that K¯0 or K0 in any decay mode is usually CLEOtags theflavorofD bythedecayD∗+→D0π+.
measured as K and thus DCSD mode could interfere
S
with the corresponding Cabibbo-favored mode.32 As a
the main goal now is to search effects beyond the stan-
result, the oft-used relation B(K¯0X) = 2B(K X) does
S dard model, however, Cabibbo-favored modes also need
not hold. The correction is typically of order 5 to 10%,
tobechecked. Table5showsrecentmeasurementsofCP
but for some channels it could be as large as 25%. One
asymmetries of D+,0 decays. Since there is an asymme-
swuhcehreextahme pClaebiisbbthoe-fanvoorrmedalimzaotdioenDm+odeKD¯0S+K→+ iKs cSoKlo+r-, try in photo-production of D and D¯ in E687 numbers
suppressed (i.e. Class-2) but the DSC→SD mode DS+ → aDr+enormKa−lizπe+dπt+ocaonrdresDp0ondinKgC−πab+i.bbAo-lflavnourmedbedrescaayres
K0K+ is not. The exact amount of correction depends → →
consistent with zero.
on unknown FSI phase, and it is difficult to reliably es-
For D0 Kπ, CP violation in mixing introduces
timate. →
additional factor between ρ and ρ in (4) which differ
For D+,DS+ → K−K+π+ modes, we now have for D0 K+π− andD¯0 DK−π+ M(assuming that there
Dalitz plot analysis from E687.30 Figure 4 shows the → →
is no direct CP violation):
Cabibbo-suppressed mode D+ K−K+π+. The po-
sition of the K∗(892) band was→found to be shifted in a ρ qρ (D0), ρ pρ (D¯0)
way consistent with existence of K∗(1430). After the fit M → p M M → q M
including the interferences, the ratios of partial widths
where p and q are the coefficients of D0 and D¯0 for the
are found to be
mass eigenstates D :
Γ(D+→K¯∗0(892)K+) = 0.044 0.003 0.004 H,L
Γ(ΓD(D+Γ(→+D→K+K−→−πφ+πππ+++π))+) = 0.058±±0.006±±0.006. DH =pD0+qD¯0, DL =pD0−qD¯0.
If p = q, then the additional factor is in general differ-
The D+ →φπ+ mode is color-suppressed,butthe decay ent f6or D0 and D¯0 resulting in CP asymmetry in the
constant of φ (which is ‘emitted’ from the hadronic cur-
time-dependent Γ(D0 K+π−)(t) vs. its CP conjugate
rent D π in the factorization picture) is quite large →
→ channel as well as in the time-integrated rates. In the
(f 233 MeV), could bring it up to the same level as
φ
D+∼ K∗0K+ which is a Class-1 decay. limit of ℑ(aD/a) = 0 and δγ = 0, there is no term lin-
→ ear in t in the expression (4). Even then, CP violation
in mixing would give rise to a term linear in t which is
2.2 CP Violation
also CP odd. Such asymmetry that increases linearly
CP asymmetries in D decays can occur through 1) di- with time would indicate both CP violation and mixing
rect CP violation21,22, 2) mixing31, or 3) interference simultaneously35. The table also lists asymmetries for
of Cabibbo-favoredmode and DCSD in modes involving CP self-conjugate final states; the results are all consis-
K 32. The asymmetries are expected to be quite small tent with zero.
S
in the standard model (10−3 level or less); any asymme-
try much larger is thus a signal of physics beyond the 3 Summary
standard model.
Direct CP violation should involve at least two The charm physics has matured. We now see rare de-
quark-level diagrams with different CKM phases and cays such as pure leptonic decay and isospin violating
different FSI phases. The two diagrams may be two decay. A few Doubly-Cabibbo-Suppressed decays have
spectators21, spectator plus penguin22, or spectator plus been observed, and detailed studies of singly-Cabibbo-
annihilation23. Atleastinthestandardmodel,theasym- suppressed modes have been done and ongoing. Most
metries are larger for Cabibbo-suppressed modes; since of the modes are qualitatively understandable in terms
of the color-suppressionand the destructive interference (1984) 1037.
together with known SU(3) breaking effects such as the 24. M.Artusoet al. (CLEO),apapersubmittedto this
differences in decay constants. The experimental sen- conference (EPS0181).
sitivities for CP asymmetries are still a few orders of 25. P. Frabetti et al. (E687), Phys. Lett. B340 (1994)
magnitudeawayfromthelevelexpectedbythestandard 254;P. Frabetti et al. (E687), Phys. Lett. B321
model. (1994) 295.
26. M.Selenet al. (CLEO),Phys. Rev. Lett. 71(1993)
1973.
Acknowledgements: The author would like to thank 27. P. Frabetti et al. (E687), Phys. Lett. B346 (1994)
I. Bigi, S. P. Ratti, F. Muheim and V. Jain for useful 199;
andstimulatingconversations. Thisworkwaspartlysup- 28. J. Adler et al., Phys. Rev. Lett. 63 (1989) 1211.
ported by the U.S. department of energy. 29. X.-Y. Pham, Phys. Lett. B193 (1987) 331.
30. P. Frabetti et al., (E687), Phys. Lett. B351 (1995)
References
591,
1. The derivation can be found in, J. Kaplan and J.H. 31. I. Bigi and A.I. Sanda, Phys. Lett. B171 (1986)
Ku¨hn, Phys. Lett. 78B (1978) 252. 320.
2. S. Aoki et al. (WA75), Prog. Th. Phys. 89 (1993) 32. I. Bigi and H. Yamamoto, Phys. Lett. B349 (1995)
131. 363.
3. D. Acosta et al. (CLEO), Phys. Rev. D49 (1994) 33. P. Frabetti et al. (E687), Phys. Rev. D50 (1994)
5690. 2953.
4. J. Bai et al. (BES), Phys. Rev. Lett. 23 (1995) 34. J. Bartelt et al. (CLEO), to be published.
4599. 35. L. Wolfenstein, Phys. Rev. Lett. 75 (1995) 2460;G.
5. D.Gibautet al. (CLEO),a papersubmitted to this Blaylock, A. Seiden, and Y. Nir, Phys. Lett. B355
conference (EPS0184). (1995) 555;T. Browder and S. Pakvasa, University
6. S. Menary, a private communication. of Hawaii Preprint UH-511-828-95-ReV.
7. F. Muheim and S. Stone, Phys. Rev. D49 (1994)
3767.
8. Particle Data Group, Phys. Rev. D50 (1994) 1206.
9. P. Cho and M.B. Wise, Phys. Rev. D49 (1994)
6228.
10. J. Gronberg et al. (CLEO), Phys. Rev. Lett. 75
(1995) 3232.
11. Seeforexample,M.FrankandP.J.O’Donnell,Phys.
Lett. 159B (1983) 174.
12. M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C34
(1987) 103.
13. J. Gronberg et al. (CLEO), Phys. Rev. Lett. 75
(1995) 3232.
14. P. Frabetti et al., (E687), Phys. Lett. B359 (1995)
403.
15. M. Purohit (E791) talk presented at 1994 ICHEP
Glasgow, FERMILAB-Conf-94/186.
16. P. Frabetti et al., (E687), to be published.
17. J. Anjos et al. (E691), Phys. Rev. Lett. 69 (1992)
2892.
18. M. Adamovich et al. (WA82), Phys. Lett. B305
(1993) 177.
19. J. Anjos et al. (E691), Phys. Rev. Lett. 60 (1988)
1239.
20. P. Frabetti et al., (E687), Phys. Lett. B331 (1994)
217,and references therein.
21. M. Golden and B. Grinstein Phys. Lett. B222
(1989) 501.
22. F. Buccella et al., Phys. Lett. B302 (1993) 319.
23. L.-L. Chau and H.-Y. Cheng, Phys. Rev. Lett. 53