Charm Leptonic and Semileptonic Decays

0.15 MB·English

by  Peter Zweber

Charm Leptonic and Semileptonic Decays
7
0 P. Zwebera
0
2 aUniversity of Minnesota, Minneapolis, Minnesota 55455 USA

n
a Experimental results for the pseudoscalar decay constants fD and fDs are reviewed. Semileptonic form factor
J results from D→(pseudoscalar)lν and D→(vector)lν decays are also reviewed.

5
1
1. INTRODUCTION CKM transition matrix element. These decays
2
are helicity suppressed and, based on Eq. 1, the
8v The study of charmed meson decays are im- SM predicts Γ(D+ l+ν)=2.3 10−5 :1:2.64
1 portantforimprovingourknowledgeoftheStan- and Γ(D+ l+ν)→= 2.3 10−5×: 1 : 9.72, with
dardModel(SM). Inparticular,the study oflep- s → ×
0 l = e : µ : τ, respectively. Deviations from these
1 tonic and semileptonic decays allow us to mea-
predictions may arise from physics beyond the
0 sure the CKM matrix elements V and V to a
cs cd SM. Recent measurements of leptonic decays of
7 highlevelofprecision. Leptonicandsemileptonic the D+ and D+ are discussed in the following
0 s
decays are also used to test theoretical predic-
/ subsections.
x tions describing the strong interaction (QCD) in
-e heavyquarksystems. Charmedmesondecaysare 2.1. D+ l+ν
p a good laboratory to test Lattice QCD (LQCD) →
The BES Collaboration reported a measure-
e predictions, which can then be applied with con- ment of the D+ µ+ν branching fraction us-
h µ
: fidence to bottom meson decays. Improved theo- ing 33 pb−1 of e+→e− annihilation data collected
v retical predictions will not only lower the uncer-
on the ψ(3770) resonance with the BES II de-
Xi tainty in the CKM matrix elements mentioned tector [2]. Events are selected using the Mark
above but also V and V .
r cb ub III “D-tagging” method [3], which consists of
a fully reconstructing the D meson from e+e−
2. LEPTONIC DECAYS →
ψ(3770) DD events and studying the D de-
→
cay. In (semi)leptonic decays, the neutrino in in-
Leptonic decays of heavy mesons involve the
ferred from the missing four-momentum in the
annihilationofthe constituentquarksintoaneu-
−
event. Using a sample of 5300 taggedD decays
trino and charged lepton via a virtual W boson.
(note that charge conjugation is implied unless
The probability for the annihilation is propor-
otherwisestated)from9tagmodesandrequiring
tional to the wavefunctions of the quarks at the
one additional particle consistent with a muon,
point of annihilation and is incorporated within
3 candidates events are observed with 0.3 back-
the decay constant of the meson. The leptonic
decay partialwidth of the D+ meson within the groundevents. Thisleadstoabranchingfraction
(s) of (D+ µ+ν ) = (12+11 1) 10−4, where
SM is given by [1] B → µ −5 ± ×
the first error is statistical and the second is sys-
Γ(D+ l+ν)= tematic.
(s) →
The CLEOCollaborationreportedanupdated
G2Ff2 m2M 1 m2l V 2, (1) measurement of the D+ µ+ν branching frac-
8π D(s) l D(s)(cid:18) − MD2(s)(cid:19)| cd(s)| tion [4]. Using a 281 pb−→1 dataµsample collected
where G is the Fermi coupling constant, f at the ψ(3770) resonance with the CLEO-c de-
F D
(f )istheD+ (D+)decayconstant,M (M ) tector,asampleof158,000D− decaysfrom6tag
Ds s D Ds
is the D+ (D+) mass, m is the mass of the modes was studied using the D-tagging method
s l
chargedlepton,andV (V )isthec d(c s) described above. Candidate events are required
cd cs
→ →
1
2
to have one charged track of opposite charge A complementary CLEO analysis searched for
to the tagged D− and the track needs to de- D+ e+ν decays [4]. In this case, the charged
e
→
posit an energy in the electromagnetic calorime- trackisrequiredtobe consistentwithapositron.
ter (E ) <300 MeV, which is consistent with No signal is observed and an upper limit of
tkCC
a minimum ionizing particle. Eventswith aniso- (D+ e+ν ) < 2.4 10−5 at 90% confidence
e
B → ×
lated photon-like shower in the calorimeter with level (C.L.) is obtained.
anenergyinexcessof250MeVarerejected. Fig- The CLEO Collaboration has reported on the
ure 1 shows the missing mass squared distribu- search for D+ τ+ν ,τ+ π+ν using the
τ τ
tion for the candidate events, where the miss- same 281 pb−1→and tagged D→− sample [5]. For
ing mass squared is defined as MM2 (E minimum ionizing pions with E <300 MeV,
b tkCC
≡ −
E )2 ( p p )2, where E is the beam en- the signal region is defined as 0.05 < MM2 <
erµgy,p− −istDhe−moµmentumofthbetaggedD−,and 0.175 GeV2, above D+ µ+ν signal region
D µ
→
E (p ) is the energy (momentum) of the muon. andbelowtheD+ K0π+ background(seeFig.
µ µ → L
The signal region, defined by MM2 < 0.05 1). Pions which hadronize in the calorimeter are
| |
GeV2, contains 50 candidate and2.8 background studied by requiring the track to have E >
tkCC
events, of which 1.1 events are determined from 300MeV,beinconsistentwithapositron,andre-
the SM prediction for D+ τ+ν ,τ+ π+ν . side in the region -0.05 < MM2 < 0.175 GeV2.
τ τ
→ →
The result corresponds to (D+ µ+ν ) = Eventsarerejectedinboth casesifitcontainsan
µ
(4.4 0.7 0.1) 10−4. B → isolatedphoton-like showerwith an energyin ex-
± ± ×
cess of 250 MeV or if the candidate pion is more
consistent with being a charged kaon. No sig-
nificant enhancement is observed in either case,
resulting in an upper limit of (D+ τ+ν ) <
τ
120 1630905-009 2.1 10−3 (90% C.L.). UsingBthe C→LEO result
×
for D+ µ+ν above, an upper limit for the ra-
15 → µ
100 tio (D+ τ+ντ)/ (D+ µ+νµ) of 1.8 times
B → B →
10 that of the SM prediction is placed.
2
V80 5
1 Ge 2.2T.heDs+Ba→Bal+rνCollaboration analyzed a 230.2
0.060 0.05 0 0.05 fb−1 data sample taken at or near the Υ(4S)
s / resonance to study the decay process D+
Event40 µD+∗+νµD[6]., wThehreeyDstudiaerde 1th6efupllryocreescsones+tersu−ct→→ed
s tag tag
D0,D−,D−, and D∗− decays and D∗+
20 s s →
γD+ γ(µ+ν ), using a method similar to an
s → µ
earlier CLEO measurement [7]. Figure 2 shows
0 the resultant ∆M M(D∗+) M(D+) dis-
0 0.25 0.50 ≡ s − s
MM2 (GeV2) tribution. With 489 55 signal events, they
±
determine Γ(D+ µ+ν )/Γ(D+ φπ+) =
s → µ s →
0.143 0.018 0.006. Usingthe recentBaBarre-
± ±
sult (D+ φπ+)=(4.71 0.46)%[8],theyde-
Figure 1. CLEO MM2 distribution for D+ termBineasb→ranchingfraction±of (D+ µ+ν )=
µ+νµ decays [4]. The inset shows the signal r→e- (0.67 0.08 0.03 0.07)%,wBheresth→e last eµrror
gion, defined by the arrows, in more detail. The arises±from t±he D+± φπ+ normalization uncer-
background peak at MM2 0.25 GeV2 is con- tainty. s →
∼
sistent with D+ K0π+ decays and is substan- As part of the CLEO-c run plan, the energy
→ L
tially displayed from the signal region. region3.97 - 4.26 GeV was scanned to determine
3
2c 300
V/ 12 (i)
Ge 250
1
0.0 200
Entries/ 110500 8
50
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
∆M (GeV/c2) 2 4
V
e
G
1
0
Fµ+igνuµrede2c.aysB[a6B].aTrh∆eMsoliddislitnreibiusttihonefiftotredDss+ign→al ents/ 0. 60 (ii)
v
and background distribution, while the dashed E
line is the backgrounddistribution alone. 4
2
0
the best energy for Ds production. The energy (iii)
1
√s = 4.170 GeV was found to be the location
0
with the highest production rate of D mesons, 0 0.25 0.50
s
but the D mesons are predominately produced Missing Mass squared (GeV 2 )
s
in the processes e+e− D∗−D+,D−D∗+. The
→ s s s s
tagging procedure becomes more complicated by
the presence of the transition photon from the Figure 3. CLEO MM2 distributions for D+
radUiasitnivgeade1c9a5yppbr−oc1esdsaDtas∗s→amDplseγ.collected near tl+aiνnsdtercaacykss,wwihtherEe l = e<,µ3,0τ0[M9].eVF,iFguigr.e33iiisccoo→nn--
tkCC
√s = 4.170 GeV, the CLEO Collaboration re- tains tracks with E > 300 MeV and incon-
tkCC
portedpreliminarybranchingfractionsforDs+ → sistent with the positron hypothesis, while Fig.
l+ν decays, where l = e,µ,τ, and with the tau 3iii contains tracks which are consistent with the
decaying via τ+ π+ντ [9]. Events are selected positron hypothesis.
− →
with 8 D tag modes and the detection of the
s
transition photon. The missing mass squared for
D+ is defined as MM2 (E E E
s ≡ CM − Ds − γ −
E )2 ( p p p )2, where E is the for the positron decay channel in Fig. 3iii. The
tk − − Ds − γ − tk CM
center-of-mass energy, E (p ) is the energy D+ µ+ν signal region contains 64 candidate
(momentum) of the taggeDds D−Ds, E (p ) is the ansd→7.3 bacµkground events, of which 5.3 events
s γ γ
energy(momentum)ofthetransitionphoton,and aredeterminedfromtheSMpredictionforD+
s →
E (p ) is the energy (momentum) of the can- τ+ν ,τ+ π+ν . Using events with candidate
tk tk τ τ
→
didate track. The signal side, consisting of one tracks inconsistent with the positron hypothesis
chargedtrack,isreconstructedusingthesamecri- and outside of the D+ µ+ν signal region, 36
s → µ
teria as the CLEO D+ l+ν analyses described candidateand4.8backgroundD+ τ+ν events
→ s → τ
above, but with the exceptions of increasing the are found. The preliminary branching fractions
D+ e+ν andD+ τ+ν MM2signalregions are (D+ e+ν ) < 3.1 10−4 (90% C.L.),
s → e s → τ B s → e ×
to0.20GeV2andincreasingthemaximumshower (D+ µ+ν ) = (0.66 0.09 0.03)%, and
B s → µ ± ±
energyto300MeV.Figure3showstheMM2dis- (D+ τ+ν )=(7.1 1.4 0.3)%.
B s → τ ± ±
tributions. Signals are apparent in Figs. 3i and A complementary CLEO analysis of (D+
B s →
3ii, while no signal is observed near MM2 = 0 τ+ν ) was reported using the decay mode τ+
τ
→
4
Table 1
Experimental and theoretical results for the decay constants f and f .
D Ds
f (MeV) f (MeV) f /f
Ds D Ds D
CLEO[9,10]a[4] 280(12)(6)a 222.6(16.7)+2.8 1.26(11)(3)a
−3.4
BaBar[6] 283(17)(4)(14)
BES[2] 371+129(25)
−117
Unquenched LQCD[11] 249(3)(16) 201(3)(17) 1.24(1)(7)
Quenched LQCD[12] 266(10)(18) 235(8)(14) 1.13(3)(5)
Quenched LQCD[13] 236(8)+17 210(10)+17 1.13(2)+4
−14 −16 −2
Quenched LQCD[14] 231(12)+6 211(14)+10 1.10(2)
−1 −12
QCD Sum Rules[15] 205(22) 177(21) 1.16(1)(3)
QCD Sum Rules[16] 235(24) 203(23) 1.15(4)
Quark Model[17] 268 234 1.15
Quark Model[18] 248(27) 230(25) 1.08(1)
Potential Model[19] 253 241 1.05
Isospin Splittings[20] 262(29)
aThe CLEO f result is the average of the 3 preliminary measurements described in the text.
Ds
e+ν ν [10]. This analysis reconstructs the
taggeedτD− but does not require detection of the 50 Data
s MCTotal
transition photon. Events are selected with a
MC Signal
positron with opposite charge to the tag and re- 40
MC Background
quires the summed energy of all isolated showers V
e MC K 0 e+ ν
in the calorimeter (Eextra) < 400 MeV. The pre- M e
CC 0 30
liminary branching fraction is B(Ds+ → τ+ντ) = s /5
(6.3 0.8 0.5)% and, while the CLEO D+ nt
τ+ντ±,τ+ ±π+ντ analysishassmallersystemsat→ic Eve20
→
uncertainty, this result has a smaller statistical
uncertainty. 10
2.3. Decay Constants f and f
D Ds 0
Table 1 summarizes the experimental results
forfD andfDs alongwithvarioustheoreticalpre- 0 0.5 1.0 1.5
dictions. The experimental results are consistent E e x t r a (GeV)
CC
with most theoretical models. The decay con-
stant ratio from the CLEO results is f /f =
Ds D
1.26 0.11 0.03,whichisconsistentwiththeun-
± ± Figure 4. Eextra energy distribution from the
quenchedLQCD[11] prediction1.24 0.01 0.07 CC
± ± CLEO D+ τ+ν ,τ+ e+ν ν analysis [10].
and slightly larger than other predictions. s → τ → e τ
3. SEMILEPTONIC DECAYS
3.1. Inclusive D Decays positron momentum spectra from the D0 and
The CLEO Collaboration reported measure- D+ decays are similar, as expected. They deter-
ments of the inclusive branching fractions for mine branching fractions of (D0 Xe+ν ) =
e
B →
D0 X e+ν andD+ X e+ν decaysandthe (6.46 0.17 0.13)% and (D+ Xe+ν ) =
e e e
→ → ± ± B →
corresponding positron momentum spectra from (16.13 0.20 0.33)%. After subtracting the
the 281 pb−1 ψ(3770) data sample [21]. The known±exclusiv±e semileptonic decay modes [22],
5
Table 2
Preliminary CLEO branching fraction measurements of rare semileptonic D decays. Results are at the
10−4 level and upper limits are at 90% C.L.
CLEO [23] PDG[22] ISGW2[24] HQS[25]
(D+ η e+ν ) 12.9(1.9)(0.7) < 70 16a 10
e
B(D+ →η′ e+ν ) < 3.0 < 110 3.2a 1.6
e
B →
(D+ φ e+ν ) < 2.0 < 209
e
B →
(D+ ω e+ν ) 14.9(2.7)(0.5) 16+7 13
B(D0 →K−π+eπ−e+ν ) 2.9+1.5(0.5)b <−126
B(D0 →K−(1270) e+eν , −1.1
B K−(→12701) K−π+πe−)b 2.2+1.4(0.2)b 5.6(6)c
1 → −1.0
aPrediction assumes 10◦ η η′ mixing angle. bSignal observed at a 4.5σ significance.
cPrediction includes experi−mental uncertainties from K−(1270) K−π+π− decay[22].
1 →
the unobserved semileptonic branching fractions intheevent. TheBelleresult[29]usesa282fb−1
are (0.3 0.3)% and (1.1 0.7)% for the D0 sample collected at or near the Υ(4S) resonance
± ±
and D+, respectively. It is apparent that the with signal events reconstructed from the decay
known exclusive decays almost completely satu- process D∗+ D0π+. For comparison, a recent
→
rate the inclusive branching fractions. Combin- unquenchedLQCDresultisalsolistedinTable3.
ing these branching fractions with the world av- The experimental results for D0 K−(π−)l+ν
→
eragefortheD+/0lifetimes[22],thepartialwidth are approaching the precision of 2% (4%), while
ratio is Γ(D+ Xe+ν )/Γ(D0 Xe+ν ) = the LQCD predictions are at the 20% level.
e e
→ → ∼
0.985 0.028 0.015, consistent with isospin in-
± ±
variance.
Table 3
3.2. Rare D Decays BranchingfractionsforthedecaysD0 K−e+ν
e
TheCLEOCollaborationhassearchedforvar- and D0 π−e+ν . Results are given→in percent.
e
ious rare semileptonic D decays with its 281 → K− e+ν π− e+ν
pb−1 ψ(3770) sample. Table 2 lists the prelim-
PDG04[26] 3.58(18) 0.36(6)
inary branching fractions. With the exception of
BES[27] 3.82(40)(27) 0.33(13)(3)
(D+ ωe+ν ),theseresultsareeitherfirstob-
B → e CLEO-c[28]a 3.44(10)(10) 0.262(25)(8)
servationsorimproveupperlimitsbyoneorderof
Belle[29] 3.45(10)(19) 0.279(27)(16)
magnitude. The results are consistent with pre-
CLEO(Tag)b 3.58(5)(5) 0.309(12)(6)
dictions based on ISGW2 [24] and heavy quark
CLEO(NoTag)b 3.56(3)(11) 0.301(11)(10)
symmetry (HQS) [25].
LQCD[31] 3.8(3)(7) 0.32(3)(7)
aFrom a 56 pb−1 sample using the D-tag tech-
3.3. D (pseudoscalar)l+ν
Precis→ionmeasurementsofthe D0 K− e+ν nique and is a subset of the other CLEO results.
andD0 π− e+ν branchingfraction→shavebeene bPreliminary results, not to be averaged.
e
→
measuredandarelistedinTable3. TheBES[27]
and preliminary CLEO(Tag) [23] analyses, using
33 pb−1 and 281 pb−1 ψ(3770)data samples, re-
The differential partial width for D
spectively, use the Mark III tagging method. An K(π)l+ν decays is governed by one form facto→r,
alternative CLEO analysis, CLEO(NoTag) [30], f (q2), and is given by
+
does not use the D-tagging technique but “re-
constructs” the neutrino by fully reconstructing dΓ G2 2
= F p3 V 2 fK(π)(q2) , (2)
the semileptonic decay from all decay products dq2 24π3 K(π) | cs(d)| (cid:12) + (cid:12)
(cid:12) (cid:12)
(cid:12) (cid:12)
6
Table 4
Simple pole and modified pole fit results from D K(π)l+ν decays.
→
mD→K (GeV) mD→π (GeV) αD→K αD→π
pole pole
FOCUS[35] 1.93(5)(3) 1.91+0.30(7) 0.28(8)(7)
−0.15
CLEO III[36] 1.89(5)+0.04 1.86+0.10+0.30 0.36(10)+0.03 0.37+0.20(15)
−0.03 −0.06−0.03 −0.07 −0.31
BaBar[37]a 1.854(16)(20) 0.43(3)(4)
Belle[29] 1.82(4)(3) 1.97(8)(4) 0.52(8)(6) 0.10(21)(10)
CLEO-c(Tag)b 1.96(3)(1) 1.95(4)(2) 0.22(5)(2) 0.17(10)(5)
CLEO-c(NoTag)b 1.97(2)(1) 1.89(3)(1) 0.21(4)(3) 0.32(7)(3)
LQCD[31] 1.72(18) 1.99(17) 0.50(4) 0.44(4)
aPreliminary results. bPreliminary results, not to be averaged.
where p (p ) is the kaon (pion) momentum in tagged analyses) use isospin averaging of D0
K π
the D rest frame and q2 is the invariant mass of K−e+ν and D+ K0e+ν decays for D →K
the lepton-neutrino pair. studieseandD0 →π−e+Sν anedD+ π0e+ν→de-
e e
→ →
Various parameterizations of the form factor cays for D π studies. The recent unquenched
→
have been proposed. The earliest is in terms of a LQCD result [31] is also listed in Table 4. The
simple pole model given as measurements of the pole masses as determined
using the simple pole model are all lower than
fK(π)(0)
fK(π)(q2)= + , (3) the expected vector states. The results for α are
+ 1 q2/ mD→K(π) 2 inconsistent with the null result, but present ex-
− (cid:16) pole (cid:17) perimental accuracy does not constrain it well.
where the pole mass is expected to be the Table 5 lists recent results for fK(π)(0). The
D0K+ (D0π+) vector state M(D∗+) = 2.112 form factor model for CLEO result+s use the Hill
s
(M(D∗+)= 2.010) GeV. Becirevic and Kaidalov series parameterization with three parameters,
[32] proposed a modified pole model, which ex- while the BES and Belle results use the modi-
plicitlyincorporatestheD∗+ massesbutincludes fied pole model. While variations exist between
(s)
a term α to account for deviations from the vec- theexperimentalresults,theyareconsistentwith
tor masses. Becher and Hill [33] proposed a less the unquenched LQCD result.
model-dependentwayofdealingwiththeanalytic
singularities at q2 = m2 . They project the
pole
q2 dependence into a different parameter space, Table 5
which pushes the cut singularities far from the Results for the f+K(π)(0) form factors. The form
physical q2 region, and the corresponding form factorsaresimilarlyderivedusingthe2006global
factorcanberepresentedbyarapidlyconverging fit values for Vcs and Vcd [22], with the exception
Taylorseries. Hill [34]extended the procedureto of the Belle result.
fK(0) fπ(0)
explicitly describe semileptonic D decays. | + | | + |
BES[27] 0.80(4)(3) 0.72(14)(3)
Table 4 lists the recent experimental results
Belle[29] 0.695(7)(22) 0.624(20)(30)
for the simple and modified pole variables.
CLEO(Tag)a 0.761(10)(7) 0.660(28)(11)
The FOCUS result [35] is determined from
13000 D∗+ D0π+ decays, where D0 ≈ CLEO(NoTag)a 0.749(5)(10) 0.636(17)(13)
K−(π−) µ+ν→. The CLEO III [36], BaBar [37→], LQCD[31] 0.73(3)(7) 0.64(3)(6)
µ
and Belle [29]results studiedD0 decaysfromthe aPreliminary results, not to be averaged.
decay process D∗+ D0π+ using 7 fb−1, 75
fb−1, and 282 fb−1 →data samples, respectively,
collected at or near the Υ(4S) resonance. The Using the unquenched LQCD prediction for
preliminary CLEO results (both tagged and un- fK(π)(0)[31]allowsforanexperimentalmeasure-
+
7
ment of the CKM matrix elements V and V . D+ decays and find R =1.40 0.25 0.03 and
cd cs V
± ±
ThepreliminaryV resultfromtheCLEOtagged R =0.57 0.18 0.06. This analysis represents
cs 2
± ±
(untagged) analysis is V = 1.014 0.013 the first form factor measurement of a Cabibbo
cs
± ±
0.009 0.106(0.996 0.008 0.015 0.104),where suppressed vector decay mode in the charm sys-
± ± ± ±
thelastuncertaintyarisefromthetheoreticalun- tem.
certaintyinf+K(0). ThepreliminaryCLEOresult 3.4.2. D+ K∗l+ν
for V is 0.234 0.010 0.004 0.024 (0.229
cd ± ± ± ± The CLE→O collaboration, using the 281 pb−1
0.007 0.009 0.024). For comparison,the 2006
± ± ψ(3770) data sample and the D-tagging tech-
global fit values are V =0.97296 0.00024 and
cs
± nique, reported a non-parametric form factor
V = 0.2271 0.0010 [22]. The experimental
cd
± analysisusingtheFOCUSmethod[38]forthede-
uncertainties for V and V are at the 2% and
4% level, respectivcesly, whilcedthe theoretical un- cay process D+ K∗e+νe (K−π+)e+νµ [39].
→ →
certainty is on the order of 10%. When future CLEO confirms the presence of the s-wave inter-
theoretical predictions achieve higher precision, ference in the K−π+ final state and determines
semileptonic decays will be an ideal environment results for the formfactors to be consistwith the
to precisely measure V and V . FOCUS analysis. CLEO did not observe any ev-
cd cs idence of d- or f-wave interference in the K−π+
3.4. D (vector)l+ν system.
→
While the semileptonic D decays to vector
mesons are an additional method to measure Vcs 4. CONCLUSION
and V , they are complicated by the presence
cd
of three form factors associated with the three The recent experimental results for leptonic
helicity states of the final state meson. The and semileptonic decaysof charmmesons are be-
spectroscopic pole dominance model proposes to ginning to improvetheir accuracyto point where
parametrize the vector mesons in terms of a vec- theoreticalerrorsare dominating the uncertainty
tor and two axial vector form factors, which are inthedeterminationoftheVcs andVcd CKMma-
defined as trixelements. Thesemeasurementsprovidestrin-
genttestsoftheoreticalmodels,whichinturnwill
V(0) A (0)
V(q2)= 1 q2/m2 , Ai(q2)= 1 qi2/m2 , (4) improve the models as to lower their uncertainty
− V − Ai but are also used to “fine-tune” the models so
where mV = 2.1 GeV and mA1 = mA2 = 2.5 theycanbeappliedwithconfidencetobeautylep-
GeV.The normalizedformfactorsaredefined by tonic and semileptonic decays. The experimental
two ratios, the vector to first axial vector RV = precision will continue to improve from the final
V(0)/A1(0) and the second to first axial vector CLEO-c D and Ds data samples and the begin-
R2 =A2(0)/A1(0). ningofdatacollectionwiththeupgradedBES-III
and BEPC-II facilities in 2008.
3.4.1. D ρ e+ν
e
→
The CLEO Collaboration reported prelimi-
5. ACKNOWLEDGEMENTS
nary results for the decay processes D+/0
ρ0/−e+ν (π+π−/0)e+ν using the 281 pb−→1
e e I wish to thank Neville Harnew, Guy Wilkin-
→
ψ(3770)datasampleandtheD-taggingtechnique
son,andallofthe organizersforanengagingand
[23]. They determine the most precise branch- enjoyable conference. This work was supported
ing fractions of (D+ ρ0e+ν ) = (2.32
e bytheU.S.NationalScienceFoundationandDe-
0.20 0.12) 10B−3 and→ (D0 ρ−e+ν ) ±=
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(1.56± 0.16 ×0.09) 10−3.BUsing→theworldaver-
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