Measurements of the exclusive branching fractions B(D^0→π^-e^+ν_e) and B(D^0→K^-e^+ν_e), using data collected at the ψ(3770) with the Mark III detector at the SLAC e^+e^- storage ring SPEAR, are used to determine the ratio of the Kobayashi-Maskawa matrix elements │V_(cd)/V_(cs)│^2  =0.057_(-0.015)^(+0.038)±0.005

Adler, J.

Coffman, D.

DeJongh, F.

Dubois, G. P.

Eigen, G.

Hauser, J.

Hitlin, D. G.

Matthews, C. G.

Mincer, A. I.

Richman, J. D.

Weinstein, A. J.

Wisniewski, W. J.

Zhu, Y.

English

Caltech Authors - Main

VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
Measurement of the Branching Fractions for D 0 ---+ 1r - e + v e and D 0 ---+ K - e + Ve 
and Determination of I Ycd !Yes I 2 
J. Adler, J. J. Becker, G. T. Blaylock, T. Bolton, J.-C. Brient, T. Browder, J. S. Brown, K. 0. Bunnell, 
M. Burchell, T. H. Burnett, R. E. Cassell, D. Coffman, V. Cook, D. H. Coward, F. DeJongh, D. E. Dorfan, 
J. Drinkard, G. P. Dubois, G. Eigen, K. F. Einsweiler, B. I. Eisenstein, T. Freese, C. Gatto, G. Gladding, 
C. Grab, R. P. Hamilton, (a) J. Hauser, C. A. Hensch, D. G. Hitlin, J. M. Izen, P. C. Kim, L. Kopke, A. Li, 
W. S. Lockman, U. Mallik, C. G. Matthews, A. I. Mincer, R. Mir, P. M. Mockett, R. F. Mozley, 
B. Nemati, A. Odian, L. Parrish, R. Partridge, D. Pitman, S. A. Plaetzer, J. D. Richman, H. F. W. 
Sadrozinski, M. Scarlatella, T. L. Schalk, R. H. Schindler, A. Seiden, C. Simopoulos, A. L. Spadafora, 
I. E. Stockdale, W. Stockhausen, W. Toki, B. Tripsas, F. Villa, S. Wasserbaech, A. Wattenberg, A. J. 
Weinstein, S. Weseler, H. J. Willutzki, D. Wisinski, W. J. Wisniewski, R. Xu, andY. Zhu 
(The Mark III Collaboration) 
California Institute of Technology, Pasadena, California 91125 
University of California at Santa Cruz, Santa Cruz, California 95064 
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 
University of Iowa, Iowa City, Iowa 52242 
Stanford Linear Accelerator Center, Standford, California 94309 
University of Washington, Seattle, Washington 98195 
(Received 30 December 1988) 
Measurements of the exclusive branching fractions B(D 0 --+ n-e +v,) and B(D 0 --+ K- e +v,), using 
data collected at the 1f1(3770) with the Mark III detector at the SLAC e + e- storage ring SPEAR, are 
used to determine the ratio of Kobayashi-Maskawa matrix elements I VcdiVcs 12 =0.057 ~8:8H ± 0.005. 
PACS numbers: 13.20.Fc, 12.15.Ff, 14.40.Jz 
Present knowledge of the Kobayashi-Maskawa (KM) 
matrix element Vcd has been derived from a measure-
ment of neutrino-induced charm production. 1 This 
determination, however, depends on the production cross 
sections for D 0 , D +, and to a lesser degree, other 
charmed particles. It also depends on the semimuonic 
branching ratio and fragmentation function of each par-
ticle type. While determinations of I Vcd I using hadron-
ic decays of D mesons are free from uncertainties in the 
production mechanism, they suffer from the effects of in-
terference and final-state interactions. 2 In contrast, 
semileptonic decays are free of these complications. We 
report herein measurements of the branching fractions 
B(D 0 -+ n-e +ve) and B(D 0 - K- e +ve) and use their 
ratio to determine I VcdfVcs I 2. 3 
The data were collected with the Mark III detector 4 at 
the SLAC e + e - storage ring SPEAR near the peak of 
the lf/(3770), which decays predominantly to DD. The 
data contain about 27 700 produced D 0i5° events. 5 Can-
didate events are selected by first reconstructing a i5°, 
called a tag, in the following modes: K + n-, 
K+n-n+n-, K~n+n-, and K+n-n°. The absolute 
branching fractions B (D 0 --+ n-e + Ve) and B (D 0 
--+ K - e + v e ) are then measured by reconstructing these 
decay modes in the system recoiling from the tagged 
-o 6 D. 
measured i5° momentum. All events with a beam-
constrained mass greater than 1.8 GeV/c 2 are retained. 
A signal region is defined from 1. 8 54 to 1. 8 7 4 Ge VIc 2; 
events in a sideband from 1.830 to 1.850 GeV /c 2 are 
used to evaluate the background under the peak. 80% of 
events in the signal region have a unique tag; the 
remainder contain an average of 2.5 tags per event. 
Multiple tags are most often found in the K + n- n° 
mode; they arise from the use of photon candidates 
whose source is hadronic showers or charged-kaon de-
cays. To determine the total number of events with at 
least one tag, we plot in Fig. 1 (a) the beam-constrained 
mass of the tag from the mode having the least back-
ground per event, starting with the lowest-multiplicity 
decay, K + n-, and continuing through K + n- n + n-, 
K~n+n-, and K+n-n°. Multiple K+n-n+n- or 
K~n + n- tags are resolved by selecting the tag whose 
lowest-momentum track has the largest momentum. The 
preferred K + n-n° tag is selected by means of a con-
strained fit of the photons to the n° mass. Figure 1 (a), 
which shows the results of this procedure, contains a sin-
gle entry per event. There are 3636 ±54± 195 events 
(Ntag) above background. 
A D 0-+ n-e +Ve or D 0-+ K- e +ve decay candidate 
recoiling against a tag is required to contain two oppo-
sitely charged tracks, one of which is identified as an 
Tagged events are selected by 
constrained mass, (E6eam- piJo) 112, 
using the beam- electron. The sign of the charge of the lepton must be 
where Pl5o is the opposite the charm of the tag. 7 Electrons are identified 
© 1989 The American Physical Society 1821 
VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
"' 0 
> <I> (') 
C\1 
0 
0 
~ 
!!l 
c 
<I> 
> UJ 
1500 
1000 
500 
0 
20 
10 
0 
(c) 
2 
0 
1.80 1.84 1.88 
Beam Constrained Mass (GeV/c 2 ) 
FIG. I. (a) Beam-constrained mass of i5° hadronic tags. 
(b) Beam-constrained mass of i5° hadronic tags for K-e +v. 
events. (c) Beam-constrained mass of i5° hadronic tags for 
1r-e + v, events. 
using information from the time-of-flight (TOF) 
counters and the barrel electromagnetic calorimeter. 
For momenta below 0.3 GeV/c, TOF alone is used. 
Above 0.4 GeV /c, an algorithm using shower energy and 
shower shape 8 is used to distinguish electrons from pions. 
Between 0.3 and 0.4 GeV/c, electrons identified by either 
technique are accepted. Electron candidates with a kaon 
TOF identification are rejected. In this analysis, 75% of 
electrons are correctly identified; 7% of muons and 5% of 
pions are misidentified as electrons. 
Two independent methods are used to identify the 
recoiling hadron. The kinematics of a fully reconstruct-
ed semileptonic decay permit the identification of the 
hadron as either a pion or kaon. The quantity U 
=E missing- I Pmissing I' calculated for both the pion and 
kaon hypotheses, is expected to be zero for the correct 
choice since a single massless particle is undetected. For 
events with multiple tags, U is calculated separately for 
each. Monte Carlo studies indicate that the choice of 
the correct assignment has the minimum I U 1. The hy-
pothesis with the smallest value of I U I is accepted, and 
then only if the kinematic identification agrees with the 
TOF identification. 9 For the K- e + Ve analysis, we also 
accept kinematically identified kaons even when no TOF 
information is present. These may be tracks which do 
not enter the TOF system, tracks which have decayed 
before reaching the TOF counters, or tracks which enter 
1822 
~3 
(') 
~ 2 
0 
ci 
~ 
c 
~ 
w 0 
·0.2 0 0.2 
U (GeV) 
FIG. 2. Distribution of U (n °- 1r-e + v. hypothesis) calcu-
lated for n°- 1r-e + v. candidates (histogram), for recon-
structed Monte Carlo n °- 1r-e + Ve decays (solid curve), and 
for the principle background, n°- K- e + Ve decays interpret-
ed as n°-1r-e+v, (shaded). The curves are not normalized 
to the data. 
a counter close to the position of another track. For the 
1r-e + Ve analysis, we require that the pion be identified 
both kinematically and by TOF. 
Next, backgrounds from hadronic and other semilep-
tonic decays of the recoil D 0 must be suppressed. The 
decay D 0-K-1r+ is removed by requiring that the in-
variant mass calculated by interpreting the hadron and 
electron as a kaon and pion be less than 1.7 GeV/c 2• 
Less than 5% of K- e + Ve events fail to meet this re-
quirement. Recoiling decays with neutral pions (e.g., 
D 0- K -Kol + v1) are suppressed by rejecting events 
with photons other than those used in the hadronic tag. 
A visual scan is performed to prevent the elimination of 
events with showers caused by hadronic interactions or 
hadronic decays: Six additional K - e + Ve events contain-
ing hadronic showers classified as photons are recov-
ered. 10 No additional 1r-e + Ve events are recovered by 
the scan. 
Seven 1r-e + Ve candidates 11 and 56 K- e + Ve candi-
dates are retained, and their U distributions are shown in 
Figs. 2 and 3, respectively. Monte Carlo simulations are 
used to predict signal and background U distributions. 
The solid curves in Figs. 2 and 3 are the expected distri-
butions for reconstructed signal events. The shaded area 
in Fig. 2 shows the expected distribution for D 0 
> ~ 10 
0 0.2 
U (GeV) 
FIG. 3. Distribution of U (n°-K-e+v. hypothesis) cal-
culated for n°- K- e +ve candidates (histogram), for recon-
structed Monte Carlo n °- K - e + ve decays (solid curve, nor-
malized to the data), and for the background ( x I 00) from 
n°- K -Jr0e + Ve decays (shaded). 
VOLUME62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
---+ K- e + Ve events, where each event is interpreted in-
correctly as D 0 ---+ 1r-e + Ve. The shaded area in Fig. 3 
shows the expected feed-down of K -1r0e + ve events with 
an undetected 1r0 into the K- e + Ve sample. The require-
ment I U I < 0.1 Ge V is imposed to reduce these back-
grounds and other backgrounds with undetected massive 
neutral particles. One K- e + Ve candidate is rejected by 
this cut. 
The beam-constrained mass distributions forK- e + Ve 
and 1r-e + Ve events passing the particle identification 
and background rejection requirements are shown in 
Figs. 1 (b) and 1 (c). Events in the sideband region are 
used to evaluate the background due to incorrectly 
reconstructed tags. A Monte Carlo simulation incor-
porating a complete model of D 0 decays 5•12 is used to 
evaluate backgrounds occurring with a correct tag. 
Backgrounds are enumerated in Table I. The effic-
iencies for reconstructing semielectronic decays in the 
TABLE I. Number of background and observed events. 
Decay 
K -e +v, 
K- J1 +vi' 
n--e+v, 
n-- J1 +vi' 
1r + 1r -n-o 
K -n-+ 
K*-e+v, 
K-p+ 
K*-n-+ 
Sideband 
N background 
Nobserved 
0.44 
0.03 
N.A. 
N.A. 
0.03 
0.04 
0 
0.53 
7 
N.A. 
N.A. 
0.06 
0.02 
0.05 
0.13 
0.19 
0.06 
1.51 
55 
recoil to a tag are e,.-e+v, ==0.38 and eK-e+v, =0.37. The efficiencies for reconstructing semimuonic decays as their cor-
responding semielectronic decays are e,-JJ+v~' ==0.050 and EK-JJ+v~' =0.052. Lepton universality implies nearly identical 
semielectronic and semimuonic branching fractions; semimuonic events need not, therefore, be subtracted as a back-
ground. Instead, acceptance and background corrections are made using the expression 
B(DO- X- e + Ve) = Nobserved- Nbackground [1- Etag'I:.B(D 0 - tag modes) ) ' 
<ex-e+v. +ex-JJ+vi')Ntag 2 
where X is a 1r or K and Etag is the average tag reconstruction efficiency. We find 
B(D 0 - 1r- e +ve) =(0.39:!:8:H ± 0.04)% 
(Ref. 13) and 
B(D 0 ---+ K- e+ve) =(3.4±0.5 ±0.4)%. 
Systematic errors arise from uncertainties in the simulation of backgrounds (50% of the subtracted background), deter-
mination of the number of tags (5.3%), electron identification efficiency (2%), photon reconstruction efficiency (5%), 
visual scan efficiency (5%), track reconstruction efficiency (2%), and TOF identification of hadrons (5%). These errors 
are added in quadrature. The technique of tagging with hadronic i5° decays eliminates any dependence on the charm 
production cross section or the integrated luminosity. 
The ratio I Vcd /Vcs I 2 is obtained from B (D 0 ---+ 1r-e + Ve) and 
I 
Vcd 12 = [J/),.(0)) 2 f£mJ;/(mJ;-t)J2(Eg-mg) 312dt 
Vcs f~(O) f£mJ./(mJ.-t)J2(E;-mi)3/2dt 
under the assumption that the t dependence of the vector 
form factor is described by a single pole. 8•14 The ratio of 
the integrals is 0.507. While the individual form factors 
Jlf,. (O) and f~ (O) are expected to deviate substantially 
from unity due to SU(4) symmetry breaking, the ratio 
Jlf,. (0)/f~ (O) is expected to deviate from unity 15 by only 
-10% due to SU(3) symmetry breaking. Nevertheless, 
taking Jlf,. (0)/f~ (O) to be unity, the ratio of the KM 
matrix elements is I VcdfVcs I 2 -0.057 :!::8:8?~ ± 0.005, 
where no systematic error is included for the uncertainty 
in Jlf,. (0)/f~ (0), and the statistical error is a two-sided 
68.3% likelihood interval. 16 The systematic error for 
I VcdiVcs I 2 is independent of the detection efficiency and 
the number of tags; only the background subtraction and 
the visual scan contribute. 
We gratefully acknowledge the dedicated efforts of the 
SPEAR storage ring and linear accelerator operating 
staffs, and the continued support of the Directorate of 
the Stanford Linear Accelerator Center for the SPEAR 
high-energy physics program. This work was supported 
in part by the Department of Energy, under Contracts 
No. DE-AC03-76SF00515, No. DE-AC02-76ER01195, 
No. DE-AC03-81ER40050, No. DE-AM03-
1823 
VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
76SF00034, and No. DE-AC02-87ER40318, and by the 
National Science Foundation. 
(a) Deceased. 
1 H. Abramowicz et a/., Z. Phys. C 15, 19 (1982); K. Klein-
knecht and B. Renk, Z. Phys. C 34, 209 (1987). The papers 
are based on analyses of the same data. The first finds 
I Vcd I =0.24 ± 0.03 using an average semimuonic branching 
fraction of (7 .I ± 1.3 )%. The second finds I Vcd I -0.21 ± 0.03 
using an updated estimate for the average semimuonic branch-
ing fraction of (9.3 ± 1.0)%. 
2 B. Guberina et a/. , Phys. Lett. 89B, Ill ( 1979); I. I. Bigi, 
SLAC Report No. SLAC-PUB-4455, 1987 (unpublished). 
3Reference to a state shall henceforth also imply reference to 
its charge conjugate. 
40. Bernstein et at., Nucl. Instrum. Methods Phys. Res., 
Sect. A 226, 301 (1984). 
5J. Adler eta/., Phys. Rev. Lett. 60, 89 (1988). 
6As the four-momentum of the semileptonic decay candidate 
is known, the event can be reconstructed with no kinematic 
ambiguity, in spite of the undetected neutrino. 
7A K~Jr+Jr- can come either from the decay of a D 0 or a 
i5°; hence both electron signs are accepted. 
so. M. Coffman, Ph.D. thesis, California Institute of Tech-
nology, 1986 (unpublished). 
9 J. S. Brown et a/. , N ucl. Instrum. Methods Phys. Res., 
Sect. A 221, 503 (1984). The TOF alone provides more than 
1824 
2.0a 1r-K separation over the entire kinematic range. 
10Showers that start in the first three radiation lengths of the 
calorimeter and deposit more than 0.1 Ge V are classified as 
photons if they are further than 18° from the nearest charged 
track. 
11 If the TOF criteria are removed, one additional 1r-e + v. 
candidate is accepted. 
12J. Adler et at., Phys. Lett. B 196, 107 (1987); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 56, 2136 (1986); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 55, !50 (1985); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 54, 1976 (1986). 
13The statistical probability that 0.53 event (the expected 
background) would produce 7 or more observed events is 
1.5x 10-6• 
14J. C. Anjos et at., Phys. Rev. Lett. 62, 1587 (1989). 
They measure r(D 0-+K-e+v.)/r(D 0-+K-n-+)=0.91 
±0.07±0.11. 
15M. Wirbel, B. Stech, and M. Bauer, Z. Phys. C 29, 637 
(1985); C. A. Dominguez and N. Paver, Phys. Lett. B 207, 199 
(1988); B. Grinstein, M. B. Wise, and N. Isgur, California In-
stitute of Technology-University of Toronto Report No. 
CALT-68-1311, UTPT-85-37, 1985 (unpublished); B. F. L. 
Ward, Nuovo Cimento 98A, 401 (1987). 
16A. G. Frodesen, 0. Skjeggestad, and H. T0fte, Probability 
and Statistics in Particle Physics (Universitetsforlaget, Ber-
gen, 1979). The marginal likelihood function for I Vcd!Vcs 12 is 
obtained from the joint likelihood function for B(D 0 
-+ 1r-e +ve) and B(D 0 -+ K-e + v.). Our point estimate for 
I Vcd!Vcs I 2 is the value which maximizes the marginal likeli-
hood function. 


Measurement of the Branching Fractions for D^0 → π^-e^+v_e and D^0 → + K^-e^+V_e and Determination of │V_(cd)/V_(cs)│^2

VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
Measurement of the Branching Fractions for D 0 ---+ 1r - e + v e and D 0 ---+ K - e + Ve 
and Determination of I Ycd !Yes I 2 
J. Adler, J. J. Becker, G. T. Blaylock, T. Bolton, J.-C. Brient, T. Browder, J. S. Brown, K. 0. Bunnell, 
M. Burchell, T. H. Burnett, R. E. Cassell, D. Coffman, V. Cook, D. H. Coward, F. DeJongh, D. E. Dorfan, 
J. Drinkard, G. P. Dubois, G. Eigen, K. F. Einsweiler, B. I. Eisenstein, T. Freese, C. Gatto, G. Gladding, 
C. Grab, R. P. Hamilton, (a) J. Hauser, C. A. Hensch, D. G. Hitlin, J. M. Izen, P. C. Kim, L. Kopke, A. Li, 
W. S. Lockman, U. Mallik, C. G. Matthews, A. I. Mincer, R. Mir, P. M. Mockett, R. F. Mozley, 
B. Nemati, A. Odian, L. Parrish, R. Partridge, D. Pitman, S. A. Plaetzer, J. D. Richman, H. F. W. 
Sadrozinski, M. Scarlatella, T. L. Schalk, R. H. Schindler, A. Seiden, C. Simopoulos, A. L. Spadafora, 
I. E. Stockdale, W. Stockhausen, W. Toki, B. Tripsas, F. Villa, S. Wasserbaech, A. Wattenberg, A. J. 
Weinstein, S. Weseler, H. J. Willutzki, D. Wisinski, W. J. Wisniewski, R. Xu, andY. Zhu 
(The Mark III Collaboration) 
California Institute of Technology, Pasadena, California 91125 
University of California at Santa Cruz, Santa Cruz, California 95064 
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 
University of Iowa, Iowa City, Iowa 52242 
Stanford Linear Accelerator Center, Standford, California 94309 
University of Washington, Seattle, Washington 98195 
(Received 30 December 1988) 
Measurements of the exclusive branching fractions B(D 0 --+ n-e +v,) and B(D 0 --+ K- e +v,), using 
data collected at the 1f1(3770) with the Mark III detector at the SLAC e + e- storage ring SPEAR, are 
used to determine the ratio of Kobayashi-Maskawa matrix elements I VcdiVcs 12 =0.057 ~8:8H ± 0.005. 
PACS numbers: 13.20.Fc, 12.15.Ff, 14.40.Jz 
Present knowledge of the Kobayashi-Maskawa (KM) 
matrix element Vcd has been derived from a measure-
ment of neutrino-induced charm production. 1 This 
determination, however, depends on the production cross 
sections for D 0 , D +, and to a lesser degree, other 
charmed particles. It also depends on the semimuonic 
branching ratio and fragmentation function of each par-
ticle type. While determinations of I Vcd I using hadron-
ic decays of D mesons are free from uncertainties in the 
production mechanism, they suffer from the effects of in-
terference and final-state interactions. 2 In contrast, 
semileptonic decays are free of these complications. We 
report herein measurements of the branching fractions 
B(D 0 -+ n-e +ve) and B(D 0 - K- e +ve) and use their 
ratio to determine I VcdfVcs I 2. 3 
The data were collected with the Mark III detector 4 at 
the SLAC e + e - storage ring SPEAR near the peak of 
the lf/(3770), which decays predominantly to DD. The 
data contain about 27 700 produced D 0i5° events. 5 Can-
didate events are selected by first reconstructing a i5°, 
called a tag, in the following modes: K + n-, 
K+n-n+n-, K~n+n-, and K+n-n°. The absolute 
branching fractions B (D 0 --+ n-e + Ve) and B (D 0 
--+ K - e + v e ) are then measured by reconstructing these 
decay modes in the system recoiling from the tagged 
-o 6 D. 
measured i5° momentum. All events with a beam-
constrained mass greater than 1.8 GeV/c 2 are retained. 
A signal region is defined from 1. 8 54 to 1. 8 7 4 Ge VIc 2; 
events in a sideband from 1.830 to 1.850 GeV /c 2 are 
used to evaluate the background under the peak. 80% of 
events in the signal region have a unique tag; the 
remainder contain an average of 2.5 tags per event. 
Multiple tags are most often found in the K + n- n° 
mode; they arise from the use of photon candidates 
whose source is hadronic showers or charged-kaon de-
cays. To determine the total number of events with at 
least one tag, we plot in Fig. 1 (a) the beam-constrained 
mass of the tag from the mode having the least back-
ground per event, starting with the lowest-multiplicity 
decay, K + n-, and continuing through K + n- n + n-, 
K~n+n-, and K+n-n°. Multiple K+n-n+n- or 
K~n + n- tags are resolved by selecting the tag whose 
lowest-momentum track has the largest momentum. The 
preferred K + n-n° tag is selected by means of a con-
strained fit of the photons to the n° mass. Figure 1 (a), 
which shows the results of this procedure, contains a sin-
gle entry per event. There are 3636 ±54± 195 events 
(Ntag) above background. 
A D 0-+ n-e +Ve or D 0-+ K- e +ve decay candidate 
recoiling against a tag is required to contain two oppo-
sitely charged tracks, one of which is identified as an 
Tagged events are selected by 
constrained mass, (E6eam- piJo) 112, 
using the beam- electron. The sign of the charge of the lepton must be 
where Pl5o is the opposite the charm of the tag. 7 Electrons are identified 
© 1989 The American Physical Society 1821 
VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
"' 0 
> <I> 
(') 
C\1 
0 
0 
~ 
!!l 
c 
<I> 
> 
UJ 
1500 
1000 
500 
0 
20 
10 
0 
(c) 
2 
0 
1.80 1.84 1.88 
Beam Constrained Mass (GeV/c 2 ) 
FIG. I. (a) Beam-constrained mass of i5° hadronic tags. 
(b) Beam-constrained mass of i5° hadronic tags for K-e +v. 
events. (c) Beam-constrained mass of i5° hadronic tags for 
1r-e + v, events. 
using information from the time-of-flight (TOF) 
counters and the barrel electromagnetic calorimeter. 
For momenta below 0.3 GeV/c, TOF alone is used. 
Above 0.4 GeV /c, an algorithm using shower energy and 
shower shape 8 is used to distinguish electrons from pions. 
Between 0.3 and 0.4 GeV/c, electrons identified by either 
technique are accepted. Electron candidates with a kaon 
TOF identification are rejected. In this analysis, 75% of 
electrons are correctly identified; 7% of muons and 5% of 
pions are misidentified as electrons. 
Two independent methods are used to identify the 
recoiling hadron. The kinematics of a fully reconstruct-
ed semileptonic decay permit the identification of the 
hadron as either a pion or kaon. The quantity U 
=E missing- I Pmissing I' calculated for both the pion and 
kaon hypotheses, is expected to be zero for the correct 
choice since a single massless particle is undetected. For 
events with multiple tags, U is calculated separately for 
each. Monte Carlo studies indicate that the choice of 
the correct assignment has the minimum I U 1. The hy-
pothesis with the smallest value of I U I is accepted, and 
then only if the kinematic identification agrees with the 
TOF identification. 9 For the K- e + Ve analysis, we also 
accept kinematically identified kaons even when no TOF 
information is present. These may be tracks which do 
not enter the TOF system, tracks which have decayed 
before reaching the TOF counters, or tracks which enter 
1822 
~3 
(') 
~ 2 
0 
ci 
~ 
c 
~ 
w 0 
·0.2 0 0.2 
U (GeV) 
FIG. 2. Distribution of U (n °- 1r-e + v. hypothesis) calcu-
lated for n°- 1r-e + v. candidates (histogram), for recon-
structed Monte Carlo n °- 1r-e + Ve decays (solid curve), and 
for the principle background, n°- K- e + Ve decays interpret-
ed as n°-1r-e+v, (shaded). The curves are not normalized 
to the data. 
a counter close to the position of another track. For the 
1r-e + Ve analysis, we require that the pion be identified 
both kinematically and by TOF. 
Next, backgrounds from hadronic and other semilep-
tonic decays of the recoil D 0 must be suppressed. The 
decay D 0-K-1r+ is removed by requiring that the in-
variant mass calculated by interpreting the hadron and 
electron as a kaon and pion be less than 1.7 GeV/c 2• 
Less than 5% of K- e + Ve events fail to meet this re-
quirement. Recoiling decays with neutral pions (e.g., 
D 0- K -Kol + v1) are suppressed by rejecting events 
with photons other than those used in the hadronic tag. 
A visual scan is performed to prevent the elimination of 
events with showers caused by hadronic interactions or 
hadronic decays: Six additional K - e + Ve events contain-
ing hadronic showers classified as photons are recov-
ered. 10 No additional 1r-e + Ve events are recovered by 
the scan. 
Seven 1r-e + Ve candidates 11 and 56 K- e + Ve candi-
dates are retained, and their U distributions are shown in 
Figs. 2 and 3, respectively. Monte Carlo simulations are 
used to predict signal and background U distributions. 
The solid curves in Figs. 2 and 3 are the expected distri-
butions for reconstructed signal events. The shaded area 
in Fig. 2 shows the expected distribution for D 0 
> 
~ 10 
0 0.2 
U (GeV) 
FIG. 3. Distribution of U (n°-K-e+v. hypothesis) cal-
culated for n°- K- e +ve candidates (histogram), for recon-
structed Monte Carlo n °- K - e + ve decays (solid curve, nor-
malized to the data), and for the background ( x I 00) from 
n°- K -Jr0e + Ve decays (shaded). 
VOLUME62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
---+ K- e + Ve events, where each event is interpreted in-
correctly as D 0 ---+ 1r-e + Ve. The shaded area in Fig. 3 
shows the expected feed-down of K -1r0e + ve events with 
an undetected 1r0 into the K- e + Ve sample. The require-
ment I U I < 0.1 Ge V is imposed to reduce these back-
grounds and other backgrounds with undetected massive 
neutral particles. One K- e + Ve candidate is rejected by 
this cut. 
The beam-constrained mass distributions forK- e + Ve 
and 1r-e + Ve events passing the particle identification 
and background rejection requirements are shown in 
Figs. 1 (b) and 1 (c). Events in the sideband region are 
used to evaluate the background due to incorrectly 
reconstructed tags. A Monte Carlo simulation incor-
porating a complete model of D 0 decays 5•12 is used to 
evaluate backgrounds occurring with a correct tag. 
Backgrounds are enumerated in Table I. The effic-
iencies for reconstructing semielectronic decays in the 
TABLE I. Number of background and observed events. 
Decay 
K -e +v, 
K- J1 +vi' 
n--e+v, 
n-- J1 +vi' 
1r + 1r -n-o 
K -n-+ 
K*-e+v, 
K-p+ 
K*-n-+ 
Sideband 
N background 
Nobserved 
0.44 
0.03 
N.A. 
N.A. 
0.03 
0.04 
0 
0.53 
7 
N.A. 
N.A. 
0.06 
0.02 
0.05 
0.13 
0.19 
0.06 
1.51 
55 
recoil to a tag are e,.-e+v, ==0.38 and eK-e+v, =0.37. The efficiencies for reconstructing semimuonic decays as their cor-
responding semielectronic decays are e,-JJ+v~' ==0.050 and EK-JJ+v~' =0.052. Lepton universality implies nearly identical 
semielectronic and semimuonic branching fractions; semimuonic events need not, therefore, be subtracted as a back-
ground. Instead, acceptance and background corrections are made using the expression 
B(DO- X- e + Ve) = Nobserved- Nbackground [1- Etag'I:.B(D 0 - tag modes) ) ' 
<ex-e+v. +ex-JJ+vi')Ntag 2 
where X is a 1r or K and Etag is the average tag reconstruction efficiency. We find 
B(D 0 - 1r- e +ve) =(0.39:!:8:H ± 0.04)% 
(Ref. 13) and 
B(D 0 ---+ K- e+ve) =(3.4±0.5 ±0.4)%. 
Systematic errors arise from uncertainties in the simulation of backgrounds (50% of the subtracted background), deter-
mination of the number of tags (5.3%), electron identification efficiency (2%), photon reconstruction efficiency (5%), 
visual scan efficiency (5%), track reconstruction efficiency (2%), and TOF identification of hadrons (5%). These errors 
are added in quadrature. The technique of tagging with hadronic i5° decays eliminates any dependence on the charm 
production cross section or the integrated luminosity. 
The ratio I Vcd /Vcs I 2 is obtained from B (D 0 ---+ 1r-e + Ve) and 
I 
Vcd 12 = [J/),.(0)) 2 f£mJ;/(mJ;-t)J2(Eg-mg) 312dt 
Vcs f~(O) f£mJ./(mJ.-t)J2(E;-mi)3/2dt 
under the assumption that the t dependence of the vector 
form factor is described by a single pole. 8•14 The ratio of 
the integrals is 0.507. While the individual form factors 
Jlf,. (O) and f~ (O) are expected to deviate substantially 
from unity due to SU(4) symmetry breaking, the ratio 
Jlf,. (0)/f~ (O) is expected to deviate from unity 15 by only 
-10% due to SU(3) symmetry breaking. Nevertheless, 
taking Jlf,. (0)/f~ (O) to be unity, the ratio of the KM 
matrix elements is I VcdfVcs I 2 -0.057 :!::8:8?~ ± 0.005, 
where no systematic error is included for the uncertainty 
in Jlf,. (0)/f~ (0), and the statistical error is a two-sided 
68.3% likelihood interval. 16 The systematic error for 
I VcdiVcs I 2 is independent of the detection efficiency and 
the number of tags; only the background subtraction and 
the visual scan contribute. 
We gratefully acknowledge the dedicated efforts of the 
SPEAR storage ring and linear accelerator operating 
staffs, and the continued support of the Directorate of 
the Stanford Linear Accelerator Center for the SPEAR 
high-energy physics program. This work was supported 
in part by the Department of Energy, under Contracts 
No. DE-AC03-76SF00515, No. DE-AC02-76ER01195, 
No. DE-AC03-81ER40050, No. DE-AM03-
1823 
VOLUME 62, NUMBER 16 PHYSICAL REVIEW LETTERS 17 APRIL 1989 
76SF00034, and No. DE-AC02-87ER40318, and by the 
National Science Foundation. 
(a) Deceased. 
1 H. Abramowicz et a/., Z. Phys. C 15, 19 (1982); K. Klein-
knecht and B. Renk, Z. Phys. C 34, 209 (1987). The papers 
are based on analyses of the same data. The first finds 
I Vcd I =0.24 ± 0.03 using an average semimuonic branching 
fraction of (7 .I ± 1.3 )%. The second finds I Vcd I -0.21 ± 0.03 
using an updated estimate for the average semimuonic branch-
ing fraction of (9.3 ± 1.0)%. 
2 B. Guberina et a/. , Phys. Lett. 89B, Ill ( 1979); I. I. Bigi, 
SLAC Report No. SLAC-PUB-4455, 1987 (unpublished). 
3Reference to a state shall henceforth also imply reference to 
its charge conjugate. 
40. Bernstein et at., Nucl. Instrum. Methods Phys. Res., 
Sect. A 226, 301 (1984). 
5J. Adler eta/., Phys. Rev. Lett. 60, 89 (1988). 
6As the four-momentum of the semileptonic decay candidate 
is known, the event can be reconstructed with no kinematic 
ambiguity, in spite of the undetected neutrino. 
7A K~Jr+Jr- can come either from the decay of a D 0 or a 
i5°; hence both electron signs are accepted. 
so. M. Coffman, Ph.D. thesis, California Institute of Tech-
nology, 1986 (unpublished). 
9 J. S. Brown et a/. , N ucl. Instrum. Methods Phys. Res., 
Sect. A 221, 503 (1984). The TOF alone provides more than 
1824 
2.0a 1r-K separation over the entire kinematic range. 
10Showers that start in the first three radiation lengths of the 
calorimeter and deposit more than 0.1 Ge V are classified as 
photons if they are further than 18° from the nearest charged 
track. 
11 If the TOF criteria are removed, one additional 1r-e + v. 
candidate is accepted. 
12J. Adler et at., Phys. Lett. B 196, 107 (1987); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 56, 2136 (1986); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 55, !50 (1985); R. M. Bal-
trusaitis et at., Phys. Rev. Lett. 54, 1976 (1986). 
13The statistical probability that 0.53 event (the expected 
background) would produce 7 or more observed events is 
1.5x 10-6• 
14J. C. Anjos et at., Phys. Rev. Lett. 62, 1587 (1989). 
They measure r(D 0-+K-e+v.)/r(D 0-+K-n-+)=0.91 
±0.07±0.11. 
15M. Wirbel, B. Stech, and M. Bauer, Z. Phys. C 29, 637 
(1985); C. A. Dominguez and N. Paver, Phys. Lett. B 207, 199 
(1988); B. Grinstein, M. B. Wise, and N. Isgur, California In-
stitute of Technology-University of Toronto Report No. 
CALT-68-1311, UTPT-85-37, 1985 (unpublished); B. F. L. 
Ward, Nuovo Cimento 98A, 401 (1987). 
16A. G. Frodesen, 0. Skjeggestad, and H. T0fte, Probability 
and Statistics in Particle Physics (Universitetsforlaget, Ber-
gen, 1979). The marginal likelihood function for I Vcd!Vcs 12 is 
obtained from the joint likelihood function for B(D 0 
-+ 1r-e +ve) and B(D 0 -+ K-e + v.). Our point estimate for 
I Vcd!Vcs I 2 is the value which maximizes the marginal likeli-
hood function. 


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Measurement of the Branching Fractions for D^0 → π^-e^+v_e and D^0 → + K^-e^+V_e and Determination of │V_(cd)/V_(cs)│^2

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