. . . _

SLAC-PUB-95-6746

BEPC-EPl-95-01

January 1995

A.Direct Measurement of the Pseudoscalar Decay Constant, fo,* _

J. 2. Bai,’ 0. Bardon,’ I. Blum,” A. Breakstone,g T. Burnett,i2 G. P. Chen,i H. F. Chen,4

i J. Chen5 S. J. Chen,l S. M. Chen,r Y. Chen,i Y. B. Chen,l Y. Q. Chen,’ B. S. Cheng,r

R. F. Cowan,’ H. C. Cui,’ X. Z. Cui,’ H. L. Ding,’ Z. Z. Du,r W. Dunwoodie,’ X. L. Fan,’

J. Fang,.r M. Fero, 6 C. S. Gao,l M. L. Gao,i S. Q. Gao,l W. X. Gao,r P. Gratton,il

J. H. Gu,r S. D. Gu,l W. X. Gu,r Y. F. Gu,i Y. N. Guo,l S. W. Han,’ Y. Han,r

F. A. Harris,g M. Hatanaka, J. He,i K. R. He,’ M. He,7 D. G. Hitlin,3 G. Y. Hu,l

H. B. Hu,’ T. Hu,’ X. Q. Hu,r D. Q. Huang,l Y. Z. Huang,’ J. M. Izen,ir Q. P. Jia,5

C. H. Jiang,i Y. Jin,l L. Jones,3 S. H. Kang,r M. H. Kelsey,3 B. K. Kim,ri Y. F. Lai,’

H. B. Lan,’ P. F. Lang,’ A. Lankford, lo F. Li,l J. Li,r P. Q. Li,l Q. Li,7 R. B. Li,’ W. Li,l

W. D. Li,i W. G. Li,r X. Li,r X. N. Li,i S. Z. Lin,i H. M. Liu,i J. H. Liu,l Q. Liu,l

R. G. Liu,’ Y. Liu,’ Z. A. Liu,’ X. C. Lou,ll B. Lowery,‘l J. G. Lu,’ A. M. Ma,’

E. C. Ma,’ J. M. Ma,l H. S. Mao, r Z. P. Mao,’ R. Malchow,5 M. Mandelkerqi’

X. C. Meng,r H. L. Ni,’ J. Nie,’ S. L. Olsen,g J. Oyang,3 D. Paluselli,g L. J. Pan,g

J. Panetta,3 F. Porter,3 E. Prabhakar,3 N. D. Qi,’ Y. K. Que,’ J. Quigley,’ G. Rang,’

. - M. Schernau,l’ B. Schmid,l’ J. Schultz, lo Y Y. Shao,l D. L. Shen,l H. Shen,l X. Y. Shen,r

H. Y. Sheng,i H. Z. Shi,i X. R. Shi,3 A. Smith,” E. Soderstrom,’ X. F. Song,l

J. Standifird ii D. Stoker lo F. Sun i H. S. Sun,’ S. J. Sun,r J. Synodinos,’ Y. P. Tan,’

S. Q. Tang,l W. Toki,5 G.’ L. Tong,’ E. Torrence,’ F. Wang,i L. S. Wang,r L. Z. Wang,l ’ M. Wang,’ P. Wang,’ P. L. Wang,’ S. M. Wang,’ T. J. Wang,r W. Wang,’ Y. Y. Wang,l

S. Whittaker, R. Wilsoq5 W. J. Wisniewski,13t D. M. Xi,’ X. M. Xia,’ P. P. Xie,’

D. Z. Xu,l R. S. Xu,i Z. Q. Xu, ’ S. T. Xue,l R. Yamamoto,’ J. Yan,l W. G. Yan,’

C. M. Yang,’ C. Y. Yang,’ W. Yang, l H. B. Yao,l M. H. Ye,’ S. Z. Ye,i C. S. Yu,’

C. X. Yu,i Z. Q. Yu,’ C. Z. Yuan,’ B. Y. Zhang,’ C. C. Zhang,l D. H. Zhang,’

H. L. Zhang,i J. Zhang,l J. W. Zhang,’ L. S. Zhang,l S. Q. Zhang,’ Y. Zhang,r

Y. Y. Zhang,i D. X. Zhao,l J. W. Zhao,i M. Zhao,i P. D. Zhao,l W. R. Zhao,i W. X. Zhao,l J. P. Zheng,l L. S. Zheng,’ Z. P. Zheng,l G. P. Zhou,r H. S. Zhou,r Li Zhou,l

X. F. Zhou,i Y. H. Zhou,’ Q. M. Zhu,’ Y. C. Zhu,’ Y. S. Zhu,’ B. A. Zhuang,i G. Zioulas” - The BES Collaboration

‘Institute of H’g i h Energy Physics, Beijing 100039, People’s Republic of China

2Boston University, Boston, Massachusetts 02215

3California Institute of Technology, Pasadena, California 91125

4China’s University of Science and Technology, Hefei 230026, People’s Republic of China . 5 Colorado State University, Fort Collins, Colorado 80523

6h4assachusetts Institue of Technology, Cambridge, Massachusetts 02139

7Shandong University, Jinan 250100, People’s Republic of China

‘Stanford Linear Accelerator Center, Stanford, California 94309

’ Univers y f it o Hawaii, Honolulu, Hawaii 96822

-

1

lo University f 0 California at Irvine, Irvine, California 92717

l1 University of Texas at Dallas, Richardson, Texas 75083-0688

l2 University f o Washington, Seattle, Washington 98195

13Superconducting Sup ercollider Laboratory, Dallas, Texas 75237-3946

(22 December 1994)

Abstract

The Beijing Spectrometer (BES) p ex eriment has observed purely leptonic

decays of the D, meson in the reaction e+e- + D$D; at a c.m. energy

of 4.03 GeV. Three events are observed in which one D, decays hadronically

to +r, li*“K, or K”li, and the other decays leptonically to ova or l-v,.

With the assumption of p-r universality, values of the branching fraction

Br(D, + PV~) = 1.5?~:~+~:~ %, and the D, pseudoscalar decay constant,

f& = 4.3$;:;f;:; x lo2 MeV, are obtained.

Submitted to Physical Review Letters

*Work supported in part by the National Natural Science Foundation of China under Contract

_ No. 19290400 and the Chinese Academy of Sciences under contract No. KJ85 (IHEP); by the

Department of Energy under Contract Nos. DE-FG02-91ER40676 (Boston University), DE-FGOS-

92ER40701 (Caltech), DE-FG03-93ER40788 (Colorado State University), DE-AC02-76ER03069

(MIT), DE-AC03-76SF00515 (SLAC), DE-FG03-91ER40679 (UC Irvine), DE-FG03-94ER40833

(U Hawaii), DE-FG05-92ER40736 (UT Dallas), DE-AC35-89ER40486 (SSC Lab); by the U.S.

National Science Foundation, Grant No. PHY9203212 (U niversity of Washington); and by the

Texas National Research Laboratory Commission under Contract Nos. RGFYSlB5, RGFY92B5

(Colorado State), and RCFY93-316H (UT Dallas).

tpresent address: Stanford Linear Accelerator Center, Stanford, California 94309.

2

Purely leptonic decays of the D, meson proceed via the annihilation of the charm and

anti-strange quarks to a virtual W boson. The rate of this process is determined by the

quark wavefunction at the origin, and is characterized by the pseudoscalar decay constant,

fD,. The leptonic decay width of the D, can be written as [l]

(1) -

where mD, is the D, mass, me the lepton mass, V,. = 0.974 is the c+s CKM matrix element

: [a], and GF is the Fermi constant.

Predictions for fD, and the Cabbibo-suppressed decay constant of the charged D meson,

fD, varying from 90 to 350 MeV, have been made using various theoretical models [3-71.

Many models can more reliably predict the ratios fo, : fD : fs, where fB is the decay

constant for the charged B meson [8]. S ince fB relates measured quantites, such as B’--p

mixing, to CKM matrix elements, its determination is of considerable importance. Mea-

surements of the charm decay constants will help discriminate among the different mod-

els and improve the reliability of estimates of fs. The first experimental measurement,

fo, = 232 f 45 & 20 f 48 MeV, was reported by the WA75 group [9], using muons from D,

leptonic decays seen in emulsions; the third error is due to uncertainty in the D, production

rate. The CLEO group [lo] measured fD, = 344 f 37 f 52 f 42 MeV using the decays

-0; --+ a, Ds t pv; here the third error is due to uncertainty in the normalizing D, branching fraction.

In this paper, direct, model-independent measurements of fD, and the D, leptonic . - branching fraction are reported.

Beijing e+e- Collider (BEPC), The data were obtained using the BES detector at the

and correspond to an integrated luminosity of 22.3 pb-i

(obtained from large angle Bhabha scattering events) at c.m. energy 4.03 GeV. This is just

above efe- + Q!O; threshold, but below that for oB+D; [ll]. Thus, if a D, meson

decay is fully reconstructed in a given event, the recoil system corresponds to the decay of

the charge conjugate D, meson. Events for which one D, is fully reconstructed are termed

singly-tagged. For such a data sample, the detection of the decays D, + ova or 7~~ among

the recoil systems permits an absolute measurement of fD, and the leptonic branching frac-

tions.

The BES is a conventional cylindrical detector, which is described in detail in ref. [la].

A four-layer central drift chamber surrounding the beampipe provides trigger information.

Charged tracks are reconstructed in a forty-layer main drift chamber (MDC) with a momen-

.tum resolution of 1.7%dv (p in GeV/c), and energy loss (dE/dz) resolutions of 8.5% for -

Bhabha electrons and 11% for hadrons. Scintillation counters provide time-of-flight (TOF)

w measurements, with resolutions of - 330 ps for Bhabha events and - 450 ps for hadrons.

A 12-radiation-length, lead-gas barrel shower counter (BSC), operating in limited streamer

mode, measures the energies of electrons and photons over N 80% of the total solid angle.

A solenoidal magnet provides a 0.4 T magnetic field in the central tracking region of the

detector. Three double-layer muon counters (MUC) instrument the magnet flux return, and

serve to identify muons of momentum greater than 500 MeV/c. They cover - 68% of the

total solid angle with longitudinal (transverse) spatial resolution of 5 cm (3 cm).

In this experiment, singly-tagged D, mesons are detected via hadronic decay to &r,

K*“IC, or li’Ol(, with 4 + li’+li’-, @ --+ K-a+ and li’O + Kg -+ x+T-. For a candidate -.

3

three-charged-track combination, each track must be well-reconstructed and consistent with

an origin in the interaction region (candidate pions from K$J decay need not satisfy the latter

requirement). In addition, the dE/d x and TOF information associated with each track must

be consistent with the assigned mass interpretation with a confidence level > 0.1%. Finally,

if the confidence level as a kaon is greater than that as a pion, the track is considered to be

a kaon, and vice versa.

With the resulting mass assignments, the energy sum over the candidate tracks may be

calculated; for particle-antiparticle production, this energy should be close to that of the

beam. Requiring that the energy difference be < 50 MeV selects such events without bias

’ in mass, and effectively suppresses background from D+ decay. In order to improve the

invariant mass resolution, surviving candidates are subjected to a one-constraint (1-C) fit

requiring overall event four-momentum balance and that the candidate and recoil systems

have the same (but unspecified) invariant mass. Candidates yielding fit confidence levels

> 20% are retained, and the decay mode to &r, K*“h’, or li’OK defined by requiring that

the invariant mass of the $ (li’+K-), fl (K-n+), or li’O (~T.+T-) be within 25, 50 or 15

MeV, respectively, of nominal [a]. For the I(“” sample, significant background reduction is

achieved by further requiring ) cos 8K] > 0.4, where t9K is the helicity angle of the I(- in the

K*V rest frame. Similarly, background in the h’O sample is reduced by requiring that the - K” have a significant flight-path whose direction is consistent (within 26 degrees) with the

-. -K” momentum vector.

The resulting distributions in invariant mass, calculated using the momentum vectors

from the 1-C fit, are shown in Fig. 1; each exhibits a clear signal at the D, mass position.

1- An unbinned maximum likelihood fit [13] to the combined distribution of Fig. l(d) yields a

singly-tagged 0; meson signal of 94.3f12.5 events, and a D, mass value 1968.7&0.6(stat.) f

0.5(syst.) MeV.

The search for D, leptonic decay candidates among the systems recoiling against singly-

tagged D, candidates includes all of the events of Fig. l(d), not only those in the D, signal

region. For this sample, the recoil system is required to contain a single, vertex-associated

charged track of charge opposite that of the tagging system. Events containing at least one

isolated photon [14] are removed, and for the remaining events the recoil charged track is

subjected to the following lepton identification criteria.

An electron candidate is required to have momentum 2 400 MeV/c and direction

] cos 191 5 0.75, with TOF and dE/dn: measurements consistent with the electron hypothesis.

The TOF-measured velocity of the track must be > 0.7c, and the measured &Y/&r should be

within 4g of the expected value for an electron. The energy deposition in the BSC must be

-consistent with that expected for an electron in both magnitude and distribution in depth.

w Applying these criteria to radiative Bhabha scattering events leads to an identification ef-

ficiency of more than 80% over the full momentum range, and - 90% for electrons with

momenta above 1 GeV/c. Known pions are mis-identified as electrons at a rate of N 5%,

with a modest momentum dependence.

-

A muon candidate is required to have momentum between 550 and 1250 MeV/c and

direction I cos 81 < 0.65, with TOF and dE/d II: information consistent with the muon inter-

pretation. There must be hits in the MUC detector which are well associated with the track

in transverse projection; the required number of hits is momentum dependent. For a sample

of cosmic rays, the identification efficiency is - 85%, while for a sample of well-identified

4

pions the average mis-identification rate is N 4%.

Events satisfying the above selection criteria are subjected to a visual scan. This serves

to remove events containing cosmic rays as well as those having unreconstructed low-angle

track(s), which are typically recognized by a pattern of hits in the CDC and the innermost

two layers of the MDC.

The distributions of tagging D, mass for the events of Fig. l(d) which have an identified

single electron or muon candidate are shown in Figs. 2(a) and (b), respectively. The char-

acteristics of these events are summarized in Table I; in each case the D, and sub-system

masses agree well with the expected values.

From Monte Carlo simulations, it is found that the detection efficiencies for the tagging

and leptonic D, decays are independent, to a good approximation. The expected number

of DQ 0; events for which one D, is from the signal region of Fig. l(d) and the other

corresponds to a particular leptonic decay mode is then obtained as the product of the

singly-tagged signal, the D, branching fraction to the mode in question, and the detection

efficiency for that mode. The latter efficiency is found to be 51% for the decay D, + pvp,,

6.3% for D, + TY,, r -+ pvv, and 8.2% for D, + ~TV,, r --+ eyy, including the T branching

fractions [a]. S ince the D, decay rate to ev, is negligible, leptonic events with an electron

recoil result only from the 7 decay sequence.

A Monte Carlo study shows that background contributions to the leptonic decay samples

result mainly from hadron mis-identification in the processes D, + KZK and D, + TV, with r + TV,. In the present analysis, this contribution is estimated from the singly-tagged

events in the D, signal region of Fig. l(d) which h ave a single recoil track satisfying neither

the electron nor the muon identification criteria. The tagging mass distribution for these

events is shown- in Fig. 2(c); seven events in the D, signal region satisfy the momentum

and polar angle criteria for electrons, while only six satsify those for muons. The mis-

identification rates discussed previously yield background estimates of 0.35 events for the

electron sample and 0.24 for the muon sample (of which 0.04 contribute to D, + pvp).

The values of the D, leptonic branching fractions are estimated by maximizing a like-

lihood function containing a Poisson distribution factor for the expected number of events

(including background), and a factor for the expected missing-mass-squared distribution for

‘each channel (the distributions for D, + ova DS. D, -+ TV,, 7 --+ ,LWV are well separated).

Maximizing the likelihood function for the branching fractions to pvp and rv, independently,

the values Br(D, + pvcL) = 2.0?::“7 % and Br(D, + TY,) = 12’;: % are obtained. Assum-

ing p--r universality and the theoretical prediction of the ratio B~(Q-~~)/B+v~) = 9.74,

the result is Br(D, + ,w~) = 1.5?~:~(stat.)‘~:~(syst.) %.

If in addition, the relation

-

is used with Eq. (l), the likelihood function may be maximized with respect to fo, directly,

as shown in Fig. 3. The result is

f~, = 4.3f~:i;t~:~ x lo2 MeV .

The first errors are statistical, and correspond to the 68.3% confidence interval shown in

Fig. 3; the second errors are systematic, and result from uncertainties in lepton mode de-

tection efficiencies, background estimates, and the D, lifetime [a]. -.

Although the branching fraction and fo, values obtained in the present analysis have

sizable uncertainties, it should be emphasized that the results are independent of luminosity

and D$D; cross section, and do not require model-dependent assumptions. The central

value of fo, is larger than, but consistent with current theoretical predictions, which range

from 90 to 350 MeV.

-We would like to thank the staff of the BEPC accelerator, the IHEP Computing Cen- _

ter, and the Texas High Performance Computing Center (formerly PDSF). We thank Prof.

Chaohsi Chang for useful discussions of D, physics.

REFERENCES

[l] See, for example, J. L. Rosner, Phys. Rev. D42, 3732 (1990); C. H. Chang and

Y. Q. Chen, Phys. Rev. D46, 3845 (1992) and Phys. Rev. D49, 3399 (1994).

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[7] E. V. Shuryak, Nucl. Phys. B198, 83 (1982); R. R. Mendel and H. D. Trottier, Phys.

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f - (1983).

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[l-l] Throughout the paper, reference to a particular charge configuration implies reference

to the charge conjugate configuration as well.

[12] J. Z. Bai et al., Nucl. Instr. and Methods A344, 319 (1994); J. Z. Bai et al., Phys. Rev.

Lett. 69, 3021 (1992);

[13] The D, ‘g 1 si na is represented by a Gaussian distribution, and the background by a

polynomial. Additional background in the I(OK mode resulting from D*D events is

represented by a second Gaussian at N 1940 MeV.

[14] An isolated photon is defined as an e.m. shower of energy > 60 MeV and separated by

at least 18 degrees from the direction of the nearest charged track.

I :

TABLES

TABLE I. Three Candidates for D, Leptonic Decay

1 Event 1 2 3 I

Tagging D, Decay

Subsystem mass (MeV) 1019.3 873.4 491.5 -

D, Mass (MeV) 1970.2 1970.9 1969.0

Recoil Lep t on P- P- e-

plepton (MeV/c) 751 1216 489

M$,, (GeV2) 0.778 -0.115 1.627

D, Leptonic Decay 4P 3v) P w( e 3~)

. -

FIGURES

20 15 20

> 010 $5 10

-so 0 E $10 40

w5 20

. 0 1.8 1.85 1.9

0 1.95 2 1.8 1.85 1.9 1.95 2

D, Candidate Mass (GeV) FIG. 1. The invariant mass distributions, calculated using 1-C fit momentum vectors, for (a)

&r, (b) K*VK, and (c) K°K D, decay candidates; the combined distribution is shown in (d), where

the curve corresponds to the fit described in the text.

. -

2.5 (c) &A recoil eza p > 400 MeV/c

KXI p > 550 MeV/c

1.85 1.9 1.95

D, Candidate Mass (GeV) FIG. 2. The distribution of Fig. l(d) re q uiring that the recoil system consist of a single charged

track identified as (u) an electron; (b) a muon; (c) neither an electron nor a muon. Shading in

( )’ d’ t - ‘g 1 g c m ma es si na re ion events which satisfy the lepton kinematic requirements described in the

text.

9

0 0 200 400 600 800 1000

f Ds tMeV) FIG. 3. The variation of the normalized likelihood function with respect to fD,, under the

assumption of p--r universality; the unshaded area under the curve denotes the 68.3% confidence

interval.

. -

10