Nuclear Physics B (Proc. Suppl.) 13 (1990) 227-232 227 North-Holland

SEMILEPTONIC DECAYS OF CHARMED MESONS

M.S. Witherell

University of California, Santa Barbara, CA 93106

I review the experimental status of the semileptonic decays of charm. There are new results on decay rates, polarization, and Cabibbo-suppressed decay.

1. INTRODUCTION

SemUeptonic decays of heavy quarks are of par-

ticular interest because they are the easiest decays

to interpret. For this reason, they are used to de-

termine the elements of the Kobayashi-Maskawa

matrix. For the case of charm decay, the elements

are constrained in the three-generation model to be

Vcs = 0.9743 ± 0.0006 and Vcd = 0.220 :I: 0.0002.1

At the present level of theoretical and experimental

knowledge, we can only check these values at a fairly

crude level. For comparison, the effect of the third

generation on Vcs is only 0.002, which is almost two

orders of magnitude better than the direct experi-

mental measurement.

Because the K-M matrix elements are so precisely

known, in the three-generation scheme, we can use

the measurements to tune up the form factor models.

These models should then be even more accurate in

B decays, and can be used for precise determinations

of Vcb and Vub, eventually. At the same time, the

form factors are of interest themselves as a source

of information about the wave functions of mesons

containing heavy quarks.

Exclusive semileptonic decays of charmed mesons

had been more difficult to measure than nonleptonic

decays, because no narrow mass peaks are formed.

Different techniques have been developed by E691

and Mark IH, however, to achieve good background

rejection and clean signals for these decays. The ba-

sic measurements are getting to be quite good, and

the attention is turning to more detailed measure-

ments, such as angular distributions.

The description of semileptonic decay is straight-

forward. It is assumed that it p r ~ e e ~ "..by specta-

tor decay only. In the weak interaction the charmed

quark decays c --* s(d)e +re and the light antiquark

q has no effect. All strong interaction effects are con-

tained in the form factor, which describes the prob-

ability for the sq system to be bound as a K, K*,

or other hadronic state. A simple isospin argument

shows that F(D + --* X0e+v) = F(D 0 --, X-e+~,) for

each final state, in spite of the very different lifetimes.

I will thus use partial rates rather than branching ra-

tios in comparing results with theory.

2. INCLUSIVE DECAYS

We have had for some time good measurement

from Mark HI on the inclusive semileptonlc decays. 2

They measure B(D o --* e+X) = (7.5 -I- 1.1 -I- 0.4)~

and B(D + ---, e+X) = (17.0 4- 1.9 ± 0.?)~. These can

be .combined with the lifetime measurements from

E6~13 to calculate the decay rate, r(D ° --, e+X) =

(17.4 ± 2.5 ± o.9}. m I0 s -1, and 1"(D + -, e+X} =

(lS.Z ± 1.8 ± s.e) • lO l° s -1. As expected, r(D ° --,

e+X) = r(D + -, e+X), and the average value 1"(D --~

e+X) = (16.3 ± 1.5). 10 I0 s -1.

In a simple quark decay picture,

G s _5 f ( ~ ) ,

where the function f corrects for the finite mass of the

strange quark and is about 0.5. This formula gives

the right answer for mc = 1.6 GeV, which is a rea-

sonable value. Unfortunately, the dependence on the

fifth power of the charmed quark mass means that

the rate varies by a factor of 2 for a change of 0.2

GeV in the quark mass. To do better, we must use

0920-5632/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

228 M.S. Witheteli/Semileptonic decays of charmed mesons

exclusive decays.

3. EXCLUSIVE DECAYS

The amplitude for Cabibbo-favored semileptonic

decays can be written

ACF = ~22 Vcs L ~ H~

where L~ and H/z are the leptonic and hadronic cur-

rents, respectively. For decay into a pseudesc~lar X,

D --* Xe~,, Hp = (PD + Px)p fx( t ) , in the limit of

small lepton mass. The momentum transfer variable

t = (PD -- PX) 2 is just equal to the square of the

virtual W mass, M2v. There is jdst one vector form

factor, fx( t ) , needed to describe the decay. Often one

assumes the t-dependence with a single pole form, f+X(t)=fXt0~[ 1 1 + ~ / [1-t-:~yJ' where My is the mass of the

lowest c~ resonance with JP ----- 1 - , MD~ = 2.1 GeV.

More generally, this serves as a simple parameteri-

zation of the t-dependence. Assuming a mass of 2.1

GeV, the decay rate can be expressed

r (D ° -* K-e+v) -- Iv=12lf+X(0)l 2 15.3-1010S -1 ,

where we use the value of the form-factor at t = 0 as

the normalization parameter.

A measurement for D O --* K-e+~, was recently

published from the Fermilab charm photoproduc-

tion experiment E6914 We looked at the decay chain

D*+ k_~ ~r+D 0, D O .~ K-e+~,e. We require a K - e +

pair from the secondary vertex, in association with a

~r + from the primary. The electron identification ef-

ficiency is 72%, and the mlsidentification probability

is 0.5%. Assuming that the Kx comes from the de-

cay D O --. K - e + v , one can calculate the D~r mass.

There is a clear excess in the right-sign spectrum at

the D* mass, with a total of 250 events. The result-

ing branching ratio and rates are shown in Table 1.

The t-distribution is also measured, and a fit to the

single-pole form gives a good fit with My = 2.1 +0.4 -0.2

GeV/c ~.

The Max~ [ ] collaboration has also measured

D O -* K - e + v in double-tagged events, in which

Table 1. Results for D O --~ K - e + v

Branching Ratio Decay Rate (~) (1010s -1)

E691 3.8 4- 0.5 4- 0.6 8.8 -I- 1.2 -I- 1.4 Mark IH 3.4 4- 0.5 -t- 0.4 7.8 4- 1.2 4- 0.4 Average 3.5 4- 0.5 8.2 -I- 1.2

m

the D O is observed in one of a number of hadronic

decays. 5 The electron identifcation efficiency is 75%,

and the misidentification probability is 5%. The vari-

able U = Emiss - [Pmiss[ should be 0 for a single

missing neutrino. Figure I shows the U distribution

and a Monte Carlo fit. The shaded region shows the

shape expected for D O -* K-~r0e+v, but at 100 times

the expected rate. The very clean signal of 56 K - e + v

events corresponds to the results shown in Table 1.

~ 1 0 -

O d ~ " 5 - C

uJ 0 =0.2

12-88 6218A3

' I , I

0

U

K-e*v e

0.2

(GeV)

FIGURE 1

Distribution of U calculated for D O --~ K-e+ve can- didates from Mark III (histogram) for Monte Carlo events (curve), and for the background (xl00) from D O --* K-Tr0e+ve (shaded).

The results from the two experiments agree and

a weighted average gives B(D 0 --, K-e+~,) = (3.5 4-

0.5)~ and a decay rate of B(D 0 - , K - e + v ) = (8.2 +

1.3) • 101°s-1. Plugging this into the decay rate for-

mula above gives the result [fK(0)[2[Vcs[ -~ = 0.54 +

0.08. Assuming [Vcsl = 0.975, the best measure-

ment of fK(0) = 0.75 4- 0.05. This agrees well with

predictions of Wirbel, Stech, and Bauer 0 (0.76) and

Dominguez and Paver 7 (0.75). There are also early

results from lattice gauge calculations, some of which

were discussed at the conference. 8 The basic result

M.S. Witherell / Semileptonic decays of charmed mesons 229

is that there is good agreement of the experimen-

tal result with the calculated form factor, assuming

[vcs[ = cos 0c.

The other dominant Cabibbo-favored dec~y is

D -4 K~rev. The first goal is to measure the decay

rate for D --+ K*ev, and compare it to the calcu-

lations. The second is to measure the size of non-

resonant Klreu, and thus get a first measure of the

importance of hadronic final states other than the K

and K*. The general picture from form factor models

is that 6,9 the K* to K ratio should be greater than 1.

The D + --* K-~r+e+Ve rate has been measured in

E691.10 Although the D* cut available for D°decay is

not available, the vertex cuts are particularly effective

because of the long D + lifetime. There is a signal

of 250 events over 62 background as measured with

the wrong sign (K-lr+e - ) sample. With tighter cuts

on electron-identification and vertex isolation, the

numbers are 155 signal and 14 background.

The K~r mass spectra for the two samples are

shown in Figure 2. There is a clean K* peak, which

clearly dominates the signal. The background con-

tribution, averaged over the K* width, is about 10~

with the standard cuts and 4 ~ with the tight cuts.

The results of the fit are shown in Table 2. Less than

20~ of the decays are nonresonant, which corresponds

to a very small fraction of the inclusive semileptonic

decay rate. The decay rate for D + --* K*0e+v com-

bined with the E691 result for D O ~ K - e + v leads to

the ratio F(D --* K*e+v) / r (D --* Ke+v) = 0.45+0.12,

which is significantly lower than expected. This calls

for a re-examination of the form factors. Ther~ is

sor~e discussion of this problem by Wirbel in his pa-

per to this conference. 11

Table 2. E691 Results for D + --* K-~r+e+v

Mode Branching Decay Rate Ratio (~ ) (101°s -~)

D + --, K*0e+v 4.5 -I- 0.7 4- 0.5 4.2 :E 0.6:1:0.5 D + --. (K-~r+)NRe+v 0.3 • 0.2 4- 0.2 < 0.7

A

f j

60

40

(.9 v

i'M 0 (5 or) I-.. Z t.~ > h i

0

4(3

20

| | | g g

fl (o)

(b)

0 ~ ' ~ - ~ M m 0.6 1.0 1.4 !.8

K'Tr MASS (GeV/c 2)

FIGURE 2

The K~r mass spectra for D + -4 K-~r+eve candi- dates from E691 w'th right-sign (solid) and wrong- sign (dashed) electrons: (a) loose cuts, (b) tight c.uts. The curves are fits used to extract the K* compo- nent.

There are preliminary results on D --* K~ev from

Mark HI. They see D O decaying into three modes,

K-~rOe+v, K-6~r-e+v, and K0----~-/z+v, for a total of

23{) M.S. Witherell / $emileptonic decays of charmed mesons

16 events signal with 4 background. They also see 11

D + decays with 4 background, in the modes K-w+e+v

and K6~r0e+t,. The corresponding decay rates are

I"(D 0 --. [X~rl-e+v) _- (14_~3 4- 2) . 1ol0s - I and

p(D + [~rl0e+v) = (~ o+1.6~ 1Ol0s-1. "-~ " ~ - - 1 . 3 ; "

The D + decay rate agrees with E691, although the

D O rate is higher by a factor of 3. Although the statis-

tics are low, the discrepancy between the D O decay

rate and the D + rate from either experiment appears

significant. A violation of the isospin relation would

be most surprising and since the results are prelim-

inary, ] will not use them in the comparisons to fol-

low.

Do the exclusive decays to pseudoe~alar and vec-

tor mesons saturate the measured inclusive rate? In

Table 3 1 list the known components of the semilep-

tonic rate. For the nonrssonant Klrev decay, I mul-

tiply the K-g+e+ve rate from E691 by the isospin

factor of 1.5. The Cabibb~suppressed decay can be

estimated by taking the Cabibbo-favored decays and

multiplying by, for example, the calculation for the

ratio ~e~/Kev from reference 5. This takes into ac-

count the Cabibbo suppression, as well as differences

in phase space and form factors, and should be quite

accurate. The sum is (14.1 -I- 1.5). 1010s - I , compared

to (16.3 4- 1.5)- 1010s - I for the inclusive average. The

missing rate is (2.2-I- 2.2). 1010s - I , which is consistent

with zero. There is not much room for D --* K1rlre~,,

K~/ev, etc.

Table 3. Semileptonic Decay Rate S-mmary

Mode Source Rate (1010s -1)

D O --, K-e+~, Mark ]]I/E691 8.2 ± 1.2 D + --* K*-e+t , E691 4.2 4- 0.8

D + --, (K~)NRev E691 0.4 -I- 0.4 D --* (~r, p)e~, tan 2 8c 1.3 -t- 0.2

Total 14.1 4- 1.5

Inclusive Mark IH 16.3 -I- 1.5

4. ANGULAR DISTRIBUTIONS IN D --+ K*et,

Returning to the problem of the low D --* K*ev

rate, the next step is to determine which of the form

factors causes the discrepancy. There are three form

factors in K*ezs decay, one vector form factor V(t)

and two axial vector form factors A1 (t) and A2(t).

Fortunately, the extra information necessary to ex-

tract the form factors is available in the angular dis-

trlbutions. There are three angles which define *,he

distribution. The K* decay angle 6 v is the angle be-

tween the lr and the D momenta in the K* center of

mass. The leptonic decay angle ee is the angle be-

tween the electron and the D momenta in the rest

frame of the virtual W. The angle between the de-

cay planes is X- The entire specification of an event is

given by ee, 0V, X, and t.

The angular distribution for the general case has six terms: 12

[Ai 2 = G2lVcsl2tx

{[(I "}" cos 0e)2[H+l 2 -I- (I ~ COS 8e)~ IS~ 12] sin2 8V

+ [ 2 ( 1 - cos 2 ee)[H0[2]~ cos 2 e v

- [2(1 - cos 2 0e)Re(H+a*_)]~ sin 2 8 v cos 2X

- ~ S i n e e [ ( 1 + cos 0e)Re(R+H~)

+ (1 - cos ee)Re(H- H~)]2 sin 0V~os 8 v cos X }.

The functions H+, ~I0, and H_ correspond to helicity

amplitudes of the virtual W +. They are related to

the form factors by the relations

H~(t) = (M D "I" h/IK,)Al(t ) -4- 2 ~ V ( t )

1 r(S2 - M 2, - t) ( S v -I- MK.)AI(t ) H0(t) = 2Mx, v~t D 2 2

Integrating over the azimuthal angle X, there are two

terms: a transverse component with sin 2 0V, and lon-

gitudinal with cos 2 0 V.

To get a first look at the relative amount of trans-

verse and longitudinal decays, E691 has analyzed

the dependence on 0 V. The distribution of cos 6 V is

M.S. Withersll/Semileptonic decays of charmed mesons 231

CJ (3

Z bJ > bJ

20

! 0 , n 1 - I .0 0 ID

COS

FIGURE 3

The cos 8 v distribution for the D + --+ K*0e+ve can- didate from E691. The curve is from a fit to back- ground plus signal and corresponds to F~/FT = 2.4.

shown in Figure 3. A fit to the form dF/d cos 0 V =

1 + ~ cos 2 8 v gives the result a = 3 8+. 3"4 This cor-

responds to a ratio of longitudinal to transverse of

r L / r T = (1 + a ) / 2 = 2.4+1:9 ? -I-0.2. This ratio would

be 0.5 for unpolarized K*'s, and was expected to be

1.0 in the BSW model. The K* is longitudinally po-

larized, somewhat more so than expected. The prob-

lem now is to find a convincing explanation for both

the low K* rate and the longitudinal polarization.

This fit uses only cosSv, and varies the relative

size of FL and F T. We will next fit the same data

sample using cos 0v, cosSe, X and t, varying the size

of AI, A2, and V. It may be possible to l ~ r n the

source of the discrepancy by measuring the inc~vid-

ual form factors directly.

5. CABIBBO-SUPPRESSED DECAY

The K-M element Vcd can be measured in two

ways: in neutrino production of charm, and in Cahibl~

suppressed charm decay. The first of two measm~

ments from neutrino experiments is the result from

CDHS 13 of [Vcd[ 2 = 0.044 =I= 0,012. In his paper

submitted to this conference, Shaevit~ 14 ~ves a new

result from the CCFR experhnent corrssponding to

[Vcd[ 2 - 0.047 -I- 0.009. These both agree with

the expected result of 0.048. The results depend on

semlmuonic branching ratios, the ratio of cross sec-

tions for D + and D 0, and the fragmentation function.

Mark HI has observed the Cabibbo-suppressed de-

cay D O -* ~r-e+v. 5 The analysis parallels very closely

that used for the Kev decay discussed e~]ic ~ The

~r/K discrimination is provided by thne-of-flight mea-

surement, and by the U variable. The b ~ u n d

is 0.5 events, or less than 10~, and the resulting

branching ratio is B(D 0 --, ~-e+~,) = (0 ~o+0.23 ~_ • "-~'-0.11 -~ 0.04)~. By taking into account the difference in

phase space, and assuming equal values of ft(0), the = n 05~+0-038 -I- 0.00 , .% derived result is ]VcjVcs] 2 v. "-0.015

which is consistent with the expected result of 0.049.

The systematics on the measurement of the ratio are

quite good, because errors in the electron efficiency or

form factor normaliz.tion cancel. The only limitation

is the small number of events in the signal.

6. CONCLUSIONS

The decay rates for the Cabibbo-favored semilep-

tonic decays of charmed mesons are now reasonably

well measured. The average rate for D O --* K - e + o is

(8.2-1-1.2).10 l0 see -1, which agrees with expectations.

The decay rate for D + --* K,(Je+~ is (4.2 ~ 0.6 -I- 0.5).

1010 sec -1, which is significantly smaller than the

predicted value, and the K* is longitudinally polar-

ized, more than had been expected. The nonresone~t

decay D --* K1rev is less than about 7% of the in-