Semileptonic decays of charmed mesons

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


    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.


    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~ee~ " 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.


    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.


    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


    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.

    ~10 -

    O d ~" 5 - C

    uJ 0 =0.2

    12-88 6218A3

    ' I , I



    K-e*v e



    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) 101s-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 Ddecay 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 (~) (101s -~)

    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


    f j



    (.9 v

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




    | | | g g

    fl (o)


    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-


    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


    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 inee[ (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


    ! 0 , n 1 - I .0 0 ID


    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

    rL / rT = (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~rn the

    source of the discrepancy by measuring the inc~vid- ual form factors directly.


    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~und

    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...