SE ILEPTONIC DECAYS OF HEAVY

Alex Nippe

Deutsches Elektroren-Synchrotron, Notkestrasse 85 . D-2000 Hamburg 52, Germany

Experimental results on exclusive semileptonic decays of B and H mesons are presented and their role as a probeof the hadronic structure of weak decays is reviewed.

1. INTRODUCTION

ileptonic decays of heavy mesons provide ab at

for testing the hadronic structureof weak decays,

From the theoretical point of viewthey are relatively simple to interpret since only twovalence quarks are involved. On the other hand, theundetected neutrino makes them difficult to study ex-perimentally. so in this review I will include a briefsketchof the various experimental techniques used to analyzesemileptonic decays . These measurements are not re-stricted to the determination of rates, but investigateother quantities, such as angular distributions, whichare more sensitive to the underlying hadronic dynamicsand are independent on the weak coupling . The under-standing of the hadronic structure is of particular inter-est for a reliable extraction of the Cabbibo KobayashiMaskawa elements from exclusive semileptonic decays .I will not go into more detail on the latter point butconcentrate on the first one .After a theoretical overview I will discuss experimentalresults on B and D decays involving b -~ c and c -* stransitions . Due to lack of statistics it is not possibleto extract information on the hadronic structure fromCabbibo suppressed channels .

ESONS

2 . THEORETICAL BACKGROUNDIn the spectator model (Fig.1), the semileptonic de-

cay of the heavy meson M into the lighter X via emis-sion of a virtuel W-boson, is described by the underlying quark transition Q -+ qlv, where this process is

0920-5632/91/$03.50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)

Nuclear Physics B (Proc. Suppl.) 21 (1991) 384-391North-Holland

not affected by the light spectator quark q, . Hadronic

qs

9s

Figure 1 : Spectator diagram for semileptonic decays

dynamics enters only as soft forces binding the quarksinto mesons . The transition amplitude is derived as :

A(M --> 1'lv) = ~VQ9 - L"H,,

(2.1)

where the leptonic current L" is calculable exactly . Incontrast the hadronic current H" =< X'IJ"IM > can-not be derived from first principals, but has to be es-timated by phenomenological models . This problemturns into the calculation of form factors appearing inthe lorentz invariant decomposition of the hadronic ma-trix element . These form factors depend only on q2, thesquare of the momentum transfer to the lepton-neutrinopair .It is expected that the total semileptonic rate is dom-inated by the two lowest lying mass states, the pseu .-doscalar P and the vectormeson V . Neglecting leptonmasses, one arrives at the following expressions for thedecay rate of these processes :

(a) pseudoscalar meson (X = P)

dI' = GFI?4a32K

3 Fr(g2)2.

(2.2)

VQq is the appropriate Cabbibo Kobayashi Maskawa ma-trix element and K the momentum of the meson V inthe frame of 111 . The decay rate depends on only onevector form factor Fl( q2 ) .

(b) Vectormeson (fi = T')The partial width can be expressed in terms of threehelicity amplitudes H� where i = (+, -, 0) refer to thetwo transverse and the longitudinal polarisation state ofV:

dT ti(IH+12 +IH_12 +IH01 2).

(2.3)

The amplitudes are given by

2

2

AlaiK

, 2H±(g) _ (Alm + 111v)AI(q)

q?(Mar + lth)t (q )

(2 .4)

Ho(g2) =1

2Mvgf(~lsr -ar~ - g

2 )(1lIAq + MI )AI(g2 )

A112fK24 Mat + MvA2(g2)) .

Here MAr and lbly denote the masses of the initial andfinal mesons ; q is -1 for positive and +1 for negativecharged quarks . One is left with the calculation of twoaxialvector form factors AI(g2) and A2(g2 ), and onevector form factor V(q2 ) .

Recently N .Isgur and M.Wise 1 have shown, that inthe so-called heavy mass limit, there exists a model in-dependent description of hadronic matrix elements : asquark masses go to infinity (the spectator quark stayslight), the velocities of the heavy quarks Q and q arenot affected by soft binding forces . Moreover the spin ofthese quarks fully decouples from its dynamics. There-fore the overlaps of the initial and final mesons, i .e .the form factors, are all equal at maximum momentumtransfer . This new spin symmetry leads to definite rela-tions between the transitions M -+ Plvand 11I --> Vlv.Model dependence enters the calculation through cor-rections to the heavy mass limit. (For further detailssee J.Körner in these proceedings.)

A. Nippe/Semileptonic decays of heavy mesons

(2.5)

One expects b --" F transitions to be close to this limit.so that the theory should be correct to within V. -_ onthe other hand for c , s transitions. the s-quark is nolonger heavy enough, to make this approximation reli-able . Here we have to rely on more pmodels, which are discussed widly in literature 2.3 .4 .5,

Although their approaches are different (e .g . nonrela-tivistic and relativistic quark models; helicity matching),the predictions are the same on the 20'`ßa level . This al-lows me to avoid discussion of individual models, and torefer to their collective results as 'theory' . (For b ---, ctransitions the models are also in a ' agreementwith the predictions of the heavy quark limit.)In the theoretical framework givers above the angulardependence of the decay rate is already integrated out.In principal there are three angles involved which, incombination with the q2 distribution . a for a directdetermination of the individual form factors . The an-gles are1. 0`r - the angle between one of the pseudoscalar decayproducts of j' and the direction of M. in the l'-frame .2. 0E - the angle between the lepton and J1 in thelepton-neutrino system .3. X - the angle between the lepton-neutrino plane. andthe plane formed by the two pseudoscalar decay prod-ucts of V, measured in the 111-frame .Instead of giving explicit formulas, I would like to point

out that 0v distinguishes between transverse and lon-gitudinal polarisation of V, and 0E between its positive

and negative helicity. ., appears only in the interference

terms of Ht , H_ and Ho.To include the q2 dependence of the decay rate into

the studies one has to make assumptions about the q2

behaviour of the form factors . Usually one assumes a

single pole dominance with, for example, a monopole

type formfactor

F( q2 ) =

F(0)

,

etc.

(2.6)1 - g2/ntporE

where the pole carries JP = 1 - quantum numbers for

vector (Fl , V (q2 )), and JP = 1+ for axialvector form

fact

(A;. A_).

Experimentally one can extract themalisations F(O) from a simultanious fit to the three

angular distributions and the q2 distribution . As we willsee later, the complication arises from the unseen neu-trino, because one has to obtain the full kinematics fromjust the observed

ay products . Therefore it has notalways

n possible to perform the full study, and onehas only restricted information in the form of the ratio

r, and the ratio of pseudoscalar to vectorme-uction . Branching ratios can be compared to

if iQq is determined independently, which holdsfor c - s transitions .

3. RESULTSIn this section I will first explain the experimental

technique used to study the decays P - D`+I_v and

-~, D'V!9 , and then discuss the theoretical impli-cati

ofthe results.Up to now there are only two experiments, AR-

GUE and CLEO, contributing measurements to semilep-tonic B meson decays . Since both produce the B'sin e+c_ annihilation via T(45) --~ BB, they use al-most the same experimental method to investgate thesedecays. This technique . the so-called 'missing-mass-method' exploits the fact, that the B's are producedalmost at rest . Therefore, all the kinematical quantitiesneeded to calculate the neutrino mass as the recoil massof the D'+I- system, are known:

M2 = E2 _ sy py

h -, clr, TRANSITIONS

- [EB - (ED. + E1)1 2 -(PB - (PD" + P1)I2

(3.1)

Using EB = Ebea,n and neglecting pB (which is about340 MeV/c) one obtains

M2 ~

= [Ebea,n - (ED* + El)] 2 - (PD" + pl)2 . (3.2)

Fig.2 shows the ARGUS9 measurement displaying therecoil mass, where one can see a clear peak ar-round M,? = 0, as expected for B --~ D'+l'v decays .

A. fppe/Semileptonic decays of heavy mesons

P,.(®- a-)

[cev2/C - ]

Figure 2 : Mrs of D`+I_ combinations from ARGUE 10The full line is a fit with a gaussian and a parametrisa-tion of the background contribution, shown as a dottedline .eie

0v`0.5z

0 .4

0 .0-1 .0 -0.5 0.0 0.5 1 .0

cos8.,

Figure 3 : Strong decay angular distribution 0v inB -+ D`+I- v (ARGUS10 ) . Fitting Eqn . (3.5) yieldsrlong/rtrans = 0.85 f 0.45 .

The background consists of uncorrelated combinations,faked leptons, faked D's, continuum and mixed events .The resulting branching ratio is listed in Table 1 (to-gether with other results discussed below) .To get deeper information on the hadronic structureof the decay process, a more detailed study has beenperformed, measuring the alignement r1ong/rtrans =

I'o/(r+ + r_) of the D'+ . This can be obtained byinvestigating the distribution of the strong decay angle9v in the decay D'+ --4 it+Do .

A. Nippe/Semileptonic decays ofheavy mesons

The experimental distribution (Fig.3) shows no pro-nounced angular dependence, thus I'oa�g ::Z rtrans-

Combining the ARGUS 10 result with a more recentmeasurement of CLE06 yields r,~g/rtrans = 0.84 ±0.29 in good agreement with the theoretical expecta-tions of about 1 .The same principal has been applied to the investiga-tion of the decayB -+ D+1- v , where the recoil massof the D+V system is calculated . Here additional back-ground arises from the decay cascadeB--+ D`+ l-v ,followed by D'+ -+ D- (y, 7r°) . These events peak atvalues slightly above zero in the recoil mass spectrum .This can be seen in Fig .4, where the missing massof D+1- is shown : points with error bars are back-ground corrected data, the curves correspond to thesignal process B --> D+l-v and the feedthrough fromB --> D'+l-v . To suppress the latter, a tight momen-tum cut of PD > 1.5 GeVlc was applied ; the remainingcontribution was not taken as a free parameter in the fit,but its form and absolute value was fixed from the studyofB -+ D'+1- v , already described above . These pro-cesses, and the corresponding decays of the chargedB's, have now also been studied by CLE07 . The latterare investigated by fitting the D° 1 - recoil mass distri-bution with theoretical predictions for the shape of theD'° and D° components simultaniously, leaving theirnormalisations as free parameters . In addition the ratioVIP was constrained to be the same for B° and B-decays .From the results listed in Table 1 one can conclude :

-2 -i 0 1 2

reco¬l

Figure 4 : 111,1,, of D+ I- combinations from ARGUS1a.The dashed curve shows the contribution from the cas.cade B -" D'+I - v --- D+(y .rr°)1-v .

Table 1 : Summary of the decay rates in B decays. Tocalculate the branching ratios.it was assumed that B-and B° are produced with equal rates from T(4S i de-cays.

(a) The ratio of vector to pseudoscalar agrees withthe theoretically predicted value of about 3 (this isnot 'naive' spin counting,r[ong/rtrans = 0-5)-(b) Adding up the vector and pseudoscalar branchingratios gives only about 70% of the inclusive branchingratio, measured to be (10 .3 f 0.5)% 8.7 . What makesup the difference? CLEO claims to see weak evidencefor B -+ D'+Xl-v at at rate of (2 .0 i 1.2)`% . Thisprocess is difficult to observe, since it appears only asa small enhancement at positive values in the D'+l-recoil mass spectrum (Fig.5) . The broadening of this

because this would imply

387

The relations

dr* - sin 29yJH_ 1 2 (3.3) N

dro - cos20t,

IH012 (3.4)60

leads to an angular dependence of the form30

dR'1 + acos2fly. 0.,;0V - (3.5)

withrlong~rtrana

1 4- n= (3.6)-30

ARGUS CLEOB --+D+1-v 1 .6t0.5±0.5 1.8i0.6=0.3B --) D*+I-v 5.4~0.9±1.3 4.6~0.5y0.7B- -->D° I-v 1.6t0.6-0.3B- -;D'°I- v 4.1~0.8~0.9

distribution due to the neglection of the B momentum

in Egn.(3.2) prevents a cleaner seperation of the differ-

ent contributions .

Figure 5:

_ ofD"1 combinationsfrom CLE06. (a)right sign,(b)gong sign combinations. The fit contributions

are described in the text . The dotted histogramin (a) is the contribution from B --+ D"+ß'1-v.

RESULTS ON c --4 slv TRANSITIONSHere I will discuss the decays D° --~ K- etv and

D+ --~ hoc'v . Some remarks on D; -~ ¢e+v arealso made.

4.1 .

THE DECAY D° -~ K-c+vResults on D° --> K- et v are published from the

MARKIII and E691 collaborations . These experimentsare different in their charm production mechanisms andtherefore in their analysis techniques. MARKIII pro-duces the D mesons in e+e' collisions via 0(3770) -4

DD. The semileptonic decays of the D's are observedusing the recoil mass of the K- e+ system . In contrastto the analogous method in B transitions, the momen-tum of the semileptonically decaying D can be fixed byreconstructing the other D meson in the event . Thecorresponding recoil mass distribution is shown in Fig.6.

r1. Nippe/Semileptonic decays ofheavy mesons

E691 . a photoproduction experiment, isolates charm

-0.2 -0.1 0

0.1 0.2 0.3U (K-e+v hypothesis) (GeV)

Figure 6: ~llree of K - c- combinations from MARKII I16(histogram) . The solid curve shows Monte CarloD' -a K c+v events (normalized to data) and the con-tribution ( x 100) from D° -4K- ;r'c+v .

decays by reconstructing well seperated secondary ver-tices . In this case they make use of the decay cascade

D'+ -+ 7r+D°, followed by D° --~ K-e+v . From thedirection of the D meson (given by the secondary ver-

tex of K-e+), the momentum of the neutrino can bedetermined up to a quadratic ambiguity. Including theneutrino momentum, the (K- c+ v) mass is constrainedto the D° mass. In combination with a a+ the whole in-variant mass of this system is required to equal the D.+

mass . Background is subtracted using wrong chargecombinations .

The results of both experiments together with the the-oretical expectation are summerized in Table 2. As a

conclusion, there is a remarkable agreement betweenthe experiments and theory .E691 has also analyzed theq2-dependence of this transi-tion . As_uming a single pole dominance as in Eqn. (2 .6)the q2 distribution was fitted, treating the pole mass

mpoce as a free parameter. Theoretically one expectsthe lowest lying ca-pole with vector quantum numbers,which is the D; at a mass of 2.11 GeVlc2.

The fitgives a mass of 2.1+0*4 GeV/c2 consistent with this pre-

0.2

diction .

10i

®w

611';1'k

~~III,p

w0 t _ r, .I

Table 2: Summary of the decay rates in D decays .The experimental rates are normalized us-ing BR(D+ -> K-7r+ar- = (9.1 ± 1.3 î 0.4)% and

4.2 .

THE DECAY D+ -+ Îs`°e+v

In 1988 the E691 Collaboration presented a studyof the decay D+ --"h°e+v , using a method similar

to the one described above. They looked for (K- ar+)e+

combinations pointing to a common vertex, and an-

alyzed the resonance structure of the (K-7r+) invari-

ant mass. Subtraction of background was mainly per-

formed by investigating (K- ar+)e- wrong charge com-

binations. The invariant mass of both charge combina-

tions is shown in Fig. 7.

Fitting the remaining distribution with a Breit Wigner

shape for the resonant part plus an s-wave nonresonant

background parametrisation yields a branching ratio of

BR(D+ -> K*Oe+v ) = (4.5 î 0.7 î 0.5)% . The non-

resonant contribution is determined to be only about

10% of the resonant .

In what follows I will talk in terms of partial widths

rather than branching ratios, making a common inter-

pretation of semileptonic D+,D° and D, decays pos-

sible. For example one expects from SU(2) invariance

that I'(D° -+ K-e+v ) equals I'(D+ -+ be+v) . This

enables a comparison of vectormeson and pseudoscalar

A. Nippe/Semileptonic decays ofheavy mesons

Figure 7: Invariant masses of Kar right charge (solidhistogram) and wrong charge (dashed) combinations

(E69113) for standard (a) and tight (b) cuts.

production in semileptonic D decays . One arrives at

I'(D+ -4 hOe`v) _ 1r(DO --i K-e+v) ^- 2'

where theory predicts a value of about 1 (not 3 as in B

decays because of a stronger phase space suppression

of the vectormeson rate).Recently this result was confirmed by ARGUS and

CLEO (for simplicity the presentation will be no longer

chronological) . These experiments have a more compli-

cated experimental enviroment, since the D's produced

in nonresonant e+e- annihilation at a center of mass

energy of 10.5 GeV are accompanied by other parti-

cles from the fragmentation process. To study semilep-

tonic decays one can exploit the relatively hard mo-

mentum spectrum of D mesons, which leads to small

opening angles between the daughter particles . Con-

389

BR(D° -> K-7r+ = (4.2 î 0.4 î 0.4)% 17.

T[10'°s-lj exp./ theoryD° -~ K-e+v 7.8 î 1 .2 î 0.9 IVIARKIII"5

8.8î1 .2î1.4 E691158.4, 8.3 theory 2,3

D+ --> K`°e+v 4.2 î 0.6 i 0.4 E6911

4.6 î 0.6 ± 1.1 ARGUS12

Do K'- c+v 3.5 î 0.9 î 0.9 CLE020

9.1, 9.5 theory238R(D; -Oe+ to < 0.45090%Gc.l . E69121BR(D, -~oir+ )

0.49 î 0.10+00 :1140 CLE0200.57 î 0.15 î 0.15 ARGUS12

1 WBS3

sequently, ARGUS12 searched for events containing a

*0 and an electron, requiring an opening angle be-

t

the combination of less than 90°. The back-

ground consists mainly of faked electrons and uncor-related combinations . Wrong charged combinations

`~c- arise from almost the same mechanism, but not

from charm decays. and are taken as a test of the back-

ground determination. The CLEO technique" to in-

vestigate D' --= fï-e~r, requires the invariant mass of

the

- t - combination to be less than the D° mass

rat

than a cut on the opening angle. The results,

suns

i ed in Table 2 are in very good agreement .Applying a similar method CLE020 and ARGUS12 ob-served the decay D; --, o;-v , with a branching ratio

relative to the channel D; ---~ o-° of 0.49 ± 0.14,,â and

0,57±0,15 =0.15, respectively. For a rough comparison

one can take the estimate from ref.19 of BR(D,' -+

6-') = (2.7

0.7) , which yields a branching ratio

for D;

oc'g, of {1,4

0.5) t

or r(D; --+ oe-v )-

(3.? ± 1,1) x 10r°s-r . From SU(3) arguments this

value should equal r(D' -->K"c'v ), but phase space

should suppress the former by about 0.8318 . The exper-

imental ratio of 0.76 ±- 0.3 agrees well with this number .

As a conclusion present form factor models are in dis-agreement with the rates for D -~ T'ev .

To understand this discrepancy a more detailed studyof the reaction D. --> Fi°e~v was performed by E691 .

As mentioned above, one can exploit the angular distri-

butions in k, (91 " , 0, and the 92 dependence to measurethe form factors. For this analysis it is necessary to know

the momentum of the unseen neutrino, which can be de-rived from the direction of the D meson. Zv91 obiainsthis from the reconstructed decay vertex (ARGUS andCLEO do not have such information) ; as a step towardsthe full analysis they presented in 1988 the measure-ment of the alignement rlong/rtrans of the _K'° . Thecorresponding distribution (Fig.8) in 0y shows a pro-nounced angular dependence, different to the situationfor B mesons . The fit to the data with a parametrisa-tion as Eqn. (3 .5) results in r,ng/rtrans = 2 .4+ 01 .7 ±0.2,

A. IN°ippe/Semileptonic decays ofheavy mesons

40

z20

W

w

01 1

1 1-1,0 0 IA

Cos

Figure 8: Distribution of 01- (E69113 )

for D} --+ Îi so et y candidates . The solid curve is thefit to the signal plus background.

whereas theory predicts 1 .

Recently the other distributions were included in theanalysis by performing a simultanious fit as discussed in

the section 2. Since (V,( is well known one can take the

total decay rate as an additional constraint, leaving only

two free parameters in the fit. Experimental complica-tions arise from the different lepton momentum spec-tra for positive and negative helicity states since clean

seperation from background requires hard cuts on thelepton momentum .

The comparison of the result with the models (Tab.3)çhowç a marked disagreement in all form factor nor-

malisations, especially in A2 . Thus the discrepancy islocalized, but not yet explained. Note that this anal-

ysis also gives a new value for rlong/rtrana with muchreduced errors . As a remark, I would like to mention,

that the authors of 18 treat one of the overlap integralsas a free parameter. Fixing this only by the total de-cay rate of D+ --+ R' {°e+v they obtain good agreementwith all measured form factors within errors . Moreover,

5. SUMMARY

A. Nippe/Semileptonic decays of heavy mesons

BR(D; ~ar' t,)the model then predicts

^- 0.45 close toBR(D, -.Q~+ )

the experimental value. However, this does not provide

further information about B meson decays .

In general one can conclude. that the model predic-

tions have to be mistrusted for semileptonic transitions

into lighter quarks, which will be especially true for

b -~ u decays. Here the measurement of form factors

for D+ -->h=*oc'v

gives an important input for future

extraction of 1L 6 from exclusive semileptonic b -4 u

transitions since Isgur and Wise 1 have shown that there

is a relation between b -~ u and c --+ s form factors.

In semileptonic B meson decays the measurments

f 1F

/1F

and BR(B--D++l -v )o

show good agree-BR(B -+D+ 1- v )

mentment with the theoretical predictions . This is expected

since b --~ c transitions are close to the heavy mass limit.

Here the full investigation of angular distributions, i.e .

the determination of the individual form factors, is de-

sireable .

The situation for c -+ s transitions is not so harmo-

nious. Only the decay D° -4 li - E+v is well described

by models . In contrast there is disagreement for the

decay D+ --~ Ii `°c+v : the rate turns out to be half

that predicted and the alignement to be about twice.

This difference is also reflected in the measurement of

the form factors for this process. Currently there is no

7. D.Cassel (CLEO Collab.) . CLNS 90/1014.

391

5. F.J .Gilman and R.L.Singelton Jr ., Phys . Rev. D41(1990) 142.

6. D.Bortoletto et al . (CLEO Collab .), Phys . Rev.Lett . 63 (1989) 1667.

8. H.Albrecht et ai . (ARGUS Collab .), DESY 90-088 .

9. H.Albrecht et al . (ARGUS Collab .), Phys . Lett .B197 (1987) 452.

10 . H .Albrecht et al . (ARGUS Collab.), Phys . Lett .B219 (1989) 121.

il . H.Albrecht et al . (ARGUS Collab.), Phys. Lett .B229 (1989) 175.

12 . H .Albrecht et al . (ARGUS Collab.), contributedpaper to Singapore 90.

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14 . J.C.Anjos et al . (TPS Collab .), FERMILAB-Pub-90/124-E .

15 . J.C.Anjos et al . (TPS Collab .), Phys. Rev. Lett .62 (1989) 1587 .

16 . J .Adler et al . (MARKIII Collab .), Phys . Rev. Lett .62 (1989) 1821 .

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19 . Particle Data Group, Phys . Lett . B239 1990 1 .

20 . J.Alexander et al . (CLEO Collab .), Phys . Rev. Lett .65 (1990) 1531 .

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Table 3: Measurerrjgqnt of the form factors forexplanation of the source of this discrepancy

D+ -, Îi °E+v (E691"*) . Result are given for q'- = 0and q2 - q2mar'

E691 IS2 BW3GS5

KS4

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