4~ * 00*9$0O~ 

can indulge yourseif with the third category; by tiiat time it is probably too late 

to worry unduly about winning ot losing. It is the second strategy t am going to 

adopt, yet it is not in my self-interest to specify which of the problems I regard as 

"easy, tough or entertaining". May I add thnt I will not cover mixing. CT violation 

or traiy rare decays. 

There exists a triple motivation for dedicated work in this field. 

J. Charm and beauty decays present us with a rather ui»<itie opportunity t<> 

learn important lessons about QCD on the interface between tin- pnttirbativr 

and non-perturbativir regimes. Open flavor states Q<i witli Q\tj\ denoting it 

heavy (light) flavor can help to bridge the gap between the light Itadtons, i;*/. 

where our understanding is rather unsatisfactory, And quarkoniaslfites, QQ. 

where potential models work increasingly well. Heavy flavor baryons Qqi<n 

offer interesting studies as well; in essence this is similar to structural studies 

with molecules into which radioactive atoms have been implanted. 

2. We want toexlract the KM parameters like V(ub), V{rb)t etc. They obviously 

represent fundamental parameters which have to be known and. hopefully, 

understood. (On a practical level it is always helpful to know what one is. 

trying to understand! The KM parameters desenbr sjstark couplings whereas 

it is ihe couplings of hadrons only that can be observed directly. The impart 

of QCD on heavy flavor decays has thus to be understood to some degree IA 

least, 

3. We all strive to find "New Physic* • -- noble cstdeavor is however ham­

pered by the sometime.-. -i..noving presence of Old Phvsics. The search for 

FASTER 
So 

fflSTWBBTIOM OF THIS DCSliwEHT JS U8LIK1TED 



/VJF *• SLAC-PUB—4455 

DE88 003606 

On C l i a r m nnd Beauty Decays - A Theoriit'a Perspective* 

I. I. Biol* 

Stanford Linear Accelerator Center, Stanford, CA 94305 

ABSTRACT 

The present understanding of charm and hot!am decays is reviewed. Special 

emphasis is placed on discussing the theoretical uncertainties in view of the partic­

ularly rich harvest of new data from the last year. A semi-quantitativedescription 

of 1) decays lias emerged enabling us to address rather dctailled and relatively 

subtle questions there, like on once and twice Cahibbo suppressed decays. Beauty 

physics having left its infancy is now in its adolescence; its future development 

towards maturity is analyzed. 

I , M o t i v a t i o n 

Giving a review talk is like playing simultaneous chess; not much attention 

is [laid to the games you win - almost everybody focuses on the ones you lose, 

an your failures, The similarity between the two situations extends also to the 

question on which strategy to adopt: Do yot' attribute the same weight to every 

opponent/problem and divide your time equally among them? Or do you exercise 

some personal judgement by dividing the field into "easy, tough and entertaining"7 

Then you proceed to run over the first kind and draw honorably with the second 

kind; that way you boost your confidence and gain in respectability. Finally you 

< This work was supported by the II. S. Department of Energy under contract number 
DE-AC03-76SFOOSU 

t Hrisetiberg K'flow-

Invited talk presented at the 
International Symposium on the Production and Decay of He<uy Flavors 

Stanford, California. September 1-5, I9S7 



Yet a more letailed look reveals a potential problem of considerable relevance: 

MARK III t i u reported"1 

jfrZ&g])* (^ - 0 . 5 7 ) ± 0 . 1 3 . (3) 

It should be noted that the quoted error is statistical only and that Eq. (3) 

does not represent a unique interpretation. The problem is not that only half 

the Kx in aemiteptonic D decays come from a K* resonance - why not? The 

problematic aspect of Eq. (3) concerns the relative weight of K and K': for 

BWS predict 

Most other models, in particular ifec one by CSrinstcin, ingttr mid Wise 

{=G1W) W , attribute even more prominence to A'* final staleH. T!xp«'n-

mentally 

I'll) -* rVA'ir) 

Using Eq- (3)» one then r onctudt:* 

044 f ° ° * . (ft) 

r( /> - • tvh} w 

If Eq. (5) were confirmed by inon- data, wo roiijil not claim to have- ncic-s-

satily a theoretical disaster at band after all there is an old prediction 

consistent with it. Yet it would constitute at least nn iieule emtarawiiimL 

in practice since all the detailed models of more n-reiil vintage point in In­

direction of Eq. (4). If Eq. (6) were to hold up in spite of the ratlier general 



the former is thus determined by the understanding of the latter. 

The outline of the talk will be as follows: 

In Section II, I will analyze charm decays, both the present understanding 

and its future refinements; in Section III, I discuss beauty decays with particular 

emphasis on |V(c6)| and |V(u&)| before concluding with some remarks on the future 

in Section IV. [n general, I will not present a comprehensive review with all numbers 

and experimental findings; those can be found in other talks at this conference.' 

Instead I will focus on the most topical features and pans theoretical judgement on 

them. 

II. The Decays of Charm 

A. Lessons on Strong Interactions in D"/D* Decays. 

1. Scmi-I^plonir D°/D* Ducays. 

Tlicsu decays tin: not expected to pomr as big a theoretical challenge as non-

It'plonir tlrrays since* Uiry involvooiity imr typtf «»f liailroiiii- inalrix clr-mrnl: 

<(.*>= 0,1 )\j,,\l) >. A host or models have been put forward to calculate 

those. A lypic-al tine was developed by Daucr, Stccli and Wirbcl (=BSW);'" 

others will l>e mentioned later: 

1'HSWI / ' - '('A*, A) ~ (15 - 20) • l O ' V c " ' (1) 

wliich coinpiircs favorably with the data 

rttt>[D -» t»K*i K) ~ {17.8 ± 2.6). l O ' V c * ' . (2) 

3 



* (OM,-|»r+) * " ' 

i,j = 1,2, ...Ne- Naively, just counting numbers, one might expect £ s 

Something has t o be d e a r l y kept in mind here: it is {trivially) tine, t h a t chain­

ing the values of c& can offset almost any change in £ {apart from (tfi + 0 2 ) I ( a ) -

«j) 3? (1 — £*)(! +C))- Y*** *'*' s observation amounts t o l t i l l c more than numerology, 

since the origins of these parameters are very different: c.± art? due to h a r d glucm 

effects, 4 on t h e other hand t o soft ghmns. 

Kq. (7) shows there are three categories of decays; 

• Class I transitions: D" — A/,' M^', only the* a% tens* contributes; 

• Class !t transitions: IP -* */{\Wf; o n ' v ^ K " i term contributes: 

- Class III transitions; D* -» htfAf?; both «i and <ii terms con­

t r i b u t e and can thus even interfere. 

If you complain that these names while being typical of scholarly tra­

dition lack a Shakespearean ring to them, you are quite right. If you 

observe further that somebody living and working in Heidelberg should 

come u p with more colorful, if not, romantic names, you are right again. 

However, such gripes should not obscure the fact t h a t these distinctions 

are very important Unfortunately, quite «ften they are misrepresented 

or at least wot appreciated tn the literature. 

Thus there are two a priori free parameters a>,«2 to be determined from 

the data plus a not insignificant amount of "poetic license" entering 

6 



expectatipu Y{B -* rVA"*) — V(D -* tvli), one had t o view t h e success of 

these models in accounting for Hie considerably more complex non-lcptonic 

decays as i% mere coincidence. Furthermore one should then tru st them even 

less itt B decays despite some early evidence t o the contrary as I will discuss 

later on. 

Considering these for a theorist - unpleasant consequences, I feel strongly 

inclined to belief t h a t lit). (6) does not represent t h e last word - t h a t instead 

it will go u p Uy a factor of two or so. 

2. NoH-leptonit- D"/D* Decays. 

(a) T h e "Art of Theoretical Engineering" 

In an effort to be practical and t o concentrate on the doable, Stech and 

coworkers have developed a. phenomenological framework to deal with 

non-leplonic decay modes. All transition amplitudes T(D —» / ) are 

expressed as a linear combination of two more elementary amplitudes 

with fixed cocH)tie»ts: 

T( D - / ) = «,T,{ D - f) + <*&{ D - / ) (7) 

fli = ^ ( c + + c . ) + | ( c + ~ c „ ) (8) 

« 2 ^ - ( c + - c . ) + | ( c + + c . ) . (9) 

T h e renomialization coefficients c± are produced by QCD radiative cor­

rections; c± = 1 holds in t h e absence of QCD. The parameter ( denotes 

t h e relative size of matrix elements in color space; e.g. 

S 



- Adding tip Tth{D — PP,PV, VV) where the D -» PP,PV modes 

have been mote or (ess confirmed experimentally and comparing it 

with r „ p ( D ) one finds 

T<£> -» F P , PV, VV) ~ 8.7 x I W ^ a S ) C13) 

!"(£>+ - £ u K / K ; PP, PV, VV)~ K } 

The two-body modes thus dominate non-lcptonic f) decays and the 

global features of D decays arc wci) reproduced. And all of this is 

achieved without any contribution from weak annihilation! 

A more detailed took reveals some phenomenological dRficiencius: 

• The predicted values for Bli{D° -* K"4>< A'*W, f<*t}} are all lowftim-

pared to the data. I do not perceive this as a major problem. They 

ail represent class II traasiliow*, i.e., are smallish — C)fJ%); llras 

even relatively small rescanning from the large class I transitions 

will have a big impart on them white affecting the* overatt picture 

very little. 

r i D ^ A ^ f * - 4 experim. 

H O " - » * + » - ) 11.4 Iheoret. 

I will come back to this point later on. 

B 



via the formfactors adopted and final state interactions(»FSl) that are 

included. 

Thift "poetic license" certainly introduce* some fuzziness into the theo­

retical description. Yet even so it is highly non-trivial - and 1 regard it 

as significant - that with 

« I = S 1 . 2 ± 0 L 1 , a j * - 0 . 5 ± 0 . l (11) 

a very decent fit is obtained to some twenty-odd EPfD* decay chan­

nels! A priori then- is no mason to expect that one set of values for 

Oi.d] should be adequate to describe so in any so diverse decays 

D -* /'P. PV 

where V\V] denotes pscudoscalar [vector] states; for the kinrmaticaland 

dynamic") environment*, i.e. phase shifts, vary very significantly. Yet we 

learn from the success of I In- fit that llirw is a simple- pattern underlying 

charm dec-ays. The specialties or individual channels can be factored 

off into the rather simple rormfarlurs and FSI employed thus allowing a 

universal value for «I,«-J. Even so soft gluon effects play an important 

role. For K.|. (II) leads to 

when adopting the usual values for t t , i.e., c + «-0.7.c_ - ' 1.9. 

Further pleasant surprises emerge from this analysis: 

7 



(c) The "High Tt Superconductor" Approach. 

There is one approach that will (hopefully) scilve all our problems and 

settle all issues once and for all - the use of lattice Monte Carlo calcula­

tions. However, like with high 7, superconductors, its benefits will not 

be reaped in the very near future; quite a few yearn will pass before it 

will yield definitive results on charm decays. 

(d) "Best AvailableTi-chnrilogy": QCD Sum Rules. 

This approach involves three ingredients 

• One employs an operator product expansion <if £(Af' — I ): 

£(AC = 1) = ] T CiO, „ (18) 

With the help of perlurbative QCD one identifies the local operators 

O, and computes their Wilson coefficients c,-. 

• Non-pcrturbative effects are introduced by allowing for nott- vanishing 

vacuum expectation values 

{010,10) s * 0 . (I!») 

• The concept of "duality" is implemented by matching up quark-

gluon amplitudes determined in the Euclidean region, with hadron 

amplitudes in the Minkowskian region. 

10 



(b) The "Mackintosh Approach": jj-

It is fair to say that the previous approach contained a few ad-hoc as­

sumptions like factorization, etc. There is another approach impressive 

in its multicoloured graphics which is based on. an expansion i.n jj, N 

hcing the number of colors. (t his some precursors' , yet the most com­

prehensive Application to charm dcrays has been given by Bm-as, Gerard 

and RucW . The transition amplitude is written down as follows: 

7 - ( Z > - / , = , / * ( * , + £ + o ( i j ) ) - (17) 

For actual calculations one retains only the leading term - bf - and 

drops all non-leading contributions bt/N, etc. This represents the basic 

assumption. From it follows: 

• £ = 0 effectively since it is of higher order in ^ : £ = jj-

- factorization holds; 

• W exchange and FSI have to be ignored. 

The description of the data obtained in this approach is not bad, though 

definitely poorer than in the Stech et al. approach. This can be traced 

back largely to the fart that FSI effects are ignored, On the other hand 

this approach is certainly more compact and obviously self-consistent 

since it is based on just one basic assumption, namely ignoring terms 

that are non-leading in ^ . This one assumption however is purely ad-

hoc. 

0 



non-rftl&tivistic potential model they are related to the hftdronic wavefunction 

at the origin 

where M denotes the meson mass. On very general grounds, one expects 

fo < h • 

Specific models yield'" (with the normalisation / , «* mw) 

ft, ~ 150 - 200 Mv.V , IF ~ I«0 - 220 Mc.V . (22) 

MARK III has obtained"" 

fo < 2<M)MeV (D0% C.L) (23) 

from their upper bound on A>+ —* ft+v. Ofcour.sc, it. h highly desirable to 

improve the sensitivity on Jo, hopefully reaching (In- level indii alrtl in K(|. 

(22); of course, it is equally desirable to obtain a comparable miinbi'i' i>n //.-. 

Yet even Eq. (23) represents a very intriguing bound, in particular if nu<> 

adopts the prescription iif non-relalivistic dynamics, [ty. (21). I'«>r in llml 

ease 

fBOi./^S.fli&n0Mr\' (24) 
V m » 

a number of great relevance in dealing with B° - Fi° mixing. 

12 

http://Ofcour.sc


Block and StuCmttn1*1 have developed and applied sneb an analysis to 

D -* PP, PV (20) 

decays, where one has six (it parameters altogether, namely three for 

&*,D+,Ds —• PP and three for EP,D*,DS -» PV, yet many more 

decay modes. 

Since the theoretical analysis involves four-point functions rather than 

two- or three-point functions, it represents a very ambitious and chal­

lenging program. Therefore one has to grant it Rome time for maturing, 

liven M> t\ lir*l »>inly»is yields very prniniNing results by producing a 

rather decent (it to the "old" MARK III Crunching ratios; in particular 

/7/f(/>° -» A'0*) - 1% ~ HRilP - . jt°ta) is obtained. Since six pa-

riunelers liave to lie filled otie has to redo the analysis with the "new" 

MA UK III luHHflmig r.iliiis, j'ct I do not anticipate a major problem 

t«i emerge. Therefore, I would like to smnniniiye why I ronirider this 

nppruacli MI) priunisiiig. A priori one doe* not make ajwumplionti like 

factorization or ignoring weak annihilation or noii'leading terms Hi j$. 

Nori-fatiorizable contribution* an' actually included and treated in an 

;iV lejwl M'iiit-tpianlitalivi* fashion. Tin- dominance of factorizable con-

lril)iilitMi> I-IIHTKCS I lien self-consistent ly from the duality match-up, yet 

other term* like W cxdi.iiipv are still present on the *» 20% level. 

I'un-Iy l.rptoiuc Decays. 

l-'roni the branching ratius O* ~* t*v,D+ —• t+v one determines very im­

portant lmdrpnic parameters, namely the decay constants fa and fp. In a 

11 



mDi7,£+K2l}mm') = O-23 * "-W ± 0.07 £691 (27) 

^ ^ ^ ^ = ^ = 0 . 2 9 * 0 . 0 7 * 0 . 0 5 £69. (28, 

and an upper limit 

Up to this conference no decay mode / had been found with 

BH{D+ -> <>*+) 

Since one estimates theoretically 

BR{Dt - • ^ r + ) - 4% 

one is then lead to the question: "Where and what are the non-leptonk Df 

decay modes?" While it is true that theoretically one tends to expect two-

body modes to be less dominant for D, than for D° decays this occurs only 

on the ~ 10% level, i.e., it is not highly significant. It was a very pleasing 

experience at this symposium to hear from both the MARK II and III groups 

about preliminary findings that 

with a possibly even large signal for D* —» q's"1 

14 



D. Cross Checks in D, Decays. 

A pleasantly simple dynamical pattern has emerged from Da, D* decays: 

< Two-body final states dominate non-lcptonic /J°, D* decays. 

• The large D* — D° lifetime ratio is dominantly though maybe not ex­

clusively produced by a destructive interference in D+ decays. 

Accepting these findings is however tantamount to giving up much flexibility 

in treating Dt decays - the model parameters have been basically fixed. D. 

decays thus offer us quite honest tests of the statement that -we have indeed 

developed a rather satisfactory understanding of D decays. 

Quite a few very interesting experimental results have been obtained in the 

last year on D, decays. As far a* the overall rates arc concerned, the news 

have been mixed. The good news has been that T(D,) has been found to 

agree with T(£J°) within quite decent errors: 

^ } - l * ± f l - » - (23) 

The bad news are that still no absolute branching ratios are known. The 

importance of D, decay modes can then be expressed only relative to the 

"standard" mode D+ -* * T + . Definite numbers have been given for three 

other modes: 

/ 0.75 db 0.12 ± 0.06 E691 
0.85 ± 0.23 MARK II 

(26) 
1.44 ±0.37 ARGUS 

V 0.6 — 0.86 theoret. 

13 



might hold. Blok and Shiftnan find large isospin cancellations in D, 

pie: 

BR{D+ -* pV*") 
BR(D+ -* WT+) £ 0.25 (33) 

with D, —• w » + still being suppressed relative to D. -+ 4>ir. Any data on 

D, -* wr are thii3 highly desirable, though hard to come by. H should 

be noted that the reaction of Eq. (31) could not contribute here. 

- Quite a new element enters it indeed 

UR(D* -» n ' * + ) ~ BR{D* -* i}**) ~ 2im(D+ -» fa*) (34) 

were found since factorization yields typically 

' BR{D* — i?V + ) ~ Stf(D+ - 7?ff+) ~ £ « ( / ? + - 0 * + ) . (35) 

Tin: presence of a nearby scalar resonance would offt*r it natural <"xi>l;i 

nation for aii enhancement in !), —» t}w,t)'Tt n\nev 

0+ — T / J 0 + / • / ' V . (.SH) 

Also it should be noted that 

0+ / • :** (37) 

Such a scalar resonance would therefore not contribute to D, —> 3ir. 

16 



While the spectre of "missing D* decays" is thus receding, many intriguing 

observations can be made: 

• The relative weight of the class II tradition D, - * R*A'+ and the class 

I transition Dt —* ^ T + is as predicted, Eq. (26), 

• The biie ti the non-resonant D, -* KKir mode is only about 20% of the 

tesonant modes, Eq. (27) - again as expected. 

• The D, does decay into final states without open or hidden strangeness, 

Eq. (28). Annihilation processes thus do occur, though with a reduced 

rate, namely with only 20-30% of the strength of spectator processes. 

• The light upper bound on D, ~» />°x+ provides some prima facie evi­

dence that D, —» ITJTT is generated by weak annihilation and not just 

by FSI. tor in the latter case one would expect BR{D+ -» p°ir+) £ 

Bfi(P* —» 7r+Jr"7T+) unless some accidental cancellations take place. 

To look at it in ,i xlighliy different way, there could be a * like, i.e., 

pseutlascalar resonance T with m , — m{Ot) that enhances apparent 

an Mill Million transitions 

Dt^rt'~*nr (31) 

whew f.' parity requires >i = odd. H would be only natural to expect 

0+ -t f(, ;jc+ Uv wc\»f Ihut way as well. 

• There is one loophole in this nrgumeiit that can be dosed by further 

observation: Tin- Beijing group has suggested that 1 " 1 

ltlt[lX* -> <&*+) - DH[Dt ~> w:r + ) 3> BR{D+ - p°v+) (32) 

15 



SU{$)FI breaking in Eqs. (38, 39) has been implemented basically via 

(//f//*)* > I, Maybe one has overlooked another important source of 

SU(Z)FL breaking. This can be checked quite clearly in /> + decays: 

nZ-22>mi'**'"n m 

where PS denotes the relative pliasespace factors and F ^ I measures 

SU{Z)FL breaking. 

Maybe FSI or weak annihilation has not been included properly. Mea­

suring 

D° ~* K°K°, arV 

while not an easy task would help greatly in disentangling these effects. 

One warning is in order here: contrary to some claims, weak annihilation 

can — despite the GIM mechanism — produce D° -+ /<°A'U due to 

SU(3)FL breaking! 

Once the first two loopholes are closed one can turn one's attention to the 

most intriguing explanation for Eqs. (38, 39) - Penguin operators! For 

they contribute to both ZJ° —» K*K~ and D° —» JT+JT- with a positive 

sign while the usual charged currents contribute v.-ith a positive [nega­

tive] sign to 0* - * K~K* [£P —» r+x~]. Therefore even a suppressed 

(coherent) Penguin amplitude can have a significant impact. 

IS 



As a final remark or appeal for data, we would like to know the scmileptonic 

branching ratio. In particular, does 

BR(D, - • ft/X) ~ BR(D° -» (vX) 

hold or 

BR{D° -*tvX)< BR(D. - tvX) < BR[D+ -* tuX) . 

Also the composition of the hadranic state X is of considerable interest: 

X = r\, t j ' , tj>, u>> IT'S . 

C. Refinements 

1. Once Cabibbo Suppressed Decays 

The oldest pu2zle in charm is represented by the following two transition 

rates 

r { / > 0 ^ K + ^ ) = | 1 - 2 i ± 9 Q - 3 x i 1 ° 1 0 - c - 1 Z , <38> 

r ^ ^ ^ o ^ l 0 ' 3 3 ^ 0 ' 1 ^ l O ' ^ e c " 1 r**" (391 
theor. 

Three mechanisms can be invoked to explain r(D° ~* K+K~) > r(D° -+ 

ff + 7T'). 

17 



The beat numbers on these KM parameters at present 

| V ( « ) | = 0.95 ± 0.15 \V(ei]\ = 0.207 ± 0.024 (43) 

are obtained ftom the di-muon signal in deep inelastic neutrino scattering. 

I am optimistic that in the foreseeable future more precise values can be 

extracted from D -*• IvK, K*tr,p. 

H I . T h e Decays of Beauty 

Dedicated studies of beauty decays promise an extremely rich harvest: The a 

priori unknown parameters V(c6). V(ub) can be extracted, ff3 - B° mixing can be 

studied, rate decays and finally CP violation can be searched for. 

This is all true in principle; in practice however a lot of very hard work of not 

necessarily the most lucid kind is required since it ia the hadrons that decay, not 

the quarks. This is the issue 1 want to address. 

A. V(th) in Semi-leptonic Decays. 

Already anticipating that |V(«6)|2 » JV(M6)J* we can write down 

The crucial question is what kiad of function is involved here. No jjencral 

answer to this question exists. Therefore we take recourse to a time-honored 

stop-gap measure. We employ different models of reasonable, though not 

always overwhelming integrity and hope that their differences in the output 

represent a good measure of the inherent uncertainties. 

20 



2. Doubly Cabibbo Suppressed Decays. 

Thews are (at least) two reasons why one wants to find and underataod AS * 

—AC transitions like 

Z>+ -» K+ff+jr~ . (41). 

• The neutral counterparts o( Eq, (41) - JD° -» jfiT+Tr-, K*T~KV - form 

an important background to present searches for D° — £fi mixing!"1 

• Such transitions can exhibit a high sensitivity to New Physics in the form 

of charged Higgs fields, For Old Physic* transitions get suppressed by 

ty*8c ~ 2.3 x 10~3 when going from AS = AC to AS = —AC processes; 

charged Higgs contributions on the other hand can get enhanced hy <v 

(m,/rru) 2 . The signal to noise ratio thus improves by ( m , / ^ ) 1 / ^ , . -v 

4 X 10* ! 

'A. Ac, etc., Decays. 

It appears to be established now that 

liolds strongly suggesting that weak annihilation drives one full half of all Ae 

decays! While it is expected on rather general grounds that weak annihilation 

is more significant in A( than in D° decays, I am somewhat surprised by its 

apparent prominence. 

19 

I , 



I a ,'• I 

saturate the total scmt-leptonic width 

?(B - t (vDJIT) 5 T(B — tvXe) . 

Jlence one extracts from the data 

. ., fO.Q4 ±0.01 GIW 
)V{d>) a* \ (48) 

10.053 ±0.01 BSW 

The exclusive modes can of course be calculated as well in such schemes: 

From the recent ARGUS measurement'1" 

BR{B° — IT-e+vt) = (7.0± 1-2± !.&)% (50) 

one concludes 
f 0 ' <0 ± O.007 \V(cb)l ~{ x (51) 
10.055 ±0.01 

in pleasantly good agreement with Eq. (48). By the way, this is one major 

reason why I fiod it hatd to believe that the same models could fail by a 

factor two to three in D —»tvK* vs. tvK. Putting everything together one 

obtains 

!

0.040 ±0.007 GIW 

0-045 ±0.008 quark level (52) 
0.055 ±0.01 BSW 

The models thus exhibit a roughly 20% internal uncertainty by themselves. 

Yet the real message of Eq. (52) is that the true overall uncertainty is much 
22 



1. Quark Level Description. 

The Spectator Ansatx leads to 

r ( B - £vX) * T{6 - iuc) = ^ ^ |K(d)|* /Y ( ^ f ) (44) 

K{x) = 1 - 8x + 8x3 - xA - 12*a log x . (45) 

From the data on TB one then deduces 

\V{cb)\Spcz 0.045 ±0.008 (46) 

where the uncertainty reflects mainly our inability to make a unique choice 

for the quark masses m& and m e . It describes only the uncertainty reithin a. 

single simple model, but not the theoretical uncertainty in general. Among 

other things one has assumed here implicitly T ( S * ) = T(B°) - an equality 

that has be>'n checked experimentally only withiD a factor of two. 

2. Hadron Level Description. 

Quite a. few different mode) descriptions have been suggested in the litera­

ture. I will concentrate here only on two of these since they seem rather 

complementary to me. These are the descriptions provided by Grinatein, 

Isgur and Wise (=GIW)"" and by Bauer, Stech and Wirbel ( = B W S ) . W 

There one finds 

T{B -, tv DfD') ~ { J ; J J ] x |V(rf)|»10» sec'* £ ™ . (47) 

ID these models one expects, cum grano satis, these two final states t o almost 

21 



onB-* li/IT. Since 

r{B+-*?t*») . f 0.391 |V(iifc)l* GIW 

one obtain') 

' V ( H j < / 0 . l 9 GIW 
| v ( 5 o r l o.n BSW . ( 5 7 ) 

quite consistent with Eq. (54). 

One important caveat ia in order here: At our present luvel of understanding 

(or limitation thereof) one has to exhibit "brand name loyalty," i.e., stay 

within o n e hadronization scheme (GIW or BSW, etc.) when quoting num­

bers ou the KM parameters. For nthrrwisc one can fall into OK: following 

trap: combining \V{cb)\ £ 0.07 as obtained from BSW with the (ilW boimrl 

|V(ub)[ £ 0.2 leads to \V{ub)\ :£ 0.014. While this value: might happen to he-

correct, its derivation was inconsistent as shown by Eq. (55). 

C, Non-leptonic Decays and the Impact of Strong Interaction... 

As in D decays, it is useful to distinguish between dims 1, 11, ami tit transi­

tions. In the following tabic, I list BSW predictions for some- tyiw'ai modes 

together with present experimental numbers: 

24 



larger, namely 

\V{cb)\ ~ 0.033 - 0.065 (53) 

i . c , a factor of two - despite the more optimistic PDG claims! I sincerely hope 

that PDG will state a more realistic evaluation of the uncertainties in their 

next report. Eq. (52) also shows that the duality concept as implemented by 

Eq. (44) is not failing - after all \V{d>)\ = 0.045 ± 0.008 is consistent with 

both the GIW and BSW value - yet it does not provide us with * surgical 

tool either. One should aim note that so far nobody has presented a proof 

why Eq, (44) should work better and better for increasing my. 

B. V(ufr) in Scmi-lcptonic Decays. 

Two methods have been used to distinguish i - m from b —* c transitions. 

I. One tries lo exploit kiiicmalical differences as exemplified by m, > m B . No 

clear signal lias hec.u found by CLEO or ARGUS. A great deal of model 

uncertainty enters when one translates this into a limit on V(ub): 

\V{ub) 
I V(cfc) 

$ 0 . 1 - 0 . 2 . (54) 

2. One attempts to identify Hie hadronic final state. CLEO has searched for 

ti* —» t*i't(f* and round no signal. Ilencconc concludes 

, , „ „ , „ fO.008'2 GIW 
^ "<")£< (55) 

U.0068 n s w , 

It i« tempting, though less than rigorous, to relate this to the ARGUS findings 

23 



Since two-body modes do not dominate non-Ieptonic B decays as they do 

with D decays, I estimate 

l S ^ S t . 2 . (58) 

Extrapolating from T(D+)/T(D°), I expect weak annihilation to be fairly 

unimportant in T{B): T(B°) should not be shortened by more than ~ 10%. 

However not everybody agrees with this expectation and in any case it has 

to be checked experimentally. 

D. Baryonic Decays of B Decays. 

Beauty mesons are sufficiently heavy to a!Jow decays into a baryon-anlibaryon 

pair possibly together with other mesons. Furthermore the weak decay pro­

duces already two quarks and two antiquarks 

bq —+ cAvq . 

Thus only one more qq pair has to be created from the vacuum to form a 

baryon-antibaryon pair and such baryonic decays should not be particularly 

suppressed. The drawback is that it poses a non-trivial problem to make 

these statements more quantitative. 

Two prescriptions have b«:en put forward to predict the inclusive baryonic 

branching ratio: both use di-quark production as a starting point although 

they treat it in a different manner. The results are1"1 

o „ , „ . f 3 ± 4 % Ref. 15 
BR{B — \ C + X)= I „ (59) 

2a 



Mode BR[%]BSW BH[%)EXP. 

Class J : oi 

# > - . £ > + * - 0.5 | ^ | 2 0,59 ± 0 . 3 

B° -» D+'Tf" 0.45 | Bg*|* 0.3S ± 0.13 ± 0.13 

Ba - • D***"*0 1.4 |Ejs£|" 2.0 ± 1.1 ± 1.1 

if TC-lfl = p" 
£!<:« / / j a* < = 0 

S O - ^ t f 0 * 0.25 0,05 0.33 ± 0.18 

Clats III : 0 ] , a j 7 £ = 0 

B " - D ° T T - « |^f 0.47 ±0.15 ± 0 . 1 0 

Considering the rather limited experimental information one cannot draw 

firm conclusions from this juxtaposition. Yet the following tentative state­

ments are suggested: 

• We appear to be off to a good start in deacribing non-leptonic B decays 

consistently with \V{cb)\ ~ 0.05. 

> { = 0 is strongly favored — like in D decays, despite the vast differences 

in kinematics, prominence of FSI, etc. 

• Relatively little negative interference occurs in the two-body modes of 

B" decays. 

25 



specific statement. The arguments can typically W phrased as foilows 

r ( f c ^ a ) = ^ . B 1 1 - C t t r ( f l
0 - p p T V ) (63) 

with 

r ( B ° — p p r * * - ) ' ~ r(B->.\N*v) 
(64) 

T(B-NrtX)' 

Just countingthe number uf available states one arrives at order of magnitude 

t'Klitnatcs 

C ~ 4 , 0„ ~ !i - 10 . ((B) 

ft, is modelled aft^r baryonic dec ays of the 7/<i'!"' 

yl„ is filiated with tlio torrcsponding number in h -•* <• transitions, Ki|. (GO): 

AU~A, ~ 1 0 . ((ifi) 

Then urn' obtains |V(nfr)/V(H>)] — 0,:j. Making "reasonable1* variations in 

our assumptions one arrives at n rather wide range 

1 V/(ct) | 

This strongly siigRcsU though docs not prove rntirhisivrly thai 

|V(ti6)/V{efc)j would be as large as it is still (barely) compatible with tin-

as 



in fine agreement with the CLGO findingn 

BR{B - A, + X) = (7-4 ± 2.9)% . (60) 

That is nice, but so what - these prescriptions are still semi-quantitative at 

best. 

Firstly, jf arguments can be invoked to improve the theoretical underpinning 

of the arguments sketched above. Secondly, data on exclusive baryonic modes 

would help trenwitdotwly t*» refine these concepts- Thirdly, the very urw 

ARC!US data uit charmless B decays force t)iin issue upon UN 

IJR(B+ ~> ppx*} = (3.7 ± 1.3± 1.4) x IO"" 
(61) 

Bli(B" -* pjiir+ir-) = (6.0 ± 2.0 ± 2 . 2 ) x lO"" 

compared I.o tin1 upper liriiits i>l>lninc<l by CMSO 

/ i « ( f i u -* -,r+T-), IJR(fP - ;ip) < 2 X IQ-* . (62) 

Sinn* I'ciiguin LransitimiB ran In- ntUtl out rather conclusively as the origin 

of IM). ((H)- 1IM-M- data, ir confirmm!, establish 

|V'(»A)|*0. 

Alas, only gui'sLiiiiatcs arc at present available to relate Eq. (€1) to a more 

27 



There are further dynamical isospin selection rules suppressing B -+ AA. 

The (valence part of the) baryonic wavefunction is antisymmetric in colur 

space. (This was the original motivation for introducing color. | There-

fore it is only the (somewhat enhanced) Fierz antisymmetric operator 

0- that contributes here: 

6 mdu . (71} 
o-

The ud pair is then in a isosifiglct state and only / = ~ baryotu. can IK-

generated from this vertex (in a one-step process): "'' 

B = [oq)-> JVA t /VAff'a (72) 

The two-body modes B —* AA are - as usual - suppressed in amplitude 

by a form factor, F{q*\ 

f V ) « ( ] + ~ y . (-si 

Applying the QCD counting rules of Brodsky and Lepage, one Arrives 

actually at n ~ 2, i . e . a dipole (instead of monopole) form factor since 

the exchange of two hard momenta is required to produce 8 —* baryon-

antibaryon. Such a highly effective- suppression can lie balanced only by 

maximizing the mass-tike parameter AJ. Thi# leads t o the very general 

30 



analysis of fcnii-leptonic decays. 

K ^ ] ~ 0 . 2 - 0 . 2 5 . m , 

I had emphasized before that in a state-of-the-art discussion of |V(ub)/V{cb)\ 

one has to specify the hadronization scheme adopted. I have refrained from 

doing so in Eq. (68) basically because there is no well-developed such scheme 

yet for baryonic B decays. All thr parameters A, B, C are rather uncertain. 

1, Naive di-quark pictures tend to yield A* < Ac\ fa arguments lead to Au ~ At 

and there is no conclusive argument against Au > Ac even. 

2. Resonance effects clearly affect BU,CU in a very significant way. 

ARGUS observes a low mass enhancement in the px spectra in Eq. (61) which 

appears consistent with i —* pir. This rases some highly intriguing questions. 

1. It is virtually impossible that a significant part of B° —* ppw+ir" is fed from 

B° -+ AA modes. 

* BR[&° —> pir~) = 5; furthermore it is almost unavoidable that 

B° +> A++A++, A ~ A ^ . (69) 

Therefore 

BR(B° -* AA) ~ 2BR(B° - A°A°) = 1&BR(B° -* PP*+K-) (70) 

i.e., unacceptably huge! 

29 



IV. Summary 

A. The Presence. 

Over the last few years we have developed a rather decent understanding of 

charm decays — one that is better than for strange decays. This development 

has been made possible by the coincidence of three factors: 

1. Nature has decided on a fairly undramatic dynamical pattern underlying 

charm decays. There is no striking feature like the A / = i rule. 

2. There have been good, comprehensive data - the "MARK III legacy.''"' 

3. Cloae feed-backs between experimentalists and llwomtx hari oVvrhipwi. 

Yet the success of our theoretical description lias not been firmly CKI aid islii'd, 

improved data could reveal grave deficiencies. 

Beauty physics on tin? other hand i*slill in its adolescent phase, rkiriiclfrizi-d 

more by promise than completed achievement: We have sUrlril In draw ;i 

rough sketch or the overall picture and to extract the i\ M i«w»itiH.eTs, 

li. The Future. 

In charm decays 

I. Important cross checks have to be performed, namely 

fa) SLi;dy /)+-° — VV transitions, 

(b) Determine absolute Dt branching ratios and (mil HHHT of lln-m. 

(c) Do the same for charm baryons. 

32 



expectation 

T{B -» NN) > T{B -» A&) (74) 

with 

N-^&r. {75) 

2. A related selection rule can be stated for B+ decays 

l'{/l + -» A + V ) » l ' { / ' + - • ;<A") (7fi) 

which is further strengthc-ru'd by f!li(A++ — px+) = J, B/f(A° - » p r ) = i . 

In all of litis we should k<vp iti mind that the apparent !ow-mMs cnhanromo.nl 

might not In* a bona fide A resonance? 

More tliiiirctiral work is nrowsiiry and proceeding, id dilfercnt places!"1 

Mill. I have li> add that further experimmtftl input is of crucial iinporlaucc 

fov mnkiiiR progress: 

(;i) Olii-ili the selection ruh-s (|-:«|. 7U, 71, T5). 

(l>) Kind or limi!. /*' •-»/I;»ST+ST"T+. 

(<) SLriTi- In identify linal H(;'1I*S containing a Jr°. 

(d) Mini exclusive modes containing charm baryons like 13 —^ \rNir for 

(theoretical) calibration purposes. 

31 

http://cnhanromo.nl


REFERENCES 

1. K. Berkelman, these Proceedings; I. I. Bigi, Invited lectures given at the 

Charm Physics Symposium, Beijing, PR China, SLAC PUB-4310 (1987); D. 

MacFarlane, these Proceedings; S. Stone, these Proceedings; M. Witliercll, 

these Proceedings; 

2. M. Bauer, B. Stech and M. Wirbel, Z- Phys. £ 2 2 (1985) 637. 

3. D. M. Coffman, Ph.D. Thesis, CALT-68-1415. 

4. B. Grinstein, N. lsgur and M. Wise, Phys. Rev. Lett. g£ (1986) 298. 

5. A. AH and T. C. Vang, Phys. Lett £Sii (1976) 275. 

G, For a recent comparison see: B. Stcch, Invited talk given at the SMJ Miitiato 

Topical Seminar on Heavy Flavors, San Miniato, 1987, preprint HD-THEP-

87-18. 

7. See for example: H- Lipkin, Les Houcbes Lectures ig68, C DeWitl, V. Gillet 

(eda.), Gordon and Breach, M. Gronau, D. G. Sutherland, Nucl. Phys. g!8^ 

(1981) 367. 

8. A. J. Butas, J.-M. Gerard and IL Ruckl, Nucl. Phys. B26S (1980) 16. 

9. B. Blok, M. A. Sb'rfman, preprints ITEP-9, 17, 37 (1986). 

10. H. Krascroann, Phys. Lett, 26B (1980) 397. 

11. J. Adler et al., SLAC-PUB-4343. 

12. X.-Y. l i , X.-Q. Li and Ping Wang, preprint AS-IIP-87-Q07. 

13. G. Gladding, these Proceedings. 

34 



2. We have to reach a higher level of sophistication in once and twice Cabibbo 

suppressed decays. 

3. All of this should eventually lead to a more precise determination of V(c&), V(cd). 

In beauty decays we have to 

1. Continue to map _.ut B decays and start on the Bt, 

2. Compare r[Bi) vs. T(B<I) VS. T(B,), and 

3. Develcp a better understanding of baryonic decay modes. 

Attaining these goals will enable us 

1. To interpret B® - &> mixing with rigor rather than just vigor, and 

2. Analyse rare decays and CP violation with considerable more confidence. 

V. Acknowledgements 

I have benefitted greatly from discussions with S. Brodskv, H. Harari, Y. Nir 

and B. Stcch. 1 want to thank the organizers, in particular, E. Bloom and A. 

Fritlman, for taking considerate care of mind and body. 

33 



14. H. Albrechtet al., preprint OESY 87-079. 

15. M.Bigi, Phys.L«tt,106B(1981)5lO 

16- H, Harari, private communications. 

17. Numbers like that have appeared also on the backs of envelopes held by 

M.Gronau, H.Harari, J.Rosner, M.Shifm&n, B.Stech and many more, 

18. D. Slech, preprint HD-THEP-87-18. 

19- Sec also M. Gronau, tliese proceedings. 

20. I Ii»ve«ini<* to praise MARK 111, not to bury them 

DISCLAIMER 

This report was prepared as an account of work sponsored by an agency of the United States 
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United States Government or any agency thereof. 

35