D0 → K0φ decay

Volume 199, number 1

PH¥SICS LETTERS B

10 December 1987

D°-~I~° 0 DECAY I B E D I A G A ~ and E P R E D A Z Z I Dtparttmento dl Flst~a Teorlca, Um~erslta dl Tormo, 1-10125 l'utm, ltah' and lstttuto Na=lonale dt Flstca Nudeare, Sezmne dt Tormo, 1-10125 Turin ltah,

Received 4 November 1986

We &scuss the decay D"~I~°0 m the framework of a model proposed recentb which mlmLcksboth quark confinement and asymptotic freedom within a distance ~ube)ond which hadromzatlon occurs The agreement with the data BR (D~'-,I¢°0) = 1% is ~er? good Predlctmns over BR( F +~np ) -~4-8% are gwen

The experimental finding [ 1 ] B R ( D ° ~ K ° , ) ,-- 1%

(1)

can be considered to be the first direct evidence of the W-exchange ( W E ) c o n t r i b u t i o n to charmed meson decays I n & c a t i o n s m this sense are also represented by the experimental difference in the lifetimes of D + and D o a difficult problem to tackle since, basically, we do not have a reliable theoretical scheme in which to describe f o r m a t m n and decay of b o u n d states of quarks and gluons A recent model [ 1-4] based on a very simple realization of quark c o n f i n e m e n t and asymptotic freedom points towards solving the m a n y open problems in charmed meson decay by naturally enhancing the W E and W A ( W - a n m h l l a t m n ) contributions as compared with the usual term W R ( W - r a d l a t m n ) The model agrees well with the data and makes new testable predlchons [4] The model assumes a wave function for the produced quarks which somehow e m b o & e s both conf i n e m e n t and asymptotic freedom by writing g/(x, t) = o ) ( P ) exp(l P/,x:' - x - / ~- x c~~ )~ ,

(2)

where xo is some typical c o n f i n e m e n t radms beyond which h a d r o n l z a t i o n occurs (the probability is not conserved in tame [2]) whereas within this &stance the quarks produced are essentially free The mare practical difference with c o n v e n t i o n a l models is that Fellow of CNPq Brazil 0370-2693/87/$ 03 50 © Elsevier Science Publishers B V ( N o r t h - H o l l a n d Physics Publishing Division)

the Dirac delta function which enforces exact threed i m e n s i o n a l m o m e n t u m conservation is replaced by a gausslan m o m e n t u m distribution which, ultimately, is responsible for the a b o v e m e n t l o n e d enh a n c e m e n t of the W E and W A contributions In this paper we show that our scheme g~ves a very reasonable explanation of the experimental value (1) and predicts a sizeable F + ~ p ° n + branching ratio One of the consequences of the model is the appearance of a new term violating the conservation of the axial current (in addition to the usual one proportional to the sum of the quark masses, which is negllglble), 1 e we have [3] O/,~/' ?,/,~5~/=l( m + m ' ) ( f

ysg/--2g/'(7.x/xo)75g/

(3) A new such term has already been recognized [ 5 ] as one possible way to enhance the decay D°-~I~°~ What as remarkable, is that our model has such a term built m automatically With the same method used previously [3,4] to investigate the decay widths of charmed pseudoscalar mesons D and F into two pseudoscalar uncharmed mesons, we replace in the hadronlc matrix element ( O IA:' ] P ) = - i f p P " - , - ifi,( q~ + q~ ) ,

(4)

where P, q~ and q2 are the f o u r - m o m e n t a of the charmed meson and of the produced quarks respectively a n d fp is the P-decay constant We take the hadronlc matrix element [6] 131

Volume 199, number 1

PHYSICS LETTERS B

(~OlA~,lq~)=i((m~. +rn,)e~

10 December 1987

W i t h the above considerations, the d o m i n a n t contrlbutlon to the decay D°--,I~°~ becomes, m our scheme

eo'qD q~_ mK+ mo

%" qD ) . + -2m, ~ q~2 F~.o(q'_, 1 )

I M ( D ° - d ~ ° ~ ) 12 = a ~ ½G2 fo,,a[ %'qD I2 X M ~ ( 2 r n ~ + 2 m 2 - M ~ ) F ~ , ( q ~ , 1+ ) c o s 4 0 ,

+ 2 1 m , %'qD qiLF~.o(q2 0 - ) , q-_

where q/~ = q~ -+.,*' - , - / ¢ j ~ eg is the p o l a n z a t l o n vector o f and F~.%(q2, JP) are the form factors for JP states In the "free q u a r k " case o f conventional models, when P,,= q~,,+ q2~,, the only n o n - v a m s h m g contribution is due to a pseudoscalar pole and the numerical estimate [5] for D ° ~ I ~ ° 0 ~s very small ( B R ~ 0 01%) Evaluating the c o n t r i b u t i o n s in (5) with the wave function (2), the second t e r m (which is the only new one c o m p a r e d with the " f r e e ' q u a r k case) gives the following c o n t r i b u t i o n 1%'q+ 12[a(2m~ + 2 m ~ - M ~ ) M ~ +b(m~ - r n ~ ) 2 ] , (6) where

a = - erf(xoMD/,f2)/M~xo

+

~-w (l+M~xo) ~/ 7[ mDxo

exp( - ~Mbx~), ' "

(7)

and b = (1 + l/M~xo) erf(xoMD/x/2) V/2 F--

\, 7r MDXo

(1 + 5Mbxg) 4 ~ , exp( - _1~2 ~ 2 ~ D~'0J

(8)

xo is the gausslan width p a r a m e t e r which has previously been d e t e r m i n e d [ 2,3] to be, roughly, xo-~ 1 GeV - j ~-0 2 f Taking MD ~ 1870 MeV, M~co-~ 2 so that one finds a-~ - 0 115 and b ~- 1 One can satisfy oneself that the t e r m leading to a in eq ( 6 ) comes from an imaginary a m p l i t u d e whereas b comes as a real a m p l i t u d e This implies that the term p r o p o r t i o n a l to b sums up to roughly zero when c o m b i n e d with the other contrxbutions m ( 5 ) (just hke in conventional models) and only the c o n t r i b u t i o n p r o p o m o n a l to a r e m a i n s 132

(9)

(5)

where a2 xs the a p p r o p r i a t e color factor ( a 2 = (2c+ c_ )/3), the c+ are the couplings o f the usual effective h a m l l t o n l a n for which we take [7,2] c+ - 0 66, c_ = 2 3 and 0 is the C a b l b b o angle fDo has been recently d e t e r m i n e d to be. within our scheme [2,3] fDo --0.2 GeV In order to agree with all the d a t a on D-decay The form factor Fk,,, is usually p a r a m e t r l z e d as -

F~.,,,(q2 1 + ) = ~ m~.m _Lq 2_ z,,

(10)

where the K, are the axial poles which can contribute to the reaction In the literature we find two possible candidates corresponding to K j ( 1 2 8 0 ) and K~(1400) The "effective" pole residue z, is expected to be o f order u m t y [8] (at least for small energy transfer) It has been recently stressed [9] that the large n u m b e r o f resonances in the region o f 1-2 G e V makes it plausible that this value m a y be significantly larger (especially since m a n y o f these resonances are fairly b r o a d ) A recent analysis o f the pseudoscalar form factor [5] estimates that an effecnve z m a y have a value up to about 3 7 without conflicting with PCAC The same analysis [ 5 ], however, estimates that, within the conventional approaches [8] to charm decay where only W R contributes, to find agreement with the experimental finding [ 1] for B R ( D ° - ~ K ° 0) (eq (1)) one would need the utterly implausible value of z -~ 30 If we plug all the known p a r a m e t e r s in eq (9) and if we take z~ ~ 1 5-2 keeping both c o n t n b u n o n s from K~(1280) and K~(1400) in (10), we find that our m o d e l gives the right order of magnitude B R ( D ° ~ I ~ ° 0 ) ~ 1%, matching quite well the experimental value [ 1] o f eq (1) We repeat once m o r e that this result, i e the c o n t r l b u n o n [9 ] originates indeed from W E , as expected on general grounds [ 10] W i t h the same k i n d of arguments and using the

Volume 199, number 1

PHYSICS LEFTERS B

axial p o l e a ~ ( 1 2 7 0 ) a n d r ( F + ) - ~ 2

8 × 1 0 -~3 s to-

g e t h e r w i t h z-~ 1 5 - 2 , we f i n d BR(F + ~p+~o)_~4_8% B R ( F + --. 9°~: + ) --- 4 - 8 %

, (1 1 )

T h i s ~s a n o t h e r [4 ] t e s t a b l e p r e & c t ~ o n o f o u r s c h e m e o f w h i c h we u r g e t h e e x p e n m e n t a h s t s to c h e c k O n e o f us (I B ) a c k n o w l e d g e s t h e h o s p i t a l i t y at t h e D l p a r t l m e n t o dl F t s l c a T e o r l c a o f t h e U n i v e r s i t y of Torlno and the financial support of CNPq-Brazll

References

10 December 1987

Mark Ill Collab, R M Baltrusaltls et al, SLAC report SLAC-PUB-3858 (1985) [2] J L Basdevant I Bedlaga and E Predazzl, to be pubbshed [3] J L Basde,~ant I Bedlaga, E Predazzl and J Tlomno, Io be pubhshed [4] I Bedlaga, E Predazzl and J Tlomno, Phys Lett B 181 (1986) 395 [5] U Baur, A J Buras, J M Gerard and R Ruckl preprmt MPI-PAE/PTh 10/86 [6] A J Buras, J M Gerard and R Ruckl, Nucl Phys B 268 (1986) 16 [ 7 ] M K Galllard and B W Lee Phys Re,~ Lett 33 (1987) 108 G Altarelll and L Malanl, Ph)s Lett B 52 (1974) 351 [8] D Faklro'~ and B Stech, Nucl Ph3s B 133 (1978) 315 [9] AN Kamal, Phys Re~ D33 (1986) 1344 [10] I I Blgl and M Fukugtta, Ph3s Lett B 91 (1980) 121

[ 1] ARGUS Collab, H Albrecht et al, Ph)s Lett B 158 (1985) 525, CLEO Collab, P A~ery et al submitted lo 1985 Lepton photon Symp (K)oto, Japan)

133