Volume 84B, number 4 PHYSICS LETTERS 16 July 1979

ON THE FREE PARTON MODEL FOR WEAK SEMILEPTONIC DECAYS OF CHARMED PARTICLES

M. GLUCK Institut far Physik, Universitdt Mainz, 6500 Mainz, I¢. Germany

Received 14 May 1979

It is argued that the fitted charmed quark mass and Fermi momentum in the free parton model for semileptonic decays of charmed particles, are unreasonably large. Furthermore, the charmed quark mass needed to explain the estimated semi- leptonic width of charmed particles is also too large (~2 GeV). It is reasoned that the failure of the free patton picture is due to strong initial and final state binding effects.

Recently, it was proposed [ 1 - 3 ] to study the semi- leptonic weak decays of charmed particles in the frame. work of a free parton model (FPM) including the first- order hard gluon corrections. By "free" one means the ineffectiveness of the "spectator" light quarks in the decaying charmed particle.

At first sight this seems to yield a quite reasonable approximation since, due to the heavy mass involved, we are in principle in the "deep" region where a free parton picture is believed to be useful. Experience with deep-inelastic scattering, however, teaches us that in order for the FPM to be useful it is not enough to be merely in the "deep", i.e. high-Q 2, region. One fur- ther needs the "inelasticity"; W 2 = Q2(1/x - 1) should be above the resonance region i.e. W 2 >~ 2 GeV 2. Only then is the description in terms of free partons or twist-two operators expected to be applicable. Other- wise correlated parton configurations or higher twist operators are important.

We shall now argue that this, in fact, is also the situation for the semileptonic decays of charmed par- ticles, i.e. we shall show that resonance effects are not negligible here in spite of the high momenta and masses involved.

Let us begin with the electron momentum spectrum dN/dP e calculated [2,3] in the a s corrected FPM. It was found [3] that the charmed quark mass needed to reproduce the data was m c = 1.7 GeV (assuming m s = 0.5 GeV). To reproduce the high Pe tail as well as the correct peak in the dN/dP e distribution an ad-hoc

Fermi momentum (Pc) of ~0 .6 GeV was introduced. An educated guess of (Pc) in the charmed D-meson would be

(Pc) ~ as(me) mumc/(mu + me) .

Taking m u ~ 0.3 GeV; m e ~ 1.5 GeV and as(me) 0.7 one gets (Pc) ~. 0.17 GeV, i.e. a factor ~3 smaller than the (Pc) of ref. [3]. Since the smearing effects depend essentially on (Pc)2 our lower (Pc) would prac- tically have no effect on dN/dP e. We conclude there- fore that for reasonable values of m c - i.e. 1.5 GeV instead of the 1 .7-1 .8 GeV of ref. [3] - and of (pc), dN/dP e is not reproduced by the a s corrected FPM. This should be contrasted with the conventional approach [4] based on the dominance o f the three exclusive decay channels D ~ Key; K*ev; Trey. Surely what is missing in the FPM is a simulation of the K* which shifts the peak in dN/dP e to its correct place. Furthermore, the abnormally high charmed mass in the FPM in fact reflects m D rather than m e.

From the above we learn that initial and final state interactions, responsible for m D and mK. , respectively, do indeed play a significant role in semileptonic charm decays and that their simulation by an inin'al state Fermi-motion correction alone leads to unreasonably high values o f (Pc). Noting furhter that the high Pe tail is due to the Cabibbo-suppressed mode D ~ trey its simulation in the FPM should proceed via c ~ deu rather than by (pc) . This would somewhat reduce (pc) but still the correct peak in dN/dP e cannot be repro- duced in a natural way in the model.

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Volume 84B, number 4 PHYSICS LETTERS 16 July 1979

In spite o f the failure to reproduce the detailed Pe spectrum because o f resonance effects perhaps the resonance "smeared" quanti ty r e ( D ) is still correctly described by the par ton model as is the case, e.g., in e+e - annihilation [5].

To check this possibility we need an independent estimate of Fe(D ). This is provided by the conventional

theoretical estimate [4] F(D ~ Key) = (1.4 +-- 0.3) X 10 -11 s -1 and the experimental P(D ~ Kev)/I~(D

-* Xev) = 0.37 -+ 0.20 obtained [6] from fits to dN/dP e based on D ~ Key, K*ev, trey, Combining these results one obtains [6] with Be(D ) = 0.1, that r D = (2.6 +- 1.5) X 10 -13 s.

To reproduce this value in the a s and mass corrected

FPM [1] one needs m c = 2.0 GeV (for m s = 0.5 GeV) or at least m c = 1.85 GeV if the highest allowed life- time is considered. It seems therefore that even the "smeared" quant i ty Fe(D ) is not correctly reproduced

by the free parton model.

References

[11 N. Cabibbo and L. Maiani, Phys. Lett. 79B (1978) 109. [2] M. Suzuki, Nucl. Phys. B145 (1978) 420. [3] A. Ali and E. Pietarinen, DESY report 79/12 (1979). [4] M.K. Galilard, B.W. Lee and J.L. Rosner, Rev. Mod. Phys.

47 (1975) 277; J. Ellis, M.K. Galliard and D.V. Nanopoulos, Nucl. Phys. B100 (1975) 313; A. Ali and T.C. Yang, Phys. Lett. 65B (1976) 275; I. Hinchliffe and C.M. Llewellyn-Smith, Nucl. Phys. B144 (1976) 45; V. Barger, T. Gotschalk and R. Phillips, Phys. Rev. D16 (1977) 746; W. Wilson, Phys. Rev. D16 (1977) 742; F. Bletzaeker, M.T. Nieh and A. Soni, Phys. Rev. D16 (1977) 732; D. Fakirov and B. Stech, Nucl. Phys. B133 (1978) 315; this is a partial list from which further references may be derived.

[5] A. DeRfjula and H. Georgi, Phys. Rev. D13 (1976) 1296; E. Poggio, H.R. Quinn and S. Weinberg, Phys. Rev. D13 (1976) 1958; R. Shankar, Phys. Rev. D15 (1977) 755.

[6] J. Kirkby, SLAC-PUB-2231 (1978).

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