The Experimental Situation in D Meson Decay

Abstract

It has been clear for some time that the simple light quark spectator model of charm quark decay¹ does not provide a satisfactory explanation of the experimental situation. It is not clear, however, which specific changes to this picture are necessary. These changes, proposed by numerous authors, fall into two broad categories. The first approach assumes the fundamental correctness of the spectator model. That is, the dominant mechanism is thought to be decay of the charmed quark via emission of a W, with subsequent decay of the W into quark pairs. The light quark component of the meson is merely a spectator. The failures of this simple picture, that is, the non-equality of D° and D ⁺ lifetimes and the erroneous prediction of suppression of the decay D° → $overline K ^\circ \pi ^\circ$ are dealt with by two basic modifications:

• 1) The change of the two QCD couplings f ₊ and f _- from their calculated values.² These coefficients have now been calculated by renormalization group techniques not only in leading log approximations but, recently, in the next-to-leading log order. The next order changes are, in fact, small, reinforcing the correctness of the leading log values (f ₊ ≅ .7, f _- ≅ 1.9, for six fermions and a mass scale of ∼2 GeV) which have been in use for several years. Nonetheless, in order to account for the experimental facts within this context, it is necessary to postulate that f _- is, in fact, very much larger than f ₊. Since the two spectator diagrams in D ⁺ decay lead to the same final quark state, they can interfere. If f _- >> f ₊, this interference can be destructive, reducing the D ⁺ decay rate and lengthening the D ⁺ lifetime. Thus, in this picture the D ⁺/D° lifetime difference is ascribed to an increase in the D ⁺ lifetime, with the D° and F ⁺ lifetimes occurring at values one would estimate by scaling from muon decay by (m _μ/m _c )⁵.

• 2) The second approach attributes the shorter D° lifetime to the importance of additional (W exchange) amplitudes, occurring only in D° decay.³ These are, naively, suppressed by helicity conservation at the light quark vertex. Either through explicit radiation of soft gluons, or through the gluon component of the quark wavefunction, the W exchange diagram is then enhanced. In this picture, the D ⁺ lifetime would occur at the “normal” value while the D° lifetime (and perhaps the F ⁺ lifetime through similarly enhanced W annihilation graphs) would be shortened. Since the W exchange process leads to I = 1/2 final states in hadronic D° decay, whereas the spectator process produces both I = 1/2 and I = 3/2 final states, reinforcement of I = 1/2 configurations would be indicative of the importance of exchange diagrams.