The Experimental Situation in D Meson Decay

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.

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.