Mechanism for the Difference in Lifetimes of Charged and Neutral D Mesons

estimated the via a pole model and finds it comparable to the purely leptonic rate. The reaction D -s+ d+ gluon is proposed as a source for the difference in the lifetimes of the charged and neutral D mesons. In a nonrelativistic bound-state model the rate for the reaction is found to depend on the ratio folm . For reasonable values of this ratio the observed difference in the lifetimes may be accounted for.

S. Kaptanoglu, Phys. Rev. D 18, 1554. "Estimates of frr have been given by S. Gershtein and M. Khlopov,Pis'ma Zh. Eksp. Teor. Fiz. 23,374 (1976) I JETP Lett. 23, 338 (1976)l; V. Novikov et al . , Phys. Rev. Lett. 38, 626 (1977); and A. Ali et al. , . Phys The reaction D -s+ d+ gluon is proposed as a source for the difference in the lifetimes of the charged and neutral D mesons. In a nonrelativistic bound-state model the rate for the reaction is found to depend on the ratio folm . For reasonable values of this ratio the observed difference in the lifetimes may be accounted for.
A number of experiments' have recently reported a significant difference in the lifetimes of the charged and neutral D mesons, with TD perhaps as much as six times as large as T&p. It has been argued that mesons containing a heavy quark c, 6, or t will decay through a mechanism where the light quark acts as a spectator' [Fig. 1(a)]. The process depicted in Fig. 1(b) can contribute only to the decay of the D'. ' However, by the usual helicity arguments the contribution of of SU(4), respectively. ' Using a, (m, ') =0. 6, we obtain f -2 and f, -0.'l, leading to as = 1.7.
In this note, we propose a mechanism that may account for the observed difference in lifetimes. It is the one depicted in Fig. 2, namely, Dos + d + y, (gluon) .
Vfe have calculated the contribution of this proc-. ess by considering the Do meson (mass = 1.86 GeV) as a nonrelativistic bound state of c and u quarks with "constituent" quark masses of m, -1.55 GeV and m"-0.3 GeV. The momentum variation of the bound-state wave function is faster than that &D(P)i J""10&=(2, )", (2~" ",, where J is the weak hadronic axial-vector current. The spectator graph leads to equal charged and neutral decay rates given by4 where e' is the polarization of the gluon and l" the weak current of the light quarks: l" =u, (q,)y "(1y, )v, (q,) .
Since we are dealing with gluon emission from a color -neutral state the gauge-invariant amplitude (4) is infrared finite. Note that the contribution for gluon emission from final-state light-quark lines will be suppressed by powers of m, ' and/or m~' and is therefore neglected.
In the nonrelativistic model that we have adopted we find F"~y (0)  Our method of calculating F"and FY of Eqs. (6) and (7) based on a nonrelativistic bound-state model are expected to work, at best, for heavyquark systems. They are totally unreliable for r or K mesons. Analogous form factors exist' for v (K) -ivy {also vyy), but they are smaller by a factor of 10' for the m case and a factor of 10 for the case of K mesons than a model as ours would suggest. For light mesons these form factors can be under stood on the basis of partial conservation of axial-vector current (PCAC) arguments. We do not expect soft-D-meson limits to work. On the other hand, nonrelativistic boundstate models have had considerable success in the heavier systems. " We expect an analogous mechanism to be important in other heavy-meson decays. Some consequences are as follows: (1) The contribution of the gluon mechanism of Fig. 2 to the width of the charmed E meson can be obtained by repla, cing a, ' with a, = ( f, -f )'/4, mv with mz, m"with m"and f~w ith fz in Eq.
(9). Note that since the W carries no color, the renormalization of the weak four-fermion vertex via gluon exchange is crucial to this contribution and it vanishes in the limit of f;f =1. We thus-obtain " -GF2 a, ' n, f~'mD'/324&'m"', (2) The lifetimes of the neutral mesons containing b and I; quarks and their semileptonic branching ratios will also be smaller than those of their char ged isospin counterparts.
(3) Of course, the strongest prediction of our model is the existence of a gluon jet in the decays of heavy mesons. Anticipating an ability to distinguish gluon from quark jets (for instance by (p~) or multiplicities), we give the energy (&u) distribution of the gluon as I ' dI' /dr=6r(1r), Recall that the contribution to this ratio from the spectator graph [ Fig. 1(a)] is highly suppressed and amounts to 4', . ' Experimentally this ratio is O. V +0.35. " If our mechanism is important for the above two-body modes, then it will also be important to Cabibbo-suppressed decays such as +~a nd Do-~+a .
In short, even a large difference in the lifetimes of charged and neutral B mesons can be explained without requiring a revision of the underlying gauge model and/or invoking exotic new interactions, provided f~/m, "2. The critical point in our calculation is the observation that in the rate for the reaction D -s+ d+ gluon, the de-where r=cu/( 4) Similar considerations should apply to radiative leptonic decays of D (Cabibbo suppressed) and E (Cabibbo allowed) decays. The rate for D' (E+) -e 'vy should be 10' times that for D' (E') -e'v.
(5) As the gluon carries no isospin our mechanism indicates that isospin--, ' final states may dominate Cabibbo-allowed D' decays. It is not clear whether this dominance would extend to the exclusive two-body channels. If it does, then it is worth pointing out that the mechanism of Fig.