ar X iv : h ep - p h / 01 06 13 1 v 1 1 3 Ju n 20 01 The Search for New Physics in D 0 → γγ Decay

We present main results of the investigation of the rare decay mode D0 → γγ, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Lagrangian we have considered the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one loop π, K diagrams. The loop contributions which are proportional to g and contain the a1 Wilson coefficient are found to dominate the decay amplitude. The branching ratio is then calculated to be (1.0 ± 0.5) × 10−8. Observation of an order of magnitude larger branching ratio could signal new physics. Contributed Paper for LPO1 In the past years the rare decays of B mesons came under the spotlights as the source of possible signals of new physics. In the meanwhile studies of rare D decays have received much less attention. Partially this is because theoretical investigations of D weak decays are rather difficult, also due to the presence of many resonances close to this energy region. The penguin effects on the other hand, which are very important in B and also in K decays, are usually suppressed in the case of charm mesons due to the presence of d, s, b quarks in the loop with the respective values of CKM elements. Nevertheless, D meson physics has produced some interesting results in the past year. Experimental results on time dependent decay rates of D0 → K+π− by CLEO [1] and D0 → K+K− and D0 → K−π+ by FOCUS [2] have stimulated several studies on the D0 − D̄0 oscillations [3]. The recently measured D* decay width by CLEO [4] has provided the long expected information on the value of DDπ coupling. Among the rare D decays, the decays D → V γ and D → V (P )l+l− are subjects of CLEO and FERMILAB searches [5]. On the theoretical side, these rare decays of charm mesons into light vector meson and photon or lepton pair have been considered lately by several authors (see, e.g., [6][11], for radiative leptonic D meson decay see [12]). The investigations of D → V γ showed that certain branching ratios can be as large as 10−5, like for D0 → K̄∗0γ, D+ s → ρ+γ [6, 11]. However, the decays which are of some relevance to the D0 → 2γ mode studied here, like D0 → ρ0γ, D0 → ωγ, are expected with branching ratios in the 10−6 range [13]. Thus, it is hard to believe that the branching ratio of the D0 → 2γ decay mode can be as high as 10−5 in the Standard Model (SM), as found by [14]. Apart from this estimation, there has been no other detailed work on D0 → 2γ prior to our analysis [15]. In addition to these theoretical studies there are experimental attempts to observe this decay rate done by CLEO and FOCUS [16]. On the other hand, in the B and K meson systems there are numerous studies of their decays to two photons. For example, the Bs → γγ decay has been studied with various approaches within SM and beyond. In SM, the short distance (SD) contribution [17] leads to a branching ratio B(Bs → γγ) ≃ 3.8 × 10−7. The QCD corrections enhance this rate to 5 × 10−7 [18]. On the other hand, in some of the SM extensions the branching ratio can be considerably larger. The two Higgs doublet scenario, for example, could enhance this branching ratio by an order of magnitude [19]. Such ”new physics” effects could at least in principle be dwarfed by long distance (LD) effects. However, existing calculations show that these are not larger than the SD contribution [20], which is typical of the situation in radiative B decays [21]. In the K0 system the situation is rather different. Here, the SD contribution is too small to account for the observed rates of KS → 2γ, KL → 2γ by factors of ∼ 3− 5 [22], although it could be of relevance in the mechanism of CP-violation. Many detailed calculations of these processes have been performed over the years (see recent refs. [22] -[25] and refs. therein), especially using the chiral approach to account for the pole diagrams and the loops. These LD contributions lead to rates which are compatible with existing measurements. Motivated by the experimental efforts to observe rare D meson decays [16], and noticing that Bs → γγ offers possibility to observe physics beyond the SM, we undertook an investigation of the D0 → γγ decay [15]. Here we present only the main results of our analyses, while the details of our work are presented in [15]. The short distance contribution is expected to be rather small, as already encountered in the one photon decays [6, 7], hence the main contribution would come from long distance interactions. In order to treat the long distance contributions, we use the heavy quark effective theory combined with chiral perturbation theory (HQχPT) [26]. This approach was used before for treating D strong and electromagnetic decays [27]-[29]. The leptonic and semileptonic decays of D meson were also treated within the same framework (see [27] and references therein). The approach of HQχPT introduces several coupling constants that have to be determined from