The Kπ and ππ S-wave from D decays

The physics of the scalar mesons has been challenging for decades. Scalar mesons are difficult to detect, since they decay isotropically and have, in general, large widths . There are many candidates with mass bellow 2 GeV/ c. Some states are now well established, while others remain controversial. In any case, there is a large overlap between states in this region of the spectrum. An additional problem arises from the richness of the low energy strong dynamics, allowing other 0 configurations than the usual qq̄. Although none of these ’exotic’ configurations has been clearly established, some would populate the 1-2 GeV/ c region, mixing with the regular qq̄ mesons. The identification of the qq̄ scalar nonet(s) is, thus, a rather complicated task, which can only be accomplished if one combines data from different types. This paper is focused on two issues: the Kπ spectrum near threshold – the kappa problem –, and the ππ spectrum between 1.2 and 1.5 GeV/ c – thef0(1370) problem. Both problems will be analysed from the perspective of the D meson decays, with some additional information from τ andB decays. Hadronic and semileptonic decays of D mesons have unique features that make them a key to light meson spectroscopy, in particular to the study of the Kπ andππ scattering amplitudes in S-wave. First, these are the only process that allows us to access the Kπ/ππ spectrum continuously from threshold up to∼ 1.5 GeV/c. In Kπ andππ scattering, the production of scalar resonances near thres hold is suppressed by the Adler zeroes. No such effect is observed inD decays. In scattering, the large nonresonant component forms a continuum background on top of which the scalar resonances are found. The interference between the broad states and this continuum distorts the resonance line shape, and is always a difficult problem to be accounted for. InD decays, the nonresonant component is usually small. InD decays, channels with two identical pions in the final state have a largely dominant S-wave component. Decay modes like D → K−π+π+ andD, D s → π−π+π+ are easy to be reconstructed and have large branching fractions. There are plenty of good data with very low background on these ’golden’ modes. In the first year of the LHCb operation, we will enter in the regime of ’infinite’ statistics. The decay of aD meson is, obviously, a very complex process. It is initiated by the c → s(d) weak transition. This transition is embedded in a strongly interacting system, in the non-perturbative regime, from which the final state hadrons emerge. No precise quantitative description based on first principles can be performed. Nevertheless, a qualitative description of such a complex process can be constructed using simple ideas. Going through the PDG listings, one realises that essentially the wholeD decay width can be explained by simple treelevel valence quark diagrams, such as the one shown in Fig. 1, connected to the well known qq̄ resonances from the Constituent Quark Model. Considering, for instance, three body decays proceeding through intermediate states having spin-1 and 2 resonances, one concludes that the regular qq̄ mesons correspond to the entire decay rate. No ’exotic’ states have been observed in D decays, which act as a qq̄ filter. Assuming the tree-level diagrams to be dominant, the available ’final state’ quarks, that is, those resulting fro m the weakc decay, determine not only which qq̄ resonances can occur, but also their relative rates. A nice example is the ’weak vector/axial-vector dominance’, a close analogy to the vector dominance in electrodynamics. Due to the V-A nature of thec quark decay, in the diagram of Fig. 1 the virtualW will couple preferentially to a vector or to an axial-veto particle, rather than to a pseudoscalar. The branching fraction for the decays D → Ka1 (1260) and D → K−ρ+(770), for instance, are three to four times larger than that of D → K−π+.