ar X iv : h ep - p h / 97 10 45 7 v 1 2 4 O ct 1 99 7 Dressing the Scalar Glueball

The hadronic dressing of the ten lightest scalar mesons is discussed. Let us imagine that we live in a world without quarks. QCD suggests there will still be a spectrum of hadrons, bound states of two or more gluons, the lightest of these being stable. Though this world is far from that explored by experiment, it is the world of the lattice calculator. There the lightest state is a scalar in the region of 1–2 GeV, just where we expect the lowest qq scalars to be. The lattice makes definite predictions for the bare glueball mass, depending on the calculational scheme : 1550 MeV from UKQCD (1), 1600 MeV from Morningstar and Peardon (2) and 1740 MeV from the GF-11 group at IBM (3). Though this state is stable in the quenched world of the lattice, the IBM group have pioneered the calculation of its coupling to 2 pseudoscalar sources and found this would correspond to a width of some 100 MeV (4). Naively, one would expect the bare glueball to couple as an SU (3) F singlet. The IBM group have calculated that in fact coupling to heavier pseudoscalars should be favoured (4). Thus the lattice makes predictions for the scalar gluestate with some element of choice about its exact mass and coupling scheme. Here we will focus on just one for ease of presentation. We will take a mass of 1600 MeV with a coupling pattern as given by the IBM group (note that this pattern is not very sensitive to the exact glueball mass). However, very similar results apply for other choices. Of course, the bare non-decaying state is not what any experiment can observe. A bare state, whether composed of glue or quarks, has to be dressed by interactions with mesons in order to decay. Thus, though we like to think of the ρ or φ as qq states, their Fock space contains important ππ and KK components , respectively, through which these hadrons decay. For most mesons, and in particular, the vectors and tensors, these hadronic dressings make rather little difference to the states. So the hadrons we observe and the underlying qq bound states are simply related and readily identifiable one from the other. However, as has been emphasised by Tornqvist (5), this is not the case for scalars. This is because their couplings are larger and because, in as much as decays to …