Systematics of qq-states in the (n, M 2 ) and (J, M 2 ) planes A.V. Anisovich, V.V. Anisovich, and A.V. Sarantsev St.Petersburg Nuclear Physics Institute, Gatchina, 188350, Russia (March 13, 2000) In the mass region up to M < 2400 MeV we systematise mesons on the plots (n, M 2 ) and (J, M 2 ), thus setting their classification in terms of n 2S+1 LJ qq states. The trajectories on the (n, M 2 )-plots are drawn for the following (IJ P C )-states: a0(10 ++ ), a1(11 ++ ), a2(12 ++ ), a3(13 ++ ), a4(14 ++ ), π(10 −+ ), π2(12 −+ ), η(00 −+ ), η2(02 −+ ), ρ(11 −− ), f0(00 ++ ), f2(02 ++ ). All trajectories are linear, with nearly the same slopes. At the (J, M 2 )-plot we set out meson states for leading and daughter trajectories: for π, ρ, a1, a2 and P ′ .In the last decade tremendous efforts have been paid to study meson spectra over the mass region 1000-2400 MeV. The collected rich information that includes the discovery of new resonances and confirmation of those discovered before needs to be systematized.We present a scheme for qq trajectories on the (n, M 2 ) and (J, M 2 ) plots (n is the radial quantum number and J is the meson spin) using the latest results [1-6] together with previously accumulated data [7].The trajectories on the (n, M 2 )-plots are presented in Figs. 1 and 2: they are linear and with a good accuracy can be represented asM 0 is the mass of basic meson and µ 2 is the trajectory slope parameter: µ 2 is approximately the same for all trajectories: µ 2 = 1.25 ± 0.15 GeV 2 . At M ≤ 2400 MeV the mesons of qq nonets n 2S+1 L J fill in the (n, M 2 )-trajectories as follows:Trajectories with the same IJ P C can be created by different orbital momenta with J = L ± 1, in this way they are doubled: these are trajectories (I1 −− ), (I2 ++ ), and so on. Isoscalar states are formed by two light flavor components, nn = (uū + dd)/ √ 2 and ss. Likewise, this also results in doubling isoscalar trajectories.The trajectories a 1 (11 ++ ) and a 3 (13 ++ ) are shown in

We present the results of the current analysis of the partial wave IJ P C = 00 ++ based on the available data for meson spectra (ππ, K K, ηη, ηη ′ , ππππ). In the framework of the K-matrix approach, the analytical amplitude has been restored in the mass region 280 MeV< √ s < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750) and the broad state f 0 (1200 − 1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, K K, ηη, ηη ′ , ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, K K, ηη, ηη ′ , we estimate the quark/gluonium content of f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750), f 0 (1200 − 1600). For f 0 (980), f 0 (1300), f 0 (1500) and f 0 (1750), their partial widths testify the q q origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f 0 (1200 − 1600) support the idea about gluonium nature of this broad state.→ ππ, K K, ηη, ηη ′ , makes us to apply the other methods to single out the states which are extra ones for the q q-systematics, namely, exotic states. The method based on the consideration of trajectories in the (n, M 2 )-plane (n is radial quantum number of the q q state and M its mass) is discussed in Section 5.On the basis of the extracted partial widths for the channels ππ, K K, ηη, ηη ′ , the following properties of resonances f 0 (980), f 0 (1300), f 0 (1500), f 0 (1750) and broad state f 0 (1200 − 1600) are to claim:1. f 0 (980): This resonance is dominantly the q q state, q q = nn sin ϕ + ss cos ϕ, with a large ss component. Under the assumption that the admixture of the glueball component is

We perform the K-matrix analysis of meson partial waves with IJ P C = 00 ++ , 10 ++ , 02 ++ , 12 ++ basing on GAMS data on π − p → π 0 π 0 n, ηηn, ηη ′ n together with BNL data on π − p → K Kn and Crystal Barrel data on pp(at rest) → π 0 π 0 π 0 , π 0 ηη, π 0 π 0 η. The positions of the amplitude poles (physical resonances) are determined as well as the positions of the K-matrix poles (bare states) and the values of bare state couplings to two-meson channels. Nonet classification of the determined bare states is discussed.

BARYONS S y s t e m a t i z a t i o n a n d M e t h o d s o f A n a l y s i sMesons and Baryons Downloaded from www.worldscientific.com by 18.236.120.13 on 05/10/18. For personal use only. British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. PrefaceThe notion of quarks appeared in the early sixties just as a tool for the systematisation of the growing number of experimentally observed particles. First it was understood as a mathematical formulation of the SU(3) properties of hadrons, but soon it became clear that hadrons have to be considered as bound states of quarks (objects which we call now "constituent quarks"). The next steps in understanding the quark-gluon structure of hadrons were made in the framework of Quantum Chromodynamics, a theory of coloured particles, as well as in the study of hard processes (i.e. in the study of hadron structure at small distances). We know that hadrons are, definitely, composed of large numbers of quarks, antiquarks and gluons. We have learned this from deep inelastic scattering experiments, and this picture is proven by many experiments on hard collisions and multiparticle production. At small distances quarks and gluons interact weakly, obeying the laws of QCD. An important fact is that a coloured quark or a gluon alone cannot leave the small region of the size of a hadron (i.e. that of the order of 10 −23 cm): they are confined -they can fly away only in groups which are colourless.In the fifties and sixties of the last century virtually the whole physics of "elementary particles" (at that time also hadrons were considered as such) was devoted to the consideration of these distances. With the progress of experimental physics very soon even smaller distances were reached at which hard processes were investigated, giving a strong basis to Quantum Chromodynamics -a theory in the framework of which coloured particles can be considered perturbatively. This, and the hope that the key for understanding the physics of strongly interacting quarks and gluons was hidden just here, initiated research towards smaller and smaller distances, skipping the region of strong (soft) interactions. We accumulated a very serious amount of knowledge on the hadron structure at extremely small distances. But looking back to the region of standard hadron sizes, 10 −24 -10 −23 cm, we realize now that, in fact, the physics at ∼ 10 −23 cm in its essential domains remains unknown [1, 2]. We left behind the hadron distances without really understanding all the observed phenomena. We have learned only a small part of what could be learned from the experimental results in that region, not to mention that experiments which could be easily carried out were also abandoned. The physics community just skipped some p...