The lightest scalar glueball

Abstract

Recently performed investigations of meson spectra allow us to determine the resonance structure for the waves IJ P C = 00 ++ , 10 ++ , 02 ++ , 12 ++ = IJ P = 1 2 0 + in the mass region up to 1900 MeV, thus establishing the meson multiplets 1 3 P0qq and 2 3 P0qq. Experimental data demonstrate that there are five scalar/isoscalar states in this mass region. Four of them are qq states, that is, members of the 1 3 P0qq and 2 3 P0qq nonets, while the fifth state is an extra one not accomodated by qq systematics; it has the properties of the lightest scalar glueball. Analysis of the 00 ++ -wave performed within the framework of the dispersion relation technique allows us to reconstruct the mixing of a pure gluonium with neighbouring scalar qq states belonging to 1 3 P0qq and 2 3 P0qq nonets: three scalar mesons share the gluonium state between each other -those are two comparatively narrow resonances f0(1300) and f0(1500) and a broad resonance f0(1530 +90 −250 ). The broad state is a descendant of the gluonium, keeping about 40-50% of its component.1 Introduction: retrospective view and the current state of the problem A great variety of the currently observed mesons and baryons represent systems built of quarks. These are baryons, which are three-quark systems (qqq), and mesons, which are quark-antiquark bound states (qq). More than 20 years ago the problem arose [1] whether additional hadrons exist which are built out of another fundamental QCD particle, the gluon. An intensive search for the glueball -a particle consisting of gluons -was carried out throughout these decades. First evaluation of the glueball masses for different J P C was done in the bag model [2]. According to it, the lightest glueballs are scalars and tensors, 0 ++ and 2 ++ ; then follow pseudoscalar and pseudotensor glueballs, 0 −+ and 2 −+ .Recently considerable progress has been achieved in Lattice QCD calculations. The UKQCD collaboration [3] obtained the following mass values for the lightest gluodynamical glueballs (i.e. the glueball without quark degrees of freedom taken into account):Systematic errors are not included into the values given in Eq. (1.1); they are of the order of 100 MeV.The IBM group obtained a slightly different value for the mass of the lightest scalar glueball [4]:m G (0 ++ ) = 1740 ± 71 MeV , (1.2)The result of Ref.[5] is as follows:m G (0 ++ ) = 1630 ± 60 ± 80 MeV , m G (2 ++ ) = 2400 ± 10 ± 120 MeV .(1.3)

The meson spectrum in a covariant quark model

“…A brief discussion concerning spin-orbit effects in both models is given in part C. In the last part of section III, we focus on the pseudoscalar and scalar mesons by adding the residual 't Hooft interaction which only acts for mesons with vanishing total angular momentum. There we will also comment on a set of K-matrix poles found by V. V. Anisovich and coworkers [22][23][24][43][44][45] by comparing to our results. Finally we give a summary and conclusion in section IV.…”

“…This effect was illustrated by carrying out the nonrelativistic reduction of both Dirac structures and it turned out that the Salpeter equation in model A reduces to the usual Schrödinger equation whereas in model B the negative energy components do not vanish even in this limit. By virtue of these observations one can conclude that any quark model should account for the correct treatment of relativistic effects not only in the calculations of deeply bound state masses (M ≪ m 1 + m 2 ) but also in the case of higher radial excitation states 16 There exists a second K-matrix solution for the 2 3 P0qq nonet: the authors in [22][23][24][43][44][45] find a third scalar isoscalar bare state between 1200-1600 MeV, the f bare 0 (1235 ± 50), which, instead of the f bare 0 (1600 ± 50), can also be used to complete the 2 3 P0qq nonet. So, one of the scalar isoscalar bare states in the mass region 1200-1600 MeV is superfluous for theqq classification and may be connected to the lightest scalar glueball.…”

Modified Breit–Wigner formula for mesonic resonances describing OZI decays of confined $q\bar{q}$ states and the light scalar mesons

“…Especially the real part of the mass shift is strongly affected by higherorder corrections. In a recent K-matrix analysis [51], as well as in a covariant quarkonium model [52], it is indeed also found that the bare state might be appreciably lower than the central resonance position for the K * 0 (1430). The K * 0 (727) singularity (23) does not have a direct relation to any of the states stemming from the confinement mechanism.…”

The calculation of the differential cross section of hadron elastic scattering by transferred four-momentum within the perturbation theory

“…Тому в цьому сенсi опис зв'язаних ґлюонiв може мало вiдрiзнятися вiд опису зв'язаних кваркiв. Опосередковано про це говорить схожiсть властивостей ґлюболiв i кварк-антикваркових систем [53][54][55][56][57]. Наявнiсть енерґетичного порога народження зв'язаних ґлюонiв приводить до того, що якщо енерґiя взаємодiї ґлюонiв у ґлюболi менша за цей порiг, то новi зв'язанi ґлюони народжуватися не зможуть i ми матимемо систему з фiксованою кiлькiстю частинок.…”