The current situation for vector meson spectroscopy is outlined, and it is
shown that the data are inconsistent with the generally-accepted model for
meson decay. A possible resolution in terms of exotic (hybrid) mesons is given.
Although this hypothesis resolves some of the issues, fresh theoretical
questions are raised. It is argued that high-precision $e^+e^-$ annihilation
data provide an excellent laboratory for studying many aspects of
nonperturbative QCD.Comment: Paper T05 presented at the Workshop on e+e- Physics at Intermediate
  Energies, SLAC, May 200

Donnachie, A

English

arXiv

The current situation for vector meson spectroscopy is outlined, and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms of exotic (hybrid) mesons is given. Although this hypothesis resolves some of the issues, fresh theoretical questions are raised. It is argued that high-precision $e^+e^-$ annihilation data provide an excellent laboratory for studying many aspects of nonperturbative QCD

Donnachie, Alexander

CERN Document Server

LIGHT VECTOR MESONSPECTROSCOPYA. Donnachie, University of Manchester, EnglandJune 19, 2001AbstractThe current situation for vector meson spectroscopy is outlined,and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms ofexotic (hybrid) mesons is given. Although this hypothesis resolvessome of the issues, fresh theoretical questions are raised. It is ar-gued that high-precision e+e− annihilation data provide an excellentlaboratory for studying many aspects of nonperturbative QCD.1 THE PROBLEMIt is now 15 years since it was rst suggested [1, 2] that the 0(1600), asit was then known, is in fact a composite structure, consisting of at leasttwo states: the (1450) and (1700). Their existence, and that of theirisoscalar counterparts, the !(1420) and !(1650), and of an associated hidden-strangeness state, the (1680), is now well established [3]. The key data indetermining the existence of the two isovector states were e+e− ! +−[4] and e+e− ! ! [5]. These original data sets have subsequently beenaugmented by data on the corresponding charged channels in  decay [6, 7,8, 9], to which they are related by CVC. These new data conrm the earlierconclusions. The data on e+e− ! +−+− [10, 11] and e+e− ! +−00[10, 12] (excluding !) and the corresponding charged channels in  decay[7, 8] are consistent with the two-resonance interpretation [13, 14], althoughthey do not provide such good discrimination. Itwas also found that thee+e− ! +− cross section is better tted with two interfering resonances1than with a single state [15]. Independent evidence for two JP = 1− states isprovided in a high statistics study of the  system in −p charge exchange[16]. Decisive evidence for both the (1450) and (1700) in their 2 and 4decays has come from the study of pp and pn annihilation [17]. The datainitially available for the study of the !(1420) and !(1600) were e+e− !+−0 [11, 18] (which is dominated by ) and e+e− ! !+− [18]. Thelatter cross section shows a clear peak which is apparently dominated by the!(1600). The former cross section is more sensitive to the !(1420). Morerecent and more precise data [19] on e+e− ! +−0 below 1.4 GeV conrm[14] the !(1420).However, although there is general consensus on the existence of thesestates, there is considerable disparity on the masses and widths of theseresonances. Information on the vector states comes principally from e+e−annihilation and  decay, but there are problems with much of the data: inconsistencies, even in recent high-statistics data restricted energy ranges, e.g. Novosibirsk and CLEO poor statistics in some channels and missing channels inadequate knowledge of multiparticle nal states ∑ exclusive > inclusiveIn fact the only channel with really consistent data sets over a wide energyrange is the  channel, although even that runs out of statistics at theupper end of the energy range. The comparatively low statistics of the olderdata, the restricted energy range of the newer data with higher statistics,and persisting inconsistencies in data from dierent experiments rule outprecision ts.There are also theoretical uncertainties which aect the analysis of e+e−annihilation and  decay, and which present data are insuciently precise toresolve. Firstly there is the \tail-of-the-" problem. In some channels, mostnotably  and !, there is strong interference between the high-energytail of the  and the higher-mass resonances. The magnitude and shape ofthis tail are not known with any precision. They can only be specied inmodels and strictly should be part of the parametrisation. Dierent modelsyield dierent results for the masses and widths of the resonances. A relatedproblem is the question of the relative phases. These can be specied insimple models, but we know that these models are not precise and leavingthe phases as free parameters has a major eect.Thus only the qualitative features emerge, and apparent precision is inreality the result of implicit, or explicit, theoretical assumptions.2Despite these diculties, the existence of the higher-mass states is not indoubt, and a natural explanation for them is that they are the rst radial,23S1, and rst orbital, 13D1, excitations of the  and ! and the rst radialexcitation of the , as the generally-accepted masses [3] are close to thosepredicted by the quark model [20]. However this interpretation faces a fun-damental problem. The data on the 4 channels in e+e− annihilation arenot compatible with the 3P0 model [21, 22, 23, 24], which is accepted as themost successful model of meson decay. The model works well for decays ofestablished ground-state mesons: widths predicted to be large, are found to be so widths predicted to be small, are found to be so calculated widths agree with data to 25− 40% signs of amplitudes are correctly predictedAs far as one can ascertain the 3P0 model is reliable, but it has not beenseriously tested for the decays of excited states.The 3P0 model predicts that the decay of the isovector 23S1 to 4 isextremely small:Γ2S!a1pi  3 MeV Γ2S!h1pi  1 MeV (1)and for the isovector 13D1 the a1 and h1 decays are large and equal:Γ1D!a1pi  Γ1D!h1pi  105 MeV (2)As h1 contributes only to the +−00 channel in e+e− annihilation, anda1 contributes to both +−+− and +−00, then after subtraction ofthe ! cross section from the total +−00 the 3P0 model predicts:(e+e− ! +−00) > (e+e− ! +−+−) (3)This contradicts observation over much of the available energy range. Below 1:6 GeV (+−+−)  2(+−00), although at higher energies(+−00) is the larger. Further, and more seriously, it has been shownrecently by the CMD collaboration at Novosibirsk [25] and by CLEO [8]that the dominant channel by far in 4 (excluding !) up to  1:6 GeV isa1. This is quite inexplicable in terms of the3P0 model. So the standardpicture is wrong for the isovectors, and there are serious inconsistencies inthe isoscalar channels as well. One possibility is that the 3P0 model is simplyfailing when applied to excited states, which is an intriguing question in itself.An alternative is that there is new physics involved.32 A SOLUTIONA favoured hypothesis is to include vector hybrids [26, 27], that is qqg states.The reason for this is that, rstly, hybrid states occur naturally in QCD,and secondly, that in the relevant mass range the dominant hadronic decayof the isovector vector hybrid H is believed to be a1 [27]. The massesof light-quark hybrids have been obtained in lattice-QCD calculations [28,29, 30, 31], although with quite large errors. Results from lattice QCD andother approaches, such as the bag model [32, 33], flux-tube models [34],constituent gluon models [35] and QCD sum rules [36, 37], show considerablevariation from each other. So the absolute mass scale is somewhat imprecise,predictions for the lightest hybrid lying between 1.3 and 1.9 GeV. Howeverit does seem generally agreed that the mass ordering is 0−+ < 1−+ < 1−− <2−+.Evidence for the excitation of gluonic degrees of freedom has emergedin several processes. Two experiments [38, 39] have evidence for an ex-otic JPC = 1−+ resonance, ^(1600) in the 0− channel in the reaction−N ! (+−−)N . A peak in the  mass spectrum at  1400 MeV withJPC = 1−+ in −N ! (−)N has also been interpreted as a resonance[40]. Supporting evidence for the 1400 state in the same mode comes frompp ! −+ [41]. There is evidence [42] for two isovector 0−+ states in themass region 1.4 to 1.9 GeV; (1600) and (1800). The quark model predictsonly one. Taking the mass of the 1−+  1:4 GeV, then the 0−+ is at  1:3GeV and the lightest 1−− at  1:65 GeV, which is in the range required forthe mixing hypothesis to work. Of course if hybrids are comparatively heavy,that is the ^(1600) is the lightest 1−+ state, and the (1600) presumably thecorresponding 0−+ hybrid (or at least with a signicant hybrid component)then the vector hybrid mass  2:0 GeV making strong mixing with the radialand orbital excitations unlikely.Two specic models for the hadronic hybrids are the flux-tube model[27, 34] and the constituent gluon model [43, 44]. There are some substantialdierences in their predictions for hybrid decays. For the isovector 1−− theflux-tube model predicts a1 as essentially the only hadronic mode, and awidth of  100 MeV. The constituent gluon model predicts dominant a1,but with signicant ()S and ! components, and a larger width. Forthe isoscalar 1−− the flux-tube model predicts  as essentially the onlyhadronic mode, with a width of  20 MeV. The constituent gluon modelpredicts dominant , a signicant !()S component and a larger width.4The general conclusion is that the e+e− annihilation and  -decay data re-quire the existence of a \hidden" vector hybrid in the isovector and isoscalarchannels (assuming that the 3P0 results are qualitatively reliable). The mix-ing required is non-trivial, although schemes can be devised which are qual-itatively compatible with the data [45]. The unseen physical states are \o-stage", in the 1.9 to 2.1 GeV mass region. Nonetheless, it appears dicult toachieve quantitative agreement with data (within the constraint of specicmodels) unless the hybrids and the 13D1 states have direct electromagneticcoupling. At the simplest level they do not, but these couplings can be gen-erated by relativistic corrections at the parton level [20] or via intermediatehadronic states, for example hybrid ! a1 ! \" ! e+e−.To extract the information will require excitation curves for a wide rangeof hadronic nal states: ! a1 h1  ()S K K K K    (4)Note that the nn states can decay to K K, K K etc. with signicant partialwidths:Γ2S!KK¯  30MeV Γ1D!KK¯  40MeV (5)so isospin separation is necessary in these channels, and there can be mixingbetween the isoscalar nn states and the ss states.Radiative decays allow a clean separation of the 2S and 1D states. Pre-liminary widths in keV are [46]:Γ(S) Γ(!S) Γ(D) Γ(!D)a1γ  80  750  200  1800a2γ  100  900  10  100f1γ  650  70  1700  200f2γ  1200  130  120  15Obviously the f2γ channel selects the S state uniquely. 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Light Vector Meson Spectroscopy

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