Two-photon collisions at the e$^+$e$^-$ colliders allow to investigate the
formation and the properties of resonant states in a very clean experimental
environment. A remarkable number of new results have been recently obtained
giving important contributions to meson spectroscopy and glueball searches. The
most recent results from the LEP collider at CERN and CESR at Cornell are
reviewed here.Comment: 10 pages, invited talk presented at Meson2000, Cracow, Poland, May
  200

Braccini, Saverio

English

arXiv

Two-photon collisions at the e$^+$e$^-$ colliders allow to investigate the formation and the properties of resonant states in a very clean experimental environment. A remarkable number of new results have been recently obtained giving important contributions to meson spectroscopy and glueball searches. The most recent results from the LEP collider at CERN and CESR at Cornell are reviewed here

Braccini, S

CERN Document Server

RESONANCE FORMATIONIN TWO-PHOTON COLLISIONSSaverio BRACCINIyUniversity of Geneva,24, Quai Ernest-Ansermet, CH-1211 Geneve 4, SwitzerlandE-mail: Saverio.Braccini@cern.chTwo-photon collisions at the e+e− colliders allow to investigate the for-mation and the properties of resonant states in a very clean experimentalenvironment. A remarkable number of new results have been recently ob-tained giving important contributions to meson spectroscopy and glueballsearches. The most recent results from the LEP collider at CERN andCESR at Cornell are reviewed here.1. IntroductionTwo-photon collisions at electron positron storage rings are a good lab-oratory to investigate the properties of meson resonances and play a crucialrole in glueball searches.A resonant state R can be formed by the collision of two photons via thereaction e+e− ! e+e−R (g. 1). The outgoing electron and positron areusually scattered at very small angles and are not detected (no-tag mode).In this case the two photons are quasi real and the resonant state R mustbe neutral and unflavoured with C=1 and J6=1. If one of the two photonsis highly virtual, the outgoing electron or positron can be detected at lowangle and the spin of the resonant state is allowed to be one (single-tagmode). In both cases the two outgoing particles carry nearly the full beamenergy and the mass of the resonant state is much smaller than the e+e−centre of mass energy. This fact allows a clean separation between the two-photon and the annihilation process by using a cut in the visible energy.Since there are no particles produced other than R, the reconstruction ofthe nal state can be performed in a very clean experimental environment.The cross section for this process is given by the convolution of the QEDcalculable luminosity function L, giving the flux of the virtual photons, with† Talk given at Meson2000, Cracow, Poland, May 2000.(1)2Fig. 1. Diagram of the formation of aresonant state in two-photon collisionsat e+e− colliders.Events / 40 MeV L3m(pi+pi-pio) (GeV)02550751001250.5 1 1.5 2 2.5Fig. 2. The +−0 mass spectrum.the two-photon cross section (γγ ! R) that is expressed by the Breit-Wigner function(γγ ! R) = 8(2J + 1) Γγγ(R)Γ(R)(W 2γγ −m2R)2 +m2RΓ2(R)(1)where Wγγ is the invariant mass of the two-photon system, mR, J, Γγγ(R)and Γ(R) are the mass, spin, two-photon partial width and total width ofR, respectively. This leads to the proportionality relation(e+e− ! e+e−R) = K  Γγγ(R) (2)that allows to extract the two-photon width from the cross section. Theproportionality factor K is evaluated by a Monte Carlo integration.In the single tag-mode the high virtuality of one of the two photons istaken into account by multiplying the Breit-Wigner function by a VDMpole transition form factorF 2(Q2) =(11 +Q2=2)2(3)where Q2 is the four vector squared of the virtual photon and  is a param-eter to be measured experimentally.Since gluons do not couple directly to photons, the two photon widthof a glueball is expected to be very small. A state that can be formed in3a gluon rich environment but not in two photon fusion has the typical sig-nature of a glueball. According to lattice QCD predictions [1], the groundstate glueball has JPC= 0++ and a mass between 1400 and 1800 MeV. The2++ tensor glueball is expected in the mass region around 2200 MeV whilethe 0−+ pseudoscalar glueball is predicted to be heavier. Since several 0++states have been observed in the 1400-1800 MeV mass region, the scalarground state glueball can mix with nearby quarkonia, making the search forthe scalar glueball and the interpretation of the scalar meson nonet a com-plex problem [2] [3] [4]. The results from two-photon formation representtherefore a fundamental piece of information for glueball searches.In order to distinguish ordinary quarkonia from glueballs, a parametercalled stickiness has been introduced [5]. The stickiness is an estimate ofthe ratio j < Rjgg > j2=j < Rjγγ > j2 evaluated from the the ratio Γ(J= !γR)=Γ(R! γγ) corrected by a phase space factor. The ss mesons have thelargest stickiness among quarkonia (14.7 for the f02(1525)) while much largervalues are expected for glueballs.Because of the large mass of the charm quark, the study of the forma-tion of charmonium states allows to test non-relativistic perturbative QCDcalculations and to measure s at the charm scale.Two e+e− colliders have collected a large amount of data in the lastfew years. The four LEP experiments ALEPH, DELPHI, L3 and OPAL atCERN have collected approximately 150, 55, 175, 240 pb−1 each atps  91,183, 189, 191-202 GeV respectively. The CLEO experiment at CESR (Cor-nell) has collected about 3000 pb−1 atps  10.6 GeV. Since the luminosityfunction L increases with the beam energy, the higher energy allows LEPto partially compensate the smaller luminosity by a larger cross section.In this paper the most recent results on resonance formation and glueballsearches obtained at LEP and CESR are reviewed.2. The pi+pi−pi0 final stateA study of the reaction γγ ! +−0 is performed by L3 [6] [7] usingonly untagged events. The mass spectrum (g. 2) is dominated by the for-mation of the a2(1320) tensor meson. A clear enhancement is visible around1750 MeV where the study of the total transverse momentum distributionshows evidence for an exclusive process. The study of the angular distri-butions shows that the a2 formation is dominated by a JPC=2++ helicity2 wave. The radiative width is found to be Γγγ(a2) = 0:98  0:05  0:09keV. A spin-parity analysis in the mass region above the a2(1320) showsthat also this region is dominated by a JPC=2++ helicity 2 wave, con-rming the observation of the CERN-IHEP collaboration [8] and in con-tradiction with CELLO [9] and Crystal Ball [10] measurements. This can401002003004000.5 1 1.5 2m(pi+pi−γ) [GeV]Events/10 MeVDataFitBkga2L3Fig. 3. The +−γ mass spectrum forQ2 < 0:01 GeV2.051015201 1.5 2 051015201 1.5 201020301 1.5 2L3a)          Mass ,  GeVNevents / 50 MeV L3b)          Mass ,  GeVL3c)          Mass ,  GeVNevents / 50 MeV L3d)          Mass ,  GeV051015201 1.5 2Fig. 4. The K0sK mass spectrumfor Q2 <0.02 GeV2 (a), 0.02< Q2 <0.2GeV2 (b), 0.2< Q2 <1.0 GeV2 (c) and1.0< Q2 <7.0 GeV2 (d).be interpreted as the formation of a radial recurrence of the a2 for whichΓγγ(a02(1765))BR(a02(1765) ! +−0) = 0:29 0:04 0:02 keV in agree-ment with theoretical predictions [11]. The JPC=2−+ wave contribution isfound compatible with zero.3. Pseudoscalar mesons and their form factorsThe reaction γγ ! 0 ! +−γ is studied by L3 [12] in both theno-tag and single-tag mode. The +−γ mass spectrum (g. 3) shows aprominent peak due to the formation of the 0(958) while the enhancementaround 1250 MeV is due to the process γγ !a2(1320)! +−0 when onephoton from the 0 goes undetected. For the two-photon width, Γγγ(0) =4:17 0:10 0:27 keV is measured. The electromagnetic form factor of the0 is studied using tagged and untagged events. For the untagged events Q2can be measured as (pt)2, as demonstrated by a Monte Carlo study. A lowgluonic component in the 0(958) is found by comparing the data with thetheoretical predictions [13]. The value 0:9000:0460:022 GeV is obtainedfor the parameter .The transition form factors for the three pseudoscalar mesons 0,  and0 are studied by CLEO [14] using only the single-tag mode. The values0=0.7760.0100.0120.016 GeV, =0.7740.0110.0160.022 GeV,′=0.8590.0090.0180.020 GeV are measured. Data are consistentwith a similar wave function for the 0 and . The non-perturbative prop-5[width=0.45]g5.eps [width=0.45]g6.epsFig. 5. The +− mass spectrum for Q2 <0.02 GeV2(left) and Q2 >0.02GeV2(right).[width=0.45]g7.eps [width=0.45]g8.epsFig. 6. The K0sK0s mass spectra measured by L3 (left) and CLEO (right).erties of the 0(958) are found to be dierent from those of the 0 and. According to T. Feldmann [15], another interpretation of these resultsleads to the conclusion that 0, 0 and 0 mesons behave similarly in hardexclusive reactions.Interesting new preliminary results on the K0sK and the +− -nal states are obtained by L3 [16]. The K0sK mass spectrum is stud-ied as a function of Q2 (g. 4). A prominent signal is present at 1470MeV at low and at high Q2. At very high Q2 another signal appearsaround 1300 MeV due to the formation of the f1(1285). The study ofthe cross section as a function of Q2 in the 1470 MeV region reveals thatboth the 0−+ and 1++ waves are needed to t the data. The 0−+ waveis due to the formation of the (1440) and largely dominates at low Q2while at high Q2 the formation of the f1(1420) is found to be dominant.The value Γγγ((1440))  BR((1440) ! KK) = 234  55  17 eV isobtained by using data at low Q2. This rst observation of the (1440)in untagged two-photon collisions disfavours its interpretation as the 0−+glueball in agreement with the lattice QCD calculations. The (1440)can therefore be interpreted as a radial excitation [17]. The +− -nal state shows no evidence for the formation of the (1440) at low and athigh Q2 (g. 5). A prominent signal due to the formation of the 0(958)is present in the two spectra while the f1(1285) is visible only at highQ2. The upper limits Γγγ((1440))  BR((1440) ! ) < 88 eV andΓγγ((1295)) BR((1295) ! ) < 61 eV at 90% C.L. are obtained.4. Glueball searches in the K0sK0s and pi+pi− final statesA study of the reaction γγ ! K0sK0s is performed by L3 [7] [18]. Themass spectrum is shown in g. 6(left). The 1100-1400 MeV mass regionshows destructive f2(1270) { a2(1320) interference in agreement with the-oretical predictions [19]. The spectrum is dominated by the formation ofthe f20(1525) tensor meson in helicity 2 state as clearly shown by the an-gular distribution in the K0SK0S center of mass. The preliminary valueΓγγ(f 02(1525))  BR(f 02(1525) ! KK)= 0.076  0.006  0.011 keV is ob-tained. A clear signal is present in the 1750 MeV mass region due to theformation of the fJ(1710). The presence of a 0++ ss meson would supportthe glueball interpretation of the f0(1500) [2]. The study of the angulardistribution in the 1750 MeV mass region favours the presence of a 2++,6helicity 2 wave. This is consistent with the interpretation of the fJ(1710)as a radial recurrence of the f20(1525) [11]. The presence of a 0++ wavecannot however be excluded. The BES Collaboration [20] reported thepresence of both 2++ and 0++ waves in the 1750 MeV region in K+K−in the reaction e+e− ! J= ! K+K−γ. No signal for the formation ofthe (2230) [21] tensor glueball candidate is observed. The upper limitΓγγ((2230))BR((2230) ! K0SK0S) < 1:4 eV at 95% C.L. is obtained.The stickiness is found to be S(2230) > 73 at 95% C.L.The (2230) is searched by CLEO in the K0sK0s [22] and +− [23] -nal states. The K0sK0s mass spectrum (g. 6(right)) shows similar featuresrespect to the L3 data. The upper limits Γγγ((2230))  BR((2230) !K0SK0S) < 1.3 eV and Γγγ((2230))  BR((2230) ! +−) < 2.5 eV at95% C.L. are obtained. Combining these two results the stickiness is foundto be S(2230) > 102 at 95% C.L. The very large lower limits for S(2230)obtained by CLEO and L3 give a strong support to the interpretation ofthe (2230) as the tensor glueball. A conrmation of its existence in gluonrich environments becomes now very important.The +− nal state is studied by ALEPH [24]. The mass spectrum(g. 7) shows a signal due to the formation of the f2(1270) tensor meson.No other signals are present. Assuming the f0(1500) and the fJ(1710) tobe scalars, the upper limits Γγγ(f0(1500))  BR(f0(1500) ! +−) < 310eV and Γγγ(fJ(1710))  BR(fJ(1710) ! +−) < 550 eV at 95% C.L.are obtained. Interference eects with the +− continuum are not takeninto account. According to A.V.Anisovitch et al. [25], interference with the+− continuum should make the f0(1500) appear as a dip.5. Charmonium formationThe formation of the c(2980) is studied by L3 [26]. Since the c decaysin many dierent nal states with small branching fractions, the simulta-neous study of several decay channels is mandatory. The mass spectrumshown in g. 8 is obtained by summing nine dierent nal states. The valueΓγγ(c) = 6.9  1.7 (stat.)  0.8 (sys.) 2.0 (BR) keV is measured. De-spite the limited statistics, the study of the formation of the c(2980) as afunction of Q2 allows to exclude a VDM  pole transition form factor. Dataare consistent with a J/ VDM pole form factor, as expected.From the reaction γγ ! c2(3555) ! J= γ ! l+l−γ with l = e; , thetwo-photon width of the c2 is measured by OPAL[27]. The signal is seen inthe distribution of the mass dierence m(l+l−γ) { m(l+l−) when m(l+l−) iscompatible with the mass of the J= (g. 9). The value Γγγ(c2) = 1.76 0.47 (stat.)  0.37 (sys.) 0.15 (BR) keV is obtained. The value Γγγ(c2)= 1.02  0.40 (stat.)  0.15 (sys.) 0.09 (BR) keV is measured by L3 [28]7010002000300040005000600070008000Events / 20 MeV ALEPH(a)-50005000.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4pipi invariant mass (GeV/c2)(b)Fig. 7. The +− mass spectrum: theonly signal is due to the formation ofthe f2(1270).2.5 3.0 3.5 4.00100200300400Mass [GeV]Number of Events / 50 MeVAll untagged dataηc Monte CarloL3Fig. 8. The mass spectrum of the sum ofnine dierent nal states. The signalsof the c(2980) and the c0(3415) arevisible.02468101214160.2 0.4 0.6 0.8 1 1.2 Ml l γ  - Ml l   [ GeV/c2 ]Events / 50 MeVOPAL√see= 91 and 183 GeVFig. 9. The signal of the formation ofthe c2(3555) from the mass dierencem(l+l−γ)-m(l+l−).Fig. 10. The mass spectrum of the sumof ve dierent decay channels.using the same method.The measurements of the two-photon width of the c performed in two-photon collisions are in good agreement with the ones obtained in pp anni-hilations [29]. For the c2 the agreement is not good and the two-photonmeasurements are signicantly higher than the value Γγγ(c2) = 0.31 0.05  0.04 keV measured by E835 at Fermilab [30] in pp annihilations.This value is in agreement with a previous measurement by E760 [31]. Thereason for this is not known but it is interesting to remark that all the two-photon measurements are performed by using the same nal state and the8Resonance Experiment Final state JPC Γγγ Ref.0(958) L3 +−γ 0−+ 4.170.100.27 keV [12]a2(1320) L3 +−0 2++ 0.980.050.09 keV [6]f′2(1525) L3 K0sK0s 2++ 0.0850.0070.012 keV [18]c(2980) L3 9 chan. 0−+ 6.91.7.0.8 keV [26]0c L3 9 chan. 0−+ < 2:0 keV [26]c2(3555) L3 l+l−γ 2++ 1.020.400.15 keV [28]c2(3555) OPAL l+l−γ 2++ 1.760.470.37 keV [27](1440) L3 K0sK 0−+ 234y5517 eV [16]fJ(1710) L3 K0sK0s (?)++ [18]a02(1752) L3 +−0 2++ 0.29y0.040.02 keV [6]f0(1500) ALEPH +− 0++ < 310y eV [24]f0(1710) ALEPH +− 0++ < 550y eV [24](2230) CLEO +− 2++ < 2:5y eV [23](2230) CLEO K0sK0s 2++ < 1:3y eV [22](2230) L3 K0sK0s 2++ < 1:4y eV [18]Table 1. The most recent results on the two-photon width of mesons, charmonia,radial excitations and glueball candidates. (y the value is given times the decaybranching ratio)same experimental method.No signal for the formation of the 0c is observed at LEP. Five dierentdecay channels are examined by DELPHI [32] as shown in g. 10. Theformation of the c(2980) is clearly observed while no signal is present inthe 0c mass region. The upper limitΓγγ(′c)Γγγ(c)< 0:34 at 90% C.L. is obtained.The upper limit Γγγ(0c) < 2:0 keV at 95% C.L. is obtained by L3 [26] usingnine dierent decay modes.6. ConclusionsA remarkable progress on the study of resonance formation in two-photon collisions has been achieved in the last few years. Data from theLEP collider at CERN and CESR at Cornell allowed to improve signicantlythe precision on the two-photon widths of several resonances, to study thetransition form factors, to identify some radial excitations and to searchfor glueball candidates. All these results are summarised in Table 1. Theyrepresent an important contribution to meson spectroscopy and glueballsearches.97. AcknowledgementsI would like to acknowledge the two-photon physics groups of the ALEPH,CLEO, DELPHI, L3 and OPAL collaborations. I would like to thank M.N.Focacci-Kienzle, J.H. Field, M. Wadhwa, I. Vodopianov, A. Buijs, H. P.Paar, C. Amsler, L. Montanet, U. Gastaldi and P. Minkowski for the veryconstructive discussions and suggestions. I would like to express my grati-tude to B. Monteleoni, recently deceased.REFERENCES[1] C. Michael, Nucl. Phys. A 655 (1999) 12 and references therein.[2] C. Amsler and F. E. Close, Phys. Rev. D 53 (1996) 295.[3] P. Minkowski and W. Ochs, Frascati Physics Series Vol.XV (1999) 245 andhep-ph/9905250.[4] U. Gastaldi et al., LNL-INFN(rep) 148/99 and QCD99 proceedings, Montpel-lier, France.[5] M. Chanowitz,“Resonances in Photon-Photon Scattering”, Proceedings of theVIth International Workshop on Photon-Photon Collisions, World Scientic,1984.[6] L3 Collab., Phys. Lett. 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Resonance Formation in Two-Photon Collisions

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