Using multihadronic Z0 decays recorded in 1991-1995 by the OPAL detector in
e+e- collisions at LEP1, experimental analyses were made of the following
subjects: (a) Bose-Einstein correlations; (b) Intermittency and correlations;
(c) rho and omega spin alignments; (d) A search for the tensor glueball
candidate fj(2200).Comment: 6 pages, 5 Encapsulated Postscript figures, uses APS revtex.sty To be
  published in the proceedings of American Physical Society (APS) Meeting of
  the Division of Particles and Fields (DPF99), Los Angeles, CA, 5-9 Jan 199

Giacomelli, G.

English

arXiv

Using multihadronic Z0 decays recorded in 1991-1995 by the OPAL detector in e+e- collisions at LEP1, experimental analyses were made of the following subjects: (a) Bose-Einstein correlations; (b) Intermittency and correlations; (c) rho and omega spin alignments; (d) A search for the tensor glueball candidate fj(2200)

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arXiv:hep-ex/9903021v2  17 Apr 1999Recent OPAL measurements in non-perturbative QCDG. GiacomelliDipartimento di Fisica dell’Universita’ di Bologna and INFN, Sezione di Bologna,Viale B. Pichat 6/2, 40127 Bologna, Italyfor the OPAL CollaborationAbstract. Using multihadronic Z0 decays recorded in 1991 - 1995 by the OPAL detector in e+e− collisions at LEP1, experi-mental analyses were made of the following subjects: (a) Bose-Einstein correlations; (b) Intermittency and correlations; (c) ρand ω spin alignments; (d) A search for the tensor glueball candidate fj(2200).1 IntroductionThe large sample of multihadronic (MH) Z0 decays recorded by the OPAL detector at LEP1 offers the possibilityto study several aspects of non perturbative QCD.Bose-Einstein correlations (BEC) give an estimate of the size and shape of the identical bosons emitting region;more recently BEC have been used to yield information on the hadronization process.Intermittency and multiparticle correlations are studied in terms of the scaled normalized factorial moments and ofcumulants vs rapidity y, azimuthal angle φ, and transverse momentum Pt. Intermittent behaviour is seen in y and φas an increase of the moments with decreasing bin size. Genuine multiparticle correlations exist. They are containedin the used Monte Carlos.Little is known on the role of spin in the hadronization process. At LEP, this can be investigated by studying theproperties of vector mesons produced in hadronic Z0 decays. New results are presented on the helicity density matrixelements for the ρ(770)± and ω(782) mesons.QCD predicts the existence of glueballs; lattice gauge theories predict the mass of the ground state glueball (twoleading gluons with antiparallel spins) to be ≃ 1.5 GeV. Some glueball candidates have been reported; the inter-pretation of data in this mass region is difficult because of mixing with conventional mesons. This difficulty is lesspronounced for the tensor glueball, expected with m ≃ 2.2 GeV. A search for this state is here reported.The OPAL data at LEP1 concern 4.1 million MH events. The analyses use charged particles detected by thetracking chambers in the magnetic field. Standard quality cuts are applied to each track and to each multiparticleevent. Photons are detected in the electromagnetic calorimeter, or as γ → e+e−.2 Bose-Einstein CorrelationsBose-Einstein correlations (BEC) between identical bosons lead to an enhancement of the number of identicalbosons when they are close in phase space. LEP1 data allowed to study: (i) correlations for π±π±, K0K0, K±K±,(ii) the multiplicity dependence of the 2π emitting region, (iii) multi-pion BECs, (iv) two-dimensional ππ BEC [1].LEP2 data allowed to study (v) BEC in e+e− → W+W− for identical charged pion pairs. For two pions we usethe notation in terms of Q2 = −(P1 − P2)2 = m2ππ − 4m2π. The distribution in Q of the like-charge pairs has to benormalized to a Q-distribution which does not contain BEC, for instance the distribution of unlike-charge pairs or toa Monte Carlo prediction [2]:C′(Q) = (N++ +N−−)/N+− , C(Q) = (N++ +N−−)/(N++ +N−−)MC (1)Various parametrizations are used in the literature to interpret the data. We use the Goldhaber parametrization:C(Q) = N(1 + λ e−Q2R2)(1 + ǫQ+ δQ2) (2)N is a normalization factor, λ is the chaoticity parameter (0 ≤ λ ≤ 1) and R estimates the radius of the emittingregion; (1 + ǫQ + δQ2) accounts for the long range correlations arising form charge and energy conservation andphase space constraints. The Q-dependence, corrected for Coulomb effects, of C(Q) or C′(Q) for π±π± shows anenhancement at small Q value. Fits of C(Q) to Eq. 2, eliminating the regions where there could be hadron resonanceeffects, yields R ≃ 0.793± 0.007st ± 0.015sys and λ ∼ 0.58 [2]; R and λ seem to be energy independent [1].For 2π, OPAL analyzed the dependence of R on the average charged multiplicity of MH events, and it found anincrease of R with nch (from 0.86 to 1.0 fm) and a decrease in the parameter λ [3]. Similar values of R and λ werefound for π0π0 [3], K0sK0s [4] and K±K± [5] BECs. For 3π BECs, OPAL [6] considered the ratio1R3(Q3) = N+++(Q3)/N+++MC (Q3) (3)corrected for Coulomb effects; the Monte Carlo is JETSET7.4. The effects of 2π correlations must be removed toobtain the genuine 3π correlation function:C3(Q3) = R3(Q3)−R1,2(Q3) = N+++N+++MC− δ++−N+++MC〈n+++n++−〉 (4)R1,2 = δ+++2 /N+++MC , δ+++2 is the three-pion enhancement due to the two-pion BEC; Q23 = −(q1− q2)2− (q1− q3)2−(q2 − q3)2The experimental distribution (4) was fitted to an expression similar to (2). One obtains: R3 = 0.580± 0.004st ±0.029sys fm ; λ3 = 0.504± 0.010st± 0.041sys Notice that two-pion BEC yield R2 = 0.793± 0.015 fm; assuming thatR3 ≃ R2/√2 = 0.793/√2 one has R3 ≃ 0.561± 0.011 fm which agreees with the measured R3 = 0.558 fm.BECs have been measured for 2π in the reaction e+e− → W+W− at √s = 172 and 183 GeV [7]. Three datasamples are available: (i) the four-jet hadronic sample, W+W− → qq′ qq′: here final state interactions (FSI) canoccur within a single W decay or between the two different W bosons. (ii) The two-jet (semileptonic) sample,W+W− → qq′ lνl; FSI can only occur within a single W . (iii) The leptonic sample, W+W− → l+νl l−νl. Fromthe point of view of the MW measurements, FSI are of consequence if they occur between the two W ’s in the samehadronic event. At LEP2 energies the two W -bosons decay within a distance of about 0.1 fm, which is smaller thanthe hadronization scale of ≃ 1 fm. Thus the fragmentation processes for hadrons coming from different W -bosonscould be interconnected. OPAL demonstrated the existence of BEC in W decays, Fig. 1. An attempt was madeto determine BEC for two pions originating from the same W -boson and from different W -bosons, as well as forpions from (Z0/γ) → qq events [7]. Fitting these samples together, assuming a common source radius R, we findλsame = 0.63± 0.19± 0.14 , λdiff = 0.22± 0.53± 0.14 , λZ∗ = 0.47± 0.11± 0.08 , R = 0.92± 0.09± 0.09 fm(the first error is statistical and the second one is systematic). At present it is not established whether BECs betweenpions from different W bosons exist or not.Two-dimensional, two-pion BECs are being studied; preliminary results indicate a non spherical di-pion emittershape [8].3 Intermittency and multiparticle correlationsLocal multiparticle fluctuations have been studied in final hadron states. With the word Intermittency one refersto the rise of the factorial moments with decreasing bin size. Analyses in terms of the factorial cumulant momentsreveal “genuine multiparticle” correlations. The modified factorial moments (FM)F cq = Nq〈n[q]m 〉/N [q]m (5)are used by OPAL to avoid biases in the normalization [9]. The q-th order factorial moment is nqm = nm(nm −1)...(nm − q + 1); nm is the number of particles in the m-th bin of the phase space divided into M equal bins, Nm isthe number of particles summed over all the N events, Nm =∑ni=1(nm)i The bar stands for “horizontal” averagingover the bins in each event, (1/M)∑Mm=1; the angle brackets denote “vertical” averaging over the events. The phasespace is considered in terms of the rapidity y, azimuthal angle φ and transverse momentum Pt. Non-statisticalfluctuations lead to increasing FMs with increasingM , Fq(M) ≈Mϕq , 0 < ϕq < q−1, M →∞ (power dependence,scaling law). The FMs of order q = 2÷5 have been plotted vs the number of binsM for the one-dimensional rapidity,azimuthal angle, and transverse momentum. The y and φ distributions increase with M up to M ∼ 20 and thenflatten; the Pt distribution is essentially independent of M . Thus there is an intermittency in y and φ and not in Pt.This behaviour is reasonably well predicted by the used Monte Carlos. The same behaviour, with stronger increasewith M , is exhibited in two phase space dimensions, in particular by y × φ, and in three dimensions by y × φ × Pt.The modified factorial cumulant (FC) moments areKcq = NK(m)q / N[q]m (6)The multipliers K(m)q are the unnormalized factorial cumulants (Mueller moments), and represent genuine q-particlecorrelations. This leads toF2 = K2 + 1 , F3 = K3 + 3K2 + 1 , F4 = K4 + 4K3 + 3(K(m)2 )2 + 6K2 + 1 , ... (7)2Two-particle contributions F(2)q can be expressed as F(2)3 = 3K2+)1, F(2)4 = 3(K(m)2 )2+6K2+1, F(2)5 = 15(K(m)2 )2+10K2 + 1, ... These equations can be used to search for multiparticle correlation contributions to local fluctuations.Fig. 2 shows the FCs in one, two and three dimensions for q = 4 and 5. the FCs are positive, which indicates thatmultiparticle correlations exist. The FCs exhibit stronger power-law behaviour than for FMs. Addition of phase spacedimensions, from y to y × φ and to y × φ × Pt, enhances the manifestation of multiparticle genuine correlatons [9].The results agree with the QCD jet formation dynamics, but additional contributions from other mechanisms cannotbe excluded.4 Spin alignment of ρ(770)± and ω(782) mesonsThe helicity density matrix elements for the ρ(770)± and ω(782) mesons produced in Z0 decays have been measuredby OPAL [10]. Since ρ± → π±π0, we can use as a spin analyzer the angle in the π±π0, rest frame between one of thepion momenta and the ρ± boost direction. The distribution of this angle, θH , is:W (cos θH) =34[(1 − ρ00) + (3ρ00 − 1) cos2 θH ] (8)ρ00 is the helicity density matrix element corresponding to the probability that the spin of the ρ± meson be perpen-dicular to its momentum direction. Because of unitarity and parity conservation, the probabilities that the spin beparallel or antiparallel, ρ11 and ρ−1−1, are equal ρ11 = ρ−1−1 = (1− ρ00)/2.The π± and π0 candidates are combined in pairs and three quantities are evaluated: the scaled energy of the pairxE = Emeson/Ebeam, the invariant mass mπ±π0 , and cos θH defined between the π0 and the boost of the π±π0 system.The ρ± signal in the mπ±π0 distribution is parametrized with a Breit-Wigner convoluted with the experimental massresolution in xE . The efficiency-corrected ρ± yields are evaluated for ten cos θH bins and fitted to the formula:I(cos θH) = A(1 +B cos2 θH). One has ρ00 = (1+B)/(3 +B). The parameters A, B are obtained from a linear leastsquare fit. The decay ω → π0π+π− has BR = 88.8%. In the rest frame of the π0π+π− system the momenta of thethree pions lie in a plane; the appropriate spin analyzer is the angle θH between the normal to this plane and the boostdirection. The measured values of ρ00 as a function of xE are shown in Figs. 3a and 3b for the ρ± and ω mesons,respectively. The measurements are compatible with 1/3, corresponding to a statistical mix of helicity −1, 0 and +1states. The DELPHI results for ρ0 agree with our ρ± values [11]. For 0.3 < xE < 0.6 one has ρ00 = 0.373± 0.052 and0.142± 0.114 for ρ± and ω, respectively. These results are lower than those for K⋆(890) and φ mesons [12]. Fig. 3cshows a comparison with previous data.According to the Monte Carlo, up to 10% of ρ± originate from decays of JP = 0− mesons into a ρ± (JP = 1−)and another JP = 0− meson (mainly D0 → ρ+K−, JP = 0− → 0− + 1−). The effects of the alignment of the ρ±from such decays are shown in Fig. 3a as dotted lines.In conclusion there appears to be a difference in the spin alignment properties of vector mesons, see Fig. 4, possiblydepending on their strangeness content.5 A search for the tensor glueball fj(2220)In the K0s K0s and K+ K− final states a narrow resonance with Γ ≃ 20 MeV (denoted fj(2220) was reported bythe MARK III Coll., in J/ψ decays [12], by the BES Collaboration in radiative J/ψ decays [13] and by the L3 Coll.[14] in hadronic Z0 decays in an enriched three-jet sample (and mainly coming from the lowest energy jet, enrichedin gluons). But the DM2 Coll., in J/ψ decays [15] and the CLEO Coll., in γγ collisions [16], did not find indicationsfor this state (the DM2 Coll. had indications for a broader structure). The OPAL detector is well suited for a studyof the fj(2220) → K0s K0s because of its large radius tracking chamber which allows efficient detection of K0s overa large momentum range [17]. The K0s K0s mass spectrum was investigated in the full event sample and, followingthe L3 analysis, in the three-jet sample and in individual jets of the three-jet sample. Neither in the global eventsample nor in gluon enriched samples is there any evidence for a narrow resonance (see Fig. 5). The upper limitfor the product of the inclusive production rate per hadronic Z0 decay nfJ (2220) and the branching ratio BRfJ→KKis [nfJ (2220) · BRfJ→KK ] < 0.0028, at 95% C.L. for the fj(2220) with production and decay properties as a 2++meson.6 ConclusionsMany measurements related to multihadronic non perturbative QCD have been performed by OPAL. In particular:(i) The studies of BEC is yielding a number of interesting informations; (ii) Intermittency and multiparticle correlationsare present in multihadron events; (iii) More precise experiments are needed to understand the role of spin in thehadronization process; (iv) OPAL found no confirmation for the proposed fj(2220) tensor glueball candidate.3References[1] E. A. De Wolf, Bose-Einstein Correlations, Int. Conf. High En. Phys., Glasgow (1994), Inst. Phys. Publ.(1995), p. 1281; G. Alexander and I. Cohen, Measure of π’s and Λ’s emitter radius via Bose-Einstein andFermi-Dirac statistics, TAUP 2335-98 (1998).[2] OPAL Coll., P. D. Acton et al., Phys. Lett. B267 (1991) 143; G. Alexander et al., Z. Phys. C72 (1996) 389.[3] L3 Coll., L3 98-2270, L3 98-2278, Proc. ICHEP98, Vancouver (1998).[4] OPAL Coll., P. Acton et al., Phys. Lett. B298 (1993) 456; R. Akers et al., Z. Phys. C67(1995) 389.[5] DELPHI Coll., P. Abreu et al., Phys. Lett. B379 (1996) 330.[6] OPAL. Coll., K. Ackerstaff et al., Euro. Phys. Jou. C5 (1998) 239.[7] OPAL Coll., G. Abbiendi et al., Bose-Einstein Correlations in e+e− →W+W− at 172 and 183 GeV,CERN-EP/98-174 (1998).[8] L3 Coll., A two-dimensional study of Bose-Einstein Correlation in Z decays al LEP, XXIX Int. Conf. on High En.Phys., Vancouver (1998).[9] OPAL Coll., G. Abbiendi et al., Intermittency and correlations in hadronic decays of the Z0, PN345 (1998);E.K.G. Sarkisyan, Study of Intermittency and correlations in hadronic Z0 decays, CR368.[10] OPAL Coll., G. Abbiendi et al., A study of spin alignment of ρ(770)± and ω(782) mesons in hadronic Z0 decays,OPAL PN371 (1998).[11] DELPHI Coll., P. Abreu et al., Phys. Lett. B406 (1997) 271.[12] OPAL Coll., K. Ackerstaff et al., Phys. Lett. B412 (1997) 210.[13] MARK III Coll., R. M. Baltrusaitis et al., Phys. Rev. Lett. 56 (1986) 107.[14] BES Coll., J. Z. Bai et al., Phys. Rev. Lett. 76 (1996) 3502.[15] G. Forconi, 7th Int. Conf. on Hadron Spectroscopy, Brookhaven Nat. Lab. (1997); Available at:http://hpl3sn02.cern.ch/conference/talks97.html.[16] DM2 Coll., J. E. Augustin et al., Phys. Rev. Lett. 60 (1988) 2238.[17] M. S. Alam et al., hep-ex/9805033 (1998).[18] OPAL Coll., A search for the tensor glueball candidate fJ(2220) in hadronic Z0 decays, PN357 (1998).OPAL a) W+W-→qq_qq_Chad (Q)b) W+W-→qq_ lν_Csemi (Q)c) (Z0/γ)*→qq_Q(GeV/c2)Cnon-rad.(Q)0.811.21.41.60.811.21.41.60.811.21.41.60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2FIG. 1. The BEC for like-charge pairs relative to unlike-charge pairs for three event selections: a) Chad(Q) for the fullyhadronic, b) Csemi(Q) for the semileptonic, and c) Cnon−rad.(Q) for the non-radiative events. The Coulomb-corrected dataare shown as solid points with statistical errors. The lines are the result of the simultaneous fit [7].410-210-111 10 10 210-210-111010 21 1010-111010 21 1010-111010 10 211010 210 310 410 51011010 210 310 410OPAL PreliminaryDataJETSET 7.4HERWIG 5.9KC 4y y×Φ y×Φ×pTyMKC 5y×ΦM1/2y×Φ×pTM1/3FIG. 2. The 4th and 5th FC in one, two, and three dimensions of rapidity, azimuthal angle and transverse momentum vsthe number of bins M [9].00.20.40.60.810 -1 100.20.40.60.810 -1 1xE of ρ±ρ 00Jetset ρ± (with and without L=1 mesons)OPAL ρ± (preliminary)(a)xE of ωρ 00Jetset ω (with and without L=1 mesons)OPAL ω (preliminary)(b)xE of particleρ 00OPAL ωOPAL ρ±OPAL K*(892)DELPHI ρ0(c)00.20.40.60.810 -1 1FIG. 3. Measured ρ00 values vs xE for a) ρ± mesons and b) ω mesons produced in Z0 decays [10]. The dotted lines are theρ00 values calculated assuming that JP = 0− → 0−+1− decays are the only source of alignment, and that the number of thesedecays per hadronic Z0 decays is as predicted by the Monte Carlo. In c) our data are compared with other measurements.5Helicity matrix element ρ00B*B*B*D*(2010)±φ(1020)φ(1020)K*(892)0K*(892)0K*(892)0ω(782)ρ(770)0ρ(770)±0 0.2 0.4 0.6 0.8 1 1.2DELPHIALEPHOPALOPAL c→D*DELPHI x>0.7OPAL x>0.7DELPHI x>0.4OPAL 0.3<x<0.5OPAL x>0.7OPAL 0.3<x<0.6DELPHI x>0.3OPAL 0.3<x<0.6FIG. 4. Summary of ρ00 measurements for vector mesons produced in Z0 decays [10].MKK [GeV/c2]Entries per 20 MeV/c20204060801001.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5FIG. 5. Invariant mass spectrum of K0sK0s pairs for the lowest-energy jet in the 3-jet event sample [17]. The Jetset 7.4prediction is shown by the open histogram while the lines with error bars are the data. The solid line shows the result of thefit with the 95% confidence upper limit for the signal. The shaded histogram is the expectation based on the preliminary L3result.6

Recent OPAL measurements in non-perturbative QCD

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