Chapkin, M

Chung, S U

Gavillet, P

Obraztsov, V F

Ryabchikov, D I

Sokolov, A

Todorovova-Nova, S

Uvarov, V

Weiser, C

CERN Document Server

DELPHI Collaboration DELPHI 2001-063 CONF491June 26, 2001Measurement ofInclusive f1(1285) and f1(1420) Productionin Z Decays with the DELPHI DetectorM. Chapkin, S.-U. Chung, P. Gavillet,V. Obraztsov, D. Ryabchikov, A. Sokolov, S. Todorovova-Nova,V. Uvarov, C. WeiserAbstractInclusive production of two (KK¯pi)0 states in the mass region 1.22–1.56 GeV in Zdecay at LEP I has been observed by the DELPHI Collaboration. The measuredmasses and widths are 1274 ± 4 and 29 ± 12 MeV for the first peak and 1426 ± 4and 51±14 MeV for the second. A partial-wave analysis has been performed on the(KK¯pi)0 spectrum in the mass range; the first peak is consistent with the quantumnumbers IG(JPC) = 0+(0−+/1++) and the second with IG(JPC) = 0+(1++). Thesemeasurements, as well as their total hadronic production rates per hadronic Z decay,are consistent with the mesons of the type nn¯, where n = {u, d}. They are verylikely to be the f1(1285) and the f1(1420), respectively.Contributed Paper for EPS HEP 2001 (Budapest) and LP01 (Rome)1 IntroductionThe inclusive production of mesons has been a subject of long-standing study at LEP[1][2],as it provides an insight into the nature of fragmentation of quarks and gluons to hadrons.So far the studies have been done on the S-wave mesons (both 1S0 and3S1) such as pi andρ, as well as certain P -wave mesons f2(1270) and K∗2 (1430) (i.e.3P2) and f0(980) anda0(980) (3P0). Very little is known about the production of mesons belonging to otherP -wave (i.e. 3P1 and1P1). For the first time, we present in this paper a study of theinclusive production of JPC = 1++ mesons f1(1285) and f1(1420) (i.e.3P1).There are at least four nonstrange isoscalar mesons[3], IG(JPC) = 0+(1++) andIG(JPC) = 0+(0−+), known in the mass region between 1.2 and 1.5 GeV, which couplestrongly to the decay channel (KK¯pi)0. They are f1(1285), η(1295), f1(1420) and η(1440).All are seen prominently in the peripheral production from pi−p interactions[3], indicatingthat, despite their decay into (KK¯pi)0, they are mostly nn¯ states, where n = {u, d}. Thereare possibly two additional states, IG(JPC) = 0−?(1+−) h1(1380) and IG(JPC) = 0+(1++)f1(1510), which may harbor a large ss¯ content, as they are produced with considerablecross sections in the peripheral reactions involving K−p interactions[3]. Given this com-plexity with the (KK¯pi)0 systems, it is important that one seek answers to which reso-nances among these are readily excited in inclusive hadron Z decays.The DELPHI data for this study is based on the neutral KK¯pi channel in the reactionZ → (KSK±pi∓) + X0 (1)Section 2 is devoted to the selection process for the event sample collected for this study.Sections 3 deals with a study of the KK¯pi mass spectra. A partial-wave analysis ispresented in Section 4. A discussion of the results and conclusions are given in Section 5.2 Experimental ProcedureThe analysis presented here is based on a data sample of about 3.3 million hadronic Zdecays collected from 1992 to 1995 with the DELPHI detector. Detailed description ofthe DELPHI detector and its performance can be found elsewhere[4][5].The charged particle tracks have been measured in the 1.2-T magnetic field by a set oftracking detectors. The average momentum resolution for charged particles in hadronicfinal states, ∆p/p, is usually between 0.001 and 0.01, depending on their momentum aswell as which detectors are included in the track fit.A charged particle has been accepted in this analysis—if its momentum p is greaterthan 100 MeV/c; its momentum error ∆p is less than p; and its impact parameter withrespect to the nominal crossing point is within 4 cm in the transverse (xy) plane and 4cm/sin θ along the beam direction (z-axis), θ being the polar angle of the track.Hadronic events are then selected by requiring at least 5 charged particles, with atleast 3-GeV energy in each hemisphere of the event—defined with respect to the beamdirection—and total energy at least 12% of the center-of-mass energy. The contaminationfrom events due to beam-gas scattering and to γ-γ interactions is estimated to be lessthan 0.1% and the background from τ+ τ− events less than 0.2% of the accepted events.After these cuts, there remain about 680 000, 680 000, 1 350 000 and 650 000 eventsfor the 1992, 1993, 1994 and 1995 run periods, respectively.1After the event selection, in order to ensure a better signal-to-background ratio forthe resonances in the KSK±pi∓ invariant mass spectra, tighter requirements have beenimposed on the track impact parameters with respect to the nominal crossing point, i.e.they have to be within 0.2 cm in the transverse plane and 0.4 cm/sin θ along the beamdirection.K± identification has been provided by the RICH detectors for particles with momentaabove 700 MeV/c, while the ionization loss measured in the TPC has been used for mo-menta above 100 MeV/c. The corresponding identification tags are based on the combinedprobabilities, derived from the average Cherenkov angle and the number of observed pho-tons in the Ring Imaging Cherenkov (RICH) detectors, as well as the measured dE/dx inthe Time Projection Chamber (TPC). Cuts on the tags have been applied to achieve thebest signal-to-background ratio, while rejecting e±, µ±, p and p¯ tracks. A more detaileddescription of the identification tags can be found in Ref. [1]. In the present case, the K±identification efficiency has been estimated by comparing the φ(1020) → K+K− signalin the experimental data with the simulated events generated with JETSET[6]—tunedwith the DELPHI parameters[7]—and passed through the detector simulation programDELSIM[8]. Agreement within 4% is observed between the data and the simulation.The KScandidates are detected by their decay in flight into pi+pi−. The details ofthe method and the various cuts applied are described in Ref. [9]. Our selection processconsists of taking the V 0’s passing certain criteria for quality of the reconstruction plus amass cut given by 0.45 < M(KS) < 0.55 GeV.After all the above cuts, only events with at least one KSK+pi− or KSK−pi+ com-bination have been kept in the present analysis, corresponding to a sample of 705 688events.3 KSK±pi∓ Mass SpectraA histogram of the KSK± pi∓ mass spectrum is shown in Fig. 1. Also shown in the figureis the same mass spectrum with a K∗(892) cut, which would be appropriate if the decayof a resonance had proceeded through a K∗(892) intermdediate state. Neither histogramshows visible enhancement in the mass region between 1.25 to 1.45 GeV.This is due to the enormous background in this mass region coming from the highnumber of KSK±pi∓ combinations (' 〈9〉) per event in inclusive Z decays. The key toa successful study of the f1(1285) and f1(1420)—under the circumstances—is to make amass cut M(KSK±) ≤ 1.04 GeV, as shown in Fig. 2, where two clear peaks are now seenin this mass region. There are two reasons for this: (1) the decay mode a0(980)±pi∓ isselected by the mass cut, while the general background for the KK¯pi system is reducedby a factor of ' 7 at 1.42 GeV or more at higher masses; (2) the interference effect ofthe two K∗(892) bands on the Dalitz plot at M(KK¯pi) ∼ 1.4 GeV is enhanced, if theG-parity is positive[12].In order to measure the resonance parameters for these two states, we have first gen-erated a Monte Carlo sample, deleting—from the existing MC package—all mesons witha major decay mode into (KK¯pi)0 in the mass region 1.25 to 1.45 GeV, i.e. f1(1285),h1(1380) and f1(1420), which is then passed through the standard detector simulationprogram. The smooth curve shown in Fig. 2 has been obtained by fitting the mass spec-trum of the aforementioned MC sample between 1.15 to 1.65 GeV with a background2Figure 1: M(KSK± pi∓) distributions from the Z decays with the DELPHI detector at LEPI. The histogram with solid (open) circles is for the full data sample (with a K ∗ cut 0.822 <M(Kpi) < 0.962 GeV).functionfb(M) = (M −M0)α1 exp(α2 M + α3 M2) (2)where M and M0 are the effective masses of the (KK¯pi)0 system and its threshold, re-spectively, and αi are the experimental parameters. We have fitted the (KK¯pi)0 spectrumadding two S-wave Breit-Wigner forms to the background fb(M), given byfr(M) =Γ2r(M −Mr)2 + (Γr/2)2(3)where Mr and Γr are the mass and the width to be determined experimentally. Theresults are shown in Fig. 2 and also in Table I.3Figure 2: The same as in Fig. 1 but with a mass cut M(KSK±) < 1.04 GeV. The two solidcurves in the upper part of the histogram describe Breit-Wigner fits over a smooth background(see text). The lower histogram and the solid curve give the same fits with the backgroundsubtracted and amplified by a factor of two.Table I. Fitted parameters and numbers of eventsMass (MeV) Width (MeV) Events1274± 4 29± 12 345± 88 (stat)± 69 (sys)1426± 4 51± 14 790± 119 (stat)± 110 (sys)The main sources of systematic errors come from the various cuts and selection criteriaapplied for the V 0 reconstruction plus the charged K identification—on the one hand—and the conditions of the mass-fit procedure—on the other. To estimate the first type of4error, we have compared the KSK± mass distributions of the simulated sample with thereal data. Normalized to the same number of events, both distributions agree within 7%,in the low KSK± mass region.The f1(1285) and f1(1420) signals show up over a large background (∼ 80%). Varia-tions of the background shape and amplitude thus induce sizable fluctuations of the fittednumbers of signal events, especially in the f1(1420) mass region. To quantify this effect,we have performed a series of fits, varying the mass range of the fit, thereby allowing thebackground level to fluctuate. In this way we estimate the fit uncertainty to be 15% forthe f1(1285) and 14% for the f1(1420). The systematic errors have been added quadrati-cally and are shown in Table 1. It should be emphasized that the masses and the widthsquoted in the table are not intended to be new experimental measurements; rather, theyare merely given as an indication that our peaks are consistent with the known parameters.An in-depth analysis of such a measurement must include a relativistic Breit-Wigner formwith a mass-dependent partial width which includes orbital angular-momentum barrierfactors. In addition, one must consider the possibility that there can be more than oneresonance of different spin-parity in each mass peak. Given the high level of backgroundin our data sample, such an analysis—we believe—is not warranted at this time.4 Partial-wave AnalysisThere exists a long list of 3-body partial-wave analyses; the reader may consult PDG[3]for earlier references, for example, on a1(1260), a2(1320), K1(1270/1400) or K2(1770).For the first time, we apply the same technique to a study of the (KK¯pi)0 system fromthe inclusive decay of the Z at LEP.A short introductory remark may be in order, for the general principles involved ina spin-parity analysis of the system composed of three pseudoscalars. The descriptionof such a system requires five variables, which may be chosen to be the three Eulerangles describing the orientation of the 3-body system in its suitably-chosen rest frameand two effective masses describing the decay Dalitz plot. We have chosen to employthe so-called Dalitz plot analysis, integrating over the three Euler angles. This entailsan essential simplification in the number of parameters required in the analysis, as thedecay amplitudes involving the D-functions defined over the three Euler angles and theirappropriate decay-coupling constants, are orthogonal for different spins and parities[10].The actual fitting of the data is done by using the maximum-likelihood method, in whichthe normalization integrals are evaluated with the accepted Monte Carlo events[11], thustaking into account the finite acceptance of the detector and the event selection.The background under the two f1 is very large, some ∼ 80%. It is assumedthat this represents essentially different processes with, for example, different overallmultiplicities—so that the background does not interfere with the signals. We as-sume further that the background itself is a non-interfering superposition of a flatdistribution (on the Dalitz plot) and the partial waves IG(JPC) = 0+(1++) a0(980)pi,0+(1++) (K∗(892)K¯ + c.c.) and 0−(1+−) (K∗(892)K¯ + c.c.). We have verified that theseamplitudes give a good description of the three background regions for M(KK¯pi) in1.22 → 1.26, 1.30 → 1.38 and 1.48 → 1.56 GeV, respectively.The signal regions, for M(KK¯pi) in 1.26 → 1.30 and 1.38 → 1.48 GeV, have been fittedwith a non-interfering superposition of the partial waves IG(JPC) = 0+(1++), 0+(1+−)5and 0−(0−+), where the decay channels a0(980)pi and K∗(892)K¯ + c.c. are allowed tointerfere within a given JPC . All other possible partial waves have been found to benegligible in the signal regions. Because of a lack of phase space, the two isobars a0(980)and K∗(892) cannot be distinguished for M(KK¯pi) below 1.30 GeV, so we have keptthe a0(980)pi decay mode only. The fit results can be summarized as follows: (1) themaximum likelihood is found to be the same for IG(JPC) = 0+(1++) a0(980)pi and for0−(0−+) a0(980)pi, i.e. the 1.28- GeV region is equally likely to be the f1(1285) or theη(1295); (2) in the 1.4-GeV region, the maximum likelihood is marginally better (byabout 3 for ∆ lnL) for IG(JPC) = 0+(1++) f1(1420) than IG(JPC) = 0+(0−+) η(1440);the IG(JPC) = 0+(1+−) h1(1380) is excluded in this analysis (by about 13 for ∆ lnL).The results of the partial-wave analysis are summarized in Fig. 3. It should be empha-sized that both the mass-dependent (per 20 MeV) and the mass-independent global fitsgive compatible results. The masses, the widths and the numbers of events found in themass-independent global fit, shown as solid curves in Fig. 3, are statistically consistentwith those given in Table I, even though the overall background shape—see the dottedcurve just below the histogram with error bars—exhibit a slight dip around 1.4 GeV whichis not present in Fig. 2.6Figure 3: M(KSK± pi∓) distributions per 20 MeV with a breakdown into the partial-wavesfor the signals and the background. The signals consist of 1++ a0(980)pi for the first peak and1++ K∗(892)K¯ for the second peak. The background consists of non-interfering superpositionof isotropic distribution (1), 1++ a0(980)pi (2), 1++ K∗(892)K¯ (3) and 1+− K∗(892)K¯ (4).75 Discussion and ConclusionsWe have measured the production rate 〈n〉 per hadronic Z decay for f1(1285)/η(1295)and f1(1420). We assume for this study that both have spin 1. The results are〈n〉 = 0.132± 0.034 for f1(1285)〈n〉 = 0.0512± 0.0078 for f1(1420)(4)taking a KK¯pi branching ratio of (9.0±0.4)% for the f1(1285) and 100% for the f1(1420)[3].The production rate per spin state [i.e. divided by (2J + 1)] has been studied in Ref. [2];in Fig. 4 is given all the available data for those mesons with a ‘triplet’ qq¯ structure, i.e.S = 1 in the spectroscopic notation 2S+1LJ . To this figure we have added our two mesonsfor comparison. It is seen that both f1(1285) and f1(1420) come very close to the linecorresponding to other mesons whose constituents are thought to be of the type nn¯. Thisis suggestive of two salient facts: (1)the first peak at 1.28 GeV is very likely to be thef1(1285); (2) both f1(1285) and f1(1420) have little ss¯ content. Indeed, the two stateswhich are thought to be pure ss¯ mesons, the φ and the f ′2(1525), are down by a factorγk ≈ 1/4 (γ = 0.50 ± 0.02 and k = 2), as shown in Fig. 4. This is highly unlikely giventhe production rate (4).We have studied the inclusive production of f1(1285)/η(1295) and f1(1420) in Z decaysat LEP I. The measured masses and widths are 1274 ± 4 and 29± 12 MeV for the firstpeak and 1426 ± 4 and 51 ± 14 MeV for the second one. For the first time, a partial-wave analysis has been carried out on the (KK¯pi)0 system. The results show that thefirst peak is equally likely to be the f1(1285) or the η(1295), while the second peak isconsistent with the f1(1420). However, the hadronic production rate of these two statessuggests that their quantum numbers are very probably IG(JPC) = 0+(1++) and thattheir quark constituents are mainly of the type nn¯, where n = {u, d}. In a previous studyof the production rate[2] for the S = 1 mesons—which included 3S1,3P0 and3P2—anintriguing pattern has been found; it appears that the mesons of the type 3P1, assumingthat both f1(1285) and f1(1420) belong to the category, follow the same pattern. Finally,we conclude that the mesons η(1295), η(1440) and h1(1380) are less likely to be producedin the inclusive Z decays compared to f1(1285) and f1(1420).8Figure 4: Total production rate per spin state and isospin for scalar, vector and tensor mesonsas a function of the mass (open symbols). The two solid circles correspond to the f1(1285) andthe f1(1420).9AcknowledgementsS.-U. Chung is grateful for the warm hospitality extended to him by CERN staff duringhis sabbatical year in the EP Division.References[1] P. Abreu et al., DELPHI Collab., Phys. Lett. B449 (1999) 364.[2] V. Uvarov, Phys.Lett. B511 (2001) 136; ‘Determination of the strangeness contentof light-flavor isoscalars from its production rates in hadronic Z decays measured atLEP,’ (arXiv:hep-ph/0105185) May 2001.[3] Review of Particle Physics, Eur. Phys. J. C15, (2000) 1.[4] P. Aarnio et al., DELPHI Collab., Nucl. Inst. Meth. A303 (1991) 233.[5] P. Abreu et al., DELPHI Collab., Nucl. Inst. Meth. A378 (1996) 57.[6] T. Sjo¨strand, Comput. Phys. Comm. 82 (1994) 74.[7] P. Abreu et al., DELPHI Collab., Z.Phys. C 73 (1996) 11.[8] P.Aarnio et al., DELPHI Collab., Nucl. Instr. Meth. A 378 (1996) 57.[9] P. Abreu et al., DELPHI Collab., Z.Phys. C 65 (1995) 587.[10] See, for example, S. U. Chung, ‘Spin Formalisms,’ CERN preprint 71-8 (1971).[11] S. U. Chung et al., Phys. Rev. D60 (1999) 092001.[12] See, for example, S. U. Chung, ‘Analysis of KK¯pi systems (Version I),’ BNL-QGS-98-901 (1998), posted on the website: http://cern.ch/suchung/.10