a + 0 (980)-resonance production in the reaction pp dπ+ η close to the K K threshold

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1 a + (98)-resonance rouction in the reaction π+ η close to the K K threshol P. Feorets, 1, 2 M. Büscher, 1 V.P. Chernyshev, 2 S. Dymov, 1, 3 V.Yu. Grishina, 4 C. Hanhart, 1 M. Hartmann, 1 V. Hejny, 1 V. Kleber, 5 H.R. Koch, 1 L.A. Konratyuk, 2 V. Kotev, 6 A.E. Kuryavtsev, 2 P. Kulessa, 1 S. Merzliakov, 3 S. Mikirtychiants, 6 M. Nekielov, 1, 6 H. Ohm, 1 R. Schleichert, 1 H. Ströher, 1 V.E. Tarasov, 2 K.-H. Watzlawik, 1 an I. Zychor 7 1 Institut für Kernhysik, Forschungszentrum Jülich, Jülich, Germany 2 Institute for Theoretical an Exerimental Physics, Bolshaya Cheremushkinskaya 25, Moscow, Russia 3 Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, Dubna, Russia 4 Institute for Nuclear Research, 6th October Anniversary Prosect 7A, Moscow, Russia 5 Institut für Kernhysik, Universität zu Köln, Zülicher Str. 77, 5937 Köln, Germany 6 High Energy Physics Deartment, Petersburg Nuclear Physics Institute, Gatchina, Russia 7 The Anrzej Soltan Institute for Nuclear Stuies, 54 Swierk, Polan The reaction η has been measure at a beam energy of T =2.65 GeV ( =3.46 GeV/c) using the sectrometer at COSY-Jülich. The missing mass istribution of the etecte airs exhibits a eak aroun the η mass on to of a strong backgroun of multi-ion (nπ) events. The ifferential cross section 4 σ/ω Ω for the reaction η has been etermine moel ineenently for two regions of hase sace. Emloying a ynamical moel for the a + rouction allows one then to euce a total cross section of σ( a+ π+ η) = (1.1 ±.3 stat ±.7 sys) µb for the rouction of η via the scalar a + (98) resonance an σ( η) = (3.5 ±.3 stat ± 1. sys) µb for the non-resonant rouction. Using the same moel as for the interretation of recent results from for the reaction K + K, the ratio of the total cross sections is σ( (K + K ) L= )/σ( a + π+ η) =.29 ±.8 stat ±.9 sys, which is in agreement with branching ratios in the literature. I. INTRODUCTION One of the rimary goals of haronic hysics is the unerstaning of the internal structure of mesons an baryons, an their rouction an ecay, in terms of quarks an gluons. The non-erturbative character of the unerlying theory Quantum Chromo Dynamics (QCD) hiners straightforwar calculations. QCD can be treate exlicitly in the low momentum-transfer regime using lattice techniques [1], which are, however, not yet in the osition to make quantitative statements about the light scalar mesons. Alternatively, QCDinsire moels, which emloy effective egrees of freeom, can be use. The constituent quark moel is one of the most successful in this resect (see e.g. [2]). This aroach treats the lightest scalar resonances a /f (98) as conventional q q states. However, more states with quantum numbers J P = + have been ientifie exerimentally than woul fit into a single SU(3) scalar nonet: the f (6) (or σ), f (98), f (137), f (15) an f (171) with I=, the κ(8) an K (143) (I=1/2), as well as the a (98) an a (145) (I=1) [3]. Consequently, the a /f (98) have also been associate with K K molecules [4] or comact qq- q q states [5]. It has even been suggeste that a comlete nonet of four-quark states might exist with masses below 1. GeV/c 2 [6]. The first clear observation of the isovector a (98) resonance was achieve in K interactions [7], an in subsequent exeriments it has also been seen in annihilations [8], in π collisions [9], an in γγ interactions [1]. Exeriments on raiative φ-ecays [11, 12] have been analyse in terms of the a /f rouction in the ecay chain φ γa /f γπ η/π π. In collisions the a (98) resonance has been measure at = 45 GeV/c via f 1 (1285) a ± π ecays [13] an in inclusive measurements of the X + reaction at = 3.8, 4.5, an 6.3 GeV/c [14]. Desite these many exerimental results, the roerties of the a (98) resonance are still far from being establishe. The Particle Data Grou gives a mass of m a = (984.7 ± 1.2) MeV/c 2 an a with of Γ a = (5 1) MeV/c 2 [3]. The main ecay channels, πη an K K, are quote as ominant an seen resectively. An exerimental rogramme has been starte at the Cooler Synchrotron COSY-Jülich [15] aiming at exclusive ata on the a /f rouction from, n, an interactions at energies close to the K K threshol [16]. The final goal of these investigations is the extraction of the a /f -mixing amlitue, a quantity which is believe to she light on the nature of these resonances [17, 18]. As a first stage the reaction K + K has been measure at T =2.65 GeV, corresoning to an excess energy of Q=46 MeV above the K + K threshol, using the sectrometer [19]. The ata, which have been ecomose into artial waves, show that more that 8% of the kaons are rouce in a relative s wave, corresoning to the a + channel [2]. In this aer we reort on the analysis of the reaction η, which was measure in arallel. II. THE SPECTROMETER AND DATA ANALYSIS Fig. 1 shows the layout of. It consists of three iole magnets (D1 D3), installe at an internal tar-

2 2 get osition of COSY. D1 an D3 eflect the circulating COSY beam from an back into the nominal orbit. The C-shae sectrometer iole D2 searates forwar-going reaction roucts from the COSY beam. The angular accetance of covers ϑ h 1 horizontally an ϑ v 3 vertically for the etecte euterons ( > 13 MeV/c), an ϑ h 12 an ϑ v 3.5 for the ions. An H 2 cluster-jet target [21], lace between D1 an D2, has been use, roviing areal ensities of cm 2. The luminosity has been measure using elastic scattering, recore simultaneously with the ata. Protons in the angular range ϑ = have been selecte, since the accetance changes smoothly in this region an the elastic eak is easily istinguishe from the backgroun in the momentum istribution. The average luminosity uring the measurements has been etermine as L = (2.7±.1 stat ±.7 syst ) 1 31 s 1 cm 2, corresoning to an integrate value of L int = 3.3 b 1 at a roton beam intensity of u to x y 1m D1 z Target TOF-Start MWPC1,2 D Focal-surface telescoes Positive ejectiles Negative ejectiles MWPC3-5 Scintillator hooscoe SD FD #6 #1 D3 TOF-Sto COSY beam FIG. 1: To view of the sectrometer an simulate tracks of ions an euterons from η events. Two charge articles, an, were etecte in coincience. Their trajectories, simulate with the - GEANT rogram ackage [22], are shown in Fig. 1. Positively charge ions in the momentum range π = (6 11) MeV/c were ientifie in the sie etection system (SD) [19, 23], consisting of one layer of 23 start time-of-flight (TOF) scintillation counters, two multiwire roortional chambers (MWPCs) an one layer of 6 counters for TOF-sto. Pions were selecte by a timeof-flight technique (Fig. 2. The fast euterons with momenta = (13 28) MeV/c (an elastically scattere rotons with 34 MeV/c) hit the forwar etection system (FD) [19, 24], which inclues three MWPCs an two layers of scintillation counters. Twoimensional istributions t vs. momenta of forwar articles have been use for the euteron ientification. t was calculate as the time ifference between the etection of a ion in the TOF-sto counter an a fast forwar-going article in the first layer of the FD scintillators. Two istinct bans corresoning to rotons an euterons are seen in this istribution (Fig. 2. The selection of euterons was achieve by cutting along the euteron ban. N, a.u TOF (Start18-Sto4) [44 s/ch.] t [ch.] momentum [MeV/c] FIG. 2: Time-of-flight of articles etecte in TOF start counter 18 an sto counter 4; time ifference t between fast forwar-going articles in the FD an mesons as a function of the momentum of the forwar article. The ashe lines inicate the criteria for euteron ientification. The tracking efficiency for ions in the SD MWPCs was calculate as the ratio of articles in the roer TOF range with an without requiring a reconstructe track. The efficiency eens on the SD sto-counter number (i.e. momentum) an varies between 53% an 76%. For the FD MWPCs the efficiency has been etermine for each of the six sensitive lanes (two er chamber). At least two vertical an horizontal lanes were emane for track reconstruction an for the calculation of the intersection oint with the remaining lane. Each lane has been ivie in 2 2 subcells, an the efficiency of each cell has been calculate from the resence an absence of a hit in the reconstructe intersection. The average FD MWPC track efficiency for euterons is 73%. The efficiencies of the scintillators an TOF criteria are larger than 99% [23]. The efficiency correction is one on an event-by-event basis. III. RESULTS FOR THE REACTION η The missing mass istributions mm(, ) an mm(, ) for the selecte airs are resente in Fig. 3. In the (, ) missing mass istribution a clear eak is observe aroun m(η)=547 MeV/c 2 with about 62 events. The eak sits on to of a smooth backgroun from multi-ion rouction (nπ) (n 2). After selecting the mass range (53 56) MeV/c 2 aroun the η eak, the missing mass sectrum mm(, ) exhibits a shouler at 98 MeV/c 2 (Fig. 3a, otte), where the eak from the a + (98) resonance is execte. Table I resents the ifferential cross sections for η for two regions of hase sace where the accetance of is essentially 1% for this reaction. Six variables in the lab. system have been chosen to escribe these rectangular areas: the vertical (θ y ) an horizontal (θ x ) angles an momenta of the two etecte articles, euteron an. These angles are efine as tan(θ y ) = y / z, tan(θ x ) = x / z.

3 3 N/m [a.u.] 12x1 3 4x1 3 8x1 3 4x1 3 x 6 3x1 3 2x mm(,) [MeV/c 2 ] mm(, ) [MeV/c 2 ] FIG. 3: Missing mass istributions ( mm(, ), ( mm(, ) for the reaction X. The otte histogram in mm(, ) (scale by factor 6) corresons to the selecte area aroun the η eak (53 56 MeV/c 2 ) in mm(, ) (inicate by arrows). 4 σ/ω Ω variables, lab. system µb/(sr GeV/c) 2 θ y, eg. θ x, eg., GeV/c euteron variables 71 ± 6 stat ± 2 sys ( 3, +3 ) ( 3.5, +3.5 ) (1.4, 1.6) ion variables ( 4, +4 ) ( 11, 3 ) (.65,.95) euteron variables 3 ± 4 stat ± 9 sys ( 3, +3 ) ( 6, 2 ) (1.8, 2.7) ion variables ( 4, +4 ) ( 11, 3 ) (.65,.95) TABLE I: Differential rouction cross sections for the reaction η. In both regions of hase sace a + an non-resonant η rouctions contribute. For the momentum range = ( ) GeV/c the non-resonant η rouction shoul be ominant, because this momentum range corresons to low masses of the η system, where the a + rouction is suresse. Unfortunately, ue to the limite hase-sace coverage of, a artial wave ecomosition of the tye erforme in Ref. [2] is not ossible in this case. Thus, in orer to interret the ata in terms of a + an non resonant η rouction, we nee to emloy a moel. This investigation will be escribe in the next section. IV. INTERPRETATION OF THE RESULTS The η final state can be rouce via the a + resonance, a + π+ η (resonant rouction), or through the irect reaction η (non-resonant rouction). The rouction mechanism for the a + has been stuie theoretically in Refs. [25 29]. Accoring to Refs. [25, 26], the cross section for a + rouction at T =2.65 GeV is execte to be 1µb while, for the non-resonant η rouction, ifferent reictions exist, ranging from (.6 1.4) µb [3] an ( )µb [31] u to one orer of magnitue more [26]. The ifferential cross sections from Table I contain contributions from both the resonant an the non-resonant reactions. We have erforme a moel-eenent analysis using the calculate momentum istributions of the rouce euterons (see Figs. 4a,. The calculations are base on moels escribing the resonant rocess within the Quark-Gluon Strings Moel (QGSM) (Fig. 5 [32] an the non-resonant (Fig. 5 rouction via N - an -resonance excitation [29, 31, 33]. The momentum istribution for the resonant reaction is narrower, because low ( η) masses are suresse for a + rouction. The momentum istributions within the accetance are shown in Figs. 4c,. N/ [a.u.] N/ [a.u.] 6x1 4 5x1 4 4x1 4 3x1 4 2x1 4 1x >a + () [GeV/c] ->a + accetance c) () [GeV/c] 4x1 4 3x1 4 2x1 4 1x ) -> η () [GeV/c] -> η accetance () [GeV/c] FIG. 4: Simulate accetance for the euteron momentum for the resonant (a,c) an the non-resonant (b,) η rouction. Uer row: the initial moel istributions [29, 31 33]; lower row: momentum istributions within the accetance. q 5q a + (π ) ++ ( + ) FIG. 5: Diagrams escribing the resonant η rouction within the QGSM [32] ( an the non-resonant via N an excitations [29, 31, 33] (. Within the moels the non-resonant backgroun has a negligible πη s wave contribution an thus oes not interfere with the resonant amlitue. As a consequence, in the range = ( ) GeV/c, the contribution of the non-resonant rocess ominates whereas the resonant η (n) n()

4 4 art is negligibly small (see shae areas in Figs. 4c,). Thus, the cross section of the non-resonant contribution in this momentum range can be efine by fitting the η eak in mm(, ) (Fig. 6 an extracting the number of η events. The missing mass sectra have been escribe by the sum of a Gaussian istribution an a 4 th orer olynomial. N/m [a.u.] x1 3 χ 2 /nf=.9 χ 2 /nf=1.1 3x mm(, ) [MeV/c 2 ] 2x1 3 1x mm(, ) [MeV/c 2 ] FIG. 6: Missing mass istribution mm(, ) for the momentum ranges = ( ) GeV/c ( an = ( ) GeV/c (. In the momentum range = ( ) GeV/c, where both the resonant an the non-resonant reactions contribute, it is ossible to calculate the number of events from the non-resonant rouction taking into account the ifferent accetances. Then the number of a + events is the ifference between the total number of events uner the η eak (Fig. 6 an the calculate amount of non-resonant η events. Incluing all corrections, total cross sections σ a = (1.1 ±.3 stat ±.7 sys ) µb for the a + rouction an σ n.r. = (3.5±.3 stat ±1. sys ) µb for the non-resonant η rouction have been obtaine. It is obvious, that these numbers coul change if ifferent assumtions were mae on the artial wave ecomosition of the (non )resonant contributions. However, we here refrain from investigating further the uncertainty inuce by the moel assumtions. Figure 7a resents the results of GEANT simulations of the accetance for multiion backgroun ( (nπ) (n 2)), an for resonant an non-resonant rouction of the η final state. The number of initial events for each reaction is roortional to the known cross sections for multiion rouction [34] an the values of the total cross sections for the resonant an nonresonant η rouction given above. The shae of the simulate missing mass istribution mm(, ) incluing all channels is in goo agreement with the exerimental ata (Fig. 7. Data for the secon a + ecay channel, a+ K+ K, have been obtaine at in the reaction a + K+ K, simultaneously with the η ata. The measure total cross section is σ( K + K ) = (38 ± 2 stat ± 14 sys ) nb an the contribution of the (K + K ) L= channel is 83% [2]. Assuming that s wave (K + K ) rouction rocees fully via the a + (98) resonance, in accorance with the reictions of the moels iscusse above, the ratio of the total cross sections is N/m [a.u.] sum nonres. 3π 5π a 4π x geant (sum) ex mm(,) [GeV/c 2 ] mm(,) [GeV/c 2 ] FIG. 7: GEANT simulations for multi-ion backgroun ( (nπ) (n 2)), an for resonant an non-resonant rouction of the η final state in the accetance. comarison between the simulate missing mass istribution mm(, ) an exerimental ata. R = σ(a + (K + K ) L= )/σ(a + π+ η) =.29 ±.8 stat ±.9 sys. Ratio T =2.65 GeV Q=46 MeV Q,GeV FIG. 8: Ratio of the total cross sections σ(a + K + K )/σ(a + π+ η) as function of Q. The error bar shows the statistical error only. For measurements at an excess energy Q >> Γ a (5 1) MeV, the ratio of the total cross sections R = σ(a + K+ K )/σ(a + π+ η) shoul not een uon Q. However, when Q is of the orer of Γ a, the contribution from the a + K+ K ecay channel ecreases more strongly ue to the roximity of the K + K threshol an the consequently limite available hase sace. The calculate ratio of the two cross sections as a function of Q is resente in Fig. 8. The calculation is normalise to R((K K)/(πη)) =.23 ±.5, which has been measure at Crystal Barrel in the reaction a π at Q = 768 MeV [35]. The arameters of the Flatté istribution [36] m = 999 ± 2 MeV/c 2, g πη = (324 ± 15) MeV an r = gkk 2 /g2 πη = 1.3 ±.14 are also taken from Ref. [35]. The errors of the Flatté arameters efine the range of ossible R values (shae area in Fig. 8). Our result is in agreement with the calculate value.

5 5 V. CONCLUSIONS To summarize, ata on the reaction η at T = 2.65 GeV are resente. Differential cross sections for limite regions of hase sace, corresoning to forwar emission of the an in the laboratory system, have been extracte. Dynamical moels for the reaction were emloye to obtain the total cross sections for the resonant η rouction via the a + (98) an for the non-resonant η channel. For a + rouction the value for the total cross section a + π+ η is in agreement with theoretical reictions base on the value for the (K + K ) L= reaction recently measure at [2] an the branching ratio BR(K K/πη) from the literature. Our results, together with those from on the ecay channel a + K+ K, are the first evience for a + rouction in collisions, obtaine in a simultaneous exclusive measurement of both a + ecay channels. We are grateful to C. Wilkin for critical iscussions an a careful reaing of the manuscrit. We woul like to thank to W. Borgs, C. Schneier an the IKP technicians for the suort uring the beamtime. One of the authors (P.F.) acknowleges suort by the COSY-FFE rogram (grant FFE ). The work at has artially been suorte by: BMBF (grants WTZ- RUS , 211-, 691-1, GEO-1-99, POL-7-99, 15-1), DFG (436 RUS 113/444, 63, 733,787), DFG- RFBR , (436 RUS 113/652), Polish State Committee for Scientific Research (2 P3B 11 19), Russian Acaemy of Science (RFBR 6518, ), ISTC (1861, 1966). [1] T. Kunihiro et al. [SCALAR Collaboration], arxiv:heh/ [2] D. Morgan, Phys. Lett. B 51, 71 (1974); K.L. Au, D. Morgan, an M.R. Pennington, Phys. Rev. D 35, 1633 (1987); D. Morgan an M.R. Pennington, Phys. Lett. B 258, 444 (1991); D. Morgan an M.R. Pennington, Phys. Rev. D 48, 1185 (1993); A.V. Anisovich et al., Eur. Phys. J. A 12, 13 (21); S. Narison, he-h/ [3] S. Eielman et al. (Particle Data Grou); Phys. Lett. B 592, 1 (24). [4] J. Weinstein an N. Isgur, Phys. Rev. Lett. 48, 659 (1982); Phys. Rev. D 27, 588 (1983); Phys. Rev. D 41, 2236 (199); G. Janssen et al., Phys. Rev. D 52, 269 (1995); J.A. Oller an E. Oset, Nucl. Phys. A 62, 438 (1997) [Erratum-ibi. A 652, 47 (1999)]. [5] N.N. Achasov, he-h/21299; R.J. Jaffe, Phys. Rev. D 15, 267 (1977); J. Vijane et al., Proc. Int. Worksho MESON 22, May 24 28, 22, Cracow, Polan, Worl Scientific Publishing, ISBN ,.51, he-h/ [6] F.E. Close an N.A. Törnqvist, J. Phys. G 28, R249 (22). [7] J.B. Gay et al., Phys. Lett. B 63, 22 (1976). [8] A. Abele et al., Phys. Lett. B 327, 425 (1994); A. Abele et al., Phys. Rev. D 57, 386 (1998); A. Bertin et al., Phys. Lett. B 434, 18 (1998). [9] S. Teige et al., Phys. Rev. D 59, 121 (1999). [1] P. Achar et al., Phys. Lett. B 526, 269 (22). [11] N.N. Achasov et al., Phys. Lett. B 485, 349 (2); Phys. Lett. B 479, 53 (2). [12] A. Aloisio et al., Phys. Lett. B 536, 29 (22); Phys. Lett. B 537, 21 (22). [13] D. Barberis et al., Phys. Lett. B 44, 225 (1998); Phys. Lett. B 488, 225 (2). [14] M.A. Abolins et al., Phys. Rev. Lett. 25, 469 (197). [15] R. Maier, Nucl. Instr. an Methos Phys. Res., Sect. A 39, 1 (1997). [16] M. Büscher, Acta Phys. Pol. B 35, 155 (24). [17] C. Hanhart, Phys. Ret. 397, 155 (24). [18] N.N. Achasov et al., Phys. Lett. B 88, 367 (1979). [19] S. Barsov et al., Nucl. Instr. an Methos Phys. Res., Sect. A 462, 364 (21). [2] V. Kleber et al., Phys. Rev. Lett. 91, (23). [21] R. Santo et al., Nucl. Instr. an Methos Phys. Res., Sect. A 386, 228 (1997); A. Khoukaz et al., Eur. Phys. J. D 5, 275 (1999). [22] I. Zychor, Acta Phys. Pol. B 33, 521 (22). [23] M. Büscher et al., Nucl. Instr. an Methos Phys. Res., Sect. A 481, 378 (22). [24] V. Komarov et al., Phys. Lett. B 553, 179 (23). [25] V.Y. Grishina et al., Phys. Lett. B 521, 217 (21). [26] H. Müller, Eur. Phys. J. A 11, 113 (21). [27] E. Oset et al., Eur. Phys. J. A 12, 435 (21). [28] E.L. Bratkovskaya et al., J. Phys. G 28, 2423 (22). [29] L.A. Konratyuk et al., Phys. At. Nucl. 66, 152 (23) (Ya. Fiz., 66, 155 (23)). [3] V.E. Tarasov an A.E. Kuryavtsev, rivate communication. [31] V.Y. Grishina et al., Annual Reort 2 of the IKP, FZ Jülich,.3. [32] V.Y. Grishina et al., Eur. Phys. J. A 21, 57 (24). [33] A.E. Kuryavtsev et al., Phys. At. Nucl. 66, 1946 (23) (Ya. Fiz., vol. 66, 1994 (23)). [34] A. Balini, Lanolt-Börnstein, New Ser. I, Vol. 12, 97 (1988), reactions 71,72 an 73. [35] A. Abele et al., Phys. Rev. D 57, 386 (1998). [36] S. Flatté, Phys. Lett. B 63, 225 (1976).