Search for Direct Production of A2 (1320) and F2 (1270) Mesons in E+ E-Annihilation

arXiv:hep-ex/0009048v1 22 Sep 2000 ∗ Keywords PACS a:+(82326;emi:[email protected] e-mail: +7(3832)342163; Fax: fteemsn eeotie t9 ofiec level: confidence % 90 at obtained were mesons these of a efre ihSDdtco tVEPP-2M at detector SND with performed was ..Bgacio,AV ohnk ..Bkn ..Burdin, S.V. Bukin, D.A. Bozhenok, A.V. Bogdanchikov, A.G. ..Slio,SI eenao,VA ioo,ZK Silaga Z.K. Sidorov, V.A. Serednyakov, S.I. Salnikov, A.A. ..Iacek,AA oo,MS ootlv ..Koshuba S.V. Korostelev, M.S. Korol, A.A. Ivanchenko, V.N. ..Ahsv ..Br,KI eoooo,AV Berdyugin, A.V. Beloborodov, K.I. Baru, S.E. Achasov, M.N. ..Kkrsv ..Pktsv,AA oui,EE Pyata, E.E. Polunin, A.A. Pakhtusova, E.V. Kukartsev, G.A. erhfrdrc rdcino -vnresonances C-even of production direct for search A : ..Srnk,VV hr,Y..Sauo,AV Vasiljev A.V. Shatunov, Yu.M. Shary, V.V. Skrinsky, A.N. 34.p 36.i 38.m 14.40.Cs 13.85.Rm; 13.65.+i; 13.40.Gp; and erhfrdrc rdcinof production direct for Search : e + ..Dmv,AA rzesy ..Druzhinin, V.P. Drozdetsky, A.A. Dimova, T.V. ..Dboi,IA aoek,VB Golubev, V.B. Gaponenko, I.A. Dubrovin, M.S. e f − 2 olsos esrmsn Detector meson; Tensor collisions; 17)msn in mesons (1270) ukrIsiueo ula Physics, Nuclear of Institute Budker ooiis tt University, State Novosibirsk ooiis,609,Russia 630090, Novosibirsk, arnivAeu,11, Avenue, Lavrentiev Γ( Γ( a f 2 2 (1270) (1320) Abstract → → e e e 1 + + + e e e − − − ) ) oldr h pe iiso lcrncwidths electronic of limits upper The collider. < < a e 2 .1eV. 0.11 .6eV, 0.56 12)and (1320) + e − annihilation f 2 17)in (1270) a 2 (1320) e + e − annihilation dze, ∗ , 1. Introduction At present only branching ratios of pseudoscalar mesons η µ+µ− [5] and π0 e+e− [6] are + − → → Traditional subject of study in e e collisions measured with accuracies of 15% and 8% respec- PC −− are vector states with J =1 . Direct produc- tively. PC −+ ++ ++ tion of C-even mesons (J =0 , 0 , 2 ,... The energy range of the electron-positron col- ) is also possible via two-photon annihilation (fig.1) lider VEPP-2M [7] allows to perform a search for although it is suppressed by a factor of α2 for ∼ production of the lightest tensor mesons f2(1270) tensor mesons. Production of scalar and pseu- + − and a2(1320) in e e annihilation. Using the ex- doscalar states is further suppressed by additional 2 + − perimental values [5] of the two-photon widths of ’chirality’ factor me/s. Nevertheless, e e collid- these mesons, one can estimate their electronic ing beam technique remains one of the most sensi- widths in the unitarity limit: tive methods of measurement of electronic widths of C-even resonances (X) with masses around 1GeV + − −2 Γ(a2(1320) e e )ul 1 10 eV, (2) [1, 2]. → ∼ · + − −2 Γ(f2(1270) e e )ul 3 10 eV (3) → ∼ · The only experimental attempt to measure these - widths was taken in the ND experiment at VEPP- e 2M collider [8] in the search for the reactions: + − 0 e e a2(1320) ηπ , (4) → → + − 0 0 e e f2(1270) π π (5) X → → As a result the following upper limits at 90 % con- + − fidence level were obtained: Γ(a2(1320) e e ) < + − → + 25eV, Γ(f2(1270) e e ) < 1.7 eV [1, 2]. e →

2. Detector and experiment

In the present work the search for the reactions (4, 5) was continued. The experiments [9] were carried out in 1997 and 1999 at VEPP-2M e+e− collider with the SND detector [10, 11]. Four Figure 1: The diagram of direct production of successive scans of the energy range 2E0=1.04– + − C-even resonance in e e collision. 1.38 GeV with the step ∆(2E0)=0.01GeV were performed. The total integrated luminosity of 9 pb−1 was uniformly distributed over this energy In the unitarity limit [3] when both virtual range. For present analysis only the data with photons (ﬁg.1) are on the mass shell the leptonic 2E0 above 1.15 GeV with an integrated luminos- −1 width is completely determined by imaginary part ity of 6.5 pb was used. of the X e+e− transition amplitude which is The SND detector is a universal nonmagnetic → related to the X two-photon width [4]. Taking detector. Its main part is a three-layer electro- into account both real and imaginary parts of the magnetic calorimeter consisted of 1630 NaI(Tl) X e+e− transition amplitude Z, the branch- crystals covering 90% of 4π solid angle. The en- → − ing ratio of X e+e decay can be written as ergy resolution of the calorimeter for photons with → follows: energy E can be described by the function σE /E = 2 4 + − 2α 4.2%/√E, GeV , the angular resolution is close to Br(X e e )= Br(X γγ) ◦ 0 → 9 · → · 1.5 , the resolution over π invariant mass is ap- proximately 8 %. For measurement of charged 1 + (ReZ)2/(ImZ)2 (1)

2 1 four photons and no charged particles are found in an event;

, pb + -→ →π0π0 0 e e f2(1270) σ 0.8 energy deposition in the calorimeter Etot > 0.7 (2 Ebeam); · · 0.6 total momentum of an event measured by the calorimeter Ptot < 0.3 (2 Ebeam/c). · · 0.4 A total of 12.6 thousand events satisfying the + -→ →ηπ0 e e a2(1320) above criteria were found. Main background for the processes (4, 5) comes 0.2 from the following reactions with a 3 order of magnitude larger cross sections:

0 − 1 1.1 1.2 1.3 1.4 e+e 4γ (QED), (7) → 2E0 , GeV − e+e ωπ0 π0π0γ, (8) Figure 2: Energy dependences of the cross sec- → → + − 0 0 tions of the reactions e e f2(1270) π π , where the reaction (8) produces events satisfying + − 0 → → e e a2(1320) ηπ calculated in the uni- 4γ selection cuts due to merging of close photons → → tarity limit. or loss of soft photons through openings in the calorimeter. Other background processes are the reactions with emission of hard photon at large angle by one particles directions the system of two central cylin- of the initial particles and subsequent production rical drift chambers is used. More detailed de- of ρ, ω, or φ meson: scription of the SND detector can be found in [11]. A search for the reaction (5) was carried out − e+e Vγ π0γγ, ηγγ, V = ρ,ω,φ (9) taking into account the diﬀerential cross section → → calculated in [12]: Their cross sections are 1–2 orders of magnitude

6 larger than these of the processes under study (4, dσ √s 5) [13]. = 12.5 dΩ · m ! · Additional background comes from the QED 2 processes: Γ Bee B 0 0 · · π π sin2(2θ), (6) 2 2 2 2 − (m s) + m Γ · e+e 2γ, 3γ (10) − → 2 where s = 4E ; m, Γ, B , and B 0 0 are the 0 ee π π with detection of additional stray photons of beam f2-resonance mass, width, and branching ratios background. Energy spectrum and angular dis- of its decays into e+e− and π0π0. The cross sec- tribution of such photons were studied on special tions of the reactions (4) and (5), calculated in the class of events with trigger from external gener- unitarity limit, are shown in the ﬁg.2. Expected ator. Analysis of these events shows that stray numbers of events, corresponding the collected lu- photons mainly concentrate at small angles with minosity distribution, are 1 and 4 for the reactions respect to the beam axis and their spectrum de- (4) and (5) respectively. creases sharply with increase of energy. To suppress a contribution from the processes (10) with 3. Events selection extra photons, the following restrictions on angle θγ and energy Eγ of each photon in the event were For the primary selection of events the follow- applied: ing cuts were applied: ◦ ◦ 27 <θγ < 153 , Eγ > 0.1 Ebeam. ·

3 Although these cuts reduce eﬃciency for the ω πo processes under study (4, 5) by 30 %, they strongly, 100

by about five times, suppress contribution of the Events QED processes (7, 10). After all above listed cuts (πoπo+ηπo)x100 2036 events were selected, which correspond to 80 the total detection cross section 0.3 nb. 4γ (QED) ∼ To suppress background events with merged 60 photons the special parameter ζ [14] was used. This parameter is a measure of likelihood of the 40 hypothesis that given transverse energy deposition profile of a photon cluster in the calorimeter can be attributed to a single photon emitted from 20 the beam interaction point. The requirement 0 ζ <0 0 1 2 3 4 5 6 7 ο ξωπ for all photons in an event allows to suppress significantly the contribution of events with merged photons and events of the process Figure 3: Distribution of 842 experimental events over the parameter ξ 0 (circles with error + − 0 0 ωπ e e KSKL π π KL (11) → → bars). The clear histogram is the sum of expected contributions of the main background processes (7 with nuclear interaction of K . This cut reduces L – 9), shaded histogram is an expected signal of the the number of experimental events by 40 % while processes under study (4, 5) multiplied by 100. the detection efficiencies for the processes (4) and Dashed and dotted lines show individual contri- (5) decrease by only 6 % and 4 % respectively. butions of the main background processes (8) and For the events left, kinematic fit with require- (7) respectively. ment of energy-momentum conservation was performed and corresponding value of χ2 was calculated. For further analysis 842 events with were calculated. Here m1, depending on the com- χ2 <20 bination being considered, is either invariant mass were selected. This number is in a good agree- of three photons or recoil mass of two photons, m2 ment with expected contribution of the background is an invariant mass of two photons for a given processes (7 - 9) obtained by simulation. About combination; mω and mπ0 — the masses of ω and 0 65% of it comes from the process (8). π mesons respectively. The parameter ξωπ0 was To suppress contribution of the process (8) defined as 2 the special parameter ξ 0 was constructed tak- 0 ωπ ξωπ = ln(1 + mini(χi )), i =1,..., 24. (13) ing into account the topology of the process (8) It is seen from ξ 0 distributions in the fig.3 that with only four photons detected. Three hypothe- ωπ events of the process (8) concentrate in the left ses were considered: 0 side of the plot while processes under study (4, 5) 1) undetected photon is from recoil π (12 possi- have flatter and wider spectrum allowing the use ble combinations); of this parameter for further cuts. 2) undetected photon is the recoil photon from ω Similarly to eq. 12,13 the parameters ξ 0 , ξ 0 0 decay (6 possible combinations); ηπ π π 0 and ξ 0 , ξ , ξ , ξ 0 for selection of the 2) undetected photon comes from π in ω decay ωπ γ ωηγ φηγ φπ γ processes (4), (5) and (9) respectively were con- (6 possible combinations). structed. For all 24 possible combinations of photons the values of 2 2 4. Final events selection and results 2 (m1 mω) (m2 mπ0 ) χi = −2 + −2 (12) σω σπ0 To select candidate events of the reaction (5)

4 50 80 4γ (QED) 4γ (QED) Events Events πoπo 40 η πo 60 x100 x1000 o ω π 30 ω πo 40 20

20 10

0 0 0 2 4 6 8 0 1 2 3 4 5 6 ξ πo πo ξ η πo

Figure 4: The ξπ0π0 distributions: circles with Figure 5: The ξηπ0 distributions: circles with error bars — experimental data; clear histogram error bars — experimental data; clear histogram — expected contribution of the background pro- — expected contribution of the background processes (7 - 9), shaded histogram — expected signal cesses (7 - 9), shaded histogram — expected signal of the process (5) multiplied by 100. In addition of the process (5) multiplied by a factor 1000. In the individual contributions of main backgrounds, addition, individual contributions of main back- (8) — dashed line and (7) — dotted line, are grounds, (8) — dashed line — and (7) — dotted shown separately. Arrow shows the cut ξπ0π0 <2 line, are shown separately. Arrow shows the cut used for ﬁnal selection. ξηπ0 <2 used for ﬁnal selection.

the following cuts were imposed: We used the following formulae to obtain the ξωπ0 > 1.5, ξωπ0γ > 2, ξπ0π0 < 2. (14) upper limits of branching ratios of electronic decays of tensor mesons T = a2(1320), f2(1270): The ξ 0 0 distribution before the last cut from π π + − k0 (14) is shown in fig. 4. No experimental events Br(T e e ) < . (16) → Nexpt passed selection cuts, while 0.7 events of the pro- Here Nexpt = ∆L(Ei) σ(Ei) (1 + δ) ǫ(Ei) cess under study (5) (in the unitarity limit) and · · · 1.4 events of the background processes are ex- is expected number of events of the process un- P + − der study with Br(T e e ) = 1 , k0=2.44 is pected from simulation. The selection efficiency → for the process (5) is close to 17 %. a 90 % CL Poisson limit in case of none experi- To search for the reaction (4) the following mental events observed ( [5], p. 177), ∆L(Ei) is cuts were applied to 842 experimental events se- an integrated luminosity at the energy Ei, σ(Ei) lected above: and ǫ(Ei) are the cross section and the selection efficiency of the process under study, calculated ξ 0 > 2, ξωηγ > 2, ξφηγ > 1, ξ 0 < 2. ωπ ηπ by MC simulation, δ is a radiative correction. In (15) the table (1) upper limits at 90 % CL on branch- The ξηπ0 distribution before the last cut from (15) ing ratios and electronic widths of a2(1320) and is shown in fig. 5. Here again no experimental f2(1270) calculated according to eq.(16) as well as events were found. Expected number of events of the process under study (4) is 0.05, the selection efficiency is about 5 % taking into account all decay modes of η meson. Calculated contribution of the background processes (7 – 9) is 5.5 events.

5 Table 1: The upper limits of branching ratios and electronic widths of tensor mesons a2(1320) and f2(1270) obtained in this work as compared with current experimental data and theoretical calculations in the unitarity limit [3].

this work ND’91 [2] calculation in the (SND’2000) (PDG’98 [5]) unitarity limit [3] + − −9 −7 −10 Br(a2 e e ) < 6 10 < 2.3 10 1.1 10 → + − · −10 · −9 · −10 Br(f2 e e ) < 6 10 < 9 10 1.6 10 → + − · · · Γ(a2 e e ), eV < 0.56 < 25 0.012 → + − Γ(f2 e e ), eV < 0.11 < 1.7 0.029 → theoretical predictions are presented. [4] V.N. Novikov and S.I. Eidelman, Sov. J. Nucl. Phys. 21 (1975) 1029. 5. Discussion [5] Review of Particle Physics, Eur. Phys. J. C

+ − 3 (1998). The upper limits of the a2 e e and f2 − → → e+e branching ratios obtained in this work are [6] E799-II / KTeV Collaboration, Phys. Rev. respectively 45 and 15 times lower than previous Lett. 83 (1999) 922, hep-ex/9903007. experimental values [1]. Our limit for the elec- [7] G.M. Tumaikin et al., Proceedings of the 10- tronic width of f2(1270) is only four times higher th International Conference on High Energy than its unitarity limit. It allows for the first time Particle Accelerators, Serpukhov, v.1, 443 to place a meaningful experimental limit for the + − (1977). ratio of the real and imaginary parts of f2 e e → transition amplitude: [8] V.B. Golubev et al., Nucl. Instr. and Meth- ods 227 (1984), p.467. (ReZ)2/(ImZ)2 < 2.8 (17) [9] M.N. Achasov et al., Novosibirsk preprint at 90 % confidence level. Unfortunately, we could Budker INP 98-65 (1998). not find any theoretical estimates for this parameter. To observe the process (5) with SND detector [10] V.M. Aulchenko et al., SND - Detector for it is necessary to increase integrated luminosity by VEPP-2M and Phi-Factory, in: Proc. Work- 1–2 orders of magnitude. shop on Physics and Detectors for DAFNE (Frascati, April 1991), p.605.

Acknowledgments [11] M.N. Achasov et al., Nucl. Instr. and Meth. A 449 (2000) 125, hep-ex/9909015. This work is supported in part by Russian Fund for Basic Researches, grants No. 00-02-17481 [12] A.A. Belkov, E.V. Kuraev and V.N. Per- and 00-15-96802, and STP “Integration” No. 274. vushin, Yad. Fiz. 40 (1984) 1483. [13] M. Benayoun, S.I. Eidelman, V.N. References Ivanchenko and Z.K. Silagadze, Mod. Phys. Lett. A 14, No. 37 (1999) 2605. [1] P.V. Vorobyev et al., Sov. J. Nucl. Phys. 48 [14] A.V. Bozhenok, V.N. Ivanchenko and Z.K. (1987) 436. Silagadze, Nucl. Instr. and Meth. A 379 [2] S.I. Dolinsky et al., Phys. Rep. 202 (1991) (1996) 507. 99. [15] E.A. Kuraev and V.S. Fadin, Sov. J. Nucl. [3] A.I. Vainshtein and I.B. Khriplovich, Yad. Phys. 41 (1985) 466. Fiz. 13 (1971) 620.