The CELSIUS/WASA setup is used to measure the 3pi0 decay of eta mesons
produced in pp interactions with beam kinetic energies of 1.36 and 1.45 GeV.
The efficiency-corrected Dalitz plot and density distributions for this decay
are shown, together with a fit of the quadratic slope parameter alpha yielding
alpha = -0.026 +/- 0.010(stat) +/- 0.010(syst). This value is compared to
recent experimental results and theoretical predictions.Comment: 4 pages, 7 Postscript figures, uses revtex4.st

A. Kupść

A. Kuznetsov

A. Povtorejko

A. Turowiecki

A. Yamamoto

B. Borasoy

B. Höistad

B. Morosov

B. Shwartz

C. Ekström

C. Pauly

D. Bogoslawsky

E. Jiganov

F. Capellaro

G. Ivanov

G. J. Wagner

H. Calén

H. Clement

H. Pettersson

I. Koch

J. Stepaniak

J. Zabierowski

J. Złomańczuk

K. Fransson

K. Schönning

L. Demirörs

L. Gustafsson

M. Bashkanov

M. Jacewicz

M. Wolke

P. Marciniewski

P. Thörngren Engblom

R. J. M. Y. Ruber

R. Meier

S. Giovannella

S. Keleta

S. Kullander

T. Johansson

T. Skorodko

U. Wiedner

V. Sopov

V. Tchernyshev

V. Tikhomirov

W. Oelert

W. Scobel

Y. Petukhov

English

arXiv

The CELSIUS-WASA setup is used to measure the 3π0 decay of η mesons produced in pp interactions with beam kinetic energies of 1.36 and 1.45 GeV. The efficiency-corrected Dalitz plot and density distributions for this decay are shown, together with a fit of the quadratic slope parameter α yielding α = −0.026 ± 0.010(stat) ± 0.010(syst). This value is compared to recent experimental results and theoretical predictions.</p

Bashkanov, M.

Bogoslawsky, D.

Calén, Hans,

Capellaro, Filippo,

Clement, H.

Demirörs, L.

Ekström, Curt,

Fransson, Kjell,

Gustafsson, Leif,

Höistad, Bo,

Ivanov, G.

Jacewicz, Marek,

Jiganov, E.

Johansson, Tord,

Keleta, Samson,

Koch, Inken,

Kullander, Sven,

Kupsc, Andrzej,

Kuznetsov, A.

Marciniewski, Pawel,

Meier, R.

Morosov, B.

Oelert, W.

Pauly, C.

Petukhov, Y.

Pettersson, Henrik,

Povtorejko, A.

Ruber, Roger J. M. Y.,

Schönning, Karin,

Scobel, W.

Skorodko, T.

Shwartz, B.

Sopov, V.

Stepaniak, J.

Tchernyshev, V.

Thörngren Engblom, Pia,

Tikhomirov, V.

Turowiecki, A.

Wagner, G.J.

Wiedner, Ulrich,

Wolke, Magnus,

Yamamoto, A.

Zabierowski, J.

Zlomanczuk, Jozef,

Swepub

Measurement of the slope parameter for the η → 3π0 decay in the pp → ppη reaction

Crossref

Measurement of the slope parameter for theη→3π0decay in thepp→ppηreaction

The CELSIUS-WASA setup is used to measure the 3 pi(0) decay of eta mesons produced in pp interactions with beam kinetic energies of 1.36 and 1.45 GeV. The efficiency-corrected Dalitz plot and density distributions for this decay are shown, together with a fit of the quadratic slope parameter alpha yielding alpha = -0.026 +/- 0.010(stat) +/- 0.010(syst). This value is compared to recent experimental results and theoretical predictions

Jacewicz, M.

Johansson, T.

Keleta, S.

Koch, I.

Kullander, S.

Kupsc, A.

Marciniewski, P.

Calen, H.

Pettersson, H.

Ruber, R.J.M.Y.

Schönning, K.

Capellaro, F.

Thörngren Engblom, P.

Wagner, G. J.

Wiedner, U.

Wolke, M.

Zlomanczuk, J.

Ekström, C.

Fransson, K.

Gustafsson, L.

Höistad, B.

Juelich Shared Electronic Resources

arXiv:0708.2014v1  [nucl-ex]  15 Aug 2007Measurement of the Slope Parameter for the η → 3pi◦ Decay in the pp→ ppη ReactionM. Bashkanov1, D. Bogoslawsky2, H. Cale´n3, F. Capellaro4, H. Clement1, L. Demiro¨rs5, C. Ekstro¨m3, K. Fransson3,L. Gustafsson4, B. Ho¨istad4, G. Ivanov2, M. Jacewicz4, E. Jiganov2, T. Johansson4, S. Keleta4, I. Koch4,S. Kullander4, A. Kups´c´3, A. Kuznetsov2, P. Marciniewski3, R. Meier1, B. Morosov2, W. Oelert6, C. Pauly5,Y. Petukhov2, H. Pettersson4, A. Povtorejko2, R.J.M.Y. Ruber3, K. Scho¨nning4, W. Scobel5, T. Skorodko1,B. Shwartz7, V. Sopov8, J. Stepaniak9, V. Tchernyshev8∗, P. Tho¨rngren Engblom4, V. Tikhomirov2,A. Turowiecki10, G.J. Wagner1, U. Wiedner4, M. Wolke4,6, A. Yamamoto11, J. Zabierowski9, J. Z loman´czuk41Physikalisches Institut der Universita¨t Tu¨bingen Tu¨bingen,Germany2Joint Institute for Nuclear Research Dubna,Russia3The Svedberg Laboratory, Uppsala, Sweden4Institutionen fo¨r Ka¨rn- och Partikelfysik Uppsala University, Uppsala, Sweden5Institut fu¨r Experimentalphysik Universita¨t Hamburg,Hamburg, Germany6Institut fu¨r Kernphysik Forschungszentrum Ju¨lich Germany7Budker Institute of Nuclear Physics,Novosibirsk,Russia8Institute of Theoretical and Experimental Physics,Moscow,Russia9Soltan Institute of Nuclear Studies,Warsaw and Lodz, Poland10Institute of Experimental Physics,Warsaw,Poland11High Energy Accelerator Research Organization,Tsukuba,Japan(CELSIUS-WASA Collaboration)(Dated: February 16, 2013)The CELSIUS/WASA setup is used to measure the 3pi◦ decay of η mesons produced in pp inter-actions with beam kinetic energies of 1.36 and 1.45 GeV. The efficiency-corrected Dalitz plot anddensity distributions for this decay are shown, together with a fit of the quadratic slope parameterα yielding α = −0.026 ± 0.010(stat) ± 0.010(syst). This value is compared to recent experimentalresults and theoretical predictions.PACS numbers: 13.25.-k, 14.40.Aq, 12.39.Fe, 13.75.-nI. INTRODUCTIONIsospin violating decays into three pions are two of themost probable η meson decay modes: BR(η → 3pi◦) =32.5% and BR(η → pi◦pi+pi−) = 22.6% [1]. It appearsthat contribution of electromagnetic processes is sup-pressed [2, 3] and the decays are driven by an isospinviolating term of the QCD Lagrangian proportional tomd − mu. The partial width of the η → pi◦pi+pi− de-cay calculated using current algebra (PCAC) is 66 eV[4], much below the experimental value 294±16 eV [1].Second order contributions in the low energy expansionof the QCD Lagrangian (Chiral Perturbation Theory –CHPT) were calculated by Gasser and Leutwyler increas-ing the result to 160 eV [5]. The big change with respectto the first order calculations implies the importance ofpipi interaction in the final state. An elegant method ofincluding the interaction up to higher orders is providedby dispersion relations. There are two calculations usingthis technique [6, 7] but employing different formalism.They lead consistently to an enhancement of the decayrate by about 14%. A free parameter in this approachis the value of the so called subtraction point and it was∗Deceasedconstrained using CHPT calculations.The decay width can be expressed in the factorizedform:Γ =(QDQ)4Γ¯ (1)where the dependence on the md −mu is contained onlyin the Q term:1Q2=m2d −m2um2s −14(md +mu)2. (2)Normally the calculations of Γ are performed using theDashen theorem [8] where Q = QD ≡ 24.1. Since Γ issensitive to the exact value of Q, it was suggested thatthe decay might provide precise constrain for the lightquark mass ratios [9]. Namely Q determines the majoraxis of the ellipse in the mu/ms, md/ms plane. Oneimportant prerequisite is the reliability of the Γ¯ calcula-tions. The calculations can be tested by comparing theratio Γ(η → 3pi◦)/Γ(η → pi+pi−pi◦) and the density dis-tributions in the respective Dalitz plots with experiment.Recently Q was derived from preliminary KLOE data onη → pi+pi−pi0 decay [10, 11], by determining the subtrac-tion point within the dispersion relation approach of [7],yielding a Q value 22.1 [12].This letter describes an exclusive measurement of kine-matical distributions of the pi◦’s from the η → 3pi◦ chan-2TABLE I: Experimental and theoretical results for the slopeparameter αα Comment Ref.-0.052 ± 0.017(stat) ± 0.010(syst) Exp (CBarrel) [18]-0.031 ± 0.004 Exp (CBall) [19]-0.013 ± 0.004(stat) ± 0.005(syst) Exp (KLOE) [10]0 PCAC [4]+0.015 CHPT,1loop [5, 20]-0.007...-0.014 CHPT+dispersive [7]-0.007 UCHPT [13]-0.031 ± 0.003 UCHPT/fit [21]nel. The phase space of the decay can be represented bya Dalitz plot employing symmetrized variables as shownin Fig. 1(left). The amplitude can then be expressed interms of polar coordinates ρ and φ, where due to sym-metry φ is restricted to 0 < φ < 60◦. Instead of ρ anormalized dimensionless variable 0 ≤ z ≤ 1 is used:z ≡ρ2ρ2max=233∑i=1(Ti− < T >< T >)2. (3)where Ti is kinetic energy of a pi◦ in the η rest frame and< T > is the average kinetic energy.The slope parameter, α, is defined as a coefficient inthe leading term of the decay amplitude expansion in z:| A(z, φ) |2= c0(1 + 2αz). (4)The situation for the α measurement is unsettled withinconsistent experimental results and disagreement withCHPT predictions (Table I). In lowest order CHPTα = 0. The deviation is caused by the pi◦pi◦ interactions.All calculations beyond one loop predict a negative valueof α. Dispersion relations [7] and U(3) chiral effectivefield theory with rescattering [13] give consistently a lowvalue for the |α| of about 0.007. Most recent calcula-tions with U(3) effective Lagrangian and Bethe-Salpeterequations include more general rescattering graphs andparameters are fitted to the scattering data for the pseu-doscalar mesons [14]. The calculations are able to explainthe large experimental values for |α|. However in that ap-proach a change of the Q value can be compensated byother fit parameters and could even be equal to QD.A special feature of the η → 3pi◦ decay is that thephysical region extends below threshold of the pi0pi0 →pi+pi− reaction. Therefore a cusp structure should bevisible in invariant mass distribution of two pi0 around2mpi± (dashed lines in Fig. 1(left)), in analogy to therecent observation in K+ → pi+pi0pi0 decay [15, 16, 17].The exact parameters of the cusp in the K+ → pi+pi0pi0decay provide one of most precise determinations of thepipi scattering length (a2 − a0).The experimental determination of the α requires thatbackground contribution to the η production process andother systematic errors are well under control. All recent [MeV]3)/2-T1(T-40 -20 0 20 40 [MeV]3<T>-T-40-2002040φ ρFIG. 1: (Left) Symmetrized Dalitz plot for η → 3pi◦ decay.(Right) radial density distribution (right) for the MC (shadedarea) and experimental data (closed symbols).experiments on the decay η → 3pi◦ rely solely on pho-ton detection with close to 4pi electromagnetic calorime-ters. The Crystal Barrel experiment used the final statewith 10γ (pp → η2pi◦) [18], Crystal Ball used the reac-tion pi−p → nη where only the 6γ from the decay weremeasured [19]. KLOE [10] used the decay φ → ηγ as asource of the η mesons leading to 7γ in the final state.The α values differ by more than three standard devia-tions between the experiments. We have performed anindependent measurement using the reaction pp → ppη[22]. The main advantage is that the excellent missingmass resolution of the forward going pp pair can be usedto tag the process.II. MEASUREMENT AND DATA REDUCTIONThe analysis is based on data taken with the WASAdetector at CELSIUS [23] using a pellet target systemthat provides small (30 µm diameter) hydrogen pelletsthat cross the proton beam of nominal 1.36 GeV and1.45 GeV kinetic energy (the corresponding center ofmass excess energies are 41 MeV and 75 MeV respec-tively). The WASA detector system comprises a mul-tilayered forward detector (FD) for the measurement ofcharged particles emerging in the scattering angle rangeof 2.5◦-18◦, and a central deteector (CD) composed ofan electromagnetic calorimeter of 1012 CsI(Na) crystalsand a drift chamber/solenoid combination for the mea-surement of particles from η decays in the angular rangeof 20◦−140◦.The basic criteria for the selection of the final η → 3pi◦state are (i) two protons detected in the FD and (ii) sixγ hit clusters (from pi◦ → γγ) detected in the CD asneutrals with a minimum of 20 MeV deposited energy.The experimental proton-proton missing mass distribu-tion can be compared to Monte Carlo (MC) simulateddata for the reaction channels pp→ pppi◦pi◦pi◦, pp→ ppη,and pp → pppi◦pi◦. The procedure is described in detailin [22], the result for 1.36 GeV kinetic energy is shownin Fig. 2. The good agreement in shape that is obtainedalso for other kinematical proton variables and of theabsolute cross sections for the η channel with existing3]2PP missing mass [GeV/c0.30 0.35 0.40 0.45 0.50 0.55 0.60)2events/(7 MeV/c10210310410T=1.36 GeVExperimentMC sum)0pi0pi0pi →(η pp→pp 0pi0pi0pi pp→pp 0pi0pi pp→pp FIG. 2: Experimental pp missing mass distribution for recon-structed pppi◦pi◦pi◦ final states with a fit of the MC distribu-tions for 2pi◦, 3pi◦ and η production (from [22]). The verticallines indicate the η selection.data, demonstrates that the detector and its efficiencyare well under control. The missing mass resolution ofthe FD (5 MeV/c2 FWHM at 1.36 GeV) therefore allowsselection of the pp → ppη reaction (the condition 535MeV/c2 < MMpp <560 MeV/c2 was applied) such thatthe remaining background, mostly from direct pp→ pp3pireaction, is about 5%.All possible combinations (15) of the 6 reconstructedgammas to form 3 pi◦ → γγ pairs are sorted by meansof a parameter χ2 =∑3i=1(IMi −mpi◦)2/σ2i , where IMiis the invariant mass of the i-th pair of a combination,and σi the resolution. At most two combinations withthe lowest χ2 are selected for a kinematical fit of the fullevent with 8 constraints: four-momentum conservation,the pi◦ → γγ constraints and the η → 3pi◦ constraint.A cut on the χ2 of the most probable combination isapplied to further suppress background and to increasethe combinatorial purity. Three different data sets wereindividually analyzed, the combined result is based on75000 events in the Dalitz plot after all cuts.III. DALITZ PLOT AND SLOPE αThe reconstructed experimental z distribution is shownin Fig. 1(right) together with MC simulation includingpp → ppη and pp → pppi◦pi◦pi◦ reactions. The detectorresponse function for the reconstructed z was determinedfrom MC: it has a gaussian distribution with a standarddeviation (RMS) 0.067. The resolution in the pi◦pi◦ in-variant mass (Mpipi) is approximately constant and equalto 6 MeV/c2 (RMS).The acceptance corrected |A|2 dependence on the zvariable is obtained by dividing the measured distribu-tion by the MC prediction with α set to 0. A fit ofthe function (4) is performed to extract the parameterFIG. 3: Extracted experimental |A|2/c0 dependence on the zvariable for a subset of the T = 1.36 GeV (left) and for all 1.45GeV (right) data together with a fit of the slope parameterα. Only statistical errors are shown.TABLE II: Statistical errors of α fitted for data subsets ob-tained by parameter variation for selection criteria and recon-struction procedure.Condition α± σstat eventsAll data, 0.1≤ z ≤ 0.9 -0.026 ± 0.010 74700All data, 0.0≤ z ≤ 0.9 -0.014 ± 0.009 74700Analysis of subsets:Subset I T = 1.36 GeV -0.023 ± 0.018 20700Subset II T = 1.36 GeV -0.041 ± 0.018 18000Subset T = 1.45 GeV -0.019 ± 0.015 36000Subset I, variation of MMpp cut:0.530 ≤MMpp ≤ 0.575 -0.019 ± 0.018 213000.535 ≤MMpp ≤ 0.560 -0.023 ± 0.018 207000.540 ≤MMpp ≤ 0.555 -0.025 ± 0.018 18800Subset I, variation of χ2kinfit cut:χ2kinfit ≤ 999 -0.023 ± 0.015 27900χ2kinfit ≤ 50 -0.021 ± 0.017 23600χ2kinfit ≤ 30 -0.023 ± 0.018 20700χ2kinfit ≤ 15 -0.021 ± 0.020 15200χ2kinfit ≤ 15, χ2second/χ2first ≥ 1.2 -0.038 ± 0.024 10800Subset I, alternative parameterizationof kin. fit -0.023 ± 0.019 17000FIG. 4: Extracted experimental |A|2/c0 dependence on the zvariable for all data together with a linear fit to of the slopeparameter α. Only statistical errors are shown.4]2 [GeV/cpipiM0.28 0.30 0.32 0.34 0.36 0.38 0.40ratio0.900.951.001.051.10FIG. 5: Ratio of the Mpipi distribution to the MC predictionswith α = 0: points – data; line – CHPT calculations fromreference [16].α. The MC data are normalized to obtain c0 = 1. Forthe final result α = −0.026± 0.01(stat)± 0.01(syst) thefirst bin was excluded due to large systematic uncertaintyand the last bin due to low statistics. The estimate of thesystematic errors is obtained by variation of all essentialcuts applied in the reconstruction: χ2 for the kinematicfit, the combinatorial purity of the sample, the missingmass and the z range. For each subsample a fit to α wasperformed: an example is shown in Fig. 3 and the sum-mary is given in Table II. The overall systematical errorwas obtained by comparing central values of the fits forthe subsamples and it takes into account the influence ofthe first bin for the α value [24].We have also performed a search for a cusp structurein the invariant mass distribution of the two pi◦ (Fig. 5).An eventual observation would require at least two ordersof magnitude larger data sample.The presented result for α is limited by the availablestatistics which determines also attainable systematicalaccuracy (due to the size of the subsamples used for thetests). Within the errors it is compatible both with theresult from Crystal Ball [19], based on 106 events, andwith the preliminary KLOE result [10] listed in Table I.The reconstruction methods developed for the purpose ofthis experiment are now being used in analysis of recentlycollected data from the followup experiment with WASAdetector located at COSY ring (FZ Juelich) [25] withmuch larger statistics.AcknowledgmentsWe wish to acknowledge the support of the personnelat The Svedberg Laboratory throughout this experiment.This work has been supported by BMBF (06HH152,06TU261), by Russian Foundation for Basic Research(Grant RFBR 02-02-16957), and the European Com-munity Research Infrastructure Activity (FP6, HadronPhysics, RII-CT-2004-506078).[1] W. M. Yao et al. (Particle Data Group), J. Phys. G33,1 (2006).[2] D. G. Sutherland, Nucl. Phys. B2, 433 (1967).[3] R. Baur, J. Kambor, and D. Wyler, Nucl. Phys. B460,127 (1996), hep-ph/9510396.[4] W. A. Bardeen, L. S. Brown, B. W. Lee, and H. T. Nieh,Phys. Rev. Lett. 18, 1170 (1967).[5] J. Gasser and H. Leutwyler, Nucl. Phys. B250, 539(1985).[6] A. V. Anisovich and H. Leutwyler, Phys. Lett. B375,335 (1996), hep-ph/9601237.[7] J. Kambor, C. Wiesendanger, and D. Wyler, Nucl. Phys.B465, 215 (1996), hep-ph/9509374.[8] R. F. Dashen, Phys. Rev. 183, 1245 (1969).[9] H. Leutwyler, Phys. Lett. B378, 313 (1996), hep-ph/9602366.[10] S. Giovannella et al. (KLOE), KLOE results on f0(980),a0(980) scalars and eta decays (2005), hep-ex/0505074.[11] F. Ambrosino et al. (KLOE) (2007), arXiv:0707.2355[hep-ex].[12] B. V. Martemyanov and V. S. Sopov, Phys. Rev. D71,017501 (2005), hep-ph/0502023.[13] N. Beisert and B. Borasoy, Nucl. Phys.A716, 186 (2003),hep-ph/0301058.[14] B. Borasoy and R. Nissler, Eur. Phys. J. A26, 383 (2005),hep-ph/0510384.[15] N. Cabibbo, Phys. Rev. Lett. 93, 121801 (2004), hep-ph/0405001.[16] J. Belina, Master’s thesis, Universita¨t Bern (2006), URLhttp://www.itp.unibe.ch/diploma_thesis/belina/totalcor.pdf .[17] J. R. Batley et al. (NA48/2), Phys. Lett. B633, 173(2006), hep-ex/0511056.[18] A. Abele et al. (Crystal Barrel), Phys. Lett. B417, 193(1998).[19] W. B. Tippens et al. (Crystal Ball), Phys. Rev. Lett. 87,192001 (2001).[20] J. Bijnens and J. Gasser, Phys. Scripta T99, 34 (2002),hep-ph/0202242.[21] B. Borasoy and R. Nissler, Acta Phys. Slov. 56, 319(2006), hep-ph/0511290.[22] C. Pauly et al. (CELSIUS-WASA), Phys. Lett. B649,122 (2007), nucl-ex/0602006.[23] J. Zabierowski et al. (CELSIUS/WASA), Phys. ScriptaT99, 159 (2002).[24] C. Pauly, Ph.D. thesis, Hamburg University (2006).[25] H. H. Adam et al. (WASA-at-COSY) (2004), nucl-ex/0411038.

Measurement of the slope parameter for the n->3pi0 decay in the pp ->ppn reaction

Measurement of the slope parameter for the
                    
                      
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