b

Physics Letters B 623 (2005) 192–199

www.elsevier.com/locate/physlet

Search for the decayK+ → π+γ γ in theπ+ momentum regionP > 213 MeV/c

E949 Collaboration

A.V. Artamonova, B. Bassalleckb, B. Bhuyanc,1, E.W. Blackmored, D.A. Brymane,S. Chend,2, I.-H. Chiangc, I.-A. Christidi f, P.S. Cooperg, M.V. Diwanc, J.S. Frankc,

T. Fujiwarah, J. Hud, D.E. Jaffec, S. Kabei, S.H. Kettellc, M.M. Khabibullinj,A.N. Khotjantsevj, P. Kitchingk,3, M. Kobayashii, T.K. Komatsubarai,∗, A. Konakad,

A.P. Kozhevnikova, Yu.G. Kudenkoj, A. Kushnirenkog,4, L.G. Landsberga, B. Lewisb,K.K. Li c, L.S. Littenbergc, J.A. Macdonaldd,�, J. Mildenbergerd, O.V. Mineevj,

M. Miyajima l, K. Mizouchih, V.A. Mukhin a, N. Muramatsum, T. Nakanom,M. Nomachin, T. Nomurah, T. Numaod, V.F. Obraztsova, K. Omatai, D.I. Patalakhaa,

S.V. Petrenkoa, R. Poutissoud, E.J. Rambergg, G. Redlingerc, T. Satoi,T. Sekiguchii, T. Shinkawao, R.C. Strandc, S. Sugimotoi, Y. Tamagawal,R. Tschirhartg, T. Tsunemii,5, D.V. Vavilov a, B. Virenc, N.V. Yershovj,

Y. Yoshimurai, T. Yoshiokai,6

a Institute for High Energy Physics, Protvino 142 280, Moscow Region, Russiab Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA

c Brookhaven National Laboratory, Upton, NY 11973, USAd TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2A3

e Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1f Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA

g Fermi National Accelerator Laboratory, Batavia, IL 60510, USAh Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

i High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801, Japanj Institute for Nuclear Research RAS, 60 October Revolution Pr. 7a, 117312 Moscow, Russia

k Centre for Subatomic Research, University of Alberta, Edmonton, Canada T6G 2N5l Department of Applied Physics, Fukui University, 3-9-1 Bunkyo, Fukui 910-8507, Japan

m Research Center for Nuclear Physics, Osaka University, 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japann Laboratory of Nuclear Studies, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan

o Department of Applied Physics, National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan

Received 29 May 2005; accepted 22 July 2005

Available online 8 August 2005

Editor: W.-D. Schlatter

0370-2693/$ – see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2005.07.057

E949 Collaboration / Physics Letters B 623 (2005) 192–199 193

nts

” cor-

Abstract

We have searched for theK+ → π+γ γ decay in the kinematic region withπ+ momentum close to the end point. No evewere observed, and the 90% confidence-level upper limit on the partial branching ratio was obtained,B(K+ → π+γ γ, P >

213 MeV/c) < 8.3× 10−9 under the assumption of chiral perturbation theory including next-to-leading order “unitarityrections. The same data were used to determine an upper limit on theK+ → π+γ branching ratio of 2.3 × 10−9 at the 90%confidence level. 2005 Elsevier B.V. All rights reserved.

PACS: 13.20.Eb; 12.39.Fe; 11.10.Nx

Keywords: Kaon rare decay; Chiral perturbation theory; Unitarity corrections; Non-commutative theories

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We report the results of a search for the rdecayK+ → π+γ γ in the π+ momentum regionP > 213 MeV/c from the E949 experiment[1]at the Alternating Gradient Synchrotron (AGS)Brookhaven National Laboratory. The first obsvation of the decay in theπ+ momentum region100–180 MeV/c was reported[2] by the E787 ex-periment at the AGS with a partial branching ratioB(K+ → π+γ γ, 100 MeV/c < P < 180 MeV/c) =(6.0 ± 1.5(stat) ± 0.7(syst)) × 10−7. In the regionP > 215 MeV/c no K+ → π+γ γ decays were observed and, assuming a pure phase-space kinemdistribution, a 90% confidence-level (C.L.) upper limof 5.0× 10−7 was set on the total branching ratio[2].This established that theK+ → π+γ γ background tothe rare decayK+ → π+νν [3] was negligible.

In an effective-field approach to low-energy hdronic interactions called chiral perturbation theo(ChPT)[4], there is noO(p2) (“tree-level”) contribu-

* Corresponding author.E-mail address: takeshi.komatsubara@kek.jp

(T.K. Komatsubara).1 Also at the Department of Physics and Astrophysics, Univer

of Delhi, Delhi 110007, India.Present address: Department of Physics and Astronomy, Univeof Victoria, Victoria, British Columbia, Canada V8W 3P6.

2 Present address: Department of Engineering Physics, TsinUniversity, Beijing 100084, PR China.

3 Present address: TRIUMF, Canada.4 Present address: Institute for High Energy Physics, Protv

Russia.5 Present address: Research Center for Nuclear Physics, O

University, Japan.6 Present address: International Center for Elementary Par

Physics, University of Tokyo, Tokyo 113-0033, Japan.� Deceased.

c

tion toK+ → π+γ γ or its neutral counterpartK0L →

π0γ γ ; the leading contributions start atO(p4) [5].For K+ → π+γ γ , both the branching ratio and thπ+ spectrum shape atO(p4) are sensitive to the undetermined coupling-constantc. There is no completecalculation at the next-to-leading order,O(p6). Thedominant effects[6] are one-loop “unitarity” corrections, deduced from an empirical fit to the decay aplitude of K+ → π+π+π− and containing the samconstantc, and vector-meson exchange. InK+ →π+γ γ vector-meson exchange is expected to be nligible compared to unitarity corrections. The corretions result in a slightly different prediction for thπ+ spectrum (Fig. 1). Separate fits to the measurπ+ spectrum from[2] with and without the unitaritycorrections yieldedc = 1.8 ± 0.6 andc = 1.6 ± 0.6,respectively, but slightly preferred their inclusion. FK0

L → π0γ γ , the amplitude atO(p4) is determinedwithout any undetermined coupling-constant, butmeasured branching ratio,(1.41± 0.12) × 10−6 [7],is twice as large as predicted atO(p4); the vector-meson contribution in the next-to-leading order callation (sometimes parametrized by an effective cpling constantav) is considered to be important to thdecay[8].

One of the consequences of the unitarity corrtions to K+ → π+γ γ is a non-zero amplitude ithe kinematic region close to the end point ofP =227 MeV/c, where the two-photon invariant mamγγ = 0 MeV/c2, as shown inFig. 1. The partialbranching ratioB(K+ → π+γ γ, P > 213 MeV/c),corresponding tomγγ < 108 MeV/c2, is predicted tobe 6.10+0.16

−0.12×10−9 for c = 1.8±0.6 including unitar-

ity corrections and 0.49+0.23−0.18 × 10−9 for c = 1.6± 0.6

without the corrections. Observation of the decay

194 E949 Collaboration / Physics Letters B 623 (2005) 192–199

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a partial branching ratio larger than predicted woindicate the contribution of vector-meson exchanor other new dynamics toK+ → π+γ γ . The kine-matic region close to the end point inK0

L → π0γ γ isknown to be crucial to understand the CP-conservcomponent to theK0

L → π0e+e− decay through theK0

L → π0γ γ → π0e+e− amplitude, but experimentaresults onav in K0

L → π0γ γ [9,10] are inconsisten(see Refs.[11,12] for theoretical discussions).

E949 was designed primarily to measure thecay K+ → π+νν [13]. The AGS delivered kaons o710 MeV/c to the experiment at a rate of 12.8 ×106 per 2.2-s spill. Kaons, detected and identifiedCerenkov, tracking, and energy-loss counters, w

Fig. 1. Predictions for theπ+ momentum for the ChPT parameter c = 1.8 including unitarity corrections (solid line) and foc = 1.6 without the corrections (dashed line) as described intext. The ratios of the partial branching ratio in the kinematicgionP > 213 MeV/c, indicated by the arrow, to the total branchinratio are 5.77× 10−3 and 0.515× 10−3, for c = 1.8 andc = 1.6respectively.

slowed by BeO and active degraders, and came toand decayed in a scintillating-fiber target. The exsure of kaons in each spill was recorded by a scwhich counted the number of kaons entering theget during the time the data acquisition system wready to accept data.Fig. 2 shows a diagram of thapparatus. Measurements of charged decay prodwere made using the target, a central drift chamand a cylindrical range stack (RS) composed of 18ers of plastic scintillator with two embedded layerstracking chambers. The RS counters in the first la(T -counters inFig. 2) were 0.635-cm thick and 52-cmlong; the subsequent RS counters were 1.905-cm tand 182-cm long. The pion from theK+ → π+γ γ

decay was identified by observation of theπ+ →µ+ → e+ decay sequence in the RS using 500-Mwaveform digitizers based on flash analogue-to-digconverters[14]. Trigger counters surrounding the taget (I-counters inFig. 2 which were 0.64-cm thickand the T-counters surrounding the drift chamberfined the fiducial region. Counters (0.95-cm thick) srounding the RS helped to suppressed the muonsK+ → µ+ν and K+ → µ+νγ decays by identify-ing long-range muons that had completely traverthe RS. A hermetic calorimeter system surroundedcentral region. The photons fromK+ → π+γ γ weredetected in a lead/scintillator sandwich barrel dete(BV) surrounding the RS, while two endcap calorimters and other subsystems (collar, “UPV”, “AD”, an“DPV” in Fig. 2) were used for detecting extra parcles. A solenoid surrounding the BV provided a 1magnetic field along the beam line.

nerncluded the

(a) (b)

Fig. 2. Schematic side (a) and end (b) views of the upper half of the E949 detector.C: Cerenkov counter; B4: energy-loss counters; I and T: inand outer trigger scintillation counters; RSSC: RS straw-tube tracking chambers. New or upgraded subsystems for E949 (shaded) ibarrel veto liner (BVL), collar, upstream photon-veto (UPV), active degrader (AD), and downstream photon-veto (DPV).

E949 Collaboration / Physics Letters B 623 (2005) 192–199 195

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The AGS proton-beam intensity, and the E9beam line and apparatus were improved over thused in E787[15] for theK+ → π+γ γ study, whichwas performed in 1991.7 The new beam line[16] in-corporated two stages of electrostatic particle seption which improved the acceptance for kaons as was theK+ to π+ ratio. The target, central drift chamber, and RS tracking chambers were replaced by atarget consisting of 0.5-cm square fibers, a new lomass drift chamber[17], and straw-tube chamberrespectively. One third of the RS scintillation couters were replaced to increase the light output. A nphoton detector, the barrel veto liner (BVL), wasstalled to add 2.3 radiation lengths of lead/scintillasandwich material to the BV. The endcaps wereplaced by new fully active detectors consistingundoped-CsI crystals[18] with significantly increasedlight output, and both the target and endcaps wread out using 500-MHz waveform digitizers basedcharged coupled devices[19] to improve timing anddouble-pulse resolution. Additional ancillary photoveto systems[20] and a flasher system of light emittindiode to aid in the RS energy calibration were alsotroduced.

The 2002 data set used for this analysis derifrom a total exposure of kaons entering the tarNK = 1.19 × 1012. The trigger required a kaon arest in the target to decay at least 1.5 ns later inpositively charged particle which subsequently cato rest in the RS, accompanied by coincident eltromagnetic showers in both the BVL and BV, ano extra energy in the endcap or RS counters.decay particle was required to penetrate the RSat least the 16th layer to suppress backgrounds fthe monochromaticK+ → π+π0 decay(Kπ2) withP = 205 MeV/c, and no further than the 17th layersuppress decays into muons. In the RS counter wthe particle came to rest, called the “stopping counta π+ → µ+ decay was identified online based on tpulse shape information from the waveform digitizeon the RS. An improved trigger system[21] includ-ing a programmable trigger board reduced the ondead time. A total of 1.1 × 107 events met the triggerequirements.

7 Many of the improvements were made in the E787 apparafter 1991.

The momentum, equivalent range in plastic scinlator (R), and kinetic energy (E) of the charged trackwere reconstructed with information from the targdrift chamber and RS. Tracks were accepted forregion defined by 213 MeV/c < P < 234 MeV/c,33.5 cm < R < 41.3 cm, and 116 MeV< E <

135 MeV, where the lower limits corresponded3.3, 2.3, and 2.6 standard deviations, respectivabove theKπ2 peak (P = 205 MeV/c, R = 30.4 cm,and E = 108 MeV). The larger search region (P >

213 MeV/c) compared with E787 (P > 215 MeV/c)resulted from improved kinematic reconstructiowhich also removed the requirement of a constraifit for consistency withK+ → π+γ γ kinematics thatwas used in E787[2].

The timing and energy (Eγ ) of the photons weredetermined by grouping adjacent hit modules inBVL and BV to classify isolated photon showe(“clusters”). The hit position in each module alonthe beam axis (z) was calculated from the end-to-entime and energy differences; the azimuthal angleφ)of the hit position in the end view of the detectwas determined by the segmentation of the moduThe location of the photon shower inz and φ wasobtained by an energy-weighted average of the hitsitions and was used, in conjunction with the kadecay vertex position in the target, to determinepolar and azimuthal angles of the photon as well asopening angles between the photon and the chatrack in the side view (θπ+γ ) and in the end view(φπ+γ ). In approximately half of theK+ → π+γ γ

decays the two photons were unresolved and apas a single cluster in the BVL and BV, since the oping angle between two photons fromK+ → π+γ γ

gets smaller for the events withπ+ momentum closeto the kinematic end point. The events with eithone or two clusters were accepted; at least one cter with 50 MeV< Eγ < 320 MeV, θπ+γ > 155◦,andφπ+γ > 155◦ was required. For events with twclusters, the lower-energy cluster had to haveEγ >

10 MeV.Background sources from kaon decays at rest w

classified into three types:

“mismeasured”: Kπ2 decays with mismeasuremenof theπ+ and the two photons,

“overlap”: Kπ2 decays with the lower-energy photooverlapping theπ+ track in the RS, causin

196 E949 Collaboration / Physics Letters B 623 (2005) 192–199

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“muon”: K+ decays with aµ+ misidentified as aπ+ and with photons in the final state (e.gK+ → µ+νγ , K+ → π0µ+ν andKπ2 withπ+ decay in flight).

Another background source was due to kaon decaflight:

“DIF”: Kπ2 decay-in-flight before the kaon camerest in the target.

Beam-related backgrounds (e.g., multiple beam pacles scattering into the detector) were found to negible.

These backgrounds were studied from the dataimposing offline selection criteria (“cuts”). The requirements on theπ+ momentum, range and kinetenergy provided large suppression of all of the bagrounds from kaon decays at rest. Several cuts,ferred to as “γ selection cuts”, were imposed to supress themismeasured background. These includecuts on the following quantities:

• the cut on the invariant mass of two phototo reject events with two clusters andmγγ >

100 MeV/c2,• the cut on additional coincident energy to reje

events with activity not associated with theπ+and the candidate signal photons,8 and

• the cut on the photon clusters to reject events wtwo photons from aπ0 which hit the same or adjacent modules in BVL and BV and form a singcluster9 [22].

In addition, only those events whose total photoshower energy was deposited in the BVL and B

8 The extra activity was identified in the various subsystems,cluding the RS, as hits in the counters in coincidence with theπ+track within a few ns and with energy above a threshold of typic1 MeV.

9 Due to the kinematics ofKπ2 and subsequentπ0 → γ γ decays,the two photons must hit the modules at differentz positions alongthe beam axis. An event was rejected if the maximum discrepaamong thez-position measurements in the modules of the cluwas larger than 113 cm.

calorimeters were accepted. Cuts ondE/dx in theRS to reject events with a RS counter in whichmeasured energy was larger than expected fromreconstructed range in that counter were imposesuppress theoverlap background[22]. The cuts onthe relation between the range measured in theand the momentum measured in the drift chambewell as the cuts on theπ+ → µ+ → e+ decay se-quence, recorded in the RS stopping counter, wereimposed to suppress themuon background. TheDIFbackground was suppressed by requiring a delay oleast 2 ns between the time of the kaon coming toin the target and its subsequent decay, and by iming the cuts on the timing between theπ+ in the RSand theK+ in theCerenkov counter.

To study and measure these backgrounds, twodependent sets of cuts were established for each bground source. At least one of these cuts was inveto enhance each background collected by theK+ →π+γ γ trigger as well as to prevent candidate evefrom being examined before the background studwere completed. To avoid contamination from othbackground sources, all the cuts except for thoseing studied were imposed on the data. Possibilitiea correlation between the two sets of cuts or of a biaestimate of the effectiveness of the cuts were studand were found to be negligible. The signal acctance and background levels were studied as a funcof cut severity. A comparison of the observed baground levels near but outside the signal region wmade to the predicted background in these regionsof these studies[23] were performed in the same maner as theK+ → π+νν analyses of E787[24] andE949 [13]. Table 1summarizes the background leels measured with the final analysis cuts and thesets of cuts for studying each background sourcetotal, 0.197± 0.070 background events were expecin the signal region.

The acceptance (A) and the single event senstivity (SES) for K+ → π+γ γ in the kinematic re-gion P > 213 MeV/c were derived from the acceptance factors inTable 2and the total kaon exposuNK = 1.19× 1012 times theK+-stopping efficiency,which is the fraction of kaons entering the target tcame to rest before decaying. The efficiency was msured to be 0.754± 0.024 with theKπ2 events col-lected with theK+ → π+γ γ trigger and selecteusing all the analysis cuts except those designe

E949 Collaboration / Physics Letters B 623 (2005) 192–199 197

round was

ample

ous to the

Table 1Expected background levels in the signal region and the two sets of cuts for studying each background source. The total backg0.197± 0.070 events

Source Background level Two sets of cuts

Mismeasured 0.017± 0.006 π+ accepted region (P , R, E) γ selectionOverlap 0.065± 0.065 π+ accepted region (P , R) π+ dE/dx

Muon 0.090± 0.020 π+ accepted region (P , R, E) π+ → µ+ → e+π+ range-momentum relation

DIF 0.025± 0.014 Delay in the target RS–C timing

Table 2Acceptance factors for theK+ → π+γ γ decay in the kinematic regionP > 213 MeV/c, for c = 1.8 including unitarity corrections (“UC”)and forc = 1.6 without the corrections (“w/o UC”), and the samples used to determine them. “MC” in the rightmost column means the sgenerated by Monte Carlo simulation. “KB ”, “ Kµ2”, “ Kπ2”, and “πscat” mean the data samples of kaons entering the target,K+ → µ+ν

decays,Kπ2 decays, and scattered beam pions, respectively; these samples were accumulated by calibration triggers simultanecollection of signal candidates

Acceptance factors UC w/o UC Samples

Trigger 0.0623 0.0407 MC,KB

π+ reconstruction and fiducial cuts 0.980 0.935 MC,Kµ2π+ accepted region (P , R, E) 0.912 0.667 MCπ+ stop without nuclear interaction 0.492 0.524 MC

or decay-in-flightdE/dx and kinematic cuts 0.537 0.537 Kπ2, πscatπ+ → µ+ → e+ cuts 0.349 0.349 πscatγ reconstruction and fiducial cuts 0.530 0.492 MC,Kπ2γ selection cuts 0.216 0.177 MC,Kπ2Other cuts on beam and target 0.507 0.507 Kµ2

Total acceptance 2.99× 10−4 1.10× 10−4

cnce

an-

re-

iv-

na-

nt

ess

b-

ad

settio

ticde-ithforesentit

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removeKπ2 events. Thus the sensitivity forK+ →π+γ γ was normalized toKπ2 and many systematiuncertainties in the measurement of the acceptafactors, in particular in the trigger acceptance, cceled. We obtainedA = (2.99 ± 0.07) × 10−4 andSES = (3.72±0.14)×10−9 for c = 1.8 including uni-tarity corrections andA = (1.10± 0.04) × 10−4 andSES = (1.01± 0.05) × 10−8 for c = 1.6 without thecorrections. The former sensitivity was below the pdicted branching ratio of 6.10×10−9, giving an expec-tation of 1.6 events. In order to verify that the sensitity estimations were correct, a sample ofK+ → µ+ν

decays accumulated with a calibration trigger was alyzed. The branching ratio of 0.628± 0.020 measuredwith the sameK+-stopping efficiency was consistewith the Particle Data Group value[7]. The systematicuncertainty in the sensitivity was estimated to be lthan 10%.

After imposing all analysis cuts, no events were oserved in the signal region (Fig. 3). The group of 74

events aroundR = 32 cm andE = 110 MeV are dueto the Kπ2 background. Taking 2.24 events insteof zero according to the unified approach[25] withthe background contribution of 0.197 events, wea 90% C.L. upper limit on the partial branching raB(K+ → π+γ γ, P > 213 MeV/c) as 8.3× 10−9 forc = 1.8 including unitarity corrections and 2.3× 10−8

for c = 1.6 without the corrections. The systemauncertainty was not taken into consideration inriving the limits. For the purpose of comparison wthe previous E787 results, a 90% C.L. upper limitthe totalK+ → π+γ γ branching ratio assuming thphase-space distribution was calculated; the prelimit 6.0×10−8 is 8.3 times lower than the same limin E787(5.0× 10−7).

The data described above were also used to seupper limit on the branching ratio forK+ → π+γ

decay, which is forbidden by angular-momentum cservation and gauge invariance, but is allowed in ncommutative theories[26]. The signature ofK+ →

198 E949 Collaboration / Physics Letters B 623 (2005) 192–199

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Fig. 3. Range (equivalent cm of plastic scintillator) vs. kineticergy (MeV) plot of the events with all analysis cuts imposed. Tbox indicates the signal region for theK+ → π+γ γ decay. Thedark points represent the data. The simulated distribution ofpected events fromK+ → π+γ γ for c = 1.8 including unitaritycorrections is indicated by the light dots.

π+γ was a two-body decay of a kaon at rest with227-MeV/c π+ track in the RS and a 227-MeV photon emitted directly opposite to it and observed inBVL and BV calorimeters. The trigger, event recostruction, and offline selection criteria in the studyK+ → π+γ γ had been designed so that the same dwere available to the search forK+ → π+γ . Sincethe background levels were already small, theπ+ ac-cepted region was not reduced for theK+ → π+γ

analysis. The previous limit from the E787 study w3.6 × 10−7 [22] (90% C.L.) from data collected i1996–1997 with a highly prescaled trigger with rlaxed trigger-conditions resulting in the total kaon eposure of 6.7 × 108. The new 90% C.L. upper limifrom E949, using the acceptance forK+ → π+γ of(1.08± 0.02) × 10−3, is 2.3× 10−9.

The results from this study cannot confirm nor ruout the unitarity corrections of ChPT, but the upplimits obtained are the most restrictive yet achievon K+ → π+γ γ and as well as onK+ → π+γ . TheE949 experiment has been shown to be suitable fostudy ofK+ → π+γ γ in the π+ momentum regionclose to the end point. The experimental uncerta

is limited by statistics; additional data is requiredmore stringently test the predictions of ChPT for tdecay. The possibility to observe theK+ → π+γ γ

decay in the kinematic region, if the ChPT includiunitarity corrections is correct, gives further impetfor additional data collection.

Acknowledgements

We gratefully acknowledge the dedicated effof the technical staff supporting E949 and of tBrookhaven CA Department. We are also gratefuG. D’Ambrosio, F. Gabbiani, G. Isidori, and G. Valencia for useful discussions. This research was sported in part by the US Department of Energy,Ministry of Education, Culture, Sports, Science aTechnology of Japan through the Japan–US Cooative Research Program in High Energy Physicsunder Grant-in-Aids for Scientific Research, the Nural Sciences and Engineering Research Councilthe National Research Council of Canada, the RusFederation State Scientific Center Institute for HEnergy Physics, and the Ministry of Science and Ecation of the Russian Federation.

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