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PHYSICS LETTERS B
ELSEVIER
Physics Letters B 352 (1995) 487-497
One-prong r decays with neutral kaons
L3 Collaboration
M. Acciarri2, A. Adamaq, O. Adriani13, M. Aguilar-Benitezy, S. Ahlen j, B. Alpatag,
J. Alcarazy, J. Allabyq, A. Aloisioab, G. Alversonk, M.G. Alviggiab, G. Ambrosiag, Q. Anr,
H, Anderhubat, V.P. Andreevak, T. Angelescu^, D. Antreasyanh, A. Arefievaa, T. Azemoon0,
T. Aziz1, P.V.K.S. Babar, P. Bagnaiaaj,q, L. Baksayap, R.C. Ballc, S. Banerjee1, K. Baniczaq,
R. Baiillèreq, L. Baroneaj, P. Bartaliniag, A. Baschirottoz, M. Basileh, R. Battistonag, A. Bayv,
F. Becattinip, U. Becker0, F. Behnerat, Gy.L. Benczem, J. Berdugoy, P. Berges0, B. Bertucciq,
B.L. Betevat, M. Biasiniag, A. Bilandat, G.M. Bileiag, R. Bizzarri^, J.J. Blaisingq,
G.J. Bobbinkb, R. Bocka, A. Böhma, B. Borgiaaj, A. Bouchamd, D. Bourilkovat,
at
M. Bourquins, D. Boutignyd, B. Bouwensb, E. Brambilla0, J.G. Bransona£, V. Brigljevic
I.C. Brockah, A. Bujakaq, J.D. Burger0, WJ. Burgers, C. Burgosy, J. Busenitzap,
A. Buytenhuijsad, X.D. Cair, M. Capell0, G. Cara Romeoh, M. Cariaag, G. Carlinoab,
A.M. Cartaceip, J. Casausy, G. Castellinip, R. Castello2, N. Cavalloab, C. Cecchis,
M. Cerraday, F. Cesaroni^, M. Chamizoy, A. Chanav, Y.H. Changav, U.K. Chaturvedir,
M. Chemarinx, A. Chenav, C. Chenf, G. Chenf, G.M. Chenf, H.F. Chen H.S. Chenf,
M. Chen0, G. Chiefariab, C.Y. Chiene, M.T. Choia0, L. Cifarellih, F. Cindolo'1, C. Civininip,
I. Clare0, R. Clare0, T.E. Coanw, H.O. Cohnae, G. Coignetd, N. Colinoq, V. Commichaua,
S. Costantiniaj, F. C otorobaiB . de la Cruzy, X.T. Cuir, X.Y. Cuir, T.S. Dai0,
R. D’Alessandrop, R. de Asmundisab, H. De Boeckad, A. Degréd, K. Deiters“ , E. Dénesm,
P. Denesai, F. DeNotaristefani^, D. DiBitontoap, M. Diemozaj, C. Dionisia’, M. Dittmarat,
A. Dominguez^, A. Doriaab, I. Dorned, M.T. Dovar’4, E. Dragoab, D. Duchesneauq,
P. Duinkerb, I. Duranara, S. Dutta1, S. Easoag, Yu. Efremenkoae, H. El Mamounix, A. Englerah,
F.J. Eppling0, F.C. Ernéb, J.P. Ernenweinx, P. Extermanns, R. Fabbrettiar, M. Fabrear,
R. Facciniaj, S. Falcianoaj, A. Favarap, J. Fayx, M. Felciniat, T. Fergusonah, D. Fernandezy,
G. Fernandezy, F. Ferronia->, H. Fesefeldta, E. Fiandriniag, J.H. Field8, F. Filthauta\
P.H. Fisher0, G. Forconi0, L. Fredjs, K. Freudenreichat, M. Gailloudv, Yu. Galaktionovaa,°,
S.N. Ganguli‘, P. Garcia-Abiay, S.S. Gauk, S. GentileaJ, J. Gerald6, N. Gheordanescu
S. Giaguaj, S. Goldfarbv, J. Goldstein\ Z.F. Gong1, E. Gonzalezy, A. Gougase, D. Goujon8,
G. Grattaaf, M.W. Gruenewaldg, C. Gur, M. Guanzirolir, Y.K. Guptaai, A. Gurtu1,
H.R. Gustafsonc, L.J. Gutayaq, B. Hartmann3, A. Hasanac, J.T. H ef, T. Hebbekerg, A. Hervéq,
K. Hilgers3, W.C. van Hoekad, H. Hoferat, H. Hoorani5, S.R. Houav, G. Hur, M.M. Ilyasr,
Elsevier Science B.V.
SSDI 0370-2693(95)00509-9
488
13 Collaboration / Physics Leiters B 352(1995) 487-497
V. Innocenteq, H. Janssend, B.N. Jinf, L.W. Jonesc, P. de Jong0,1. Josa-Mutuberriay,
A. Kasserv, R.A. Khanr, Yu. Kamyshkovae, P. Kapinosas, J.S. Kapustinsky w, Y. Karyotakisd,
M. Kaurr, S. Khokharr, M.N. Kienzle-Focacci5, D. Kime, J.K. Kimao, S.C. Kimao,
Y.G. Kimao, W.W. Kinnisonw, A. Kirkbyaf, D. Kirkbyaf, J. Kirkby^, S. Kirschas, W. Kittelad,
A. Klimentov °’aa, A.C. Königad, E. Koffemanb, O. Kornadt3, V. Koutsenko 0,aa,
A. Koulbardisak, R.W. Kraemerah, T. Kramer0, W. Krenza, H. Kuijtenad, A. Kunin°’aa,
P. Ladrón de Guevaray, G. Landip, C. Lapoint0, K. Lassila-Periniat, P. Laurikainen u,
M. Lebeauq, A. Lebedev0, P. Lebrunx, P. Lecomteat, J. Lecoqd, P. Lecoqq, P. Le Coultreat,
J.S. Leeao, K.Y. Leeao, C. Leggettc, J.M. Le Goffq, R. Leiste“ , M. Lentip, E. LeonardiaJ,
P. Levtchenkoak, C. Li '-r, E. Liebas, W.T. Linav, F.L. Lindeb, B. Lindemanna, L. Listaab,
Y. Liur, Z.A. Liuf, W. Lohmannas, E. Longoa-i, W. Luaf, Y.S. Luf, K. Lübelsmeyer a, C. Luci a-i,
D. Luckey0, L. Ludovici aJ, L. LuminariaJ, W. Lustermannar, W.G. Mal, A. Macchiolop,
M. M a i t y L. Malgeri3-*, R. Malikr, A. Malinin 3a, C. Mañay, S. Mangla1, M. Maolinbayat,
P. Marchesiniat, A. Marinj, J.P. Martin x, F. Marzanoaj, G.G.G. Massarob, K. Mazumdar1,
D. McNallyq, S. M eleab, M. Merkah, L. Merolaab, M. Meschinip, W.J. Metzgerad, Y. M i v,
A. Mihule, A.J.W. van M ilad, Y. Mirr, G. Mirabelli*, J. Mnichq, M. Möller3, V. Monacoaj,
B. Monteleonip, R. Moorec, R. Morandd, S. Morganti3-*, N.E. Moulair, R. Mountaf,
S. Müller3, E. Nagy ra, S. Nahn0, M. Napolitanoab, F. Nessi-Tedaldiat, H. Newmanaf,
M.A. Niaz1, A. Nippe3, H. Nowak35, G. Organtiniaj, R. Ostonen“, D. Pandoulas3,
S. Paolettia>, P. Paolucci3b, G. Pascale^, G. Passalevap, S. Patricelliab, T. Paulag,
M. Pauluzziag, C. Paus3, F. Paussat, YJ. Peia, S. Pensotti2, D. Perret-Gallixd, A. Pevsner®,
D. Piccoloab, M. Pierip, J.C. Pinto3h, P.A. Pirouéai, E. Pistolesip, V. Plyaskin33, M. Pohlat,
V. Pojidaevaa,p, H. Postema0, N. Produits, K.N. Qureshir, R. Raghavan1, G. Rahal-Callotat,
P.G. Rancoitaz, M. Rattaggiz, G. Ravenb, P. Razisac, K. Read3e, M. Redaelliz, D. Ren3t,
Z. Renr, M. Rescignoaj, S. Reucroftk, A. Ricker3, S. Riemannas, B.C. Riemers aq, K. Rilesc,
O. Rindc, H.A. Rizvir, S. Roao, A. Robohm3t, J. Rodin0, F.J. Rodriguezy, B.P. R oec,
M. Röhner3, S. Röhner3, L. Romeroy, S. Rosier-Leesd, Ph. Rosseletv, W. van Rossumb,
S. Roth3, J.A. Rubioq, H. Rykaczewski3t, J. Salicioq, J.M. Salicioy, E. Sanchezy,
A. Santocchia3g, M.E. Sarakinos“, S. Sarkar', G. Sartorellir, M. Sassowsky3, G. Sauvaged,
C. Schäfer3, V. Schegelsky3k, D. Schmitz3, P. Schmitz3, M. Schneegansd, B. Schoeneich33,
N. Scholz31, H. Schopper3“, DJ. Schotanusad, R. Schulte3, K. Schultze3, J. Schwenke3,
G. Schwering3, C. Sciacca3b, R. Sehgalr, P.G. Seilerar, J.C. Sens3v, L. Servoli3g,
S. Shevchenkoaf, N. Shivarov3", V. Shoutko33, J. Shuklaw, E. Shumilov33, D. Son30,
A. Sopczakq, V. Soulimovab, B. Smith0, T. Spickermann3, P. Spillantinip, M. Steuer0,
D.P. Sticklandai, F. Sticozzi0, H. Stoneai, B. Stoyanov 3,1, K. Strauch", K. Sudhakar1,
G. Sultanovr, L.Z. Sunt>r, G.F. Susinnos, H. Suter31, J.D. Swainr, A.A. Syed3d, X.W. Tangf,
L. Taylork, R. Timellinih, Samuel C.C. Ting0, S.M. Ting0, O. Toker3®, M. Tonutti3,
S.C. Tonwar1, J. Tóthm, A. Tsaregorodtsevak, G. Tsipolitisah, C. Tullyai, H. Tuchschererap,
J. Ulbricht31, L. Urbán"1, U. Uwer3, E. Valenteaj, R.T. Van de Wallead, I. Vetlitsky3a,
G. Viertel31, P. Vikasr, U. Vikasr, M. Vivargentd, R. Voelkert38, H. Vogelah, H. Vogt35,
L3 Collaboration / Physics Letters B 352 (1995) 487-497
489
I. Vorobievaa, A.A. Vorobyov**, An.A. Vorobyovak, L. Vuilleumierv, M. Wadhway,
W. Wallraff0, J.C. Wang0, X.L. Wang', Y.F. Wang0, Z.M. Wangr-', A. Webera, R. WeilT,
C. Willmotty, F. Wittgensteinq, S.X. Wur, S. Wynhoff“, J. Xuj, Z.Z. Xu', B.Z. Yang',
C.G. Yangf, G. Yangr, X.Y. Yaof, C.H. Yer, J.B. Ye', Q. Yer, S.C. Yehav, J.M. Youah,
N. Yunusr, M. Yzermanb, C. Zaccardelliaf, An. Zaliteak, P. Zemp8', J.Y. Zengf, M. Zengr,
Y. Zenga, Z. Zhangf, Z.P. Zhang '-r, B. Zhouj, G.J. Zhouf, J.F. Zhoua, Y. Zhouc, G.Y. Zhuf,
R.Y. Zhuaf, A. Zichichih^ r, B.C.C. van derZwaanb
a ƒ. Physikalisches Instituí, RWTH, D-52056 Aachen, FRG 1
III.
Physikalisches Instituí, RWTH, D-52056 Aachen, FRG 1
b National Institute fo r High Energy Physics, NIKHEF, NL-1009 DB Amsterdam, The Netherlands
c University of Michigan, Ann Arbor, MI 48109, USA
ü Laboratoire d ’Annecy-le-Vieux de Physique des Particules, LAPP,IN2P3~CNRS, BP 110, F-74941 Annecy-le-Vieux CEDEX, France
e Johns Hopkins University, Baltimore, MD 21218, USA
f Institute o f High Energy Physics, IHEP, 100039 Beijing, China
s Humboldt University, D~10099 Berlin, FRG 1
h INFN-Sezione di Bologna, 1-40126 Bologna, Italy
1 Tata Institute of Fundamental Research, Bombay 400 005, India
j Boston University, Boston, MA 02215, USA
k Northeastern University, Boston, MA 02115, USA
*
Institute o f Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania
m Central Research Institute fo r Physics o f the Hungarian Academy o f Sciences, H-1525 Budapest 114, Hungary 2
n Harvard University, Cambridge, MA 02139, USA
0 Massachusetts Institute of Technology, Cambridge, MA 02139, USA
P INFN Sezione di Firenze and University o f Florence, 1-50125 Florence, Italy
q European Laboratory fo r Particle Physics, CERN, CH-1211 Geneva 23, Switzerland
r World Laboratory, FBUA Project, CH-1211 Geneva 23, Switzerland
s University of Geneva, CH-1211 Geneva 4, Switzerland
1
Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China
u SEFT, Research Institute fo r High Energy Physics, P.O. Box 9, SF-00014 Helsinki, Finland
v University o f Lausanne, CH-1015 iMiisanne, Switzerland
w Los Alamos National Laboratory, Los Alamos, NM 87544, USA
x Instituí de Physique Nucléaire de Lyon, IN2P3-CNRS,Università Claude Bernard, F-69622 Villeurbanne Cedex, France
y Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040 Madrid, Spain 3
z INFN-Sezione di Milano, 1-20133 Milan, Italy
aa Institute o f Theoretical and Experimental Physics, ITEP, Moscow, Russia
ab INFN-Sezione di Napoli and University o f Naples, 1-80125 Naples, Italy
ac Department of Natural Sciences, University of Cyprus, Nicosia, Cyprus
acl University o f Nymegen and NIKHEF, NL-6525 ED Nymegen, The Netherlands
ae Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
af California Institute of Technology, Pasadena, CA 91125, USA
as INFN-Sezione di Perugia and Università Degli Studi di Perugia, 1-06100 Perugia, Italy
ah Carnegie Mellon University, Pittsburgh, PA 15213, USA
ai Princeton University, Princeton, NJ 08544, USA
aJ INFN-Sezione di Roma and University of Rome, “La Sapienza ”, 1-00185 Rome, Italy
^ Nuclear Physics Institute, St. Petersburg, Russia
ai University of California, San Diego, CA 92093, USA
am Dept, de Fisica de Partículas Elementales, Univ. de Santiago, E-15706 Santiago de Compostela, Spain
an Bulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria
00 Center for High Energy Physics, Korea Advanced Inst of Sciences and Technology, 305-701 Taejon, Soufh Korea
ap University of Alabama, Tuscaloosa, AL 35486, USA
aq Purdue University, West Lafayette, IN 47907, USA
™ Paul Scherrer Instituí, PSI, CH-5232 Villigen, Switzerland
“ DESY-Institut für Hochenergiephysik, D-15738 Zeuthen, FRG
*
490
L3 Collaboration / Physics Letters B 352 (1995) 487-497
at Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerland
au University of Hamburg, D-22761 Hamburg, FRG
av High Energy Physics Group, Taiwan, ROC
Received 4 April 1995
Editor: K. Winter
Abstract
We have analyzed one-prong r decays with neutral kaons using the information from a fine-grained hadron calorimeter.
The data sample consists of 43 500 Z
7-V~(y) events collected by the L3 detector at LEP in 1991, 1992 and 1993.
The following branching fractions are measured: B(t~~ —+ iy 7r“ K°) = 0.0095 ± 0.0015(stat) ± 0.0006(syst); B ( t —>
vri r " 7r°K°) = 0.0041 ± 0.0012(stat) ± 0.0003(syst) and 2?(r' -> pTir~K°K°) = 0.0031 ± 0.0012(stat) ± 0.0004(syst).
1. Introduction
Measurements of the branching fractions of rlepton decays with neutral kaons are important for
understanding t decays [ 1 ], in particular the compat
ibility of inclusive and exclusive branching fractions.
They also provide new information on the dynam
ics of neutral kaon production which is not yet well
understood. Many factors affect the calculation of
the branching fractions for these decays, such as
Cabibbo-suppression for modes with odd numbers
of kaons, very limited phase space for the modes
with two kaons, QCD anomalies and uncertainties in
the resonant structure. Their interplay prevents firm
theoretical predictions from being made [2,3].
In this paper we present an analysis of the following
decay modes: t~ —>
, t ~~ —» vTir"“7T°K°, and
r“
^r 7r “ K°K°s where the charge conjugate decays
are also implied here and throughout this paper. The
fine-grained hadron calorimeter of L3 is used to detect
neutral kaons and to measure their energies and direc
tions. The selection of r decays with neutral kaons is
based on the coincidence of high energy deposition in
the hadron calorimeter and a low momentum charged
track detected in the central tracker. The L3 detector
1 Supported by the German Bundesministerium für Bildung, Wis
senschaft, Forschung und Technologie.
2 Supported by the Hungarian OTKA fund under contract number
2970.
3 Supported also by the Comisión Interministerial de Ciencia y
Technología.
4 Also supported by CONICET and Universidad Nacional de La
Plata, CC 67, 1900 La Plata, Argentina.
is well suited to this measurement as the efficiencies
for detecting the KL and Ks components of K° are
comparable due to the small decay volume.
The data sample used in this analysis corresponds
to an integrated luminosity of 69 pb *” 1 collected at
s/s ft M z during the 1991, 1992 and 1993 LEP run
ning periods.
2. The L3 detector
The L3 detector is described in detail in Ref. [4].
The e+e~ collision point is surrounded by a tracking
chamber, a high resolution electromagnetic calorime
ter, a cylindrical shell of scintillation counters, a
hadron calorimeter, and a muon chamber system. The
detector is installed in a large magnet providing a
uniform 0.5 Tesla field.
The hadron calorimeter (HCAL) is the key sub
detector for this measurement. It covers the polar
angle range 5° < 6 < 175° and consists of depleted
uranium absorber plates interleaved with proportional
wire chambers oriented alternately parallel and per
pendicular to the beam direction. The readout, which
is grouped into cells in both of these projections
as well as in depth, provides a three dimensional
pattern for hadronic showers. The energy resolu
tion of the calorimeter for 7 is determined to be
5 5 %/ y f E( Gt V) + 8 % in the central region. The an
gular resolution is better than 40 mrad in both the
polar and azimuthal projections for hadronic showers
above 6 GeV, which is approximately the minimum
energy of K°’s from r decays at LEP. The detailed
L3 Collaboration / Physics Letters B 352 (1995) 487-497
study of the hadron calorimeter prototype is described
elsewhere [5].
The electromagnetic calorimeter (ECAL) is com
posed of bismuth germanate crystals in the shape
of truncated pyramids pointing to the interaction re
gion. The ECAL barrel has a polar angle coverage of
42° < 6 < 138°, while the end-caps cover the regions
12° < 0 < 38° and 142° < 0 < 168°.
The central tracking detector consists of a time ex
pansion chamber (TEC) with high spatial resolution
in the plane normal to the beam direction. TEC is sur
rounded by a Z-chamber which supplements the r - ^
measurement with a z -coordinate measurement. The
transverse momentum resolution of the tracking cham
ber is c r ( l / P j ) = 0.018 (G eV /c ) ” 1 in the central
region (| c o s # t e c | < 0.7). The position resolution of
a track extrapolated to the calorimeters is 0.2 mm in
the plane transverse to the beam direction and 1.5 mm
along the beam axis.
491
detector response5 . The main source of inefficiency is
the geometric acceptance. The Z —* r +r ~ ( y ) Monte
Carlo sample contains 674000 generated events,
which corresponds to nine times more Z —> r +r ’" (y )
events than in the data sample. The background
contamination from non-r sources includes 1.9 % of
e+e“ (y ), 1.0% of
0.4% of Z —» hadrons
events, 0.4% of two-photon reactions, and 0.2%
of cosmic muon events and beam-gas interactions.
These estimates are derived primarily from the data
using either the side opposite to the selected decay or
global event characteristics. The corresponding Monte
Carlo simulation for the background [7,11] is used
only to verify these estimates. The total number of
Z —» r +r ~ ( y ) events in the sample is estimated to be
43497±60, where the error includes the uncertainty
in the background evaluation.
4. Selection of r decays with neutral kaons
3. Selection of Z —►r +r (y) events
The selection of r decays is done independently in
two hemispheres separated by the plane perpendicular
to the thrust axis of the event. Particle identification in
each hemisphere is based upon the topological prop
erties of the energy deposition in the electromagnetic
and hadron calorimeters with respect to the trajectory
of the charged track.
The selection of r decays proceeds in three steps.
First, a sample of low multiplicity, back-to-back events
is selected, consisting mainly of leptons from Z de
cays. This preselection suppresses such backgrounds
as hadronic Z decays, two-photon interactions, cos
mic muons, and beam-gas interactions. In the second
step, the individual r decays are identified. Finally, re
quirements are placed on the hemisphere opposite to
the identified r decay candidate in order to suppress
the remaining non-r background. The selection pro
cedure is described in detail in Ref. [ 6 ]. A sample
of 45 262 events is selected in the fiducial volume
46 ° < 6 < 134°.
The selection efficiency for Z —►r +r ~ ( y ) events
is calculated to be 57.8% using the KORALZ Monte
Carlo program [7,8] with a full simulation of the L3
To select a r~ —►vTK°X~ candidate6, exactly one
track is required in the hemisphere. This track must be
consistent with originating from the interaction point
in the plane perpendicular to the beam direction. The
expected energy deposition of the track in the HCAL is
estimated from its momentum in the TEC and energy
in the ECAL associated to it using the reconstruction
technique described in Ref. [ 6 ]. Any HCAL energy
deposition exceeding this estimate, A 2 ? h c = ^ h c ~~
^h c ^ 0 * could be due to a fluctuation in the charged
hadron shower, which is approximately proportional
to y/P^j or due to the presence of neutral kaons. In
order to suppress fluctuations, the ratio A ^ h c / v ^ t
must be greater than 5 (GeV ) 1/ 2 (Fig. la ). This cut
rejects a large fraction of r decays with no K° and
almost all residual background from non-r sources. No
r decays with the charged particle momentum greater
than 15 GeV / c survive this cut.
The dominant backgrounds after the previous cut
are r~ —►p ~ v r and r “ —>a^ vT decays with rr° leak
age from the ECAL to the HCAL. This background
is suppressed by requiring the energy in the first three
5 The L3 detector simulation is based on GEANT Version 3,14;
see Ref. [9]. The GHEISHA program [10] is used to simulate
hadronic interactions.
6 The hadronic system X*“ contains a single charged hadron and
any number of neutral hadrons.
L3 Colîoboration / Physics Letters B 352 (1995) 487-497
492
ing r decays contribute to the signal: r~ —►
r “ -+ ^rK "K 0, r~ -> j'7.77’~7r°K0, r~
^r K _ 7r°K0,
and r~ -> pt 7t~ K °K 0. The efficiencies are esti
mated to be 13.0%, 5.3%, 8 .8 %, 3.7% and 19.8%
in the fiducial volume respectively. The composition
of the selected sample of K0,s corresponds to 68 %
p t K ~ K° and
K£ and 32% Kg. The modes r~
z'rK ~ 7r°K0 have significantly lower efficiency
than the corresponding modes with charged pions due
to less advantageous energy sharing between K“ K°
in the laboratorv frame compared to t t ” K° 7 .
10
1
50
cn
5. Determination of the branching fractions
O 25
<L>
Q
0
40
20
0
cl
*
(rad)
*jiK
Fig. 1. (a) The spectrum of the ratio A £hc/\/^V f°r the pre
selected decays. The hatched area corresponds to the contribu
tion of the r~ —►vTir ~K°,
ivK K°, r —v Pj'fr 7T°K0
tqK°
t
—> Vr'ir ~ t
7rw
is.“, r —> i^r K“ 7t0K° decay modes, (b) The
spectrum of the fraction of the HCAL energy deposited in the first
three layers. The cut on the ratio AEhc / y/Pw is already applied,
(c) The separation angle between the charged hadron and cluster
in the HCAL. All other cuts are already applied. The arrows in
(a)-(c) indicate the corresponding values of the applied cuts.
HCAL layers ( 18Xo) to be less than 80% of the total
energy deposition in the HCAL (Fig. lb). The angu
lar separation between the ir~ and K°, ov-k°> is esti
mated as the difference between the center of gravity
of the HCAL cluster and impact position of the track
in the HCAL. It is required to be 0.03 < o^-ko <
0.2 rad (Fig. l c ) . This cut improves the purity of the
selected sample.
After applying these selection criteria, 247 r~
ptK°X~ candidate decays remain with 27.7 decays
expected from the modes without K°’s. The follow
K° decays from
In order to distinguish r
vttt~ K°K° decays, the
*V7r'~7r°K° and r~
selected decays are classified into three categories:
V t 7T 7 T ° K 0
(i) Decays with a i r candidate ( r~
candidates).
These decays are required to have an energy
cluster in the ECAL of greater than 6 GeV and
a transverse shower shape consistent with a tr°.
A typical candidate is shown in Fig. 2.
(ii) Decays with extra neutral hadronic energy
(T~ — > V r 7T~ "K°K° candidates).
Two high energy hadronic showers from a K°K°
pair are not separated in angle but are often
separated in depth (Fig. 3). Therefore, they are
characterized by a more uniform energy depo
sition than a single neutral hadronic shower. In
order to select these decays, the energy deposi
tion in the ECAL, and in the front and back parts
of the HCAL are each required to exceed 10%
of the total energy associated to neutral kaons.
(iii) Remaining decays ( r “ —►vr7r~¥^ candidates).
For each category, the total number of decays
is a linear combination of the signal channels:
pt7t~KP, t~~ —> V
Mj.K“
Ku, tt ~ —> pT7T~7r[JK [ .
tjYL K°,
t ~ —> vTK~~7r°K?, and r~ —> pt7t~ K ° k 9 and the
background channels. Only the coefficients for the
modes r~ —> ^r 7r - K°, r ”
^T7r ” 7r°K°, and
^t 7T_ K°K0 are allowed to vary in the fit.
7 In the K~ K° final state the energy is on average divided equally
between the charged and neutral kaons, leading to small values
of the ratio A£hc/%/At* In the case of the 7 r ’"'K0 final state, the
(heavy) neutral kaon has more energy in the laboratory frame than
the (light) charged pion, leading to large values of A ^ h c /V ^ t-
L3 Collaboration / Physics Letters B 352 (1995) 487-497
Run#
461204
Event# 604
R u n #
509715
E v e n t#
U
P
493
2452
B
OfloO
d
B
B
DO
•W
■q P □ 0
□
a
a
g*
0 C B
Fig. 2. A r ' -> vTi t~ 7r°K° candidate decay. In the upper hemi
sphere, the 1.36 GeV/c changed track is well separated in space
from the 12.0 GeV 7r° detected in the ECAL and the 12.6 GeV
neutral hadron shower in the HCAL. The neutral hadron shower
starts after 3 HCAL layers (about OJA).
The other coefficients are fixed to the central val
ues from the recently published measurements [ 12 ]:
B { t ~ - * vrK~K9 ) = 0.0029 ± 0.0012 and B ( t ~
j/t K-77-°K0) = 0.0005 ± 0.0005.
In order to increase the separation power between
the channels, the coefficients of the linear combination
are fit to a 10-bin histogram of the 7r° energy for the
vr7r~7r°K° sample. A 5 x 3 binned histogram
of total decay energy versus invariant mass of the ob
served r decay products is used for the r ~ —►vr'ir~K°
and r~ —> ^T7r"K °K 0 samples. We use a binned max
imum likelihood function which accounts for the finite
statistics both in the data and in the Monte Carlo.
The spectrum used for the fit of the r ”
vT7r~7r°K0 sample is shown in Fig. 4a together with
the best fit Monte Carlo distributions. The total en
ergy and invariant mass distributions for the r~
¿V77~K°K0 and r~
vT7r~K° samples are shown in
Figs. 4b and 4c respectively together with the best fit
Monte Carlo distributions.
The number of decays expected from the different
channels is shown in Table 1 together with the corre
sponding number of data decays. The numbers of data
(jnrp a
H C A L
0
J& l !g
0
1
Fig. 3. A r ~ —+ ¿y7T- K0K0 candidate decay. In the upper hemi
sphere, the 2.39 GeV/c charged track is separated in space from
the 9.4 GeV cluster in the ECAL and the 33.6 GeV neutral hadron
shower in the HCAL. The neutral hadron shower has two distinct
local maxima: about 12 GeV in the front part of the HCAL and
20 GeV in the back part. The shower shape of the neutral energy
cluster in the ECAL is inconsistent with being a 7r°.
decays in each channel from the fit are
N (r
vTir~Ÿ?) =112.0 ± 17.7
N ( r " ->• v T7r~ir°K0) =33.1 ± 9.7
N ( r - -» iy 7r-K °K 0) =55.8 ± 21.4
and the correlation coefficients between the fitted
channels are
p ( ir - K ?, 7r - ir°K°) =0.01
O
tf-O
-y
_
p ( ir " K ° , 7r - K uKu) =0.68
p(7r- 7r0K0 ,7 r'K °K 0) = 0.36.
The large correlation coefficient between N (r~
vT7r~K°) and N ( r ¿ v r- K°K°) results in an in
crease of the statistical errors for the corresponding
vttt~ K°K°) in
branching fractions. If we fix N ( r ”
the fit, the corresponding error for N ( r
jvtt- R 0)
is significantly reduced: N (t~ —> v T7r~~K°) = 112,0±
12.8, Therefore, it is important to account for this cor
relation.
L3 Collaboration / Physics Letters B 352 (1995) 487-497
494
30
20
10
20
c/3
&
o
(S 5
10
10
0
0
0
0
E ( n ) (GeV)
0.
M(7f K°) (GeV)
E( tc_)+E(K ) (GeV)
Fig. 4. (a) The spectrum of the 7r° energy for the sample enriched with r
energies of the observed r decay products for the sample enriched with r~
the 7t_ K° system for the sample enriched with r ” —►¿v7r“ K° decays.
-*> ^r 7 r ' 7 TuKu decays, (b) The spectrum of the sum of
iyn'"~K°K° decays, (c) The invariant mass spectrum of
Table 1
The numbers of decays detected in the three subsamples along with the best fit Monte Carlo expectations. For the t ~ —> ^TK“ K° and
r “- —> vTY irifiY ? channels, the numbers of expected decays correspond to the branching fractions measured in Ref. [12]
Data
r~
t
—> vTir~ K °
~ -+
K°
7”
— ►Z'T7T‘ ~77'0 K f)
T~
> ^ rK ~ 7 T °K 0
T ~ - > V t TT~ K ° K °
Background
MC total
7T K°K° sample
Total
41
92
247
71.9
10.0
3.5
0.4
18.9
11.8
2.4
0.1
20.3
0.3
4.9
7.5
37,7
3.8
9.3
1.0
32.0
8.4
112.0
13.9
33.1
1.7
55.8
27.7
116.5
35.5
82.2
244.2
7T K° sample
7
114
6. Systematic uncertainties
The dominant systematic errors in the measurement
arise from the uncertainties in the absolute energy cal
ibration and detector resolution functions, the back
ground estimation, and theoretical uncertainties.
The calibration uncertainties affect both the selec
tion efficiency and the shape of the final distributions
used for the fit. The accuracy of the ECAL energy
scale for electrons and photons is estimated to be 1%
at 1 GeV from the measurement of the position of the
7T° mass peak and 0.1% at 45 GeV from a study of
Z —» e+e ~ (y ) events. The momentum scale of the
central tracker is verified to 1% accuracy from 1 to
45 GeV using low energy electrons as well as muons
r 7t°K0 sample
from r and Z decays. The absolute energy scales of the
ECAL and HCAL for hadrons are each known to 1.5%
in the central region from the position of the p mass
peak. The corresponding uncertainties in the number
of signal decays propagated through the selection and
fitting procedures are listed in Table 2.
The resolution function of the HCAL is verified us
ing test beam data and r ”
p~ v Tdecays. The spectra
of the ratio A £ h c /V ^ » as measured in the test beam
for single pions of different energies, are compared
with the Monte Carlo expectations in Fig. 5. No dis
crepancy between data and Monte Carlo is observed
within the achieved statistical errors, limiting possi
ble uncertainty of the non-K° background to ±2.1 de
cays. The uncertainty in the number of decays with
L3 Colloboration / Physics Letters B 352 (1995) 487-497
Table 2
Summary of the systematic uncertainties in the numbers of fitted
decays
Source
AN^- tjûro ANtt- K0R0
Calibration
HCAL
ECAL
TEC
3.5
1.0
1.0
0.9
1.6
0.8
4.3
2.5
0.6
2.0
1.5
3.4
0.2
0.8
0.5
0.2
0.8
0.6
0.6
2.4
0.9
matrix element 3.9
CP(K°K°)
1.2
4.0
2.7
Background 7T°
w± /K ±
ANk_ ko
a n k-
Theory
^ k°
AN8*81
Total
—
6.9
2.6
7.4
(a)
4 GeV %
f\
10
—
!c
10
MC single 7t
10
t
t
1
i
C/2
o
e
D
>
W 10
10
a e hc / a/p*
1*
10
8 GeV n
u
20
(GeV1/2)
(b)
1
k
•
10
15
Data
1 1 MC single 7i~
495
is estimated by varying their branching
fractions according to the uncertainties quoted in
Ref. [12], Uncertainties in the number of 7r0,s from
r~ -+ p ~ v T and r~ —> a J v T decays leaking to the
HCAL are estimated using a sample enriched with
7r°’s with abnormally high energy deposition in the
first three layers of the HCAL (seen as a peak at
£ 3l / £ h c ~ 1 in Fig. lb). This uncertainty is es
timated to be 20 % of the number of r~ —►p ~ v T
and r~ —> a f vr decays predicted by Monte Carlo
simulation.
The theoretical error due to the uncertainty in the
matrix element for the r decays into three particles
with one or two kaons arises from the non-uniformity
of the selection efficiency over the phase space. In
the Monte Carlo program [ 8 ] used to simulate r de
cays, assumptions are made about the chiral structure
of the weak hadronic current and the resonant struc
ture of these decays. By varying these assumptions,
we estimate the possible change of the efficiencies to
be of the order 10%, depending slightly on the decay
channel; the exact numbers are listed in Table 2, An
other source of systematic error is the uncertainty in
the CP phase of the K°K° system in the decay r~ —>
z/r 7r"K°K°. The systematic error is assigned accord
ing to the difference in the fit results assuming that
the K°K° sample consists of only CP-odd or only CPeven components. In the final fit, used to derive the
branching fractions, the following proportion is as
sumed Kl Kl : KSKs : KsKL = 0.25 : 0.25 : 0.5.
Table 2 summarizes the study of the systematic er
rors for the numbers of fitted decays. When combining
the systematic errors of a given channel, all sources
are assumed to be independent.
ptK-77»K°
W
10
«
1
*
0
it
..........
..
10
,
I/O20
AEhc/ # tc(GeV ;)
\5
Fig. 5. The spectra of the ratio AEhc / v ^ t for (a) 4 GeV and
(b) 8 GeV single pions as measured in the test-beam (dots) and
predicted by the Monte Carlo (solid histogram).
7. Discussion and conclusions
From the fit results presented in Table 1, the selec
tion efficiencies, and the total number of observed r
decays, we extract the following branching fractions:
B (t
K°’s due to inefficiency of the HCAL is estimated to
be 1% of the number of fitted decays from a study of
fjb+ ¡ul~ (y ) events.
Z
The systematic error due to the uncertainty in
the rate of the decays r~ —> ^TK “ K° and r " —>
K° ) = 0.0095 ± 0.0015(stat)
± 0.0006 (syst)
B (r
jV7T~7r 0K0) = 0.0041 ± 0.0012(stat)
± 0 .0 0 0 3 (syst)
L3 Collaboration / Physics Letters B 352 (1995) 487-497
496
20
20
15
(C)
-
15
15
S' 10
Q
10
10
5
5 -
5
0
0
0
M(7t V ) (GeV)
1_
:
M(tTK0
M ( r f ) (GeV)
0
-
0
M(tc 71°K0) (GeV)
Fig. 6. (a) The invariant mass spectrum of the 7 r - 7 ru system for the sample enriched with t ~ —> v t i t ~ 7r°£° decays, (b) The invariant
mass spectrum of the 7r - K° system for the sample enriched with r - —* i'T7r~7r0K0 decays, (c) The invariant mass spectrum of the
7T~7r°K[) system for the sample enriched with r~ —*■pT7r^7r0K0 decays.
B ( t~
vr7r~K°K°) = 0.0031 ±0.0012(stat)
± 0.0004 (sy st).
These results are consistent with other recent measure
ments [12-15] and comparable in accuracy.
Despite the absence of explicit identification of the
final state charged hadron, these measurements are
largely independent of the assumed branching frac
tions for r~ —►*vK- K0 and r~ —►pTK~7pY?. This
is due to the fact that the selection efficiencies for
these modes are significantly lower than the corre
sponding efficiencies for modes with charged pions,
r ~ —> pt7t~K° and r~ —> ^r 7r“ 7r°K°, as a result of
the different kinematics of these decays.
The invariant mass spectrum of the 7t “ K° system
agrees with the model that this final state comes only
from t ~
p t K * ~ — > p t 7t ~ K ° . Assuming no other
contributions to this final state, we extract
B ( r ~ -> vrK*~) = 0.0142 ± 0 .0022 (stat)
± 0.009 (sy st).
We have also considered the production of the
7t _ K° final state from higher mass resonances or
nonresonant r ~ decays. Including these modes in the
fit of our data, the following limits are derived:
<0.0017
at 95% CL
B ( t ~ -> ^r 7r _ K 0) K. - ( 1430) < 0.0011
at 95% CL.
T
>■ Vt TT K. )nonresonant
The latter does not depend on the assumption of the
spin of the K*~(1430) resonance.
We have studied the resonant structure of the
hadronic current in the r~ —> jy 7r” 7r°K 0 decay
(Fig. 6 ). The p “ peak in the 7r~ 7r° invariant mass
distribution is well reproduced by the Monte Carlo
model [ 8 ] as shown in Fig. 6 a. However, Fig. 6 b and
Fig. 6 c indicate a possible enhancement of the decays
r " —> v7Yi\~ —>vrK*7T —> pT7r~'7r°K° in the data.
Our measurement of the branching fraction
B ( t ~ —►zy 7r_ K°K°) is insensitive to the theoreti
cal assumptions on the matrix element and the CP
phase of the K°K° system. It is consistent within the
achieved accuracy with measurements of the similar
decay
[13,15].
Acknowledgments
We wish to express our gratitude to the CERN ac
celerator divisions for the excellent performance of the
LEP machine. We acknowledge the efforts of all en
gineers and technicians who have participated in the
construction and maintenance of this experiment.
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