Table Of ContentRadiative Width of the a Meson†
2
The Selex Collaboration
V.P. Kubarovsky6, N. Akchurin17, V.A. Andreev11, A.G. Atamantchouk11, M. Aykac17, M.Y. Balatz8, N.F. Bondar11,
A. Bravar22, M. Chensheng7, P.S. Cooper5, L.J. Dauwe18, G.V. Davidenko8, U. Dersch9, A.G. Dolgolenko8, D.Dreossi22,
G.B. Dzyubenko8, R.Edelstein3, A.M.F. Endler4, J. Engelfried5,13, C. Escobar21,a, I. Eschrich9,b, A.V.Evdokimov8,
T. Ferbel19, I.S.Filimonov10,c, F. Garcia21, M. Gaspero20, S.Gerzon12, I.Giller12, G. Ginther19, V.L. Golovtsov11,
Y.M. Goncharenko6, E. Gottschalk3,5, P. Gouffon21, O.A.Grachov6,d, E. Gu¨lmez2, C. Hammer19, M. Iori20, S.Y.Jun3,
A.D.Kamenski8, H. Kangling7, M. Kaya17, C. Kenney16, J. Kilmer5, V.T. Kim11, L.M. Kochenda11, K.K¨onigsmann9,e,
I. Konorov9,f, A.A. Kozhevnikov6, A.G. Krivshich11, H.Kru¨ger9, M.A. Kubantsev8, A.I. Kulyavtsev6,3, N.P. Kuropatkin11,
9 V.F. Kurshetsov6, A.Kushnirenko3, S.Kwan5, J. Lach5, A.Lamberto22, L.G. Landsberg6, I. Larin8, E.M. Leikin10,
9 M. Luksys14, T. Lungov21,g, D.Magarrel17, V.P. Maleev11, D. Mao3,h, S.Masciocchi9,i, P. Mathew3,j, M. Mattson3,
9 V.Matveev8,E.McCliment17,S.L.McKenna15,M.A.Moinester12,V.V.Molchanov6,A.Morelos13,V.A.Mukhin6,K.Nelson17,
1 A.V.Nemitkin10, P.V.Neoustroev11, C. Newsom17, A.P.Nilov8, S.B. Nurushev6,A. Ocherashvili12, G. Oleynik5,h,Y. Onel17,
n E. Ozel17, S.Ozkorucuklu17, S.Parker16,S. Patrichev11, A. Penzo22, P. Pogodin17, B. Povh9, M. Procario3, V.A. Prutskoi8,
a E. Ramberg5, G.F. Rappazzo22, B. V.Razmyslovich11, V. Rud10, J. Russ3, P. Schiavon22, V.K. Semyatchkin8, Z. Shuchen7,
J J. Simon9, A.I. Sitnikov8, D. Skow5, P. Slattery19, V.J. Smith15,k, M. Srivastava21, V.Steiner12, V. Stepanov11, L. Stutte5,
8 M. Svoiski11, N.K. Terentyev11,3, G.P. Thomas1, L.N. Uvarov11, A.N.Vasiliev6,D.V. Vavilov6, V.S.Verebryusov8,
2 V.A.Victorov6, V.E. Vishnyakov8, A.A.Vorobyov11, K.Vorwalter9,l, Z. Wenheng7, J. You3, L.Yunshan7,M. Zhenlin7,
L. Zhigang7, M. Zielinski19, R.ZukanovichFunchal21
3
v 1 BallStateUniversity,Muncie,IN47306, U.S.A.
4 2 BogaziciUniversity,Bebek80815Istanbul,Turkey
1 3 Carnegie-MellonUniversity,Pittsburgh,PA15213,U.S.A.
4 CentroBrasileirodePesquisasF´ısicas,RiodeJaneiro,Brazil
0
5 Fermilab,Batavia,IL60510,U.S.A.
1
6 Institute forHighEnergyPhysics,Protvino,Russia
0
7 InstituteofHighEnergyPhysics,Beijing,PRChina
9 8 Institute ofTheoretical andExperimentalPhysics,Moscow,Russia
9 9 Max-Planck-Institutfu¨rKernphysik,69117Heidelberg,Germany
x/ 10 MoscowStateUniversity,Moscow,Russia
e 11 PetersburgNuclearPhysicsInstitute, St. Petersburg,Russia
- 12 TelAvivUniversity,69978RamatAviv,Israel
p 13 UniversidadAuto´nomadeSanLuisPotos´ı,SanLuisPotos´ı,Mexico
e 14 UniversidadeFederaldaPara´ıba,Para´ıba,Brazil
h 15 UniversityofBristol,BristolBS81TL,UnitedKingdom
: 16 UniversityofHawaii,Honolulu,HI96822,U.S.A.
v 17 UniversityofIowa,IowaCity,Iowa52242, U.S.A.
Xi 18 UniversityofMichigan-Flint,Flint,MI48502, U.S.A.
19 UniversityofRochester,Rochester,NY14627,U.S.A.
r 20 UniversityofRome”LaSapienza”andINFN,Rome,Italy
a
21 UniversityofSa˜oPaulo,Sa˜oPaulo,Brazil
22 UniversityofTriesteandINFN,Trieste,Italy
We present data on coherent production of the (π+π−π−)system by 600 GeV/c pion beam in the reaction
π−+A→A+(π+π−π−)for the C, Cu and Pb targets. The Primakoff formalism was used for extracting the radiative width
ofthea2 meson. WeobtainapreliminaryvalueΓ(a−2 →π−γ )=225±25(stat)±45(syst)keV.
1 Introduction is a large background from the strong decay channels
withπ0 →γγ inthefinalstatewithonelostphoton. For
thisreasonmostexperimentaldataforthesedecayshave
Radiative decay widths of mesons and baryons are pow-
beenobtainedusingproductionreactionsintheCoulomb
erful tools for understanding the structure of elemen-
field of the nuclei. Studying the inverse reaction (the
tary particles and for constructing a dynamical theory
so called Primakoff1 formalism) γ+π− →M− provides
of hadronic systems. Straightforward predictions for ra-
a relatively clean method for the determination of the
diative widths make possible the direct comparison of
radiative widths.
experimental data and theory.
The small value of the branching ratios of radiative ThePrimakoffreactionworksbetterwhentheenergy
decaysmakesitdifficulttomeasurethemdirectly,ifthere of the beam particles is increased. However, very good
1
spatialresolutionisneededtoextractthe signalatsmall
t where the electromagnetic processesdominate overthe Table1: Statisticsoftheexperiment.
Target Number of Events
strong interaction.
SELEX (E781) had a beam energy of 600 GeV and Carbon 2 760 523
hadahighresolutionvertexdetectorwhichmadeit pos- Copper 1 997 972
sible to explore the features of the Primakoff reaction. Lead 549 092
The differential cross section for the Primakoff reac-
tion
π−+Z →Z+a−, a− →π−π−π+ (1) (1) in this t-interval
2 2
canbewrittenasafunctionofthemassofthefinalstate 0.001
dσ
(M) and the square of the four-momentum transfer to σ = dt dM =Γ(a →πγ)·C, (7)
Primakoff 2
Z dt dM
the nucleus (t) as follows
tmin
whereC =27.2, 626, 4870(mb/GeV)fortheC,Cuand
3
dσ =8παZ2(2J +1)Γ M g (M)g (M) Pb targets respectively.
dt dM a2 γ(cid:16)M2−m2π(cid:17) γ a2
π2(M2−m2a2)m2+2a2mΓ2aa22ga22(M)Γ2a2 t−ttm2in|F(t)|2 (2) 2 Cuts and Statistics of the Experiment
Here α is the fine-structure constant, Z is the charge of The following cuts were applied in order to extract the
the nucleus, F(t) is the electromagnetic form factor of reaction
the nucleus, J is the spin of the a meson and t is π−+A→A+(π−π−π+) (8)
a2 2 min
the minimum four-momentum transfer:
from the exclusive trigger stream of SELEX data:
t ≈(M2−m2)2/4P2 , (3)
min π beam 1. The beam transitionradiationdetector shows that
the beam particle is a pion.
where P is the beam momentum. In our case
beam
Pbeam = 600 GeV and for the a2 meson with the mass 2. For the quasielastic peak, the difference between
1.32 GeV we have the beam particle momentum and the sum of
momenta of three secondaries must be less than
t ≈2·10−6GeV2 (4)
min 17.5 GeV/c.
Thet-distributionforthePrimakoffreactionischaracter- 3. The z-position of the interaction must be in the
izedbyasharppeakwiththemaximumneart=2·tmin. vicinity of a C, Cu or Pb target.
The influence of the nuclear form factor is small in the
regionof t<0.001GeV2 where we expect the Primakoff 4. The energy deposition in the Photon-1 detector
signal. It is less than 5% for the Pb target and 3% for must be less than 2 GeV.
the Cu target.
5. The averagedistance between the point of interac-
The mass-dependent total width and the partial
tionandalltracks(beamandsecondaries)mustbe
widths Γ(a → all), Γ(a → πγ) and Γ(a → ρπ) can
2 2 2 less than 20, 25 and 75 µm for the C, Cu and Pb
be rewritten in terms of resonance widths as follows:
targets.
Γ(a → πγ) = Γ g (M) and Γ(a → ρπ) = Γ g (M),
2 γ γ 2 ρ ρ
where gγ(ma2) = gρ(ma2) = 1. We used g(a2 → all) = The event statistics are presented in Table 1.
g(a →ρπ).
2
For the energy dependence of the widths we used
3 Primakoff Production of the a2 Meson
gγ(M)=(cid:18)kk0(cid:19)3 k22+k02k02 (5) Tishsehopw2TndiinstrFibigu.t1ioanaosfatnheex(3aπm)p-slye.stTemhefodristthriebCutuiotnarwgaest
q 5 2q2 fitted by the sum of two exponentials. The slope for
g (M)= 0 (6)
a2 (cid:18)q (cid:19) q2+q2 the coherent production was found to be close to the
0 0 previously published data2. The p2 distributions for all
T
wherek andq arethemomentaintheπγ andρπ frames, targets have an enhancement in the region of small p2 .
T
respectively. The two exponentials fit yields a slope for the second
Numerically integrating over M and t from t up termgreaterthan1000GeV−2 whichcorrespondsto the
min
to 0.001 GeV2 we get the cross section for the reaction Monte Carlo estimate for the Primakoff reaction.
2
Figure 1: Primakoff production of the a2 meson on Copper target in the reaction: π−+Cu→Cu+(π−π+π−). a. p2T distribution of
(3π)-system. ThePrimakoffsignalisclearlyseenintheregionofsmallp2T . b. M3π distribution. Thefirstcurve(light points)isforevents
withp2 <0.001GeV2,thesecondoneisforevents intheband0.002<p2 <0.0035GeV2. c. Resultofsubtractionoftwocurves(seeb).
T T
d. p2T distributionofthea2 meson.
3
Two p2 regions were defined (the shaded regions in solute crosssectionofthe reaction(1) is measured. This
T
Fig. 1a). In the first one (p2 <0.001 GeV2) the Pri- is the crucial point for the experiment. At the present
T
makoff mechanism dominates. We used the second one stageofanalysiswe usethe crosssectionforthe reaction
0.0015<p2 <0.0035 GeV2 for the estimation of the (8) from E2722. We determined the product of (L·ε)
T
background from the coherent production of the (3π)- and didn’t need to evaluate the reconstructionefficiency
system. ε alone. Here L is the luminosity. The experiment E272
The πππ mass spectra for these two regions are was done in a beam with energy 200 GeV. We assumed
shown in Fig. 1b for the Cu target. The result of the that the coherent cross section of the reaction (8) is in-
subtraction of these histograms is shown in Fig. 1c. A dependent of the beam energy. The simplest estimation
clear a meson signal is seen. The distributions were based on Regge theory confirms this assumption.
2
fitted using Eq. (2) integrated over t. The mass and We determined the absolute cross section in the
width of the resonance were determined using the com- p2 region close to zero to avoid the acceptance correc-
T
bined data from all targets: Ma2 = 1304 ± 5 MeV, tions:
Γa2 = 121± 20 MeV. The mass and the width of the tmaxdNdt
peaksareingoodagreementwiththe massandwidthof dt
the a meson. The number of a events was found to be (L·ε)= tmRin (10)
2 2 tmax
1587±480, 5170±590 and 2945±400 for the C, Cu an dσdt
dt
Pb targets, respectively. tmRin
To make sure that the a meson is produced via the
Primakoff mechanism we div2ided the data into five p2 - where ddNt is the differential t-distribution from SELEX
bins each 0.00025 GeV2 and repeated the subtractiTon data, ddσt is the differential cross section from E272
procedure. We got 5 histograms for each target similar data, tmin = 0, 0.001, 0.0015 GeV2 and tmax =
to Fig. 1c. After the fit of the mass spectra and the 0.020, 0.020, 0.006 GeV2 for three targets. (L ·ε) =
determination the number of a mesons in each bin the 881558, 149302, 17831 events/mbfortheC,CuandPb
2
p2 distributionwasextractedandshowninFig.1d. The targets, respectively.
T
slope was determined for every target. It is consistent
withthePrimakoffdistributionsmearedbytheresolution
6 Radiative Width of the a Meson
of the experimental setup. 2
The radiative width of the a mesonwas determined us-
2
4 Monte Carlo
ing the expression
A simple Monte Carlo program was written to simulate
Na
the p2 -distribution for the Primakoff production of the Γ(a− →π−γ) = 2 (11)
T 2 C·(Lε)·CG·BR·ε(subtr.)
a meson. The p resolution had these different values
2 T
for the different targets: σ(p ) = σ(p ) = 16, 17 and
Tx Ty where CG(a → ρπ)=0.5 is the Clebsch-Gordon coeffi-
2
20 MeV for the C, Cu and Pb targets, respectively.
cient, BR(a → ρπ)=0.701 is the branching ratio, C is
2
The subtraction procedure efficiency was evaluated
determined by numerical integration (see Eq. (7)), (Lε)
using the Monte Carlo simulation:
is the product of the luminosity and the reconstruction
efficiency (see Eq. (10)). The radiative width was deter-
0.001 0.0035
dσ′dt−k dσ′dt mined for all three targets: C, Cu and Pb. The results
dt dt
ε(subtr.)= R0 0.0R015 (9) are shown in Fig. 2. As can be seen from this figure
0.001
dσdt theresultsareconsistentwitheachother,confirmingthe
dt Coulombproductionofthea meson. Theaveragevalue
R0 2
over all targets is
where σ is the Primakoff cross section, σ′ is the Pri-
makoffcrosssectionsmearedbytheexperimentalresolu- Γ(a− →π−γ) =225±20(stat)±45(syst) keV (12)
tion and k is the normalizationfactor. These efficiencies 2
were found to be ε = 0.697, 0.630 and 0.488 for the C,
The major sources of uncertainty in this result are the
Cu and Pb targets.
normalizationprocedure2 and the errors in the determi-
nation of the number of a events. The PDG value for
2
5 Absolute Normalization the Γ(a− →π−γ) =295±60 keV is shown in Fig. 2 as
2
well.
The Primakoff approach gives the possibility to deter-
mine the radiative width only in the case when the ab-
4
Figure 2: The radiative width Γ(a− →π−γ ) for the C, Cu and
2
Pb targets. The average of SELEX result (with statistical and
systematicerrors)andthePDGvalueareshownaswell.
7 Conclusion
Basedona weightedaverageoverthe C, Cuand Pbtar-
gets of the values for Γ(a− →π−γ) we present the pre-
2
liminary value of 225±20(stat)±45(syst) keV for the
radiativewidth of thea meson. Our resulthas the best
2
world statistical error3,4 for the radiative width of the
a meson. Thesystematicerrorcanbereducedinthefu- †Talkpresentedatthe1998InternationalConferenceonHighEn-
2
ergyPhysics,Vancouver, B.C.,Canada,July,1998.
turebyaccuratemeasurementofthe(π+π−π−) coherent
aPresentaddress: InstitutodeFisicadaUniversidadeEstadualde
cross section using SELEX data. Campinas,UNICAMP,SP,Brazil.
bNowatImperialCollege,LondonSW72BZ,U.K.
cdeceased
dPresent address: Dept. of Physics, Wayne State University, De-
troit,MI48201, U.S.A.
ePresentaddress: Universita¨tFreiburg,79104Freiburg,Germany
fPresent address: Physik-Department, Technische Universita¨t
Mu¨nchen,85748Garching,Germany
References gCurrentAddress: InstitutodeFisicaTeoricadaUniversidadeEs-
tadual Paulista,Sa˜oPaulo,Brazil
hPresentaddress: LucentTechnologies,Naperville,IL
1. H.Primakoff, Phys. Rev. 81, 899 (1951). iNowatMax-Planck-Institutfu¨rPhysik,Mu¨nchen, Germany
jPresentaddress: MotorolaInc.,Schaumburg,IL
2. M.Zielinski et al., Z. Phys. C 16, 197 (1983).
kGenerous support of Carnegie-Mellon University is gratefully
3. S.Cihangir et al., Phys. Lett. B 117, 119 (1982).
acknowledged.
4. Particle Data Group, Phys. Rev. D 54, (1996) lPresentaddress: DeutscheBankAG,65760Eschborn,Germany
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