a r X i v :h e p -e x /0603021v 1 10 M a r 2006
Pis’ma v ZhETF
Measurement of the Pion Form Factor in the Range 1.04?1.38GeV
with the CMD-2Detector
V.M.Aulchenko a,b ,R.R.Akhmetshin a ,V.Sh.Banzarov a ,L.M.Barkov a,b ,N.S.Bashtovoy a ,D.V.Bondarev a,b ,A.E.Bondar a ,A.V.Bragin a ,A.A.Valishev a ,N.I.Gabyshev a ,D.A.Gorbachev a ,A.A.Grebeniuk a ,
D.N.Grigoriev a,b ,S.K.Dhawan d ,D.A.Epifanov a ,A.S.Zaitsev a,b ,S.G.Zverev a ,F.V.Ignatov a ,V.F.Kazanin a,b ,S.V.Karpov a ,I.A.Koop a,b ,P.P.Krokovny a,b ,A.S.Kuzmin a,b ,I.B.Logashenko a,c ,P.A.Lukin a ,A.P.Lysenko a ,
https://www.doczj.com/doc/686898916.html,stein a,b ,K.Yu.Mikhailov a ,I.N.Nesterenko a,b ,M.A.Nikulin a,b ,A.V.Otboev a ,V.S.Okhapkin a ,E.A.Perevedentsev a,b ,A.A.Polunin a ,A.S.Popov a ,S.I.Redin a ,
B.L.Roberts,N.I.Root a ,A.A.Ruban a ,N.M.Ryskulov a ,A.L.Sibidanov a ,V.A.Sidorov a ,A.N.Skrinsky a ,V.P.Smakhtin,I.G.Snopkov a ,E.P.Solodov a,b ,
J.A.Thompson e ?,G.V.Fedotovich a,b ,B.I.Khazin a,b ,V.W.Hughes d ?,A.G.Shamov a ,Yu.M.Shatunov a ,
B.A.Shwartz a,b ,S.I.Eidelman a,b ,Yu.V.Yudin a
a
Budker Institute of Nuclear Physics,Russian Acad.Sci.,Siberian Div.,Novosibirsk,630090,Russia
b Novosibirsk State University,Novosibirsk,630090,Russia
c Boston University,Boston,MA 02215,USA
d Yal
e University,New Haven,CT 06511,USA e University o
f Pittsburgh,Pittsburgh,PA 15260,USA f Weizmann Institute of Science,76100,Rehovot,Israel
Published in JETP LETTERS Vol.82No.12(2005)743-747
The cross section for the process e +e ?→π+π?is measured in the c.m.energy range 1.04÷1.38GeV from 995000selected collinear events including 860000e +e ?events,82000μ+μ?events,and 33000π+π?events.The systematic and statistical errors of measuring the pion form factor are equal to 1.2÷4.2and 5÷13%,respectively.
PACS:13.25.-k,13.40.Gp,13.66.-a,29.30.-h
INTRODUCTION
A study of the cross section for the process e +e ?→π+π?provides important information on the electro-magnetic form factor of the pion,which describes its internal structure.Moreover,precision measurement of this cross section is necessary for calculating the anoma-lous magnetic moment of the muon (g ?2)μ[1]and its comparison with precision measurements,one of which was carried out recently at BNL [2].Such comparison is an important test of the Standard Model.
EXPERIMENT
Measurements were performed at the VEPP-2M col-lider [3]with the CMD-2general purpose detector (cryo-genic magnetic detector),which combines the proper-ties of a magnetic spectrometer and good calorime-try [4,5].The coordinates,emission angles,and mo-menta of charged particles are measured by the coordi-nate system of the detector,which consists of the drift and Z chambers located inside a thin (0.38X 0)supercon-ducting solenoid with a magnetic ?eld of 1T.Cylindrical and endcap electromagnetic calorimeters based on CsI and BGO scintillation crystals ensure measurement of
energy and photon emission angles and make it possible to separate electrons and hadrons.A range system is used to identify muons.
This work continues a cycle of precision measure-ments of hadron cross sections with the CMD-2detec-tor.The results of the pion form factor measurement in the energy range 0.61÷0.96GeV were published in [6].In this work,we present the results of the measurement of the form factor in the energy range 1.04÷1.38GeV.A more detailed description of the data analysis was given in [7].
An integrated luminosity of 6pb ?1was collected in the experiment.For analysis,we selected 33000π+π?events accumulated at 35beam energy points from 520to 690MeV with a step of 5MeV.The beam energy was controlled with an accuracy not worse than δE/E ～10?3using the magnetic ?eld value in the VEPP-2M storage ring.
SELECTION OF COLLINEAR EVENTS To separate the events e +e ?→e +e ?,e +e ?→μ+μ?,and e +e ?→π+π?,the following conditions were used:
1
2CMD-2
E2
beam?4942·1.15MeV/c,300MeV/c), where p+and p?are the momenta of the positive and negative particles,respectively.
The main sources of the background for the process e+e?→π+π?are the e+e?→π+π?π0π0,e+e?→π+π?π0,e+e?→K+K?reactions and cosmic parti-cles.The physical background contribution to the pion form factor was calculated using experimental cross sec-tions[8,9]by taking into account the detection e?-ciency determined from the total simulation.The total contribution of these processes does not exceed0.8% and is taken into account as a correction to the pion form factor according to Eq.(2).The number of cosmic particle background events was determined from the dis-tribution of the event vertices over the distance from the beam interaction point.
EVENT SEPARATION
To determine the number of events of each process,we used two-dimensional distributions over the energy de-position in the CsI calorimeter(Fig.1).The number of events(Nπ,Nμ+N e)was determined by minimizing the maximum likelihood function:
L=?
events
ln i N i·f i(E+,E?) + i N i,
where f i is the probability density function for events of a given type(π,μ,e,cosmic).Electrons and positrons initiate an electromagnetic shower in a calorimeter and thereby noticeably di?er from other charged particles
Fig. 1.Distribution of collinear particles over the en-
ergy deposition in the calorimeter.
in their energy deposition.The energy depositions of
muons,cosmic particles,and pions with only ionization
losses are almost identical.For this reason,to determine the number of muons,we used additional information
on the ratio of the cross section for muon production
to the cross section for e+e?→e+e?as obtained from the QED calculation with the inclusion of the resolu-
tions and detection e?ciencies in the detector. DETERMINATION OF THE PION FORM FACTOR
The cross section for the e+e?→π+π?process in-tegrated over the detection solid angle is given by the expression:
σπ+π?=σ0π+π?·|Fπ|2
=
πα2
s
3
2·|Fπ|2,
(1)
whereσ0
π+π?
is the cross section calculated under the assumption of the absence of the internal structure of the pion.The contribution of vacuum polarization to the photon propagator is also included in the form fac-tor.
Measurement of the Pion Form Factor in the Range1.04?1.38GeV with the CMD-2Detector3 N e+e?+Nμ+μ?
×
×σ0
e+e?·(1+δe+e?)·εe+e?+σ0μ+μ?·(1+δμ+μ?)·εμ+μ?
|Fπ|2E,
MeV
490.0 1.069±0.082
2.598±0.134610.0
525.0 1.069±0.088
2.185±0.135620.0
535.00.794±0.064
1.884±0.119630.0
545.00.719±0.057
1.704±0.120640.0
555.00.571±0.042
1.449±0.146650.0
565.00.570±0.050
1.531±0.088660.0
575.00.460±0.040
1.386±0.087670.0
585.00.347±0.049
1.200±0.088680.0
595.00.424±0.078
0.983±0.079690.0
4CMD-2Collaboration
Error source √
Detection solid angle
0.5÷2%
Pion loss
0.05÷1.7%
Radiative corrections
0.6÷1.6%
Energy calibration
0.2÷1.5%1.2÷4.2%
Statistical error at the point
vacuum-chamber wall,and the resolution of the drift chamber while calculating radiative corrections.The calculated di?erence between the detection e?ciencies for e +e ?and μ+μ?,π+π?in the simulation was equal to εMIP ?εe +e ?=0.189±0.004%in good agreement with the measured value.The di?erence between the form factor obtained and the form factor used in the simulation varies from 0.2to 1.5%in dependence on the energy.The di?erence at the highest energy was equal to 1.5%and consisted of 1%for the separation procedure and 0.5%characterizing the systematic error in the inclusion of the above corrections.
DISCUSSION
Figure 2shows the results,which are in good agreement with the data obtained in the previous experiments with the detectors
OLYA[13],DM1[14],DM2[15],BCF[16],ACO[17].The form factor in this energy range was mea-sured in detail only in the experiment with the OLYA detector with a systematic error of 10÷15%.The ex-perimental energy dependence of the form factor is well reproduced in the framework of the vector-meson domi-nance model by the sum of the amplitudes of the ρ(770),ρ(1450),ρ(1700),ωand φmesons [6]:|F π(s )|2= BW GS ρ(770)(s )·
1+δωs
m 2φ
BW φ(s )
+
+β
BW GS ρ(1450)(s )
+γ
BW GS ρ(1700)(s )
/(1+β+γ)
2
,
(3)
Fig.2.Experimental data obtained for the pion form factor |F π|2in this work in comparison with other ex-periments.
Here,BW GS ρ(s )is the meson parametrization in the Gounaris-Sakurai model [18];BW ω(s )and BW φ(s )are the parametrization of the ωand φresonances,respec-tively,which were represented by the relativistic Breit-Wigner form due to a small width;δω,δφ,βand γare the model parameters describing the relative contribu-tions of the ρ?ωand ρ?φinterferences and ρ(1450)and ρ(1700)states,respectively.In order to determine the model parameters,it is necessary to use all the available data on the form factor in the energy range √
1.M.Davier and W.J.Marciano,Ann.Rev.Nucl.Part.Sci.54,115(2004).
2.G.W.Bennett et al.,Phys.Rev.Lett.92,161802(2004).
Measurement of the Pion Form Factor in the Range1.04?1.38GeV with the CMD-2Detector5