Measurement of the Pion Polarizability at COMPASS

0.3 MB·

by  Stefan Huber

Measurement of the Pion Polarizability at COMPASS
4 Stefan Huber∗†on behalf of the COMPASS collaboration
1
TechnischeUniversitätMünchen
0
2 E-mail: [email protected]

b
e
ThevalueofthepionpolarizabilityispredictedwithhighprecisionbyChiralPerturbationTheory.
F
However, the existing experimental values are at tension with this prediction as well as among

2
themselves.
1
TheCOMPASSexperimentattheCERNSPSaccessespion-photonreactionsviathePrimakoff

] effect, where high-energetic pions react with the quasi-real photon field surrounding the target
x
e nuclei. Flagship channel is the Primakoff reaction in which a single real photon is produced,
- givingaccesstopionComptonscattering. Usingthisprocessthepionpolarizabilityisextracted
p
e fromthemeasuredcross-sectionshape.
h
Endof2009COMPASSperformedameasurementofthepionpolarizabilityusinganickeltarget.
[
Thelargeamountofdatacollectedincombinationwiththepossibilitytostudysystematiceffects
2
v usingtheanalogousreactionwithamuonbeam,themostpreciseexperimentalvaluetodatewas
0 determined.
6
7
4
.
1
0
4
1
:
v
i
X
r
a
XVInternationalConferenceonHadronSpectroscopy-Hadron2013
4-8November2013
Nara,Japan
∗Speaker.
†This work was supported by the BMBF, the DFG Cluster of Excellence "Origin and Structure of the Uni-
verse" (Exc 153), and the Maier-Leibnitz-Laboratorium der Universität und der Technischen Universität München.
Participationattheconferencewasfinanciallysupportedbytheorganizersoftheconference.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
MeasurementofthePionPolarizabilityatCOMPASS StefanHuber
1. Introduction
TheCommonMuonandProtonApparatusforStructureandSprectroscopy,COMPASS[1]is
a fixed-target experiment operated at CERN’s Super Proton Synchrotron. The aim is to study the
structure and spectrum of light hadrons. Being the lightest meson, the pion is of special interest
as it is the fundamental particle in low-energy QCD described within the framework of chiral
perturbation theory. For non-point-like particles the electric and magnetic polarizabilities α and
π
β are fundamental quantities describing the behavior of the particles electromagnetic fields. For
π
thesevaluesexistpreciseexpectationsfromchiralperturbationtheory[4].
2. Primakoffreactions
Due to the short life-time of the pion it is impossible to prepare a pion target which the pho-
tons may scatter off. One possibility to study pion-photon scattering processes is to use highly
relativistic pion beams on nuclear targets, as has been proposed by Henry Primakoff [2]. In these
processes the charged pion scatters off quasi-real photons stemming from the strong electromag-
netic field surrounding heavy nuclei. The density of these quasi-real photons can be described
usingtheWeizsäcker-Williamsapproximation[3]inwhichthecross-sectioncanbewrittenas
dσEPA Z2α Q2−Q2 dσ
πNi = em F2(Q2) min πγ, (2.1)
dsdQ2dΦ π(s−m2) eff Q4 dΦ
n π n
where m is the mass of the pion, s the center-of-mass energy of the πγ-system and α the fine-
π em
structure constant with a value of about 1/137. Q , the minimal four-momentum transfer is a
min
quantitydeterminedbythereactionkinematicsandgivenbytheformula
s−m2
Q = π. (2.2)
min
2p
beam
F is the nuclear form factor and σ is proportional to the squared nuclear charge Z2. For the
eff πNi
extractionofthepionpolarizabilityweconsiderthecaseofpionComptonscatteringπ−γ →π−γ
whichisrelatedbyEq.2.1totheprocessπ−Ni→π−γNi. Thepolarizabilitiesentertheπγ cross-
sectionasgivenby.
dσ (cid:18)dσ (cid:19) α m3(s−m2)2(cid:18) s2 (cid:19)
πγ = πγ − em π π z2(α −β )+ z2(α +β ) , (2.3)
dΩ dΩ 4s(sz +m2z ) − π π m4 + π π
Born + π − π
wherez isgivenby1±cosθ respectivelyandtheθ isthescatteringangleofthepioninthe
± cm cm
center-of-masssystem.
3. MeasurementatCOMPASS
ForthismeasurementCOMPASSusesabeamofnegativelychargedhadronsconsistingmainly
of π−. A kaon contamination of about 3% is rejected using particle identification by Cherenkov
counters installed at the end of the beam line in front of the target. The pions impinge on a 3mm
thick nickel disk. The reaction π−Ni→π−γNi is identified by selecting events with one outgo-
ing charged track and one cluster in the electromagnetic calorimeter having an energy E above
γ
2
MeasurementofthePionPolarizabilityatCOMPASS StefanHuber
counts / 0.866 MeV/c1223505000000000 p r e li m i n a r (sdmCysia-mOc tNaaMuliel aPfidtA ito oSmn Sd- g a2t aN0)0i9 2counts / 5 MeV/c1122050500000000 p r e li m i n a r (sdpCysia-mOc tNaaMuliel afiPdtA ito oSpn S-d g a2 tNa0)0i9
1000
500
500
0 0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
|Q| [GeV/c] mpg [GeV/c2]
(a) (b)
nts / 250 MeV22050000 (sdpCsia-mOc tNaaMuliel afiPdtA ito oSpn S-d g a2 tNa0)0i9 counts / 0.00511222680240000000000 (sdpCsia-mOc tNaaMuliel afiPdtA ito oSpn S-d g a2 tNa0)0i9
cou1500 m i n a r y 11240000 m i n a r y
1000 p r e li 1000 p r e li
800
600
500 400
200
0 0
-30 -20 -10 0 10 20 30 0.4 0.5 0.6 0.7 0.8 0.9
D E [GeV] xg = Eg / Ebeam
(c) (d)
Figure1: Kinematicdistributionsforthereactionπ−Ni→π−γNi. Magnitude|Q|ofthefour-momentum
transfer(a),invariantmassoftheπγ system(b),energybalance(c)andrelativeenergyx ofthephoton(d).
γ
80GeV. Taking into account the resolution of the electromagnetic calorimeter the reaction is re-
(cid:12) (cid:12)
quired to be exclusive by cutting on the energy balance ∆E =(cid:12)Ebeam−Eγ−Eπ(cid:12)<15GeV figure
1c. The remaining non-exclusive background originates mainly from processes having one π0 in
thefinalstate,whereoneofthephotonsfromthedecayπ0→γγ isnotreconstructed. Thiscanbe
seenfromtheremainingρ−(770)peakintheinvariantmassdistribution.
Thecross-sectionforquasi-realphotonexchangedivergesaswithdecreasingfour-momentum-
transferQasgivenbyEq.2.1. UsingthispropertyPrimakoffeventsareselectedbyapplyingacut
onthesquaredfour-momentumtransferofQ2<0.0015(GeV/c)2. Thisalsoeffectivelysuppresses
contributions from diffractive processes, where the interaction probability drops approximately
linearly with Q2. In order to illustrate the momentum-transfer distribution, the quantity |Q| =
(cid:112)
|Q2|isshowninFig. 1a. Inordertoachievetheexperimentalresolutionnecessarytoidentifythis
process,specialcarewastakentoproperlyalignthevertexdetectorsaswellastoproperlycalibrate
the electromagnetic calorimeter. At very low scattering angles multiple scattering dominates. In
order to select only events where the interaction vertex can be properly determined, a cut on the
transverseoutgoingmomentumofthepionw.r.ttothebeamisapplied p >40MeV/c.
T
By using the approximation α =−β the ratio of the Born cross-section, which describes
π π
a point-like particle and the cross-section taking into account the polarizability contribution inte-
3
MeasurementofthePionPolarizabilityatCOMPASS StefanHuber
gratedovertheconsideredrangeoffour-momentumtransferreducestoasimpleformuladepending
onlyonthevaluex =E /E .
γ γ beam
(cid:18)dσ (cid:19)(cid:30)(cid:18)dσ0(cid:19) 3 m3 x2 dN /dx
R = =1 − · π · γ α = Born γ (3.1)
π
dx dx 2 α 1−x dN /dx
γ γ γ meas. γ
Applyingthisformulatoourmeasurementrequiresthedescriptionofthecross-sectionforapoint-
likespin-0particle. Forthatthex -distributionistakenfromaMonteCarlosimulation. Theratio
γ
between the measured π−-spectrum and the simulation is depicted in figure 2. A polarizability
valueofα =(1.9±0.7 )·10−4fm3 isextractedbyfittingEq.3.1tothisspectrum.
π stat
In order to check systematic effects on the measurement COMPASS takes advantage of the
possibilitytoeasilychangefromhadrontomuonbeam. Formuons,whicharepoint-likeparticles,
thepolarizabilityiszeroandsoameasured"falsepolarizability"valueformuonsgivesanestimate
ofthesystematicuncertaintiesstemmingfromtheMonteCarlodescriptionoftheexperiment. The
extracted uncertainty on the polarizability according to this procedure is ±0.6·10−4fm3. The
estimatedmagnitude
uncertaintysource
CL=68% [10−4 fm3]
tracking 0.6
radiativecorrections 0.3
backgroundsubtractioninQ 0.4
pion-electronscattering 0.2
quadraticsum 0.8
Table1: Systematicuncertaintiesestimatedon68%confidencelevel
systematicuncertaintyfromtheappliedbackgroundsubtractionprocedureisestimatedtobeofthe
order of ±0.4·10−4fm3. One additional contribution of background, which is not yet taken into
account, is the scattering of the pions on the electrons of the target, which then loose their energy
by photon emission and are therefore missidentified. The systematic effect due to this process is
estimatedas±0.2·10−4fm3. Allgivensystematicuncertaintiesaresummarizedintable1. Adding
upthesecontributionsquadraticallyyieldsatotalsystematicuncertainty±0.8·10−4fm3 whichin
conclusionsleadstoapreliminaryresultofthepionpolarizabilityof
α =(1.9±0.7 ±0.8 )·10−4fm3. (3.2)
π stat sys
4. Conclusion
TheCOMPASSresultbasedonthePrimakofftechniqueisintensionwithpreviousmeasure-
ments of the pion polarizability as shown in figure 3. In contrast it is in good agreement with the
theoreticalvaluefromchiralperturbationtheory.
InordertofurtherimprovetheexperimentalprecisionCOMPASShastakenabiggerdataset
duringthe2012run. Theexperimentalapproachtothisdataissimilarandwillallowanindepen-
dentextractionofα andβ . Furthermoreidentifyingthekaoncontributioninthebeamwillallow
π π
toextractthepolarizabilityvalueforkaonsaswell.
4
MeasurementofthePionPolarizabilityatCOMPASS StefanHuber
RD / MC (scaled to 1) 011...9211 απ = (1.9 ± 0.7)p× r10e−l4 fimm3 i n a r πCy−O NMi →PA πS−S γ 2 N00i9 background fraction0000....00011.68241 p r e li m i n a r pCy-O NMi fiPA Sp S- g 2 N00i9
0.8
0.04
0.7
0.02
0.6 0
0.4 0.5 0.6 0.7 0.8 0.9 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
xγ = Eγ/Ebeam xg = Eg / Ebeam
(a) (b)
Figure2: Extractionofthepolarizabilityvaluefromthebackgroundsubtracteddataa)andrelativeback-
groundfractionb).
world avg.: 7.5 – 1.6
3
m 50 c 2
-4 f10 PACHRA Babusci Serpukhov 2.70
/ p40 g Lpefibegdpe+vn DPLMU2T, OM, aDrkM I1I PMAACMHIRA 01..9413
b - ggfi p +p - COMPASS prelim.3.09
p30
a Sigma 8.14
Serpukhov
20 p Zfi p gZ MAMIg Fgifil'kpov+p - (CL=0.04)
gpfi gp +n COMPASS
Kaloshin preliminary
10 ggfi p +p - p Zfi p gZ
GIS '06
0
1980 1985 1990 1995 2000 2005 2010 2015 0 5 10 15 20 25 30 35
DMoanrokg IhIue year of publication GIS (2006) a p - b p / 10-4 fm3
(a) (b)
Figure3:Overviewoftheworlddataforthevalueα −β includingtheCOMPASSdataa)andanideogram
π π
forthesamedataasgiveninthePDG[5]wherethevalueindicatedwithGIScorrespondstotheprediction
ofchiralperturbationtheory[4]. Foradetaileddiscussionoftheexperimentalpointsreferto[6].
References
[1] P.Abbonetal.(COMPASSCollaboration),Nucl.Instrum.Meth.A577,455(2007).
[2] H.Primakoff,Phys.Rev.81,899(1951).
[3] I.Y.PomeranchukandI.M.Shmushkevich.Nucl.Phys.23,452(1961).
[4] J.Gasser,M.A.Ivanov,andM.E.Sainio.Nucl.Phys.B745,84(2006).
[5] J.Beringeretal.[ParticleDataGroup],Phys.Rev.D68,010001(2012).
[6] T.Nagel,PhDthesis,Tech.Univ.München(2012),CERN-THESIS-2012-138,
http://cds.cern.ch/record/1484476.
5