First Measurement of Chiral Dynamics in π^- γ-> π^- π^- π^+

0.36 MB·

by  M. G. Alekseev

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
COMPASS
CERN-PH-EP-2011–176
22November2011
First Measurement of Chiral Dynamics in π−γ → π−π−π+
TheCOMPASSCollaboration
2 Abstract
1
0 The COMPASS collaboration at CERN has investigated the π−γ →π−π−π+ reaction at center-
2 √
of-momentum energy below five pion masses, s<5m , embedded in the Primakoff reaction of
π
n 190GeVpionsimpingingonaleadtarget. Exchangeofquasi-realphotonsisselectedbyisolating
a the sharp Coulomb peak observed at smallest momentum transfers, t(cid:48) <0.001 GeV2/c2. Using
J
partial-waveanalysistechniques,thescatteringintensityofCoulombproductiondescribedinterms
8 √
of chiral dynamics and its dependence on the 3π-invariant mass m = s were extracted. The
1 √ 3π
absolute cross section was determined in seven bins of s with an overall precision of 20%. At

] leadingorder,theresultisfoundtobeingoodagreementwiththepredictionofchiralperturbation
x
theoryoverthewholeenergyrangeinvestigated.
e
-
p
e
h
[

2
v
4
5
Keywords: COMPASS,pion-nucleusscattering,chiraldynamics,photon-hadronscattering,meson
9
5 productionbyphotons
.
1
1
1
1
:
v
i
X
r
a
(tobesubmittedtoPhysicalReviewLetters)
TheCOMPASSCollaboration
M.G.Alekseev28,V.Yu.Alexakhin7,Yu.Alexandrov15,G.D.Alexeev7,A.Amoroso27,
A.Austregesilo10,17,B.Badełek30,F.Balestra27,J.Barth4,G.Baum1,Y.Bedfer22,J.Bernhard13,
R.Bertini27,M.Bettinelli16,K.Bicker10,17,R.Birsa24,J.Bisplinghoff3,P.Bordalo12,a,
F.Bradamante25,A.Bravar24,A.Bressan25,E.Burtin22,D.Chaberny13,M.Chiosso27,S.U.Chung17,b,
A.Cicuttin26,M.L.Crespo26,S.DallaTorre24,S.Das6,S.S.Dasgupta6,O.Yu.Denisov10,28,L.Dhara6,
S.V.Donskov21,N.Doshita2,32,V.Duic25,W.Du¨nnweber16,M.Dziewiecki30,A.Efremov7,
P.D.Eversheim3,W.Eyrich8,M.Faessler16,A.Ferrero22,A.Filin21,M.Finger19,M.Fingerjr.7,
H.Fischer9,C.Franco12,N.duFresnevonHohenesche10,13,J.M.Friedrich17,R.Garfagnini27,
F.Gautheron2,O.P.Gavrichtchouk7,R.Gazda30,S.Gerassimov15,17,R.Geyer16,M.Giorgi25,
I.Gnesi27,B.Gobbo24,S.Goertz2,4,S.Grabmu¨ller17,A.Grasso27,B.Grube17,R.Gushterski7,
A.Guskov7,F.Haas17,D.vonHarrach13,T.Hasegawa14,F.H.Heinsius9,F.Herrmann9,C.Heß2,
F.Hinterberger3,N.Horikawa18,c,Ch.Ho¨ppner17,N.d’Hose22,S.Huber17,S.Ishimoto18,d,
O.Ivanov7,Yu.Ivanshin7,T.Iwata32,R.Jahn3,P.Jasinski13,G.Jegou22,R.Joosten3,E.Kabuß13,
D.Kang9,B.Ketzer17,G.V.Khaustov21,Yu.A.Khokhlov21,Yu.Kisselev2,F.Klein4,
K.Klimaszewski30,S.Koblitz13,J.H.Koivuniemi2,V.N.Kolosov21,K.Kondo2,32,K.Ko¨nigsmann9,
I.Konorov15,17,V.F.Konstantinov21,A.Korzenev22,e,A.M.Kotzinian27,O.Kouznetsov7,22,
M.Kra¨mer17,Z.V.Kroumchtein7,F.Kunne22,K.Kurek30,L.Lauser9,A.A.Lednev21,A.Lehmann8,
S.Levorato25,J.Lichtenstadt23,A.Maggiora28,A.Magnon22,N.Makke22,G.K.Mallot10,A.Mann17,
C.Marchand22,A.Martin25,J.Marzec31,F.Massmann3,T.Matsuda14,W.Meyer2,T.Michigami32,
Yu.V.Mikhailov21,M.A.Moinester23,A.Morreale22,A.Mutter9,13,A.Nagaytsev7,T.Nagel17,
F.Nerling9,S.Neubert17,D.Neyret22,V.I.Nikolaenko21,W.-D.Nowak9,A.S.Nunes12,
A.G.Olshevsky7,M.Ostrick13,A.Padee31,R.Panknin4,D.Panzieri29,B.Parsamyan27,S.Paul17,
E.Perevalova7,G.Pesaro25,D.V.Peshekhonov7,G.Piragino27,S.Platchkov22,J.Pochodzalla13,
J.Polak11,25,V.A.Polyakov21,G.Pontecorvo7,J.Pretz4,C.Quintans12,J.-F.Rajotte16,S.Ramos12,a,
V.Rapatsky7,G.Reicherz2,A.Richter8,E.Rocco10,E.Rondio30,D.I.Ryabchikov21,
V.D.Samoylenko21,A.Sandacz30,M.G.Sapozhnikov7,S.Sarkar6,I.A.Savin7,G.Sbrizzai25,
P.Schiavon25,C.Schill9,T.Schlu¨ter16,L.Schmitt17,f,K.Scho¨nning10,S.Schopferer9,W.Schro¨der8,
O.Yu.Shevchenko7,H.-W.Siebert13,L.Silva12,L.Sinha6,A.N.Sissakian7,*,M.Slunecka7,
G.I.Smirnov7,S.Sosio27,F.Sozzi25,A.Srnka5,M.Stolarski12,M.Sulc11,R.Sulej30,P.Sznajder30,
S.Takekawa25,S.Tessaro24,F.Tessarotto24,A.Teufel8,L.G.Tkatchev7,S.Uhl17,I.Uman16,
M.Vandenbroucke22,M.Virius20,N.V.Vlassov7,R.Windmolders4,W.Wis´licki30,H.Wollny9,22,
K.Zaremba31,M.Zavertyaev15,E.Zemlyanichkina7,M.Ziembicki31,N.Zhuravlev7,andA.Zvyagin16
1 Universita¨tBielefeld,Fakulta¨tfu¨rPhysik,33501Bielefeld,Germanyg
2 Universita¨tBochum,Institutfu¨rExperimentalphysik,44780Bochum,Germanyg
3 Universita¨tBonn,Helmholtz-Institutfu¨rStrahlen-undKernphysik,53115Bonn,Germanyg
4 Universita¨tBonn,PhysikalischesInstitut,53115Bonn,Germanyg
5 InstituteofScientificInstruments,ASCR,61264Brno,CzechRepublich
6 MatrivaniInstituteofExperimentalResearch&Education,Calcutta-700030,Indiai
7 JointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russiaj
8 Universita¨tErlangen–Nu¨rnberg,PhysikalischesInstitut,91054Erlangen,Germanyg
9 Universita¨tFreiburg,PhysikalischesInstitut,79104Freiburg,Germanyg
10 CERN,1211Geneva23,Switzerland
11 TechnicalUniversityinLiberec,46117Liberec,CzechRepublich
12 LIP,1000-149Lisbon,Portugalk
13 Universita¨tMainz,Institutfu¨rKernphysik,55099Mainz,Germanyg
14 UniversityofMiyazaki,Miyazaki889-2192,Japanl
15 LebedevPhysicalInstitute,119991Moscow,Russia
16 Ludwig-Maximilians-Universita¨tMu¨nchen,Departmentfu¨rPhysik,80799Munich,Germanyf,l)
17 TechnischeUniversita¨tMu¨nchen,Physik-Department,85748Garching,Germanyf,l)
18 NagoyaUniversity,464Nagoya,Japanl
19 CharlesUniversityinPrague,FacultyofMathematicsandPhysics,18000Prague,CzechRepublich
20 CzechTechnicalUniversityinPrague,16636Prague,CzechRepublich
21 StateResearchCenteroftheRussianFederation,InstituteforHighEnergyPhysics,142281Protvino,
Russia
22 CEAIRFU/SPhNSaclay,91191Gif-sur-Yvette,France
23 TelAvivUniversity,SchoolofPhysicsandAstronomy,69978TelAviv,Israeln
24 TriesteSectionofINFN,34127Trieste,Italy
25 UniversityofTrieste,DepartmentofPhysicsandTriesteSectionofINFN,34127Trieste,Italy
26 AbdusSalamICTPandTriesteSectionofINFN,34127Trieste,Italy
27 UniversityofTurin,DepartmentofPhysicsandTorinoSectionofINFN,10125Turin,Italy
28 TorinoSectionofINFN,10125Turin,Italy
29 UniversityofEasternPiedmont,1500Alessandria,andTorinoSectionofINFN,10125Turin,Italy
30 NationalCentreforNuclearResearchandUniversityofWarsaw,00-681Warsaw,Polando
31 WarsawUniversityofTechnology,InstituteofRadioelectronics,00-665Warsaw,Polando
32 YamagataUniversity,Yamagata,992-8510Japanl
a AlsoatIST,UniversidadeTe´cnicadeLisboa,Lisbon,Portugal
b SupportedbyIAS-TUM,DFGandHumboldtfoundation
c AlsoatChubuUniversity,Kasugai,Aichi,487-8501Japanl
d AlsoatKEK,1-1Oho,Tsukuba,Ibaraki,305-0801Japan
e OnleaveofabsencefromJINRDubna
f AlsoatGSImbH,Planckstr.1,D-64291Darmstadt,Germany
g SupportedbytheGermanBundesministeriumfu¨rBildungundForschung
h SuppportedbyCzechRepublicMEYSgrantsME492andLA242
i SupportedbySAIL(CSR),Govt.ofIndia
j SupportedbyCERN-RFBRgrants08-02-91009
k SupportedbythePortugueseFCT-Fundac¸a˜oparaaCieˆnciaeTecnologia,COMPETEandQREN,
grantsCERN/FP/83542/2008,CERN/FP/109323/2009andCERN/FP/116376/2010
l SupportedbytheMEXTandtheJSPSundertheGrantsNo.18002006,No.20540299andNo.18540281;
DaikoFoundationandYamadaFoundation
m SupportedbytheDFGclusterofexcellence‘OriginandStructureoftheUniverse’(www.universe-
cluster.de)
n SupportedbytheIsraelScienceFoundation,foundedbytheIsraelAcademyofSciencesandHu-
manities
o SupportedbyMinistryofScienceandHigherEducationgrant41/N-CERN/2007/0
*Deceased
FirstMeasurementofChiralDynamicsinπ−γ →π−π−π+ 1
For hadronic interactions at low energy, quantum chromodynamics (QCD) can be formulated in terms
of an effective field theory resulting from the systematic treatment of chiral symmetry and its breaking
pattern, called chiral perturbation theory (ChPT). In this approach, the pions (π+,π0,π−) are identified
astheGoldstonebosonsassociatedwiththespontaneousbreakingofthechiralsymmetry. Propertiesand
interactionsofthepionsprovidethemostrigoroustestofChPTasthecorrectlow-energyrepresentation
ofQCD.
ChPT has accurately predicted the dynamics of low-energy ππ scattering as measured in various kaon
decay experiments, see Refs. in [1]. High-precision calculations of the pion polarizability in the πγ →
πγ reaction have been performed, which however are at large variance with the existing experimental
determinations[2].
Inviewofthissituationitisofgreatinteresttostudyotherlow-energyreactionsinvolvingpionsandpho-
tons,apartfrommeasuringthepionpolarizabilitieswithimprovedaccuracyasproposedatCOMPASS-
II[3]. Theπγ →3π reactionexaminedhereallowsfortestingthechiraldynamicsofpionsintheregion
nearthresholdwherecalculationsaremostreliable[1].
COMPASS at the CERN Super Proton Synchrotron is a large-acceptance, high-precision spectrome-
ter[4],whichisparticularlywellsuitedforinvestigationsofhigh-energyreactionsofparticlesatlowto
intermediatemomentumtransfertofixedtargets. Theapparatusacceptancefullycoversthephasespace
for reaction products emerging in forward direction. At very low momentum transfer in the process
π−Pb→X−Pb,photonexchangebecomesimportantandcompeteswithstronginteractionprocesseslike
diffractive excitation via Pomeron exchange. The separation of these two contributions is an important
aspectofthisLetter.
Primakoffreactionsareperipheralhadronicreactionsinthequasi-realphotonfieldsurroundingaheavy
nucleus[5]. Theπ-nucleuscrosssectioncanbeconnectedtotheπγ crosssectionusingthewell-known
equivalentphotonapproximation(EPA)[6]
dσEPA Z2α t(cid:48) dσ
Pb = ·F2(t(cid:48))· · γ (1)
dsdt(cid:48)dΦ π(s−m2) eff (t(cid:48)+|t| )2 dΦ
n π min n
Here, the cross section for the process π−Pb→X−Pb is factorized into the quasi-real photon density
providedbythenucleusofchargeZ,andσ ,thecrosssectionfortheembeddedπ−γ →X− scatteringof
γ
apionandarealphoton. Themassofthechargedpionisdenotedm , anddΦ isthen-particlephase-
π n
spaceelementofthefinal-statesystemX−. Fromthe4-momentumtransfersquaredt =(p −p )2,the
π X
positive quantity t(cid:48) =|t|−|t| is derived with |t| =(s−m2)2/(4E2 ) for a given final-state mass
√ min min π beam
m = s, where s =(p +p )2 is the squared centre-of-momentum energy. The lead form factor is
X π γ √
approximatedbytheequivalentsharpradiusformulaF (t(cid:48))= j (r t(cid:48))withr=6.84fm.
eff 1
For the specific reaction studied in this Letter with X− →π−π−π+, the Feynman graphs for σEPA are
Pb
depicted in Fig. 1(a). The Dalitz plot distributions given in Fig. 1(b), which represent a 2-dimensional
projection of the 5-dimensional phase space Φ , show that the momenta of the 3 outgoing pions are far
3
frombeinguniformlydistributedinthem regionnearthreshold.
3π
The data presented in the following were recorded in the year 2004 with a 190 GeV hadron beam (at
the target composed of 96.8% π−, 2.4% K−, 0.8% p¯) interacting with a 3mm lead target. The trigger
selectedeventswithatleasttwooutgoingchargedparticlesatscatteringangleslessthanabout50mrad.
In the data analysis, exactly three outgoing charged particles, assumed to be pions, were required to
form with the incoming beam particle a vertex that is consistent with an interaction within the target
volume. Neglectingthetinytargetnucleusrecoilatlowt(cid:48),theirenergysumE equalsthebeamenergy
3π
for the exclusive π−Pb→ π−π−π+Pb reaction. Taking into account the spread of the beam energy,
σ ≈1.3 GeV, E is required to lie within ±4GeV around the mean beam energy. Figure 2 shows
beam 3π
the m distribution with the requirement t(cid:48) < 0.001GeV2/c2, i.e. the Primakoff-t(cid:48) region. The main
3π
2 TheCOMPASSCollaboration
π− π− π− π∓ π− π−
π− π− π−
(a) γ π+ π± π± γ π−
γ π+
Pb Pb Pb Pb
Pb Pb
] 1.0 ] 0.25 1.0
4 0.11 4
c c
/ /
2 2
V 0.8 V 0.8
e e
(b) G 0.10 G 0.20
[3 0.6 [3 0.6
22 22
m m
0.4 0.15 0.4
0.09
0.2 0.2
0.10
0.08
0.0 0.0
0.08 0.09 0.10 0.11 0.10 0.15 0.20 0.25
m2 [GeV2/c4] m2 [GeV2/c4]
13 13
Fig.1: (a)Leading-order,i.e.tree-levelChPTdiagramsforπ−γ→π−π−π+,embeddedinthePrimakoffreaction
π−Pb→π−π−π+Pb. (b)Dalitzplotscorrespondingtotheleading-orderChPTcrosssection, normalizedtothe
respectivemaximumofthedistribution. Theleftplotisform =0.475GeV/c2,therightonefor0.642GeV/c2,
3π
i.e.atthelowerandupperendsoftheinvestigatedregion. Thequantitiesm2 andm2 arethesquaredmassesof
13 23
theπ−π+subsystems.
contributionsfromdiffractiveexcitationoftheincomingpionstothea (1260)andπ (1670)resonances
1 2
areclearlyseen. Inthehighlightedlow-massregion,m <mlim≡0.72GeV/c2,leading-orderChPTis
3π 3π
expected to be applicable [7]. The momentum transfer distribution for these low masses, excluding the
kaonpeak,isdepictedinFig.3. Thesharpincreasewitht(cid:48)→0includesthePrimakoffcontributionthat
isinvestigatedindetailinthefollowing.
Thedataareanalyzedusinganextensionofthepartial-waveanalysis(PWA)packagethatwaspreviously
usedforthehigh-t(cid:48)eventsfromthesamedataset[8]. TheX−→π−π−π+transitionismodeledasatwo-
step process with an intermediate 2π-resonance (isobar), X− →(2πisobar)0π− →π+π−π−, specified
as JPCMε(2πisobar)[L]π. Here J is the spin, P the parity andC the charge-conjugation parity of X, M
theprojectionofJ ontothebeamaxis,ε thereflectivityofthefinalstateintheGottfried-Jacksonframe
(see e.g. [8]), and L is the orbital angular momentum between the isobar and the bachelor pion. The
partialwavesfoundtoberelevantatlowm andlowt(cid:48) aresummarizedinTable1.
3π
ThenewelementofthepresentanalysisisthereplacementoftheM=1isobaricwavesatlowmassesby
asinglewavethatisgivenbythefullydifferentialformoftheChPTpredictionandcalledfromnowon
“chiral amplitude”, see Eq. (17) in Ref. [1]. Replacing only M=1 waves accommodates the transverse
nature of the quasi-real photon as exchange particle, as M=0 is forbidden for real photons and strongly
suppressed at smallt(cid:48). This replacement is based on the observation [9] that π−Pb strong interaction is
characterized by a (t(cid:48))Mexp(−b t(cid:48)) behaviour at high energy and smallt(cid:48), with the Pomeron slope pa-
Pb
rameterb ≈400(GeV/c)−2. Thusforstrongπ−Pbinteractionsatlowestt(cid:48),M=0componentsdominate
Pb
andM=1aresuppressed,whereasphotonexchangefeaturesasharpspikeatt(cid:48)≈|t| ≤8·10−5GeV2/c2
min
formassesm <mlim,duetothet(cid:48) dependencegivenbyEq.(1).
3π 3π
FirstMeasurementofChiralDynamicsinπ−γ →π−π−π+ 3
· 3
10
)
2 COMPASS 2004
c
9
V/ p -Pb fi p -p -p +Pb
e
8
M
t' < 0.001 GeV2/c2

5 7
(

/

s 6
t
n
e 2
v 5 7
.
E 0

4 =

m
lip3
m
3
2
1
0
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
m [GeV/c2]
3p
Fig. 2: Invariant mass spectrum of the final-state 3π system observed in the Primakoff region (t(cid:48) <
0.001GeV2/c2),withtheinteractionpointobservedinthetargetregion. Thekaondecayintoπ−π−π+isseenas
sharppeakatm ≈0.493GeV.Thelow-massregionofinterestforthisLetterishighlighted.
K
Table1: Wavesetsusedinthelow-mass,low-t(cid:48) region. InthefiguresshowingPWAfits,inthelow-massregion
exclusively the “chiral amplitude” is used. In addition to the indicated waves, always a background contribu-
tion that is homogeneous in phase space and the kaon decay contribution are allowed. Due to the very forward
kinematics,fortheM=1wavesbothreflectivitiesareallowed,asdiscussedinthetext.
M=0 M=1
1++1±(ππ) [P]π 
00−−++00++(ρπ[Pπ])πS[S]π 11−+++11±±ρρ[[PS]]ππS  (cid:26) chiral
1++0+ρ[S]π or
2++1±ρ[D]π amplitude
1++0+(ππ)S[P]π 2−+1±ρ[P]π 
2−+0+(ππ) [D]π 
S 2−+1±(ππ) [D]π 
S
InordertostudythemassdependenceofthepartialwavesinthePrimakoffregiont(cid:48) <0.001GeV2/c2,
thelow-mass(m <mlim)spectrumissubdividedintosevenbins. InthisregionthePWAisperformed
3π 3π
with the isobar M=0 waves of Table 1 and the chiral amplitude for M=1. Above this limit both M=0
and M=1 isobaric wave sets of Table 1 are used. In order to study the exchange mechanisms in this
low-mass region, we look at thet(cid:48) distribution extending the range up to 0.01GeV2/c2. The intensities
areobtainedfromaPWAwiththeM=0setofTable1andthechiralamplitudeforM=1bothbelowand
above0.001GeV2/c2. TheresultsoftheseanalysesareshowninFigs.4and5.
Figure4presentsthefittedpartial-waveintensitiesforthewholemassrange,summedseparatelyforM=0
and M=1. The intensities are corrected for acceptance effects that are determined by a Monte Carlo
4 TheCOMPASSCollaboration
2) 600 COMPASS 2004
c
2/ p -Pb fi p -p -p +Pb
V
e 500
G 0.51 < m < 0.72 [GeV/c2]
3p

5
-
0
1 400

·
5
(
300
/

s
t
n
e
200
v
E
100
· -3
10
0
0 1 2 3 4 5 6 7 8 9 10
2 2
t' [GeV /c ]
Fig. 3: Momentum transfer distribution of events in the investigated low-mass region. The Primakoff region
(t(cid:48)<0.001GeV2/c2)ishighlighted. Inordertosuppressthekaoncontribution,m >0.51GeV/c2isrequired.
3π
simulation and applied in the fitting process in their fully differential form in the 3-pion phase space.
This correction does not deviate more than ± 8% from the average value of 0.58 over the kinematic
rangeconsidered. About82%ofthetotalintensityisattributedtoM=0waves,whicharedominatedby
thea (1260)andπ (1670)resonances.
1 2
For the low-mass region integrated between 0.51−0.72GeV/c2, Fig. 5 shows the PWA results for the
t(cid:48) distributions separately for the M=0 and ChPT (i.e. M=1) contributions. In both cases, an expo-
nential function is fitted to the spectrum. For M=0, Pomeron exchange with the slope b as spec-
Pb
ified above is confirmed. For M=1, the exact shape expected for photon exchange can not be re-
solved experimentally since it is distorted by multiple scattering and detector resolution. The result-
ing spectrum is well described by an exp(−b(cid:48)t(cid:48)) function, where the theoretically “forbidden” for-
ward region at t(cid:48) → 0 is filled by multiple scattering. The slope fitted to the ChPT intensity shown
in Fig. 5, b(cid:48) = 1447±196(GeV/c)−2, is in good agreement with the simulation of pure photon ex-
change, b(cid:48) ≈ 1600(GeV/c)−2. Strong interaction M=1 exchange, on the other hand, would have a
sim
slowly rising ∝t(cid:48)exp(−bt(cid:48)) distribution. From additional studies performed for the neighboring t(cid:48) re-
gion, 0.001 <t(cid:48) < 0.01GeV2/c2, strong interaction M=1 contributions to the Primakoff region were
estimatedtobewellbelow5%.
The fitted chiral amplitude very efficiently replaces all M=1 waves, especially the dominant 1++1+
contributions also used as isobaric waves in PWA fit attempts of the low-mass region, see Table 1.
Fitting the chiral amplitude as M=1 contribution leads to smaller statistical uncertainties due to the
smallernumberoffreeparameters,whileitfeaturesasignalstrengthcompatiblewiththatofthesumof
the M=1 waves in the isobaric description. The PWA attributes a comparable likelihood to both cases,
whichreflectsthattherealeventdistributioninthe5-dimensionalphasespacefollowsequivalentlywell
thedistributionsexpectedfromthetwoansa¨tze. But,theobservedenhancementofM=1wavesatsmall
FirstMeasurementofChiralDynamicsinπ−γ →π−π−π+ 5
)
2 COMPASS 2004
c 5
10
V/ m p -Pb fi p -p -p +Pb
e lip3
m
M
t' < 0.001 GeV2/c2

0
4 104
(

/

y
t
i
s
n
e 103
t
n
I
M=0
M=1
102
M=1, ChPT only
(M=1 points shifted by +0.005)
6.3
0.5 1 1.5 2 2.5
m [GeV/c2]
3p
Fig.4: PWAintensitiessummedseparatelyfortheM=0andM=1components. Totaluncertaintiesareshown.
Fluctuations of the systematic uncertainties, as discussed along with Fig. 6, were smoothed in the range 0.5<
m /(GeV/c2)<1,andtheobtaineduncertaintieswereaddedquadraticallytothestatisticalones.
3π
t(cid:48) lacks a theoretical explanation other than its chiral nature, and the comparison to the fit with isobaric
wavesispresentedhereonlyasawell-knownstartingpointoftheemployedPWA.
Itisspecificfortheveryforwardkinematicsstudiedherethattheproductionplanespannedbytheincom-
ingbeamandtheoutgoingX− systembecomeslessaccuratelydefinedast(cid:48)→0. Asaconsequence,the
PWAnotonlyshowstheexpectedMε=1+ states,butalsostateswithMε=1− resultingfromthelimited
resolutionintheazimuthalorientationofthe3π-system,whichappliesonlyforM(cid:54)=0. Aspartialwaves
arealsoidentifiedbytheirsignatureintheremaining4kinematicalvariablesthatarenotdistortedbyres-
olutioneffectsinthet(cid:48)→0limit,thetworeflectivitycontributionshavebeensummedupandattributed
tothewell-motivatedandexpectedMε=1+ intensities. Thevalidityofthisapproachwasconfirmedbya
specialMonteCarlosimulation,wheretheappearanceofnegative-reflectivitycontributionsarisingfrom
purelypositive-reflectivityinputstatesthroughresolutioneffectsoftheset-upwasconfirmed.
InordertocomparetheobservedM=1strengthatm <mlimwiththeChPTcrosssectionprediction,the
3π 3π
intensities obtained from PWA must be normalized to incoming beam flux and target thickness. While
thelatterisknowntohighprecision,theeffectivebeamfluxisinfluencedbyavarietyofeffectswhichare
lesswellcontrolled. Thebeamintensitywasnotmonitoredwithhighprecision,andabsolutetriggerand
detectionefficiencieshavetobemodeled. Themethodemployedheretoovercometheseuncertaintiesis
basedonthefreedecayofthekaoncomponentinthebeam[10]. AscanbeseeninFig.2,theobserved3-
pionfinalstatecontainsacontributionfromkaondecaysK−→π−π−π+. Sincethefractionofkaonsin
thebeamandtheirdecaykinematicsareknowntoamuchbetterprecisionthanthestatisticaluncertainty,
the observed kaon strength was used to determine the effective luminosity. Uncertainties in the Monte
Carlo description of the experimental setup cancel out, since they affect the K− →π−π−π+ decay and
theπ−γ →π−π−π+ reactioninasimilarway.
6 TheCOMPASSCollaboration
· 3
10
)
2 1.4 COMPASS 2004
c
2/ p -Pb fi p -p -p +Pb
V
e 1.2
G 0.51 < m < 0.72 [GeV/c2]
3p

4
-
0 1.0
1 M=0
(

/
0.8 ChPT
y
t
i
s
n
0.6
e
t
n
I
0.4
0.2
· -3
10
0.0
0 1 2 3 4 5 6 7 8 9 10
2 2
t' [GeV /c ]
Fig.5: PWAintensitiesfortheinvestigatedlow-massrange. Eacht(cid:48) binrepresentsanindependentfittothedata,
yieldingsimulaneouslythetwovaluesfortheM=0andthechiralintensity.
In Fig. 6 the real-photon absolute cross section is shown. It has been obtained by taking into account
the effective luminosity for the chiral amplitude and dividing out the quasi-real photon density factor
as given in Eq. (1). A good agreement with the leading order ChPT prediction [1] is observed. This is
expected since in ChPT loop effects and resonances are supposed to become important only at higher
masses[7].
The systematic uncertainties shown in the figures contain the following components: (i) the variation
due to the fitting model; as different fit models gave results with similar values for the likelihood, we
attributed the corresponding variations of the wave intensities as systematic uncertainty; (ii) the uncer-
tainty originating from the luminosity determination, which is also indicated separately in Fig. 6; (iii)
thefullcalculationofthee.m.radiativecorrectionsisnotyetavailableforπ−γ →π−π−π+,incontrast
tothecaseofπ−γ →π−π0π0. Afirstestimateindicatesthatthiscorrectioniswellbelow5%[11]. All
thesesystematicuncertaintiessumuptoabout18%intotal.
Inconclusionwehavemeasuredtheπ−γ →π−π−π+crosssectionintheregionm <5m ,withatotal
3π π
uncertaintyofabout20%. ThemeasuredpointsareingoodagreementwiththeChPTprediction. Atthis
levelofaccuracy,ChPTthereforeprovidesagooddescriptionofthestrongpion-pioninteractionsatlow
energies,includingthecouplingtoquasi-realphotonsviathePrimakoffprocess.
We gratefully acknowledge the support of the CERN management and staff as well as the skills and
efforts of the technicians of the collaborating institutions. The authors thank N. Kaiser for instructive
andhelpfuldiscussions.
FirstMeasurementofChiralDynamicsinπ−γ →π−π−π+ 7
] 1.2
b COMPASS 2004
m[ p -g fi p -p -p +

g 1.0 from p -Pb fi p -p -p +Pb
s
Fitted ChPT Intensity
0.8
Leading Order ChPT Prediction
0.6
0.4
Full Systematic Error
0.2
Luminosity Uncertainty
0.0
0.45 0.5 0.55 0.6 0.65 0.7
m [GeV/c2]
3p
√
Fig.6: Crosssectionforπ−γ →π−π−π+ asafunctionofthetotalcollisionenergy s=m . Theerrorbars
3π
showonlythestatisticalerror. Theevolutionofthesystematicuncertainty,asdiscussedinthetextandsmoothed
overthebins,isindicatedasdashedline.
References
[1] N.KaiserandJ.M.Friedrich,Eur.Phys.J.A36,181(2008),arXiv:0803.0995[nucl-th].
[2] J.Gasser,M.A.Ivanov,andM.E.Sainio,Nucl.Phys.B745,84(2006),arXiv:0602234[hep-ph].
[3] COMPASS-IIProposal,http://cdsweb.cern.ch/record/1265628/files/SPSC-P-340.pdf
(2010).
[4] P.Abbonetal.(COMPASSCollaboration),Nucl.Instrum.Meth.A577,455(2007),
arXiv:0703049[hep-ex].
[5] H.Primakoff,Phys.Rev.81,899(1951).
[6] I.Y.PomeranchukandI.M.Shmushkevich,Nucl.Phys.23,452(1961)
[7] N.Kaiser,Nucl.Phys.A848,198(2010),arXiv:1007.5277[hep-ph].
[8] M.Alekseevetal.(COMPASSCollaboration),Phys.Rev.Lett.104,241803(2010),
arXiv:0910.5842[hep-ex].
[9] M.Perl,Highenergyhadronphysics,Wiley-Intersciencepublications(Wiley,1974).
[10] S.Grabmu¨ller,HADRON2011proceedings(2011),arXiv:1108.6039[hep-ex].
[11] N.Kaiser,Eur.Phys.J.A46,373(2010),andprivatecommunication.