Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
First
measurement
of
the
helicity
asymmetry
E in
η
photoproduction
on
the
proton
I. Senderovich
b,
B.T. Morrison
b,
M. Dugger
b,
B.G. Ritchie
b,
∗
,
E. Pasyuk
b,
R. Tucker
b,
J. Brock
ag,
C. Carlin
ag,
C.D. Keith
ag,
D.G. Meekins
ag,
M.L. Seely
ag,
D. Rönchen
aq,
M. Döring
l,
ag,
P. Collins
b,
f,
K.P. Adhikari
z,
D. Adikaram
z,
1,
Z. Akbar
k,
M.D. Anderson
aj,
S. Anefalos Pereira
o,
R.A. Badui
j,
J. Ball
g,
N.A. Baltzell
a,
ae,
1,
M. Battaglieri
p,
V. Batourine
ag,
I. Bedlinskiy
t,
A.S. Biselli
i,
S. Boiarinov
ag,
W.J. Briscoe
l,
W.K. Brooks
ah,
ag,
V.D. Burkert
ag,
D.S. Carman
ag,
A. Celentano
p,
S. Chandavar
y,
G. Charles
s,
L. Colaneri
q,
ac,
P.L. Cole
m,
M. Contalbrigo
n,
O. Cortes
m,
V. Credé
k,
A. D’Angelo
q,
ac,
N. Dashyan
an,
R. De Vita
p,
E. De Sanctis
o,
A. Deur
ag,
C. Djalali
ae,
R. Dupre
s,
H. Egiyan
ag,
w,
A. El Alaoui
ah,
L. El Fassi
z,
L. Elouadrhiri
ag,
P. Eugenio
k,
G. Fedotov
ae,
ad,
S. Fegan
p,
A. Filippi
r,
J.A. Fleming
ai,
2,
A. Fradi
s,
B. Garillon
s,
Y. Ghandilyan
an,
G.P. Gilfoyle
ab,
K.L. Giovanetti
u,
F.X. Girod
ag,
g,
D.I. Glazier
aj,
J.T. Goetz
y,
W. Gohn
h,
3,
E. Golovatch
ad,
R.W. Gothe
ae,
K.A. Griffioen
am,
M. Guidal
s,
L. Guo
j,
ag,
K. Hafidi
a,
H. Hakobyan
ah,
an,
C. Hanretty
al,
k,
1,
M. Hattawy
s,
K. Hicks
y,
D. Ho
e,
M. Holtrop
w,
S.M. Hughes
ai,
Y. Ilieva
ae,
l,
D.G. Ireland
aj,
B.S. Ishkhanov
ad,
D. Jenkins
ak,
H. Jiang
ae,
H.S. Jo
s,
K. Joo
h,
S. Joosten
af,
D. Keller
al,
y,
G. Khachatryan
an,
M. Khandaker
m,
x,
A. Kim
h,
F.J. Klein
f,
V. Kubarovsky
ag,
M.C. Kunkel
ao,
P. Lenisa
n,
K. Livingston
aj,
H.Y. Lu
ae,
I.J.D. MacGregor
aj,
P. Mattione
e,
B. McKinnon
aj,
C.A. Meyer
e,
T. Mineeva
ap,
V. Mokeev
ag,
ad,
R.A. Montgomery
o,
A. Movsisyan
n,
C. Munoz Camacho
s,
P. Nadel-Turonski
ag,
f,
l,
L.A. Net
ae,
S. Niccolai
s,
G. Niculescu
u,
I. Niculescu
u,
M. Osipenko
p,
K. Park
ag,
ae,
v,
4,
S. Park
k,
P. Peng
al,
W. Phelps
j,
S. Pisano
o,
O. Pogorelko
t,
J.W. Price
c,
Y. Prok
z,
al,
A.J.R. Puckett
h,
M. Ripani
p,
A. Rizzo
q,
ac,
G. Rosner
aj,
P. Roy
k,
F. Sabatié
g,
C. Salgado
x,
D. Schott
l,
j,
R.A. Schumacher
e,
E. Seder
h,
A. Simonyan
an,
Iu. Skorodumina
ae,
ad,
G.D. Smith
ai,
D.I. Sober
f,
N. Sparveris
af,
S. Stepanyan
ag,
P. Stoler
aa,
I.I. Strakovsky
l,
S. Strauch
ae,
V. Sytnik
ah,
Ye Tian
ae,
M. Ungaro
ag,
h,
H. Voskanyan
an,
E. Voutier
s,
N.K. Walford
f,
X. Wei
ag,
M.H. Wood
d,
ae,
N. Zachariou
ae,
L. Zana
ai,
w,
J. Zhang
ag,
z,
Z.W. Zhao
z,
ae,
ag,
I. Zonta
q,
ac aArgonneNationalLaboratory,Argonne,IL 60439,USAbArizonaStateUniversity,Tempe,AR 85287-1504,USA
cCaliforniaStateUniversity,DominguezHills,Carson,CA90747,USA dCanisiusCollege,Buffalo,NY,USA
eCarnegieMellonUniversity,Pittsburgh,PA 15213,USA fCatholicUniversityofAmerica,Washington,DC20064,USA
gCEA,CentredeSaclay,Irfu/ServicedePhysiqueNucléaire,91191Gif-sur-Yvette,France hUniversityofConnecticut,Storrs,CT 06269,USA
iFairfieldUniversity,Fairfield,CT06824,USA jFloridaInternationalUniversity,Miami,FL 33199,USA
*
Correspondingauthor.E-mailaddresses:senderov@jlab.org(I. Senderovich),barry.ritchie@asu.edu(B.G. Ritchie).
1 Currentaddress:NewportNews,Virginia23606,USA. 2 Currentaddress:EdinburghEH93JZ,UnitedKingdom. 3 Currentaddress:Lexington,Kentucky40506,USA. 4 Currentaddress:Norfolk,Virginia23529,USA. http://dx.doi.org/10.1016/j.physletb.2016.01.044
kFloridaStateUniversity,Tallahassee,FL 32306,USA
lTheGeorgeWashingtonUniversity,Washington,DC20052,USA mIdahoStateUniversity,Pocatello,ID 83209,USA
nINFN,SezionediFerrara,44100Ferrara,Italy
oINFN,LaboratoriNazionalidiFrascati,00044Frascati,Italy pINFN,SezionediGenova,16146Genova,Italy
qINFN,SezionediRomaTorVergata,00133Rome,Italy rINFN,SezionediTorino,10125Torino,Italy
sInstitutdePhysiqueNucléaire,CNRS/IN2P3andUniversitéParisSud,Orsay,France tInstituteofTheoreticalandExperimentalPhysics,Moscow117259,Russia uJamesMadisonUniversity,Harrisonburg,VA 22807,USA
vKyungpookNationalUniversity,Daegu702-701,RepublicofKorea wUniversityofNewHampshire,Durham,NH 03824-3568,USA xNorfolkStateUniversity,Norfolk,VA 23504,USA
yOhioUniversity,Athens,OH 45701,USA zOldDominionUniversity,Norfolk,VA 23529,USA aaRensselaerPolytechnicInstitute,Troy,NY 12180-3590,USA abUniversityofRichmond,Richmond,VA 23173,USA acUniversita’diRomaTorVergata,00133Rome,Italy ad
SkobeltsynInstituteofNuclearPhysics,LomonosovMoscowStateUniversity,119234Moscow,Russia aeUniversityofSouthCarolina,Columbia,SC 29208,USA
afTempleUniversity,Philadelphia,PA19122,USA
agThomasJeffersonNationalAcceleratorFacility,NewportNews,VA 23606,USA ahUniversidadTécnicaFedericoSantaMaría,Casilla110-VValparaíso,Chile aiEdinburghUniversity,EdinburghEH93JZ,UnitedKingdom
ajUniversityofGlasgow,GlasgowG128QQ,UnitedKingdom akVirginiaTech,Blacksburg,VA 24061-0435,USA alUniversityofVirginia,Charlottesville,VA 22901,USA
amCollegeofWilliamandMary,Williamsburg,VA 23187-8795,USA anYerevanPhysicsInstitute,375036Yerevan,Armenia
aoForschungszentrumJülich,InstitutfürKernphysik,52425Jülich,Germany apUniversityofWaterloo,InstituteforQuantumComputing,Waterloo,Ontario,Canada aqHISKPandBCTP,UniversitätBonn,53115Bonn,Germany
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Articlehistory:
Received26November2015
Receivedinrevisedform21January2016 Accepted22January2016
Availableonline26January2016 Editor:D.F.Geesaman
Keywords:
Etaphotoproduction Polarizationobservable Helicityasymmetry
Resultsarepresentedforthefirstmeasurementofthedouble-polarizationhelicityasymmetryE forthe
η
photoproduction reactionγ
p→η
p.DatawereobtainedusingtheFROzenSpinTarget(FROST)with the CLASspectrometerin HallB atJeffersonLab,covering arangeofcenter-of-mass energy W from thresholdto2.15 GeV andalargerangeincenter-of-masspolarangle.Asaninitialapplicationofthese data,theresultshavebeenincorporatedintotheJülich–Bonnmodeltoexaminethecasefortheexistence ofanarrowN∗resonancebetween1.66and1.70 GeV.Theadditionofthesedatatotheworlddatabase resultsinmarkedchangesinthepredictionsfortheE observablefromthatmodel.Furthercomparison withseveraltheoreticalapproachesindicatesthesedatawillsignificantlyenhanceourunderstandingof nucleonresonances.©2016PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Muchactivityisbeingdevotedtoestablishingthedetailsofthe excitation spectrum of the nucleon in order to deepen our un-derstanding of that fundamental strongly-interacting three-quark system.Duetothebroadwidthsofthenucleonexcitations(ofthe orderof100–300 MeV),thestatesoverlapin themassspectrum. Thus, disentangling the individual states to identify their exact massesandquantumnumbershasbeenquitedifficult.Whilesome resonancesare well established,fewer stateshave beenobserved thanmostconstituentquarkmodels andLatticeQCDcalculations predict[1].Anadditionalcomplexityarisesbecause,beyond reso-nancestateswithtypicalwidths,approachesbasedonchiralquark solitonsalsopredictstateswithfarnarrowerwidthsthando con-stituentquarkmodels,including,forexample,an N12+ state with awidthof40 MeV orless[2–6]atabout1.7 GeV;thisparticular statemay havebeenobservedin
η
photoproduction onthe neu-tron[7–9].Sincedifferentialcrosssectionmeasurementsaloneare insuffi-cienttolocatetheunderlyingresonancestatesordeterminetheir properties,attentionhasturnedtopolarizationobservables.
Polar-ization observables involve interferences between sets of ampli-tudes,sotheirmeasurementcanprovidestringenttestsfor predic-tionsofthephotoproductionprocessandhelpsortoutambiguities in the theoretical description of the reaction in terms the reso-nances involved. One such polarization observable is the helicity asymmetry E in pseudoscalar meson photoproduction, which is thenormalizeddifferenceinphotoproductionyieldwhenspinsof theincident photonandalongitudinally-polarized target are par-allel and anti-parallel. Formally, this observable is defined as a modulationofthecenter-of-massdifferentialcrosssectiond
σ
/d
0throughtherelation
d
σ
d=
dσ
d0 1
−
PzTP◦γE,
(1) where PTz specifies the degree oflongitudinal target polarization and Pγ◦ is the circular polarization fractionof the incident pho-tonbeam. Thisasymmetryisgenerallyexpressedasa functionof thecenter-of-massenergyW andthepolarangleoftheproduced mesoninthecenter-of-massframecos
θ
cm.Pion photoproduction studies have contributed greatly to the knowledge of the nucleon resonance spectrum. Recent
measure-ments ofspin observables inpion photoproduction [10–14] have illustrated the power of polarization observables to clarify that spectrum.Evenso,manyambiguitiesstillexistandmanypredicted states remain unobserved. Thoughpion photoproduction offers a largercrosssection,thephotoproductionof
η
mesonsexhibitsthe interesting feature that the process excludes contributions from resonanceswithisospinI=
3/
2,therebyisolatingtheN∗(I
=
1/
2)
states.The
η
photoproductionprocess ontheprotonthus actsas an “isospin filter” for the nucleon resonance spectrum, resulting in a useful tool fordisentangling the different states, and is es-pecially importantin finding andinvestigatingstatesthat do not couplestronglytopions.2. Theexperiment
Themeasurementsreportedhereareanintegral partofa pro-gram atJeffersonLab toachieve a“complete” experimentforthe
η
photoproductionprocess,wherebyallthehelicityamplitudesare determined forphotoproductionof that pseudoscalarmeson. The programbeganwithmeasurementsoftheunpolarizeddifferential crosssection ddσ0 [15,16] usingthelargesolid angleCEBAFLarge AcceptanceSpectrometer(CLAS)[17],andthebremsstrahlung pho-ton taggerhoused inJefferson LabHall B [18].For the measure-mentsreportedhere,circularly polarizedphotonbeamswere pro-ducedbypolarizationtransferfromthepolarizedelectronbeamof theCEBAFaccelerator,whichwasincidentonanamorphous radi-atorofthephotontagger.Thetargetnucleons forthe photoproductionprocess werefree protons in frozen butanol (C4H9OH) beads inside a 50-mm-long
targetcup [19].The protonsofthe hydrogenatomsinthis mate-rialwere dynamicallypolarizedalong thephotonbeamdirection. Thelongitudinal target polarization PTz wasdetermined with nu-clear magnetic resonance measurements, and averaged 82
±
5%. Tominimizesystematicuncertainties,theorientationofthetarget polarization directionwas flipped every few days of data-taking betweenbeingalignedandanti-alignedwiththedirectionofthe incomingphoton beam.Thehelicityofthebeamwas flippedata rateof30 Hz.Final state particles resulting from photoproduction were de-tectedusingCLAS,asetofsixidenticalchargedparticledetectors installed in a toroidal magneticfield. The principal CLAS subsys-tems requiredfor thisstudy were the drift chamber systems for tracking charged particles [20], a scintillator-based time-of-flight system [21], and a start counter array which determined when charged particles passed from the target into the detection re-gion [22]. The energy and polarization information for incident photonswasprovidedbythephotontagger.
3. Analysis
To determine the helicity asymmetry E in a discrete event countingexperiment,Eq.(1)isinvertedtoformtheasymmetry
E
= −
1|
PTz| |
Pγ◦|
N+−
N− N++
N−,
(2)wherethedetectoracceptance cancels.Thecross sectionsare re-placedbyN+andN−,whicharethenumberof
η
mesonscounted in beam-target helicity alignedand anti-aligned settings, respec-tively. The background from non-η
final states and those from events arising fromthe unpolarized nucleons within the butanol aresubtractedbeforeformingthisasymmetry.Determination of the E observable requires knowledge ofthe degree of polarization for both the photon beam and the target
proton. The photon beam polarization is calculated from the in-cident photonenergy Eγ relative tothebremsstrahlungendpoint (E
˜
=
Eγ/E
e−)viatheexpressionPγ◦
=
Pe4E
˜
− ˜
E24
−
4E˜
+
3E˜
2,
(3)where Pe isthepolarization oftheelectronbeamincidentonthe amorphous radiatorwithin the photon tagger[23]; Pe was mea-suredwiththeHallBMøllerpolarimeterduringtheexperimentto be0
.
84±
0.
01.Eventsinthedetectorwerereconstructedinthefollowing man-ner.IndividualchargedtrackswerereconstructedintheCLASdrift chambersandmatchedtohitsinthetime-of-flight(TOF)andstart counter paddles. The particle identity was determined by com-bining the information on the momentum ofthe particle, which was determined by the driftchambersfrom thecurvature ofthe particle trajectory inthemagnetic field, andonthe speed ofthe particle (
β
) asdetermined fromthe timing information provided by thetagger,startcounter,andTOFsystems.Chargedtracksthat couldnotbereconstructedbyallofthesedetectorswererejected. A track was assumed to have the particle identity that allowed theclosestmatchbetweenthe4-momentum-computedβ
andthe measuredvalueofβ
.Anadditionalrequirementthatthemeasuredβ
was within±
0.
04 of theexpectedvalue was imposed onpion candidates,significantlysuppressingtheelectronbackground.Once the particle identity was established, a correction due to energy lossinthetarget anddetectormaterialswas performed,withthe 4-vectorvaluesadjustedaccordingly.Thetracksandtheeventasa wholewereassociatedtobeamphotonsbasedonconsistencywith the projectedvertextiming.Toavoidambiguity,onlyeventswith particlesmatchingexactlyonebeamphotonwerekept.The CLAS detectoris primarily a charged particle spectrome-ter,withelectromagneticcalorimetryconfinedtoanarrowangular range.Thus,
∼
94% ofthesignalinthisanalysisreliedonmissing massreconstructionoftheneutralη
fromthemeasured kinemati-calinformationoftheprotonrecoilingintotheCLAS(thedetection ofwhichwas required),withtheremainder ofeventshavingone or both charged pions from the decayη
→
π
+π
−π
0 detected.Events withasingle detectedchargedpionwererequiredtohave a missing masssquared greater than 0
.
06 GeV2/c
4,which is theonsetofthe remainingtwo-pionphase space.Events withboth a
π
+andπ
−detectedwererequiredtohavetheremainingmissing mass squaredclosetothat oftheπ
0 within thedetectorresolu-tion:0
.
008–0.
028 GeV2/c
4.The
η
photoproductiondatawereanalyzedtoextractthe helic-ity asymmetry E in 50 MeV-wide center-of-massenergy W binsand 0.2-wide center-of-mass production
η
polar angle (cosθ
cm)bins.Binningin W beginsnearthe
η
thresholdat1.
5 GeV.These binwidthswerechosentobalancebetweenminimizingstatistical uncertainties for the extraction while achieving the best energy resolutionfortheresonancespectrumandmostthorough knowl-edgeofthepolardistributionoftheresonancedecay.Theanalysis procedures described below were performed for each kinematic binseparately.To distinguish a photoproduced
η
from the background, fits were performedtotheinvariant massspectrawithmodelsofthe signal and backgroundincluded, asshownin Fig. 1. The integral of the fit shape of the background and the uncertainty of this integral from the error matrix estimated the background contri-bution. Since thedetectorresolution dominatedthe shapeof theη
enhancement, the signal was modeled as a Gaussian. Polyno-mialswere used tomodelthe background,withtheorder ofthe polynomial increasedprogressively with every fit iteration up to fifthorderaslongasthefitimprovementwas statistically signifi-cant. Specifically,improvementintheconfidencelevelbeyond0.5Fig. 1. Analysisexampleforthekinematicbin(1650<W<1700 MeV,−0.2<cosθcm<0.0).Leftpanel:Backgroundfittothemissingmassspectraforthetwohelicities
(higheramplitudeN−isgreen).Middlepanel:Backgroundsubtractionandnetηyield.Rightpanel:Yielddifference,withfittosidebandstodetermineoverallasymmetry offset.(Coloronline.)
was considered not significant. For the two W bins near the
η
threshold(W
<
1.
6 GeV), the step function-like drop-offin pho-toproducedsystemphasespacerequiredadifferentapproach.For thosebins,theerrorfunctionerf wasusedinadditiontothe poly-nomial,withitsamplitudeandtransitionwidthasfreeparameters. Asingle fitwas performedtothespectraofbothbeam helici-ties,withacommonmodelofthebackgroundshapeandcommon positionandwidthoftheη
enhancement;anexampleisshownin theleftpanel ofFig. 1.Themiddlepanel showsbackground sub-tractiontocomputethetotalη
yield(denominatorofEq.(2)).The unpolarizedbackgroundessentiallycancelsoutinthedifferenceof theyieldinthemissingmassspectraofthetwohelicities(N+andN−)seeninthenumeratorofEq.(2).Thesmallremainingoverall verticaloffsetseenforsomekinematicbinsmaybe dueto asym-metriesinthebroadpolarizedbackground,suchastheasymmetry which might exist for the
π
+π
− final state. These offsets were determinedwithafittothesidebands(asseenintherightpanel ofFig. 1), definedas±
3σ
fromthepeak center, wherethe cen-terandσ
valueswere derived fromthepreviously performedfit oftheη
enhancement. The normalizedasymmetry was thus cal-culatedfromthiscorrected difference ofhelicitiesdividedby the overallη
yield determined withthe background subtraction de-scribedabove.Aseparate study ofphotoproduction on a pure carbon target showed no evidence of peakingin the
η
mass region. Thus, no correction for the heavier nuclei in the target was required be-yondthesmoothbackgroundfittingdescribed.Helicityasymmetry extractionwas notperformedwhen thebackgroundexhibited an extremumunder theη
peak, (i.e. within±
1σ
of the peak cen-troid) to avoid serious ambiguities between the signal and the background shape. Additionally, analysis in a kinematic bin was abandoned when the totalη
yield uncertainty was greater than 30%.Missingmassenergyresolutionforthe
η
withCLASisasmooth functionofthekinematicspaceexploredhere.Therefore,thepeak widthsseen in theinitial independent analyses of theindividual kinematicbinswerecomparedandasmoothfunctionofthepeak widthacross thekinematicspacewasextracted. Yieldextractions werethen repeatedusingtheseconstraintsonthepeak widthto enforceconsistencywiththedetectorresolution.Statisticaluncertaintiesdominatedthesystematicuncertainties inallanalyzedbins,andareshowncombinedinthepresented re-sults.The systematicuncertainties includethe target polarization
PTz uncertainty (6.1%) and photon beam polarization P◦γ uncer-tainty(3.1%).
4. Resultsanddiscussion
The resultsforthe helicityasymmetry E are showninFigs. 2 and 3 for 1
.
5≤
W≤
2.
1 GeV. At threshold, the E observable is close to unity due to the dominance of the N(
1535)
12− reso-nance [24], and the results reported here are consistent within uncertainties withthisexpectation. As W increases,the presence of other resonances and the interferences of the various ampli-tudesrelatedtothoseresonancesgeneratea W -dependent struc-ture in E, which models of the production process attempt to describe. As examples of such models, shown in Fig. 2 are pre-dictionsfromphenomenologicalfitsbySAID[25],Jülich–Bonn[26]andANL-Osaka[27].
ThefigurealsoshowsanewfitwiththeJülich–Bonndynamical coupled-channelapproachincorporatingthedatareportedhere.In that framework, thehadronic scatteringamplitude isconstructed withapotential,generatedfromaneffectiveSU(3)Lagrangian, us-ingtime-orderedperturbationtheory,andtheamplitudeisiterated inaLippmann–Schwingerequationsuchthatunitarityand analyt-icityareautomaticallyrespected.
Thisnew fitalsosimultaneously incorporatedthe world data-bases for the pion-induced production of
η
N, Kand K
fi-nal states [28] and the partial-wave solution of the GW/DAC group [29] for elastic
π
N scattering. It also includes the world databases of pion andη
photoproduction off the proton up toW
∼
2.
3 GeV [30,26], in particular the recentMAMI results onT andF in
η
photoproduction[31].In order to achieve a good fit result, all parameters tied to the resonance states and to the photon interaction had to be modified from the values reported in Ref. [26]. The inclusion of these new E data also resulted in significant changes in the ex-tracted resonancepolepositions. Forexample, withthesenew E
data, the N(1710
)
1/
2+ resonance becomes 45 MeV heavier and 20 MeV widercomparedtoRef.[26],witha40%smaller branch-ingratiointotheη
N channel. Helicitycouplingsforthehigh-spinN(2190
)
7/
2−andN(
2250)
9/
2− resonances,whosepropertiesare difficulttodetermineingeneral,changetheirpolepositionsbyup to80 MeV in therealand100 MeV in their imaginarypartsdue tothesenewE data.That the E data reported here have such a large impact on the resonanceparameters mightappear surprising.Sincethe dif-ferentspinobservableshavedifferingcombinationsofamplitudes, the various observables will have differing degrees ofimpact on reducingtheuncertainties oftheparametervaluesextractedfrom afittothe experimentaldata.Inthepresentcase, those parame-tersarethefundamentalelectromagneticpropertiesofresonances, theirhelicitycouplingsatthepole.
Fig. 2. HelicityasymmetryE forγp→ηp asafunctionofW atvariousvaluesof cosθCMcomparedtoseveralphenomenologicalpredictions.
To study the variations in the statistical impacts on the pa-rametersofthenewJülich fitthat arisethrough theuseof mea-surementsof thedifferentspin observables, we have studiedthe conditionnumber
κ
forthecovariancematrixfoundinfittingthe observeddata.Theconditionnumberκ
isastandardtestfor diag-nosingmulticollinearity and, hence,the non-orthogonality ofthe model parameters on which the fit is based [32]. The condition numberκ
isdefinedasλ
max/λ
min,thatis,theratioofthelargestandsmallesteigenvalues.Geometrically,
√
κ
determinesthe ratio ofthe longest half-axisof the statisticaluncertainty ellipsoid di-videdbytheshortestone.Alargeκ
(say,greaterthan100[32])is asignofmoderatetostrongmulticollinearity,i.e. averyelongated statistical uncertainty ellipsoid; larger values ofκ
thus connote greater uncertaintyinthe correspondinghelicity couplings deter-minedfromthefit.Forthe present E data,we found
κ
≈
50, whileforthe other spinobservables(andeventhedifferentialcrosssection),κ
ranged from50 to400.Thus,intermsofminimizingtheuncertaintiesinFig. 3. Thehelicityasymmetry E forγp→ηp usingsmallerW binstoexplore thebehaviorofthehelicityobservablenearW∼1.7 GeV.PredictionsoftheJülich– Bonnmodelasdiscussedinthetextareshownbythesolidline.
theextractedparameters,theE observablemeasurementsreported hereindeedturnouttobeparticularlyimpactful.Thisunderscores thattheobservable E in
η
photoproductionisespeciallysuitedto disentangle electromagnetic resonance properties.With relatively few data points, this measurement offers a larger impact on the baryon spectrum,helicitycouplings,andevenhadronicdecay pa-rametersthanmightbeexpected.TurningnexttotheputativeN12+resonancenearW
∼
1.
7 GeV,Fig. 3showsourresultsfortheobservableE usingfinerW bins(of 20 MeV width). Coarser,0.4-wide binningin cos
θ
cm was used tocompensateforthenarrowenergybinning.Afittothisre-binned datausingtheJülich–Bonnformalismfoundthatthestructure ob-served at
∼
1.
7 GeV for the cosθ
cm bin centered at 0.
2 is dueto interferencebetween the E0+ and M+1 multipoles, which vary rapidlyatthisenergyduetothe N(1650
)
1/
2− andN(
1720)
3/
2+ resonances.Together withtheslowly varying E−2 multipole,these threemultipolesalonedescribetheE asymmetryquitewell with-out the need for an additional narrow resonance near 1.68 GeV. A similar analysis of the multipole content for the cosθ
cm bincentered at
−
0.
6 shows that theinterference ofthe E+0 and M+2multipoles(the lattercontainingthe N
(
1675)
5/
2−) isresponsible forthedip,withE+1,E−2 andM−2 necessarytobetterapproximate the full fit.Combined withthehints seenin Refs. [7,8], thedata presentedherefurthermotivateadditionalexperimental investiga-tionslookingatotherspinobservables.Insummary,wehavepresentedthefirst measurementsofthe helicity asymmetry E in photoproduction of
η
mesons from the proton. Initial investigation ofthese resultswith theJülich–Bonn dynamical coupled-channel approach show pronounced changes in the description of this variable when thesenew data are in-cluded,anddemonstratehowthesemeasurementsareparticularly impactful in constraining analyses of the excitation spectrum of the proton. With respect to the existence of an N12+ resonance near W∼
1.
7 GeV suggested previously [2–6], the dataobtained heredonotdemandthepresenceofsuchastate,butfurther mea-surements of other polarization observableswould be helpful in gainingadditionalinsightonthatquestion.Acknowledgements
The authors gratefullyacknowledge the work of the Jefferson Lab staff, as well as the support by the National Science Foun-dation, the JSC(JUROPA) facility at FZ Jülich, the French Centre National de la Recherche Scientifique and Commissariat à l’En-ergieAtomique,theItalianIstitutoNazionalediFisicaNucleare,the ChileanComisiónNacional deInvestigación Científicay Tecnológ-ica, the Science and Technology Facilities Council of the United Kingdom,andtheNationalResearchFoundationofKorea.This ma-terial is based upon work supported by the U.S. Department of Energy,OfficeofScience,OfficeofNuclear Physicsundercontract DE-AC05-06OR23177.
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