First measurement of the helicity asymmetry E in η photoproduction on the proton

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First measurement of the helicity asymmetry E in η

photoproduction on the proton

I. Senderovich, B.T. Morrison, M. Dugger, B.G. Ritchie, E. Pasyuk, R.

Tucker, J. Brock, C. Carlin, C.D. Keith, D.G. Meekins, et al.

To cite this version:

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

a_{ArgonneNationalLaboratory,Argonne,IL 60439,USA} b_{ArizonaStateUniversity,Tempe,AR 85287-1504,USA}

c_{CaliforniaStateUniversity,DominguezHills,Carson,CA90747,USA} d_{CanisiusCollege,Buffalo,NY,USA}

e_{CarnegieMellonUniversity,Pittsburgh,PA 15213,USA} f_{CatholicUniversityofAmerica,Washington,DC20064,USA}

g_{CEA,CentredeSaclay,Irfu/ServicedePhysiqueNucléaire,91191Gif-sur-Yvette,France} h_{UniversityofConnecticut,Storrs,CT 06269,USA}

i_{FairfieldUniversity,Fairfield,CT06824,USA} j_{FloridaInternationalUniversity,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

k_{FloridaStateUniversity,Tallahassee,FL 32306,USA}

l_{TheGeorgeWashingtonUniversity,Washington,DC20052,USA} m_{IdahoStateUniversity,Pocatello,ID 83209,USA}

n_{INFN,SezionediFerrara,44100Ferrara,Italy}

o_{INFN,LaboratoriNazionalidiFrascati,00044Frascati,Italy} p_{INFN,SezionediGenova,16146Genova,Italy}

q_{INFN,SezionediRomaTorVergata,00133Rome,Italy} r_{INFN,SezionediTorino,10125Torino,Italy}

s_{InstitutdePhysiqueNucléaire,CNRS/IN2P3andUniversitéParisSud,Orsay,France} t_{InstituteofTheoreticalandExperimentalPhysics,Moscow117259,Russia} u_{JamesMadisonUniversity,Harrisonburg,VA 22807,USA}

v_{KyungpookNationalUniversity,Daegu702-701,RepublicofKorea} w_{UniversityofNewHampshire,Durham,NH 03824-3568,USA} x_{NorfolkStateUniversity,Norfolk,VA 23504,USA}

y_{OhioUniversity,Athens,OH 45701,USA} z_{OldDominionUniversity,Norfolk,VA 23529,USA} aa_{RensselaerPolytechnicInstitute,Troy,NY 12180-3590,USA} ab_{UniversityofRichmond,Richmond,VA 23173,USA} ac_{Universita’diRomaTorVergata,00133Rome,Italy} ad

SkobeltsynInstituteofNuclearPhysics,LomonosovMoscowStateUniversity,119234Moscow,Russia

ae_{UniversityofSouthCarolina,Columbia,SC 29208,USA} af_{TempleUniversity,Philadelphia,PA19122,USA}

ag_{ThomasJeffersonNationalAcceleratorFacility,NewportNews,VA 23606,USA} ah_{UniversidadTécnicaFedericoSantaMaría,Casilla110-VValparaíso,Chile} ai_{EdinburghUniversity,EdinburghEH93JZ,UnitedKingdom}

aj_{UniversityofGlasgow,GlasgowG128QQ,UnitedKingdom} ak_{VirginiaTech,Blacksburg,VA 24061-0435,USA} al_{UniversityofVirginia,Charlottesville,VA 22901,USA}

am_{CollegeofWilliamandMary,Williamsburg,VA 23187-8795,USA} an_{YerevanPhysicsInstitute,375036Yerevan,Armenia}

ao_{ForschungszentrumJülich,InstitutfürKernphysik,52425Jülich,Germany} ap_{UniversityofWaterloo,InstituteforQuantumComputing,Waterloo,Ontario,Canada} aq_{HISKPandBCTP,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 reaction

γ

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



0

throughtherelation

d

σ

d



=

d

σ

d



0



1

−

P_zTP_◦γE



,

(1) where PT

z 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.

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 d_dσ₀ [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 PT_z 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

/

Ee−)viatheexpression

Pγ_◦

=

Pe

4E

˜

− ˜

E2

4

−

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-computed

β

andthe measuredvalueof

β

.Anadditionalrequirementthatthemeasured

β

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 massreconstructionoftheneutral

η

fromthemeasured kinemati-calinformationoftheprotonrecoilingintotheCLAS(thedetection ofwhichwas required),withtheremainder ofeventshavingone or both charged pions from the decay

η

→

π

+

π

−

π

0 _detected.

Events withasingle detectedchargedpionwererequiredtohave a missing masssquared greater than 0

.

06 GeV2

/

c4_{,which is the}

onsetofthe remainingtwo-pionphase space.Events withboth a

π

+and

π

−detectedwererequiredtohavetheremainingmissing mass squaredclosetothat ofthe

π

0 _{within thedetector}

resolu-tion:0

.

008–0

.

028 GeV2

_/

_c4_.

The

η

photoproductiondatawereanalyzedtoextractthe helic-ity asymmetry E in 50 MeV-wide center-of-massenergy W bins

and 0.2-wide center-of-mass production

η

polar angle (cos

θ

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 the

Fig. 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 positionandwidthofthe

η

enhancement;anexampleisshownin theleftpanel of

Fig. 1

.Themiddlepanel showsbackground sub-tractiontocomputethetotal

η

yield(denominatorofEq.(2)).The unpolarizedbackgroundessentiallycancelsoutinthedifferenceof theyieldinthemissingmassspectraofthetwohelicities(N₊and

N₋)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

±

3

σ

fromthepeak center, wherethe cen-terand

σ

valueswere derived fromthepreviously performedfit ofthe

η

enhancement. The normalizedasymmetry was thus cal-culatedfromthiscorrected difference ofhelicitiesdividedby the overall

η

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 the

η

peak, (i.e. within

±

1

σ

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 total

η

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

PT_z uncertainty (6.1%) and photon beam polarization P_◦γ uncer-tainty(3.1%).

4. Resultsanddiscussion

The resultsforthe helicityasymmetry E are shownin

Figs. 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, K

and 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 and

η

photoproduction off the proton up to

W

∼

2

.

3 GeV [30,26], in particular the recentMAMI results on

T 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-ingratiointothe

η

N channel. Helicitycouplingsforthehigh-spin

N

(

2190

)

7

/

2−andN

(

2250

)

9

/

2− resonances,whosepropertiesare difficulttodetermineingeneral,changetheirpolepositionsbyup to80 MeV in therealand100 MeV in their imaginarypartsdue tothesenewE data.

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.Theconditionnumber

κ

isastandardtestfor diag-nosingmulticollinearity and, hence,the non-orthogonality ofthe model parameters on which the fit is based [32]. The condition number

κ

isdefinedas

λ

max

/λ

min,thatis,theratioofthelargest

andsmallesteigenvalues.Geometrically,

√

κ

determinesthe ratio ofthe longest half-axisof the statisticaluncertainty ellipsoid di-videdbytheshortestone.Alarge

κ

(say,greaterthan100

[32]

)is asignofmoderatetostrongmulticollinearity,i.e. averyelongated statistical uncertainty ellipsoid; larger values of

κ

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,intermsofminimizingtheuncertaintiesin

Fig. 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 to

compensateforthenarrowenergybinning.Afittothisre-binned datausingtheJülich–Bonnformalismfoundthatthestructure ob-served at

∼

1

.

7 GeV for the cos

θ

cm bin centered at 0

.

2 is due

to 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 cos

θ

cm bin

centered at

−

0

.

6 shows that theinterference ofthe E+₀ and M+₂

multipoles(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.

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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