First results on nucleon resonance photocouplings from the γp → π+π−p reaction

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Physics

Letters

B

www.elsevier.com/locate/physletb

First

results

on

nucleon

resonance

photocouplings

from the

γ

p

→

π

+

π

−

p reaction

CLAS

Collaboration

E. Golovatch

ai

,

∗

,

V.D. Burkert

al

,

D.S. Carman

al

,

R.W. Gothe

aj

,

K. Hicks

ad

,

B.S. Ishkhanov

ai

,

V.I. Mokeev

al

,

∗∗

,

E. Pasyuk

al

,

b

,

S. Adhikari

m

,

Z. Akbar

n

,

M.J. Amaryan

ae

,

H. Avakian

al

,

J. Ball

g

,

L. Barion

r

,

M. Bashkanov

an

,

M. Battaglieri

t

,

I. Bedlinskiy

x

,

A.S. Biselli

k

,

e

,

S. Boiarinov

al

,

W.J. Briscoe

p

,

F. Cao

i

,

A. Celentano

t

,

P. Chatagnon

w

,

T. Chetry

ad

,

G. Ciullo

r

,

l

,

L. Clark

ao

,

B.A. Clary

i

,

P.L. Cole

q

,

M. Contalbrigo

r

,

V. Crede

n

,

A. D’Angelo

u

,

ah

,

N. Dashyan

as

,

R. De Vita

t

,

E. De Sanctis

s

,

M. Defurne

g

,

A. Deur

al

,

S. Diehl

i

,

C. Djalali

aj

,

M. Dugger

b

,

R. Dupre

w

,

H. Egiyan

al

,

M. Ehrhart

w

,

A. El Alaoui

am

,

L. El Fassi

aa

,

L. Elouadrhiri

al

,

P. Eugenio

n

,

G. Fedotov

ad

,

R. Fersch

h

,

ar

,

A. Filippi

v

,

Y. Ghandilyan

as

,

G.P. Gilfoyle

ag

,

K.L. Giovanetti

y

,

F.X. Girod

al

,

g

,

D.I. Glazier

ao

,

K.A. Griffioen

ar

,

M. Guidal

w

,

L. Guo

m

,

K. Hafidi

a

,

H. Hakobyan

am

,

as

,

N. Harrison

al

,

M. Hattawy

a

,

D. Heddle

h

,

al

,

M. Holtrop

ab

,

Y. Ilieva

aj

,

p

_,

_{D.G. Ireland}

ao

_,

_{E.L. Isupov}

ai

_,

_{D. Jenkins}

ap

_,

_{H.S. Jo}

z

,

w

_,

S. Johnston

a

,

K. Joo

i

,

M.L. Kabir

aa

,

D. Keller

aq

,

G. Khachatryan

as

,

M. Khachatryan

ae

,

M. Khandaker

q

,

W. Kim

z

,

A. Klein

ae

,

F.J. Klein

f

,

V. Kubarovsky

al

,

af

,

L. Lanza

u

,

P. Lenisa

r

,

K. Livingston

ao

,

I.J.D. MacGregor

ao

,

D. Marchand

w

,

N. Markov

i

,

B. McKinnon

ao

,

C.A. Meyer

e

,

R.A. Montgomery

ao

,

A. Movsisyan

r

,

C. Munoz Camacho

w

,

P. Nadel-Turonski

al

,

S. Niccolai

w

,

G. Niculescu

y

,

M. Osipenko

t

,

A.I. Ostrovidov

n

,

M. Paolone

ak

,

R. Paremuzyan

ab

,

K. Park

al

,

z

,

O. Pogorelko

x

,

J.W. Price

c

,

Y. Prok

ae

,

aq

,

D. Protopopescu

ao

,

M. Ripani

t

,

D. Riser

i

,

A. Rizzo

u

,

ah

_,

_{G. Rosner}

ao

_,

_{F. Sabatié}

g

_,

C. Salgado

ac

,

R.A. Schumacher

e

,

Y.G. Sharabian

al

,

Iu. Skorodumina

aj

,

G.D. Smith

an

,

D.I. Sober

f

,

D. Sokhan

ao

,

N. Sparveris

ak

,

I.I. Strakovsky

p

,

S. Strauch

aj

,

p

,

M. Taiuti

o

,

J.A. Tan

z

,

N. Tyler

aj

,

M. Ungaro

al

,

i

,

af

,

H. Voskanyan

as

,

E. Voutier

w

,

R. Wang

w

,

X. Wei

al

,

M.H. Wood

d

,

aj

,

N. Zachariou

an

,

J. Zhang

aq

,

Z.W. Zhao

j

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

c_{CaliforniaStateUniversity,DominguezHills,Carson,CA90747,USA} d_{CanisiusCollege,Buffalo,NY14208,USA}

e_{CarnegieMellonUniversity,Pittsburgh,PA 15213,USA} f_{CatholicUniversityofAmerica,Washington,DC 20064,USA} g_{Irfu/SPhN,CEA,UniversitéParis-Saclay,91191Gif-sur-Yvette,France} h_{ChristopherNewportUniversity,NewportNews,VA 23606,USA} i_{UniversityofConnecticut,Storrs,CT 06269,USA}

j_{DukeUniversity,Durham,NC 27708-0305,USA} k_{FairfieldUniversity,Fairfield,CT06824,USA} l_{Universita’diFerrara,44121Ferrara,Italy}

m_{FloridaInternationalUniversity,Miami,FL 33199,USA} n_{FloridaStateUniversity,Tallahassee,FL 32306,USA} o_{UniversitàdiGenova,16146Genova,Italy}

*

Correspondingauthor.

**

Principalcorrespondingauthor.

E-mailaddresses:golovach@jlab.org(E. Golovatch),mokeev@jlab.org(V.I. Mokeev).

https://doi.org/10.1016/j.physletb.2018.10.013

0370-2693/©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

p_{TheGeorgeWashingtonUniversity,Washington,DC20052,USA} q_{IdahoStateUniversity,Pocatello,ID 83209,USA}

r_{INFN,SezionediFerrara,44100Ferrara,Italy}

s_{INFN,LaboratoriNazionalidiFrascati,00044Frascati,Italy} t_{INFN,SezionediGenova,16146Genova,Italy}

u_{INFN,SezionediRomaTorVergata,00133Rome,Italy} v_{INFN,SezionediTorino,10125Torino,Italy}

w_{InstitutdePhysiqueNucléaire,CNRS/IN2P3andUniversitéParisSud,Orsay,France} x_{InstituteofTheoreticalandExperimentalPhysics,Moscow,117259,Russia} y_{JamesMadisonUniversity,Harrisonburg,VA 22807,USA}

z_{KyungpookNationalUniversity,Daegu41566,RepublicofKorea} aa_{MississippiStateUniversity,MississippiState,MS39762-5167,USA} ab_{UniversityofNewHampshire,Durham,NH 03824-3568,USA} ac_{NorfolkStateUniversity,Norfolk,VA 23504,USA}

ad_{OhioUniversity,Athens,OH 45701,USA} ae_{OldDominionUniversity,Norfolk,VA 23529,USA} af_{RensselaerPolytechnicInstitute,Troy,NY 12180-3590,USA} ag_{UniversityofRichmond,Richmond,VA 23173,USA} ah_{Universita’diRomaTorVergata,00133Rome,Italy} ai

SkobeltsynInstituteofNuclearPhysicsandPhysicsDepartment,LomonosovMoscowStateUniversity,119234Moscow,Russia aj_{UniversityofSouthCarolina,Columbia,SC 29208,USA}

ak_{TempleUniversity,Philadelphia,PA19122,USA}

al_{ThomasJeffersonNationalAcceleratorFacility,NewportNews,VA 23606,USA} am_{UniversidadTécnicaFedericoSantaMaría,Casilla110-V, Valparaíso,Chile} an_{EdinburghUniversity,EdinburghEH93JZ,UnitedKingdom}

ao_{UniversityofGlasgow,GlasgowG128QQ,UnitedKingdom} ap_{VirginiaTech,Blacksburg,VA 24061-0435,USA} aq_{UniversityofVirginia,Charlottesville,VA 22901,USA}

ar_{CollegeofWilliamandMary,Williamsburg,VA 23187-8795,USA} as_{YerevanPhysicsInstitute,375036Yerevan,Armenia}

a

r

t

i

c

l

e

i

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Articlehistory: Received4June2018

Receivedinrevisedform26August2018 Accepted8October2018

Availableonline12October2018 Editor:M.Doser

Keywords:

Twopionphotoproduction Resonancephotocouplings Baryonstate

Wereportthefirstexperimentalmeasurementsofthenine1-folddifferentialcrosssectionsforthe

γ

p→

π

+

π

−p reaction,obtainedwiththeCLASdetectoratJeffersonLaboratory.Themeasurementscoverthe invariant mass rangeofthe final statehadrons from1.6 GeV<W< 2.0 GeV. Forthe firsttime the photocouplingsofallprominentnucleonresonancesinthismassrangehave beenextractedfromthis exclusivechannel.Photoproductionoftwocharged pionsisofparticularimportancefortheevaluation ofthephotocouplingsforthe(1620)1/2−,(1700)3/2−,N(1720)3/2+,and(1905)5/2+resonances, whichhavedominantdecaysintothe

π π

N finalstatesratherthanthemoreextensivelystudiedsingle mesondecaychannels.

©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Studiesoftheexcitationspectrumofthenucleonandthe reso-nancephotocouplingsfromtheexperimentaldataonexclusive me-sonphotoproductionrepresentan importantavenue inthe explo-rationofthestronginteractioninthenon-perturbativeregime [1]. EvaluationoftheexcitednucleonspectrumwithinLatticeQCD [2] and continuous QCD approaches [3] adds to our understanding of how to relate the experimental results on the N∗ spectrum to thedynamicsof strongQCD andits emergence fromthe QCD Lagrangian.Inthepastdecade,dataonexclusivemeson photopro-ductionoffthenucleonhavebeenobtainedatCLAS, ELSA,MAMI, GRAAL,andLEPS[4–6,8,7,9–13].Thenewdataincludedifferential cross sections,aswell assingle-, double-, andtriple-polarization asymmetries.Thiswealthofdataprovidesforrigorousconstraints onthe reaction amplitudesthat are necessaryin orderto poten-tiallyaccesstheamplitudesfortwo-bodyfinal statessuch as

π

N,

η

N,

η

N, K Y ,and K∗Y ,to constrainthe

ω

p and

φ

p amplitudes, andtoextendtheknowledgeonthereactionmechanismsforthe double-mesonchannels

π π

N and

π η

N.

A global multichannel analysis of these data by the Bonn– Gatchina group [14–16] hasprovided strong evidencefor several new baryon states that have been reported in the recent edi-tion of the Review of Particle Properties (PDG) [17]. Strong

evi-dence for the existence of the N

(

1710

)

1

/

2+, N

(

1895

)

1

/

2−, and N

(

1900

)

3

/

2+ resonances has recently become available [18]. In particular, the CLAS photoproduction data in the K Y channels [19–22] has had a decisive impact on these findings. However, the

π

+

π

−p photoproductiondataisalsosensitivetonewbaryon states [23,24] andoffersanothercomplementarychanneltosearch forsuchstates.Nucleonresonancesestablishedinphotoproduction canalsobeobservedinexclusiveelectroproductionofftheproton at differentphoton virtualities Q2_{,with Q}2_{-independentmasses}

and hadronic decay widths. This signature provides strong evi-dencefortheexistenceofnewstates.Therefore,combinedstudies of the

π

+

π

−p photo- and electroproductiondata available from CLAS [24–26] canpotentially allowforthe validationofthe exis-tenceofmissingbaryonstatesinanearlymodel-independentway. These studies have alreadyprovided substantial evidence for the existenceofthenewN

(

1720

)

3

/

2+baryonstate [24].

Furthermore,the

π π

N channelsofallchargecombinationsare also a unique source of information on the production of sev-eral well-established resonances with masses above 1.6 GeV. So far, thephotocouplingsofmostN∗ and



∗ statesreportedinthe PDG were obtained from

π

N and multichannel photoproduction [14–16]. The

π π

N photoproduction data analyzed in the mass rangeabove1.6 GeVinclude

π

0

_π

0_{p data [7,10,11],butdonotyet}

How-ever,thetwo-bodymeson-baryonphotoproductionchannelshave limitedsensitivityto manyof theresonances with massesabove 1.6 GeV, which decay preferentially into the

π π

N final states. Moreover,the

π

+

π

−p channelhasthelargestcrosssectionamong thestudied

π π

N channels [27] andisneededtoverifytheresults ofothermeson-baryonchannels[28,29].

Inthispaperwe presentthefirstdataforthenine 1-fold dif-ferential

π

+

π

−p photoproductioncrosssectionsofftheprotonat invariant mass W from 1.6 GeV to 2.0 GeV.These data have al-lowedustodeterminetheresonantcontributionsfromafitofall measured differential cross sections combinedwithin the frame-work of the updated Jefferson Lab-Moscow State University (JM) reaction model [28–30]. By employing a unitarized Breit–Wigner (BW)ansatz[28],thephotocouplingsofallprominentresonances withmassesabove1.6 GeVwereextractedfromthe

π

+

π

−p pho-toproductiondataforthefirsttime.

2. Experiment

The data were collected using the CEBAF Large Acceptance

Spectrometer (CLAS) [32] in Hall B at the Thomas Jefferson Na-tionalAcceleratorFacility duringthe“g11a”datatakingperiodin 2004.Thephotonbeamwasproducedby anunpolarizedelectron beamof4.019 GeVenergyincidentuponagold-foilradiatorwitha thicknessof10−4 radiationlengths.Thephotonenergieswere de-terminedby detectingpost-bremsstrahlungelectronsinthe coun-ters of a tagging spectrometer [33]. The tagged-photon energy rangewas20–95%oftheelectronbeamenergy.Thetagged-photon beamimpingedona40-cm-longLH2 target.Thetemperatureand

pressure of this cryotarget were monitored throughoutthe g11a run. The mean calculated density of H2 was 0.0718 g/cm3 with

relativefluctuationsofabout0.1%[34,35].

TheCLASspectrometerwasbasedonasix-coilsuperconducting torusmagnetandincludedaseriesofdetectorssituatedinthesix azimuthallysymmetricsectorsaroundthebeamline.Threeregions of drift chambers (DC) [36] allowed for the tracking of charged reaction products in the toroidal magnetic field in the range of laboratorypolaranglesfrom8◦to140◦.Asetof342time-of-flight scintillators(TOF) [37] was usedtorecord theflight timesofthe chargedparticles. Start Counter(ST) scintillators [38] surrounded thetarget cell and were usedto determine the eventstart time. Thetriggerrequiredahitinthephotontaggerincoincidencewith STandTOFhitsinatleasttwo ofthesixsectorsofCLAS.During the g11a run period, the total number of triggers collected was

∼

2

×

1010,givinganintegratedluminosityof70 pb−1. 2.1.Eventselection

We required the detection of at least two charged particles in CLAS. The event sample consisted of four mutually exclusive topologies, one with all three final state hadrons detected and threeothersinwhichoneoutofthethreefinalstatehadronswas missing. Fortheseevents the momentum ofthe missingparticle wasreconstructedfromenergy-momentumconservation.The mo-menta of the reconstructed charged particles were corrected for energylossin thetarget materials [39]. The tagged-photon ener-gieswerealsocorrectedtakingintoaccountallknowntaggerfocal planemechanicaldeformations [40].

Akinematicfitwas usedfortheeventselectionto isolatethe

γ

p

→

π

+

π

−p reaction [41].Theeventspassingthekinematicfit withconfidencelevel(CL)above0.1wereaccepted.Thepull distri-butionsofthemeasuredkinematicquantitieswerefitbyGaussians centeredat0

.

00

±

0

.

05 with

σ

=

1

.

0

±

0

.

1.

Some events passed the CL cut with one or more tracks as-signedthe wrong particleidentity. Tofurtherclean up the event

sample,weemployedatimingcut

|

Ttag

−

Tstt

|

<

1

.

5 ns,whereTtag

isthevertextimeoftheincident photonmeasuredby thetagger andTstt isthevertextimeofthefinal stateparticlemeasuredby

theST.Thekinematicfitprobedallmatchedphotons,selectingthe hitwiththemaximumCLvalue. Thephotonenergymeasuredby thetaggerwascomparedwiththetotalenergycomputedfromthe four-momenta of the final state particles. This energy difference was foundtobe within



E

/

E

≈

0

.

5%, confirmingthe accuracyof the detectorandphoton beam calibrations andthe purityof the finaleventsample.

TheCLASdetectorcontainedinsensitiveregionsforparticle de-tection.Theseinsensitiveregionswereatthelocationsofthetorus coils,as well asatvery forward(

θ <

4◦) andverybackward an-gles(

θ >

140◦)inthelabframe [32].Thefinalstateparticleswere selected to be within the “fiducial” regions with reliable particle detectionefficiency,awayfromtheinsensitiveregions.Inaddition, thekinematic regionswherethe particledetectionefficiencywas lessthan5%wereexcluded.Overall,

≈

400million

π

+

π

−p events were selectedfortheevaluationoftheintegratedanddifferential crosssectionsexceedingbyafactorof

∼

50thestatisticspreviously collected inthischannel [42].An uncertaintyof3% fortheevent selectionwasdeterminedfromthemismatchbetweenthefraction ofselected

π

+

π

−p eventsinthekinematicfitsoftheMonteCarlo (MC)sampleandthemeasureddata.

2.2. Crosssectionevaluation

Studies of the

π

+

π

−p photoproduction reaction with an un-polarizedbeamoffan unpolarizedprotontargetatagivencenter ofmass(CM)energy W canbefullydescribed bya5-fold differ-ential crosssection. This crosssection hasa uniformdistribution overtheazimuthal CManglesforallfinalstate hadrons. Integrat-ingovertheazimuthalCMangleallowsthe5-folddifferentialcross sectiontobeexpressedasa4-folddifferentialcrosssection.

The crosssectionswere definedusingthree setsof four kine-matic variables. These included the permutationsof the two in-variant masses derived from pairing two of the three final state hadrons Mi j andMjk,where i, j,andk represent thefinal state

particles

π

+,

π

−, and p. The definitions for the final state CM angular variables are given in Fig. 1. There are two relevant CM angles in each set of variables, 1)

θ

i for one of the final state

hadronsi and2)

α

[ip][jk] betweenthetwohadronicplanesdefined by the three-momentaof the initialstate proton p andthe final statehadroni,andthethree-momentaoftheremainingfinalstate hadronpair jk.Thereactionkinematics aredescribed indetailin Refs. [29,43].

Theselected

π

+

π

−p eventsweresortedinto1625-MeV-wide

bins in W in the range from 1.6 GeV to 2.0 GeV. Each W bin

contained 16 bins in the invariant massesof the two final state hadronpairs,and14binsintheangles

θ

i and

α

[ip][jk].The4-fold differentialcrosssectionswere evaluatedfromthe

π

+

π

−p event yields collected in the 4-dimensional (4-D) bins, normalizing by thedetectionefficiencyineachbinandtheoverallbeam-target lu-minosity.Afterintegrationofthe4-folddifferential crosssections overthe threedifferentsets ofthreevariables,nine 1-fold differ-entialcrosssectionsweredeterminedfor1.6 GeV

<

W

<

2.0 GeV. These1-folddifferentialcrosssectionsinclude:

a) invariantmassdistributions:

dσ dMπ+p

,

dσ dMπ+π−

,

dσ dMπ−p

;

b) angulardistributionsover

θ

:

dσ d(−cosθπ−)

,

dσ d(−cosθπ+)

,

dσ d(−cosθp)

;

Fig. 1. Angularkinematicvariablesforthereactionγp→π+π−pintheCMframe. Thevariablesetwithi=π−, j=π+,andk=pincludestheangularvariablesfor

θπ−,thepolarangleoftheπ−,andα[π−p][π+p_],whichistheanglebetweenthe planesA andB,whereplane A ([π−p])isdefinedbythe3-momentaoftheπ−

andtheinitialstateprotonandplaneB ([π+p])isdefinedbythe3-momentaof theπ+ andthefinalstateproton p.Thepolarangleθp isrelevantfor theset withi=p, j=π+,andk=π−,whilethepolarangleθπ+belongstothesetwith i=π+, j=p,andk=π−.

c) angulardistributionsover

α

:

dσ dα_[π−p][π+p]

,

dσ dα_[π+p][π−p]

,

dσ dα_[pp][π+π−]

.

Each ofthe nine 1-fold differential cross sections,while gen-eratedby a common4-folddifferential crosssection, offers com-plementaryinformation.Noneofthemcanbecomputedfromthe others.Dataonallnine1-folddifferentialcrosssectionsare essen-tialtogaininsightintotheresonantcontributionsofthe

π

+

π

−p reaction.

Parity conservationmandatesthat the 4-fold differentialcross sectionsareequalattheangles

α

and2

π

−

α

.Inthecomputation ofthe1-folddifferentialcrosssections,wehavesetthemeasured 4-folddifferentialcrosssectionsattheangles

α

and2

π

−

α

equal totheiraveragevalue.Thisprocedurealtersthe1-folddifferential cross sections well within the uncertainties of the detector effi-ciency.

Thedetector efficiencywas computedusinga detailedGEANT

simulation of the CLAS detector called GSIM [44] and an event generator based on the older JM05 reaction model [45,46]. The kinematicalgridforthereconstructed

π

+

π

−p MonteCarloevents coincidedwiththatdescribedaboveforthemeasureddataevents. Thisgridcontained802,8165-Dcells:16(W bins)

×

16(invariant massbinsofthefirstfinalstatehadronpair)

×

16(invariantmass binsofthesecondfinalstatehadronpair)

×

14(finalstatehadron

θ

angle bins)

×

14 (final state hadron

α

anglebins). About half ofthecells residedoutsideoftheboundaryofthereactionphase space, andsuch cells were removed fromthe analysis. The small size of the cells allowed us to evaluate the detection efficiency reliablyeven forapproximatemodelingoftheeventdistributions withintheJM05modelversionincorporatedintotheevent genera-tor.UncertaintiesrelatedtothemismatchbetweentheactualCLAS efficiencyandthat determined fromthe simulationwere studied as discussed in Ref. [35] by comparing the normalized yields of

ω

electroproductioneventsinthe sixsectorsofCLAS.For experi-mentswithunpolarizedbeamandtarget,allcrosssectionsshould beuniformovertheazimuthalangle.Thedifferencesbetweenthe normalized

ω

yieldsinthedifferentCLASsectorswasabout4%.

The evaluation of the CLAS detection efficiency was further checked through the comparison of the integrals of the

normal-Fig. 2. RepresentativeintegralsI overthevariablesMπ−p,Mπ+π−,andα[pp][π+π−_]

asafunctionofθp at W from1.70 GeVto1.73GeVdefinedfromtheπ+π−p normalizedyieldsinthe4-Dcells.Theintegralscontainonlythe4-Dcellswhere the eventsfromallfourtopologieswereavailable.Theirvaluesforthefour dif-ferent topologies:allfinalstate hadronsdetected(blacktriangles) andwith the reconstructedmomentaforthep(redsquares),π−(bluecircles),andπ+(green upsidedowntriangles).Theintegralsoverthetwoinvariantmasseshave dimen-sionsof GeV2_.

izedyields ofthe

π

+

π

−p events forthefourdifferentfinalstate topologies (seeSection 2.1) overthe invariantmasses _Mπ−p and

Mπ+_π−,andtheangle

α

_[pp][π+π−].Theintegralswere calculated within the limited CLAS acceptance region where the 4-D cells contained theselected events ofall four topologies.The four in-tegrals I were obtained in each bin of W as a function of the CM angle

θ

p. Thedeviationof theintegralsfromthe four

differ-ent topologies was about 4%. This variation was assigned as the systematic uncertainty for the detection efficiency (see Table 1). A representative example for comparison between the values of thefourintegralsisshowninFig.2.

Thetaggedphotonfluxonthetargetwithinthedataacquisition live time was obtained by the standard CLAS gflux method [47]. Thenumberofphotonsforeachtaggercounterwas calculated in-dependentlyasNγ

=



·

Ne−,whereNe− isthenumberofelectrons

detectedbyataggercounterand



isthetaggingratio.Thetagging ratiowasdeterminedbyplacingatotalabsorptioncounterdirectly inthephotonbeamatlowintensityanddeterminingtheratioof thenumberofbeamphotonsandthenumberofelectronsdetected incoincidenceinthetagger.Theglobalnormalizationuncertainty derivedfromtherun-to-runvarianceandtheestimated normaliza-tionvariancewiththeelectronbeamcurrenttogether werefound tobe3.5%,employingthemethoddescribedinRef. [35].

Inthedeterminationofthefullyintegratedand1-fold differen-tialcross sections,thecontributionsfromthe insensitiveareasof CLASweretakenintoaccountbyextrapolatingthe4-fold differen-tialcrosssections.Asastarting point,theevaluationofthe1-fold differential cross sections in the full acceptance was carried out inthefollowingway.Thecrosssectionvaluesdeterminedineach one-dimensional(1-D)binwithintheCLASacceptancewere multi-pliedbytheratioofthetotalnumberof4-Dbinsthatcontributed totheanalyzed1-Dbintothenumberofbinswithnon-zero effi-ciency(crosssectionset#1).

An improved extrapolation of the 4-fold

π

+

π

−p differential cross sections into the insensitive areasof CLAS was carriedout within theframework of the newJM17 model described in Sec-tion3.TheJM17modelparameterswerefittothedatawithinthe

Fig. 3. Fullyintegratedπ+π−p photoproduction crosssectionswithin theCLAS acceptance(blueopencircles) andinthe fullacceptanceafterthe initial4-fold differentialcrosssectionextrapolationintotheinsensitiveareas(blacktriangles– crosssectionset#1)andaftertheimprovedextrapolationwithintheframeworkof theJM17modelasdescribedinSection2.2(redsquares–crosssectionset#3).The CLASdataarecomparedwiththeSAPHIR[42] (greensquareswitherrorbars)and theABBHHM [48] (greencircleswitherrorbars)results.Thestatistical uncertain-tiesofourdataaresmallerthanthemarkersize,whilethesystematicuncertainties areshownbythehatchedareaatthebottomofthefigure.

Fig. 4. Representativeθp angulardistributionsat W from1.70 GeVto1.73 GeV. ResultsareobtainedwithintheCLASacceptance(bluecircles)andinthefull ac-ceptanceextrapolatingthecrosssectionintotheinsensitiveareasaftertheinitial crosssectionextrapolation(blacktriangles–crosssectionset#1)andwiththe im-provedextrapolationusingtheJM17model(redsquares–crosssectionset#3)as explainedinSection2.2.Theresultsobtainedbyextrapolatingthecrosssectioninto theinsensitiveareaswiththeinitialJM17modelparameters(crosssectionset#2) areshownbythegreenupsidedowntriangles.Theerrorbarsaredominatedbythe uncertaintyoftheextrapolationprocedure.

CLASacceptanceandthe4-folddifferentialcrosssectionsinthe in-sensitiveareaswerecomputedfromtheJM17model(crosssection set#2).Then,theJM17modelparameterswererefittoreproduce thecrosssectionsdeterminedin thefullacceptance,obtained af-ter filling the insensitive areas. The JM17 model with improved parameters was then used again for the evaluation of the cross sectionsintheinsensitiveareas ofCLAS,generatinga newsetof differential cross sections extrapolated into the insensitive areas of CLAS (cross section set #3). The uncertainties caused by this cross section extrapolation were assigned as half the difference betweenthe cross sectionsdetermined within the full andCLAS acceptances, which amounted to 12.0% for the integrated cross

Table 1

Summaryofthesystematicuncertaintiesforthefullyintegrated

π+π−p photoproductioncrosssections.The scaleuncertainties andpoint-to-pointuncertaintiesarelistedinthesecondandthird rows,respectively.

Source of uncertainty Contributiontofully

integratedπ+π−p crosssection,%

Fiducial area choice 4.0

Event selection 3.0

Run-to-runstabilityand global normalizationfactor

3.5

Efficiency from MC 4.0

ImpactoftheCLAS insensitiveareas

12.0

Total 14.0

sections.This uncertaintyisstrongly dependent onthe CM polar anglesofthefinalstatehadrons.Itwasfoundthatthetwosetsof nine1-folddifferentialcrosssectionsinthefullacceptanceagreed within theuncertainties ofthe data,accountingforboththe sta-tisticaland extrapolationuncertainties. Since thecross section of the JM17 model accountsfor the amplitude constraints imposed byparityconservation,the4-folddifferentialcrosssectionsat an-gles

α

and2

π

−

α

areequalwithintheinsensitiveareas.

Fig.3showsthefullyintegratedcrosssection withintheCLAS acceptance(bluecircles).Theotherpoints(blacktrianglesandred squares)arethecrosssectionswithinthefullacceptanceafterthe initialandimprovedcrosssection extrapolationsintothe insensi-tive areas of CLAS. Fig. 4 showsa representative example of the differentcross section angulardistributions fromthe initial cross section set#1 andthetwo subsequentcrosssection sets#2 and #3aftertheimprovedextrapolationsintotheinsensitiveareasfor the

θ

p CMangulardistributions.

Thesystematicuncertaintiesrelatedtotheselectionofthe fidu-cial areas were estimatedby comparing the cross sections com-putedwithtwodifferentminimumCLASdetectionefficiencycuts: 5%(nominal)and10%(increased).The4-folddifferentialcross sec-tioninsidetheexcludedareaswithsmalldetectionefficiencywas estimatedwithintheextrapolationproceduredescribedabove.The computedcrosssectionswiththeincreasedandnominaldetection efficiencycutsdifferbyabout4%aslistedinTable1.

The systematic uncertainties for the fully integrated

π

+

π

−p photoproduction cross sections are summarized in Table 1. The largest contributioncomes from the 4-fold differential cross sec-tionextrapolationintotheinsensitiveareasofCLAS.

3. Resultsandphysicsanalysis

Thefullyintegrated

π

+

π

−p photoproductioncrosssectionand representative examples of the nine 1-fold differential cross sec-tions are shown in Fig. 3, Fig. 5, and Fig. 6, respectively. We show the differential cross sections in the W bins centered at

1.71 GeV and 1.74 GeV, which correspond to the peak region

of the resonance-like structure observed in the W dependence of the

π

+

π

−p electroproduction cross sections [25]. The com-plete set of differential cross sections from this experiment can be found in the CLAS physics database [49]. The error bars for the cross sectionsshownin Figs. 5 and6 includethe uncertain-ties related to the extrapolation of the 4-fold differential cross sections into the insensitive areas of CLAS. The fully integrated cross sections from CLAS are consistent with the existing re-sults within the systematic uncertainties [42,48]. However, our fully integrated cross sections in the full acceptance are slightly above the existing results likely dueto the different approaches

Fig. 5. Descriptionoftheπ+π−p photoproductioncrosssectionsandthecontributionsfromtherelevantchannelsinferredfromtheCLASdatawithintheframeworkof theJM17modelforthefullyintegratedcrosssections(left)andarepresentativeexampleofthenine1-folddifferentialcrosssectionsatW from1.70 GeVto1.73 GeV (right)shownbydifferentlines:fullreactioncrosssections(solidred),π−++(dashedred),ρp (solidgreen),π+0(dashedblue),π+N(1520)3/2−(yellow),2π direct production(magenta),andπ+N(1685)5/2+(bluedot-dashed).Theerrorbarsincludethecombinedstatisticalandpoint-to-pointsystematicuncertainties.

Fig. 6. (Left)Fullyintegratedcrosssectionscomputedfromthefitsofthenine1-folddifferentialcrosssectionswith1.15<χ2

/d.p.<1.30 (redcurves)incomparison withthemeasuredintegratedcrosssections(pointswitherrorbars).Theerrorbarsincludethecombinedstatisticalandpoint-to-pointsystematicuncertainties.(Right) Representativeexampleof1-folddifferentialcrosssections(redcurves)andtheresonant/non-resonantcontributions(blue/greenbars)fromthefitswith1.15<χ2_/d.p.< 1.30 oftheCLASπ+π−p photoproductiondataatW from1.73 GeVto1.75 GeVwithintheframeworkoftheJM17model.Thequotedrangesfortheresonanceparameters wereobtainedfromthesetsoffitsthatresultedin1.15<χ2_{/d.p.<1.30 andshownbytheredcurves.}

used for the cross section extrapolations into the insensitive ar-eas. We consider estimates of the 5-fold differential cross sec-tions inthe insensitive areasfromthe JM17 model,outlined be-low, as reliable, since the nine 1-fold differential cross sections are well described within the acceptance as shown in Figs. 5

and6.

Data on theangulardistributions over thethree

α

angles de-scribedinSection2.2havebecomeavailableforthefirsttime.Also differentialcrosssectionsoverthefinalstatehadronCM

θ

i angles

(i

=

π

+,

π

−,p)offerinformationonthereactiondynamics differ-entfromthedistributionsovertheMandelstamt variableincluded in Ref. [42]. The firstresults on thenine 1-fold differential cross

Table 2

Startingvaluesforthehadronicdecaysparametersofthe excitednucleonstatesincorporatedintotheJM17model versionforthedescriptionoftheπ+π−p photoproduc-tiondata. Resonance Mass, GeV Total width, GeV Branching fractionto π πN,% N(1440)1/2+ 1.45 0.35 37 N(1520)3/2− 1.52 0.13 41 N(1535)1/2− 1.53 0.15 4 (1620)1/2− 1.63 0.15 93 N(1650)1/2− 1.65 0.14 7 N(1680)5/2+ 1.69 0.14 35 (1700)3/2− 1.70 0.30 86 N(1720)3/2+ 1.74 0.12 85 N(1720)3/2+ 1.72 0.12 68 (1905)5/2+ 1.88 0.33 87 (1910)1/2+ 1.89 0.28 12 (1950)7/2+ 1.93 0.29 61 N(2190)7/2− 2.19 0.50 40

sectionsmake itpossible toisolate theresonant contributions to the

π

+

π

−p reaction andto determinethe resonance photocou-plingsfromthischannel.

The photocouplings of the nucleon resonances in the mass

rangefrom1.6 GeVto2.0 GeVwere determined fromafitto all nine1-fold differentialcrosssectionsfrom

π

+

π

−p photoproduc-tion.First,weestablishedtherelevantmechanismscontributingto thisexclusivechannelfromtheirmanifestationsintheobservables. TheobservabledescriptionwasperformedstartingfromtheJM16 model [28,29] updated to describe the

π

+

π

−p photoproduction data(JM17model).The previousJM modelversions,described in Refs. [28–30],weresuccessfullyusedfortheextractionofthe nu-cleonresonanceelectrocouplings fromthe CLAS

π

+

π

−p electro-productiondata[31].TheJM17modelincorporatesallmechanisms thatcontributeto

π

+

π

−p electroproductionintheresonance re-gion with manifestations seen in the measured differential pho-toproductioncrosssections.Theseconsist ofthe

π

−



++,

π

+



0,

ρ

0_p,

_π

+_N

₍

₁₅₂₀

₎

₃

_/

₂−_,and

_π

+_N

₍

₁₆₈₅

₎

₅

_/

₂+ _meson-baryon chan-nels, as well as the direct production of the

π

+

π

−p final state withoutformation of intermediate unstable hadrons. The model-ingoftheseprocesseswasdescribedinRefs. [28,30,31,45,46].

Thedifferencesinthekinematicdependenceofthe

α

_[π−p][π+p]

angular distributions for

π

+

π

−p photo- and electroproduction were accountedfor inthe phenomenological parameterizationof the direct 2

π

production mechanisms of Ref. [30]. The

π

+

π

−p photoproductiondataat W

>

1

.

8 GeV requireimplementationof the

σ

p meson-baryon channel, which was parameterized by a 3-body contact term and an exponential propagator for the in-termediate

σ

meson. The magnitudes of the parameterized

σ

p photoproduction amplitudes were fit to the data in each bin of W independently.The contributionsfromall well established N∗ stateswithmasses

<

2

.

0 GeVwithobserved decaystothe

π π

N finalstates(listedinTable 2) wereincludedintothe

π



and

ρ

p meson-baryonchannelsofJM17.Theresonantamplitudeswere de-scribedinaunitarizedBreit–Wigneransatz[28] thataccountedfor restrictionsimposed by a generalunitaritycondition to the reso-nantcontributions[50].

The initial values for the

π



and

ρ

p decay widths were taken from analyses of the previous CLAS

π

+

π

−p electropro-duction data [28,29] for the N

(

1440

)

1

/

2+, N

(

1520

)

3

/

2−, and

(

1620

)

1

/

2− resonances.For other N∗ states in the massrange up to 2.0 GeV,we usedthe results ofRef. [17] forthe total de-cay widthand fromRef. [51] forthe

π



and

ρ

p decaywidths. Theparameters forthe N

(

2190

)

7

/

2− resonance weretaken from Ref. [17]. The initial resonance photocouplings were taken from

Refs. [17,24,52].Independent fitsofthe

π

+

π

−p photo- and elec-troproduction[25] crosssectionsassumingthecontributionsfrom the known resonances only, result in a factor of four difference of the branching fractions for the decays of the conventional N

(

1720

)

3

/

2+ resonance to the

ρ

N final state. Since resonance decay widths should be Q2 independent, it is impossibleto de-scribe both the

π

+

π

−p photo- and electroproductioncross sec-tions when only contributions from conventional resonances are taken into account. By implementing a new N

(

1720

)

3

/

2+ state with the mass, photo- and hadronic couplings starting from the valuesinRef. [24],asuccessfuldescriptionofall

π

+

π

−p differen-tialcross sectionsforphoto- and electroproductionwas achieved withQ2 _{independenthadronicdecaysfortheincludedresonances}

locatedatW

≈

1

.

7 GeV,thusvalidatingthecontributionfromthe N

(

1720

)

3

/

2+state [24].

Beforeextractionofthenucleonresonancephotocouplings,we validatedthemechanismsincorporatedinto theJM17model (de-scribed above) by confronting the model expectations and the measured cross sections. We consider the successful description ofthenine1-folddifferentialcrosssectionsasstrongevidencefor the proper accounting of all essential reaction contributions. We computedthenine 1-fold crosssections,aswell asthe contribu-tionsfromallmechanismsincorporatedintotheJM17model,with the model parameters adjusted to reproduce the data. A similar approach was used successfully for the extraction of the

γ

vpN∗

electrocouplings fromthe

π

+

π

−p electroproductiondata [28,29,

43] includedinthePDG [17].TheJM17modelreproduceswellthe

π

+

π

−p differentialcross sections for W

<

2

.

0 GeV (see Figs. 5

and

6

), witha

χ

2 _{per datapoint (}

_χ

2

_/

_d

_.

_{p)in individual W bins}

lessthan1.4.

As shown in Fig. 5, the individual contributing mechanisms havedistinctivedifferencesintheshapesinall nine1-fold differ-ential crosssections.The details oftheshapesof these contribu-tionsare determinedbytheunderlyingreactiondynamics. There-fore, the successful reproduction of the measured cross sections within the JM17 model provides confidence that this model in-corporatesallessentialcontributingmechanismsandoffersa rea-sonabledescriptionofthem.Furthermore,thisagreementprovides strongconfidencethatthismodelcanbeusedfortheextractionof theresonanceparameters.

The resonance photocouplings and the

π



and

ρ

p decay widthsweredeterminedfromthedatafit,wheretheywerevaried independently together with theparameters ofthe non-resonant amplitudes described in Refs. [28,29] and the magnitudes of the

σ

p photoproductionamplitudes.Theseparameters were sampled around their initial values,employing unrestricted normal distri-butionswithawidth(

σ

)ofmagnitude30%oftheirinitialvalues. Under this variation, the computed 1-fold differential cross sec-tions overlap the measured cross sections within the combined statistical uncertainties and point-to-point systematic uncertain-ties. In this way, we scanned the full space of the JM17 model resonant andnon-resonant parameters that provided comparable computed cross sections withthe data.For each trial set of the fit parameters,we computed thenine 1-fold differential

π

+

π

−p crosssectionsandestimatedthe

χ

2

_/

_d

_.

_p

_.

_{valuesinpoint-by-point}

comparisons. Theresonance photocouplings andthe

π



and

ρ

p decaywidthswererecordedfromthefitsovertheentireW range from1.6 GeVto2.0 GeVthatresultedin1

.

15

<

χ

2

_/

_d

_.

_p

_.

_<

₁

_.

_3.This

χ

2

_/

_d

_.

_p

_.

_{rangeamountsto requiringthat thecomputedcross}

sec-tionsfromthefitsbewithinthedatauncertainties.

The robustness of thefit is demonstratedin Fig.6 where the selectedcomputeddifferentialcrosssectionstogetherwiththe res-onant/non-resonantcontributionsareshownforW

=

1

.

74 GeVas a typicalexample.From theselectedfits, theuncertainties ofthe resonant contributionsare comparablewiththose forthe

experi-Table 3

Resonancephotocouplingsdeterminedfromanalysisoftheπ+π−p photoproductiondatafromthisworkincomparison withthepreviousresultsfromthePDGaverage[17] andfrommultichannelanalysis[7].

Resonances A1/2×103 fromπ+π−p GeV−1/2 A1/2×103 PDGranges GeV−1/2 A1/2×103 multichannel analysis [7] GeV−1/2 A3/2×103 fromπ+π−p GeV−1/2 A3/2×103 PDGranges GeV−1/2 A3/2×103 multichannel analysis [7] GeV−1/2 (1620)1/2− 29.0±6.2 30–60 55±7 N(1650)1/2− 60.5±7.7 35–55 32±6 N(1680)5/2+ −27.8±3.6 −18–−5 −15±2 128±11 130–140 136±5 N(1720)3/2+ 80.9±11.5 80–120 115±45 −34.0±7.6 −48–135 135±40 (1700)3/2− 87.2±18.9 100–160 165±20 87.2±16.4 90–170 170±25 (1905)5/2+ 19.0±7.6 17–27 25±5 −43.2±17.3 −55–−35 −50±5 (1950)7/2+ −69.8±14.1 −75–−65 −67±5 −118.1±19.3 −100–−80 −94±4 Table 4

Resonancemasses,totaldecaywidths,andbranchingfractionstothe

π πN finalstatesdeterminedfromtheπ+π−p photoproductiondata fortheexcitednucleonstateslistedinTable3.

Resonance Mass, GeV Total width, GeV Branching fractionto π πN,% (1620)1/2− 1.635±0.008 0.144±0.016 81–100 N(1650)1/2− 1.657±0.006 0.154±0.028 11–14 N(1680)5/2+ 1.686±0.005 0.118±0.020 20–28 N(1720)3/2+ 1.745±0.006 0.116±0.027 69–100 (1700)3/2− 1.704±0.008 0.295±0.035 79–100 (1905)5/2+ 1.883±0.019 0.327±0.069 70–100 (1950)7/2+ 1.943±0.018 0.230±0.088 37–77

mentaldata,suggestingunambiguousaccesstothesecontributions in the differential cross sections. The resonance photocouplings weredeterminedfromtheresonantcontributionsby employinga unitarizedBreit–Wigner ansatz [28]. The differences ofthe reso-nantandnon-resonantcontributions(seeFig.6)inthenine1-fold differentialcrosssections,inparticularintheCMangular distribu-tions,allowscleanresonancephotocouplingextractioneveninbins wheretheresonancecontributionissmallerthanthenon-resonant contribution.

The resonance parameters determined from the fits that fell within ourdefined

χ

2

_/

_d

_.

_p

_.

_{range were averaged andtheir mean}

valuesweretakenastheextractedresonanceparameters.The dis-persionintheseparameterswastakenastheassociatedsystematic uncertainty.

The resonance photocouplings extracted from this work are

listed in Table 3 and compared with the resonance

photocou-plingrangesandtheresultsofthemultichannelanalysisincluded in the PDG [17]. Our results were obtained with the resonance masses, total widths, and branching fractions to the

π π

N final states(

β

π πN) listedinTable 4.Theranges ofthebranching

frac-tionswerecomputedfromtherangesoftheresonancetotal(



tot)

andpartialdecaywidthstothe

π π

N finalstates(



π πN)obtained

inthedatafit.The



tot rangeslistedinTable4werecomputedas



π πN

/β

π πN withthemean



π πN valuesfromthedatafitandthe

β

π πN ranges fromthelastcolumnofTable4.Fortheresonances

with massesbelow 1.8 GeV, we employed additionalconstraints onthetotalandthe

π π

N partialdecaywidthsfromthesuccessful combinedfitofthe

π

+

π

−p photo- andelectroproductiondata [24,

25,53] with Q2-independentresonancemassesanddecaywidths. Thispowerfulconstraintconsiderablyimprovedknowledgeonthe N∗ totaland

π π

N partialdecaywidths,ascanbeseeninTable4

fromthecomparisonofthedecayparameteruncertaintiesfor res-onancesbelow1.8 GeVtothosewithmassesabove1.8 GeV.

There is good agreement in the magnitude and sign of the

photocouplingsbetweenourresultsandthephotocouplingranges in the PDG listings. On the other hand, for several resonances in Table 3, the photocouplings determined from the

multichan-nel analysisofRef. [7] aredifferentfromours.Implementationof our

π

+

π

−p photoproductiondataintothemultichannelanalyses willallowforexaminationofthesedifferencesandtoimproveour knowledge onthephotocouplingsandhadronicdecayparameters oftheresonanceslistedinTables3and

4

.

4. Summary

Thefirst resultsonnine 1-folddifferentialandfullyintegrated

π

+

π

−p photoproductioncrosssectionsofftheprotonintherange of W from1.6 GeVto2.0 GeVhavebecome availablefrom mea-surements with the CLAS detector at Jefferson Lab. These data

amount to a factor of

∼

50 increase in the number of events

from thisreaction compared to previous measurements. Analysis ofthesecrosssectionsofmuchimprovedaccuracyhasallowedus, by using theupdated JM17meson-baryon reactionmodel, to es-tablish all essentialcontributingmechanisms totheprocess from theirmanifestationsintheobservablesandtoextracttheresonant contributionstotheexperimentaldata.Thegooddescriptionofthe experimental dataachievedintheentireW rangeprovides confi-dence inthe procedurewe have usedto determine theresonant contributionstothedifferentialcrosssectionsfromthedatafit.

Using aunitarizedBreit–Wigneransatz [28,50],whichallowed us to account for the restrictions imposed by a general unitar-ity condition on the resonant amplitudes, the resonance pho-tocouplings were determined from the resonance contributions. For the first time, the nucleon resonance photocouplings for the states in the mass range from 1.6 GeV to 2.0 GeV were deter-mined fromtheanalysisofthedataon

π

+

π

−p photoproduction. The

(

1620

)

1

/

2−,

(

1700

)

3

/

2−,N

(

1720

)

3

/

2+,and

(

1905

)

5

/

2+ resonance photocouplings were extractedfromthe

π

+

π

−p pho-toproduction channelwithmuch improvedaccuracycompared to previous

π

N analyses,becauseofthepreferential decaysofthese resonancestothe

π π

N finalstateswithbranchingfractionsabove 70%. The results on

π π

N photoproduction from this work and multichannelanalyses[7,14,15] arenowthemajorsourceof infor-mation on thephotocouplings of thesestates.The resultson the N∗ photocouplingsfrom

π

+

π

−p photoproductionshowgood con-sistencywiththerangesforthephotocouplingsfromthePDG list-ings [17],whichisanimportantresultconsideringthemuchlarger cross sections of this channel in comparison with the

π

0

_π

0_p

channel, which were analyzed so far within the W range ofour measurements [27]. Implementation of our data into the cou-pled channel analyses will help to check further the extraction of theresonance photocouplingswithin the JM17model.The re-sultspresentedinthispaperpavethewayforthefuturecombined analysis of the

π

+

π

−p photo- and electroproduction data from CLAS,whichhasalreadyrevealedsubstantialevidenceforthenew N

(

1720

)

3

/

2+ baryonstate [24].

Acknowledgements

We wouldlike to acknowledge the outstandingefforts of the staffofthe Acceleratorandthe PhysicsDivisions atJeffersonLab that madethisexperiment possible.This work was supported in partbytheChileanComisiónNacionaldeInvestigaciónCientíficay Tecnológica(CONICYT), theItalianIstitutoNazionale diFisica Nu-cleare,theFrenchCentreNationaldelaRechercheScientifique,the FrenchCommissariatàl’EnergieAtomique,theU.S.Departmentof Energy,the NationalScience Foundation,the ScottishUniversities Physics Alliance (SUPA), Skobeltsyn Institute of Nuclear Physics, thePhysicsDepartmentatMoscowState University,Ohio Univer-sity,theUniversityofSouthCarolina,theUnitedKingdom’sScience andTechnologyFacilitiesCouncil(STFC),andtheNationalResearch FoundationofKorea.AuthoredbyJeffersonScienceAssociates,LLC underU.S. DOE Contract No. DE-AC05-06OR23177.The U.S. Gov-ernmentretainsa non-exclusive,paid-up,irrevocable, world-wide license to publish or reproduce this manuscript forU.S. Govern-ment purposes. This material is based upon work supported by theU.S.DepartmentofEnergy,OfficeofScience,OfficeofNuclear PhysicsundercontractDE-AC05-06OR23177.

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