Differential cross section for γd → ωd using CLAS at Jefferson Lab

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Differential cross section for γd → ωd using CLAS at Jefferson

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Article:

Chetry, T., Hicks, K., Compton, N. et al. (109 more authors) (2018) Differential cross

section for γd → ωd using CLAS at Jefferson Lab. Physics Letters B. pp. 646-651. ISSN

0370-2693

https://doi.org/10.1016/j.physletb.2018.06.003

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Differential

cross

section

for

γ

d

→

ω

d

using

CLAS

at

Jefferson

Lab

T. Chetry

a

,

∗

_,

_{K. Hicks}

a

,

∗

_,

_{N. Compton}

a

_,

_{M. Sargsian}

m

_,

_{S. Adhikari}

m

_,

_{J. Ball}

h

_,

_{I. Balossino}

r

_,

L. Barion

r

,

M. Battaglieri

t

,

V. Batourine

aj

,

z

,

I. Bedlinskiy

x

, A.S. Biselli

k

,

f

_,

_{S. Boiarinov}

aj

_,

W.J. Briscoe

p

,

W.K. Brooks

ak

,

aj

_,

_{V.D. Burkert}

aj

_,

_{D.S. Carman}

aj

_,

_{A. Celentano}

t

_,

_{G. Charles}

ad

_,

G. Ciullo

r

,

l

_,

_{L. Clark}

am

_,

_Brandon

_{A. Clary}

j

_,

_{P.L. Cole}

q

_,

_{M. Contalbrigo}

r

_,

_{V. Crede}

n

_,

A. D’Angelo

u

,

af

,

N. Dashyan

aq

,

R. De Vita

t

,

E. De Sanctis

s

,

A. Deur

aj

,

C. Djalali

ah

,

R. Dupre

w

,

A. El Alaoui

ak

,

L. El Fassi

aa

,

P. Eugenio

n

,

G. Fedotov

a

,

ag

_,

_{R. Fersch}

i

,

ap

_,

A. Filippi

v

, G. Gavalian

aj

,

ab

_,

_{Y. Ghandilyan}

aq

_,

_{K.L. Giovanetti}

y

_{, F.X. Girod}

aj

_{, E. Golovatch}

ag

_,

R.W. Gothe

ah

,

K.A. Griﬃoen

ap

,

L. Guo

m

,

aj

_,

_{K. Haﬁdi}

b

_,

_{N. Harrison}

aj

_,

_{M. Hattawy}

b

_,

M. Holtrop

ab

, Y. Ilieva

ah

,

p

_,

_{D.G. Ireland}

am

_,

_{B.S. Ishkhanov}

ag

_,

_{E.L. Isupov}

ag

_,

_{D. Jenkins}

an

_,

S. Johnston

b

,

M.L. Kabir

aa

,

D. Keller

ao

,

G. Khachatryan

aq

,

M. Khachatryan

ad

,

M. Khandaker

ac

,

A. Kim

j

,

W. Kim

z

,

F.J. Klein

g

,

V. Kubarovsky

aj

,

ae

_,

_{L. Lanza}

u

_,

_{P. Lenisa}

r

_,

K. Livingston

am

,

I.J.D. MacGregor

am

,

N. Markov

j

,

B. McKinnon

am

,

V. Mokeev

aj

,

ag

,

A. Movsisyan

r

,

C. Munoz Camacho

w

,

P. Nadel-Turonski

aj

,

S. Niccolai

w

,

G. Niculescu

y

,

M. Osipenko

t

,

A.I. Ostrovidov

n

,

M. Paolone

ai

, R. Paremuzyan

ab

_,

_{K. Park}

aj

,

z

_,

_{E. Pasyuk}

aj

,

c

_,

W. Phelps

m

,

O. Pogorelko

x

,

J.W. Price

d

,

Y. Prok

ad

,

ao

_,

_{M. Ripani}

t

_,

_{D. Riser}

j

_,

_{B.G. Ritchie}

c

_,

A. Rizzo

u

,

af

,

G. Rosner

am

,

C. Salgado

ac

,

R.A. Schumacher

f

, Iu. Skorodumina

ah

_,

G.D. Smith

al

,

D.I. Sober

g

,

D. Sokhan

am

,

N. Sparveris

ai

,

S. Stepanyan

aj

,

I.I. Strakovsky

p

,

S. Strauch

ah

,

p

_,

_{M. Taiuti}

o

_,

_{J.A. Tan}

z

_,

_{M. Ungaro}

aj

,

ae

_,

_{H. Voskanyan}

aq

_,

_{E. Voutier}

w

_,

L.B. Weinstein

ad

,

M.H. Wood

e

,

ah

,

N. Zachariou

al

,

J. Zhang

ao

,

Z.W. Zhao

ad

a_Ohio_University,_Athens,_{OH 45701,}_United_States_of_America

b_Argonne_National_Laboratory,_Argonne,_{IL 60439,}_United_States_of_America c_Arizona_State_University,_Tempe,_{AZ 85287-1504,}_United_States_of_America

d_California_State_University,_Dominguez_Hills,_Carson,_CA_90747,_United_States_of_America e_Canisius_College,_Buffalo,_NY,_United_States_of_America

f_Carnegie_Mellon_University,_Pittsburgh,_{PA 15213,}_United_States_of_America g_Catholic_University_of_America,_Washington,_D.C._20064,_United_States_of_America h_IRFU,_CEA,_{Universit’e}_{Paris-Saclay,}_F-91191_{Gif-sur-Yvette,}_France

i_Christopher_Newport_University,_Newport_News,_{VA 23606,}_United_States_of_America j_University_of_Connecticut,_Storrs,_{CT 06269,}_United_States_of_America

k_Fairfield_University,_Fairfield_CT_06824,_United_States_of_America l_{Universita’}_di_Ferrara,₄₄₁₂₁_Ferrara,_Italy

m_Florida_{International}_University,_Miami,_{FL 33199,}_United_States_of_America n_Florida_State_University,_Tallahassee,_{FL 32306,}_United_States_of_America o_Università_di_Genova,₁₆₁₄₆_Genova,_Italy

p_The_George_Washington_University,_Washington,_DC_20052,_United_States_of_America q_Idaho_State_University,_Pocatello,_{ID 83209,}_United_States_of_America

r_INFN,_Sezione_di_Ferrara,₄₄₁₀₀_Ferrara,_Italy

s_INFN,_Laboratori_Nazionali_di_Frascati,₀₀₀₄₄_Frascati,_Italy t_INFN,_Sezione_di_Genova,₁₆₁₄₆_Genova,_Italy

u_INFN,_Sezione_di_Roma_Tor_Vergata,₀₀₁₃₃_Rome,_Italy v_INFN,_Sezione_di_Torino,₁₀₁₂₅_Torino,_Italy

w_Institut_de_Physique_Nucléaire,_CNRS/IN2P3_and_Université_Paris_Sud,_Orsay,_France x_Institute_of_Theoretical_and_Experimental_Physics,_Moscow,_117259,_Russia y_James_Madison_University,_{Harrisonburg,}_{VA 22807,}_United_States_of_America z_Kyungpook_National_University,_Daegu_41566,_Republic_of_Korea

aa_Mississippi_State_University,_Mississippi_State,_MS_39762-5167,_United_States_of_America ab_University_of_New_Hampshire,_Durham,_{NH 03824-3568,}_United_States_of_America ac_Norfolk_State_University,_Norfolk,_{VA 23504,}_United_States_of_America

ad_Old_Dominion_University,_Norfolk,_{VA 23529,}_United_States_of_America

https://doi.org/10.1016/j.physletb.2018.06.003

(3)

ae_Rensselaer_Polytechnic_Institute,_Troy,_{NY 12180-3590,}_United_States_of_America af_{Universita’}_di_Roma_Tor_Vergata,₀₀₁₃₃_Rome,_Italy

ag_Skobeltsyn_Institute_of_Nuclear_Physics,_Lomonosov_Moscow_State_University,₁₁₉₂₃₄_Moscow,_Russia ah_University_of_South_Carolina,_Columbia,_{SC 29208,}_United_States_of_America

ai_Temple_University,_{Philadelphia,}_PA_19122,_United_States_of_America

aj_Thomas_Jefferson_National_Accelerator_Facility,_Newport_News,_{VA 23606,}_United_States_of_America ak_Universidad_Técnica_Federico_Santa_María,_Casilla_110-V,_Valparaíso,_Chile

al_Edinburgh_University,_Edinburgh_EH9_3JZ,_United_Kingdom am_University_of_Glasgow,_Glasgow_G12_8QQ,_United_Kingdom an_Virginia_Tech,_Blacksburg,_{VA 24061-0435,}_United_States_of_America ao_University_of_Virginia,_{Charlottesville,}_{VA 22901,}_United_States_of_America

ap_College_of_William_and_Mary,_{Williamsburg,}_{VA 23187-8795,}_United_States_of_America aq_Yerevan_Physics_Institute,₃₇₅₀₃₆_Yerevan,_Armenia

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received19February2018

Receivedinrevisedform23April2018 Accepted3June2018

Availableonline6June2018 Editor:V.Metag

Keywords:

VectorMesonDominance Differentialcrosssection Singlescattering Doublescattering

The crosssectionfor coherent

ω

-mesonphotoproduction offthe deuteronhasbeenmeasuredforthe ﬁrsttimeasafunctionofthemomentumtransfert=(Pγ−Pω)2andphotonenergyEγ usingtheCLAS detector attheThomasJeffersonNational AcceleratorFacility. Thecross sectionsare measuredin the energyrange1.4<Eγ<3.4 GeV.Amodel basedon

ω

−Nrescatteringisconsistentwiththedataat lowandintermediatemomentumtransfer,|t|.For2.8<Eγ<3.4 GeV,thetotalcross-sectionof

ω

−N scattering,basedonﬁtswithintheframeworkoftheVectorMesonDominancemodel,isintherangeof 30–40mb.

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

1. Introduction

Vectormeson photoproductionoff protonsat highenergies is welldescribed[1] theoreticallyusingthephenomenologicalVector MesonDominance (VMD)model, inwhich the photon fluctuates intoavirtuallightvectormeson(havingthesamequantum num-bersasthephoton)andthenscattersoffthetarget [2].TheVMD modelhasbeenverysuccessfulatpredictingvectormeson produc-tion athigh energies. However, atphoton energies closer to the production threshold, other diagrams, such as pseudoscalar me-sonexchangeinthet-channel,cancontribute [3].Thismakesthe reactiondynamicsofvectormesonphotoproductionoffproton tar-getsmorecomplexnearthreshold.Additionalcomplexitynearthe thresholdmaycomefromnucleonresonancesinthes-channel. Co-herent

ω

-mesonproductionoffthedeuteronavoidssuch complex-ities.Sinceboththedeuteronandtheﬁnal

ω

dstateareisosinglets, exchangeofnon-isosinglet(e.g.pseudoscalar)mesonscannot con-tribute. Hence, natural parity exchange in the t-channel, usually describedbyPomeronexchange(seeFig.1a),isexpectedto domi-nateatlowmomentumtransfer(low

|

t

|

,wheret

=

(

Pγ

−

Pω

)

2and Piisthefour-momentumofparticlei)forvectormeson

photopro-ductionoffdeuterium,thussimplifyingtheoretical interpretations ofthedata.

At higher momentum transfer (

|

t

|

>

0

.

5 GeV2

/

c2₎ _secondary scattering diagrams, where the

ω

is produced off one nucleon and scatters from the second, as shown in Fig. 1b, enable both nucleons to remain bound as a deuteron in the ﬁnal state [4]. Thesediagrams providean opportunity to extract the

ω

−

N to-tal scattering cross section,

σ

ωN, from comparisons of data and

calculations.Similarstudiesweredoneforcoherent

φ

-meson pho-toproduction from the deuteron [5,6], resulting in the ﬁrst-ever estimatesof the

φ

−

N total cross section. Information on these vector meson–nucleon total crosssections is virtually impossible

*

Correspondingauthors.

E-mailaddress:[email protected](T. Chetry).

toextractcleanlyviaother methods,duetotheshortlifetimesof thesemesons.

Experimentalinformationon

σ

ωN isofinterestcurrentlydueto

progresswithinlatticeQCD,whichcannowextractmeson–meson scatteringphase shiftsdirectly[7]. The HadronSpectroscopy Col-laboration [7] isworkingon extractingmeson–nucleonscattering phaseshifts,whicharedirectlyrelatedtothetotalcrosssections. Thisisasigniﬁcant advancebecauseitconnectsQCD calculations toexperimentalobservables,suchasthetotalcrosssections.Such adirectconnectionbetweennon-perturbativeQCDandexperiment hasbeenrareuntilnow.The

ω

mesonisaparticularlygoodchoice for these studies, since it decays into three pions about 89% of thetime.Onthelattice,thelight quarkmassesareinputs. Lattice results are often shown for pion masses heavierthan in nature, as the lattice calculations are easier to compute there. The

ω

is thusastableparticleinlatticecalculationswherethepionmassis somewhathigherthanitsphysicalvalue.Scatteringphaseshiftsof stableparticlesareeasiertoobtainonthelatticethanforunstable particles.Hence,measurementsof

σ

ωN aretimelyandcansoonbe

comparedwithpredictionsfromlatticecalculations.

Previousexperimentaldataoncoherent

ω

photoproductionare scarce.Bubblechambermeasurements[1] havelowstatistical pre-cision. The best data on this reaction are from the Weizmann Institute [8], using a photon beam of energy 4.3 GeV and at

|

t

|

<

0

.

2 GeV2

/

c2_,_which_is_too _small_to_see_the _effect_of double-scatteringasshowninFig. 1b.Data oncoherent

ρ

photoproduc-tionhavebeenmeasuredathigher

|

t

|

atSLAC[9],whichwasused toextract

σ

ρN.Nopreviousdataexistthatwouldallowan

extrac-tionof

σ

ωN.

Here,wepresentdataoncoherent

ω

photoproductionoff deu-teriumatphotonenergiesrangingfrom1.4to3.4 GeVoverawide rangeinthemomentumtransfert.Thet-dependenceofthecross section ismeasured out to

|

t

|

∼

2

.

0 GeV2

/

c2_, _which_is _compared withtheoreticalcalculationsthatincludethedouble-scattering di-agrams,allowinganextractionofthetotalscatteringcrosssection

σ

ωN.Thiscompletesthemeasurementofscatteringcrosssections

(4)

[image:4.612.78.240.64.245.2]

Fig. 1.t-Channeldiagramsshowingtwoω-mesonphotoproductionmechanismsvia

(a)Singleand(b)Doublescattering.Thephotonfluctuatestotheω,whichscatters offthenucleon(s).ThedashedlinerepresentstheexchangeofaPomeron.

2. Experiment

The g10dataset,withunpolarizedbeam, was collected inthe spring of 2004 using the Continuous Electron Beam Accelerator Facility (CEBAF) and the CEBAF Large Acceptance Spectrometer (CLAS) at the Thomas Jefferson NationalAccelerator Facility (Jef-ferson Lab). CLAS was designedaround sixsuperconducting coils arranged in a toroidal conﬁguration that produced a ﬁeld in the azimuthaldirection.Theparticledetectionsystemconsistedofsix sets of drift chambersto determine charged-particle trajectories, gas Cherenkov counters to identify electrons, scintillator coun-ters for measuring the time-of-flight (TOF) and electromagnetic calorimeters to detect neutrons andshowering particles such as electrons.Thesesegments were instrumentedindividually sothat they formedactually independentmagneticspectrometerswitha commontarget,triggeranddata-acquisitionsystem [10].

The g10 experiment used a continuous electron beam with incident electron energy, Ee

=

3

.

767 GeV. This beam produced

bremsstrahlungphotons when passed through a thin gold radia-tor[10]. Thetaggersystem[11] wasused tomeasurethe energy ofthephotons, which interactedwithan unpolarizedliquid deu-terium target measuring 24cm in length and4 cm indiameter. Thereactionproductstraversedthelargedriftchambersand tim-ingdetectors.Thethree-momentawerereconstructedbythedrift chambersandtheparticleidentiﬁcationwasdeterminedbythe ar-rivaltimeoftheproducts.

Thedataacquisitiontriggerrequiredtwochargedparticles de-tectedincoincidencewiththetaggedphoton.Thetimeofflightof aparticlewasdeterminedusingthescintillatorpaddlesinthestart counter [12] that surrounded the target and the Time of Flight (ToF)scintillatorpaddlesthatsurroundedtheexteriorofCLAS[13]. Thechargeoftheparticlewasdeterminedbyitsdirectionof bend-inginthemagneticﬁeld.Weusedthelowermagneticﬁeld(torus magnetcurrentsetat2250A) g10datasettooptimizethe accep-tanceforlow-momentumin-bending

π

−_[₁₄_].

3. Dataanalysis

Theexclusive reaction

γ

d

→

ω

dwas identiﬁed bydetecting a ﬁnal-state deuteron andtwo charged pions from

ω

→

π

+

_π

−

_π

0 decay. The unmeasured

π

0 was reconstructed from the missing mass.Chargedparticleswereidentiﬁedfromtheirmeasured three-momentumandmeasuredflighttime,using

δ

t

=

tmeasured

−

dpath

c

p2

₊

_m2

p

,

(1)

wheredpath is thereconstructedpath lengthof theparticlefrom

the event vertexto the ToF paddles, p is its momentum, andm

is the assumedmass. The time difference for a charged particle about

δ

t

=

0 wasﬁtasafunctionoftheparticlemomentumwith aGaussianfunctionforseveralmomentumbins.A3

σ

cut around thecentroidof

δ

t ineachmomentumbinwasusedtoidentifythe particlesincoincidencewithasinglephoton.

Thevertextimeforeachchargedparticlewas comparedtothe arrival time foreach photon (from the photon tagger). The pho-tonwiththetimethatmostcloselymatchedwiththevertextime was selected. In orderto remove multiplephotons linked toone event, atiming cut of

±

1 ns wasmade. Thiscut helpedtoavoid ambiguityinselectingthe“good”incidentphotonassociatedwith an eventofinterest. Theeventsrejectedbythiscutwere studied separatelyandanoverallcorrection,

γ

corr,of6.8%wasfound.

γ

corr

is theratio ofthe numberofrejectedphotons tothe total num-ber of photons associated with the ﬁnal state detected particles for each event. The measured photon energy is slightlydifferent fromtherealphotonenergyduetoaslightgeometricalmismatch, therefore photon energy correction (correction factor within 5%) explained in [15] wasalso applied to the energyof the selected photons.

With the identity of each scattered particle established, cor-rections weremadeforthe energylostby eachdetected charged particlewhiletravelingthroughdifferentmaterialsofthedetector [16].Inadditiontotheenergylosscorrectionsforthecharged par-ticletracks,slightcorrectionswerealsonecessaryforthe momen-tum ofeach track, due to uncertainties inthe magnetic ﬁeld, by requiringfour-momentum conservationusingtheexclusive

γ

d

→

π

+

_π

−_d_channel_[₁₇_]._Cuts_were_also_made_to_remove_poorly

per-formingToFpaddles.Events associatedwithbeamtrips werealso removedfromtheanalysis.

In addition to the above, fiducial region cuts were made to removeeventsthattrackedbacktonon-physicalregionsofthe de-tectorortoregionsofthedetectorwheretheefficiencywaslowor changingrapidly.Minimummomentumcutswereusedtoexclude particleswithlowdetectionefficiency.Eventsthattrackedbackto outsidethetargetregionwerealsoremoved[17].

The data analysis for

γ

d

→

ω

d consisted of two main steps: two-pion background rejection and

ω

yield extraction from the multi-meson background.The two-pionbackground isdominated by the

γ

d

→

ρ

d channel as can be seen from Fig. 2a. The majority of this background was eliminated by requiring that the missing mass from the deuteron given by, M M

(

γ

d

,

d′

₎

₌

(

Pd

+

Pγ

−

Pd′

)

2, equaled m_ω, assuming the three pion decay

modeforthe

ω

.

Amissing

π

0_peak_can_be_seen_on_top_of_a_smooth_background inFig.2b,whichwasestimatedbyemployingaLorentzianforthe peakandasecond-orderpolynomialforthebackground.A3

σ

cut, shownbytheverticaldashedlinesinFig.2b,wasappliedtoselect exclusive

ω

eventswithsomebackground.

The missing mass spectra were then divided into four Eγ

bins in 1

.

4

<

E_γ

<

3

.

4 GeV, which were further split into dif-ferent

|

t

|

bins within 0

.

3

<

−

t

<

2

.

0 GeV2

/

c2_. _A _total _of ₂₅ en-ergyandmomentumtransferbinswereusedtoextractthe num-ber of

ω

-events. The

ω

-meson yield was obtained from a ﬁt to the M M

(

γ

d

,

d′

₎

_distribution _by _a_{Gaussian-convoluted} _Lorentzian

(5)

Fig. 2. (a)The y-axis represents the missing mass, Y, in the reaction γd→

π+_π−_d′_Y _while_the_x_-axis_shows_the_distribution_of_the_missing_mass, _X_,_in_the

reactionγd→d′ _X_._(b)_Shown_is_the_y_-axis_projection_of_(a)._The_vertical_dashed

linesrepresentthepositionofthemissingmasscutmadetoselectω-eventsusing theﬁtshownbythesolidcurve.Anestimateofthepossiblebackgroundshapeis shownbytheshadedregion.

p1

+

p2x

+

p3x2waschosentoestimatethemulti-pionbackground, wherex

≡

M M

(

γ

d

,

d

)

,andthepiareﬁtparameters.Theyieldwas

determinedbyintegratingtheVoigtianfunction.Alinearfunction was used to estimate the systematiceffect of the choice of the background function. An average systematic effect of about 8.6% was founddue tothe uncertaintyof thebackground subtraction. TheﬁtforonetypicalbinisshowninFig.3.

Measurementofthedifferentialcross-sectionrequireda calcu-lationoftheCLASacceptancebaseduponthegeometrical eﬃcien-ciesof the detectorsubsystems. The CLAS acceptance was deter-mined by performing a GEANT-basedMonte-Carlo simulation. As the acceptance is reaction dependent,

γ

d

→

ω

d

→

π

+

_π

−_d′

₍

_π

0

₎

events were generated. These events underwent the same event processingasthedata.Foreachkinematicbin,theacceptancewas calculated as the ratio of the number of accepted to the gener-ated events. The simulated distributions were also ﬁt similar to thedata.Theaverageacceptanceforthischannelwasfoundtobe 8.1%.

The target luminosity was calculated from the incident pho-tonflux(Nγ)forthecollimatedphotonbeam,targetdensity(

ρ

T),

atomicweight (Md

=

2

.

014 g

/

mol) and length of the target (lT)

usingtherelation,

L

(

Eγ

)

=

ρ

T NAlT Md

[image:5.612.322.553.67.235.2]

Nγ

(

Eγ

),

(2)

Fig. 3.YieldextractionﬁtusingthemissingmassdistributionforEγ=1.4–1.8 GeV and|t|=0.94–1.15 GeV2_/_c2_._The_background_is_estimated_using_a_polynomial

[image:5.612.42.290.68.401.2]

func-tion(dashed-dotted)which,alongwiththesignal(dashed,shadedregion),describe thetotaldistribution(solidcurve).Theyieldisthenumberofeventsintheshaded regionwithintheverticaldashedlines.

Fig. 4.Differentialcrosssectionforγd→ωd.Theinnererrorbarsrepresentthe statisticaluncertaintieswhiletheoutererrorbarsincludesystematicuncertainties addedinquadraturewiththestatisticaluncertainties.

where NA is Avogadro’s number. In each energy bin, the

differ-ential crosssectionsin momentumtransfer binsofwidth t are calculatedusingtherelation,

d

σ

dt

=

YD t A

L

×

Ŵ

ω

Ŵ

_ω_→_π+_π−_π0

×

γ

corr (3)

where YD is the yield, A is the detector acceptance,

L

is the

target luminosity for the photon energy range considered and,

Ŵ

_ω_→_π+_π−_π0

/Ŵ

_ω is the branching ratio. The quantity

γ

corr is the

correctionfactorduetothephotonselectionconditionmentioned previously.Thestatisticaluncertaintyonthedifferentialcross sec-tion was propagated from the uncertainties of each quantity in Eq. (3). The differential cross section for

γ

d

→

ω

d is shown in Fig.4asafunctionof

|

t

|

foreachincidentphotonenergybin.

[image:5.612.332.541.301.518.2]

(6)

system-Table 1

Summaryof theg10 systematiceffects associated with the γd→ωdchannel,estimatingatotalaverage point-to-pointuncertainty.

Source Systematic uncertainty Luminosity/Flux Consistency 8%

Variation of Cuts/Analysis 4.4% Yield Extraction 8.6% Branching Ratio 0.7%

Total (Added in quadrature) 12.5%

Fig. 5.Differentialcrosssection ofγd→ωd asafunctionof|t|for2.8<Eγ<

3.4 GeVcomparedtothatofacalculation [21] basedon[4].Eachcurvecorresponds toaspeciﬁcb, d_dtσ

_t₌₀

,γN andσωNvalue,aslistedinTable2.Thelegendforeach curveisdeﬁnedrespectivelyfortheseparameters.Thesolidcurverepresentsthe contributionofthesinglescatteringforinputparameterscorrespondingtothatof thedashed-dottedcurve.Intheinset,thesolidpointsaretheresultsfrom[8] for anincidentphotonenergyof4.3 GeV.

atic uncertainties calculated inthisexperiment. Due tothe large variation of the statistical uncertainty involved in this analysis, a point-to-point systematicapproach was not realistic. Therefore, anestimationofthe systematicerrors wasmadeby varyingeach cut and taking the average relative difference in the ﬁnal result for each variation. These variations are summarized as different groupsinTable1.

4. Results

InFig.5,thedifferentialcrosssectionfor2

.

8

<

E_γ

<

3

.

4 GeVis comparedwithatheoreticalcalculationusingarescatteringmodel [4]. This is a three-parameter model allowing us to determine a rangeof

σ

ωN byaﬁttotheexperimentaldata.Thescattering

am-plitudeof

γ

N

→

ω

N givenby

fγN→ωN

=

σ

γ∗_ω

(

i

+

α

_γ_N

)

e −b_γ_N

2 t

_,

₍₄₎

dealswithsinglescattering.Asimilarequationcanbealsowritten forthescatteringamplitude of

ω

N

→

ω

N thatmeasuresthe con-tributionoftherescattering [4].Thequantity

σ

γ∗_ω isparametrized

usinganinputparameter d_dtσ

[image:6.612.57.264.106.406.2]

_t₌₀_,_γ_N,whichisthedifferentialcross section of

γ

N

→

ω

N reactionat t

=

0. The initial guessfor this parameterwas basedonpublisheddataon

γ

p

→

ω

p[19,20].The

Table 2

Summaryoftheoryparametersusedtocomparedatafor 2.8<Eγ<3.4 GeV.Theparametersshownherearewithin

15%ofχ2₌₁_._{0 (the}_ideal_value).

bγN=bωN

GeV−2_/_c−2 dσ

dt _t₌₀_,γ_N

[μb/(GeV2_/_c2₎_]

σωN

[mb]

χ2_/_{N D F}

7.5 15 31 1.13

8.0 14 34 1.15

8.0 15 33 1.01

8.0 16 32 0.96

8.0 17 31 1.00

8.0 18 30 1.15

8.0 19 30 0.91

8.0 19 31 0.87

8.0 20 30 1.03

8.5 16 35 1.11

8.5 16 39 1.00

8.5 17 34 1.05

8.5 18 33 1.07

9.0 19 39 0.89

9.0 20 38 0.87

other twoinputparametersarebγN orbωN and

σ

ωN.At

interme-diate andhigherphoton energies,VMDassumestheslope factors of the corresponding amplitudes,bγN andbωN,to be equal. The

variables,

α

γN and

α

ωN,deﬁnedastheratiooftherealto

imag-inarypartsofthecorresponding scatteringamplitudes,were kept ﬁxedandequaltoaphenomenologicalvalueof

−

0

.

4.At interme-diate energies, therealpartof thescatteringamplitudesfor pro-ton andneutrontargetsarenot exactlythesame,butthismodel omits thisdifference since

ω

productionfromd isdominated by isospinaveragedamplitudes [4].Now,forvariousslopefactors,the strength of single scatteringgauged by d_dtσ

_t₌₀_,_γ_N isvaried. Each setofvariationswasfedtothecalculationforvarious

σ

ωN values

asaninputparameterandthedifferentialcrosssection valuesfor aparticularenergy(bincenter)werecalculated.Theoutputs were compared withthe datausinga

χ

2 test.Table 2summarizesthe valuesoftheseparametersthatresultedinareduced

χ

2 between 0.85and1.15. The datais consistentwiththe rescatteringmodel with30

<

σ

ωN

<

40 mbintheframeworkoftheVMDmodel.

5. Conclusion

Inconclusion,wehavepresentedtheﬁrstmeasurementofthe differential crosssectionsforcoherent

ω

photoproductionon the deuteronuptot

= −

2 GeV2

_/

_c2_for_incident_photon_energies_1.4_to 3.4 GeVusingCLASatJeffersonLab.Amodelbasedonrescattering is consistent withthe data atintermediate andhigh momentum transfer. Thedifferentialcrosssection atlarge

|

t

|

shows contribu-tions from double scattering. For 2

.

8

<

Eγ

<

3

.

4 GeV, the data

is consistent with

σ

ωN within 30–40 mb. This range is typical

of hadroniccrosssections inthisenergy range.Whilemore data would be valuable, thisdataset dramatically improves the world data on the

γ

d

→

ω

d reaction andopens up the possibility for furtherstudyofthe

ω

−

N interaction.

Acknowledgements

[image:6.612.338.517.108.281.2]

(7)

Nu-cleare;theFrenchCentreNationaldelaRechercheScientiﬁque;the French Commissariat àl’Energie Atomique; the U.S. National Sci-enceFoundation; andthe NationalResearchFoundation ofKorea. Jefferson Science Associates, LLC, operates the Thomas Jefferson NationalAcceleratorFacilityfortheU.S.DepartmentofEnergy un-derContractNo.DE-AC05-06OR23177.

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