Measurements of the Neutron Structure Functions...measurement of the neutron structure function, F 2 n.n. In particular, the d/u ratio can be determined from the ratio of neutron to

Vladas Tvaskis HUGS 2006 Measurement Vladas Tvaskis HUGS 2006 Measurement of the Neutron Structure Functionsof the Neutron Structure Functions 11

Measurements of the Neutron Measurements of the Neutron Structure FunctionsStructure Functions


IntroductionIntroduction

Most of the existing nucleon structure data - from elastic form factors to deep inelastic structure functions - come from decades of experiments on readily available proton targets, measurements on the neutron are essential for a complete understanding.

A complete determination of the valence content of the nucleon can be achieved only when both its u and d quark distributions are known.

The absence of free neutron targets has meant that, until now, the usual method for extracting neutron structure information has been to use deuterium targets, and apply nuclear corrections arising from the Fermi motion and binding of the nucleons in the deuteron.

But, nuclear model uncertainties can be rather large. As a result, our knowledge of the structure of the neutron, especially in the neutron resonance region, and in the deep inelastic region at large x, is inadequate.


The three prominent resonance The three prominent resonance enhancements are obvious in the enhancements are obvious in the hydrogen data, but only a hint of the hydrogen data, but only a hint of the first (the first (the ΔΔ(1232)) is identifiable in (1232)) is identifiable in the deuterium data. At Qthe deuterium data. At Q22 > 2 GeV> 2 GeV22, , no discernible structure remains in no discernible structure remains in the deuterium data at all. Neutron the deuterium data at all. Neutron extraction from such data requires extraction from such data requires careful modeling of the resonant and careful modeling of the resonant and nonnon--resonant components for the resonant components for the neutron (as was done with the neutron (as was done with the hydrogen data). Calculations must hydrogen data). Calculations must account for the nuclear effects of account for the nuclear effects of binding, Fermi motion, and nucleon binding, Fermi motion, and nucleon offoff--shellness, and the modelshellness, and the model--dependence introduced by each of dependence introduced by each of these steps leads to a substantial these steps leads to a substantial uncertainty in the neutron resonance uncertainty in the neutron resonance structure functions.structure functions.

Physics Motivation (Neutron Resonance Structure)Physics Motivation (Neutron Resonance Structure)

Almost nothing is known Almost nothing is known about the nature of the about the nature of the resonance excitations of the resonance excitations of the neutron !!!neutron !!!


Physics Motivation (Deep Inelastic Scattering at Large x)Physics Motivation (Deep Inelastic Scattering at Large x)

For x >0.4 the contributions from the For x >0.4 the contributions from the qqqq sea are negligible, and the structure functions are sea are negligible, and the structure functions are dominated by the valence quarks.dominated by the valence quarks.Knowledge of the valence quark distributions of the nucleon at lKnowledge of the valence quark distributions of the nucleon at large x is vital for severalarge x is vital for severalreasons. reasons.

1.1. The simplest SU(6) symmetric quark model predicts that the ratioThe simplest SU(6) symmetric quark model predicts that the ratio of d to u quarkof d to u quarkdistributions in the proton is 1/2, however, the breaking of thidistributions in the proton is 1/2, however, the breaking of this symmetry in nature resultss symmetry in nature resultsin a much smaller ratio. Various mechanisms have been invoked toin a much smaller ratio. Various mechanisms have been invoked to explain why the explain why the d(xd(x))distribution is softer than distribution is softer than u(xu(x). ).

2. If the interaction between quarks that are spectators to2. If the interaction between quarks that are spectators to the deep inelastic collision the deep inelastic collision is dominated by oneis dominated by one--gluon exchange, for instance, the d quark distribution will be gluon exchange, for instance, the d quark distribution will be suppressed, and the d/u ratio will tend to zero in the limit x suppressed, and the d/u ratio will tend to zero in the limit x →→ 1, This assumption has been 1, This assumption has been built into most global analyses of parton distribution functionsbuilt into most global analyses of parton distribution functions, and has never been tested , and has never been tested independently. independently.

3. On the other hand, if the dominant reactio3. On the other hand, if the dominant reaction mechanism involves deep inelastic n mechanism involves deep inelastic scattering from a quark with the same spin orientation as the nuscattering from a quark with the same spin orientation as the nucleon, as predicted by cleon, as predicted by perturbative QCD counting rules, then d/u tends to 1/5 as x perturbative QCD counting rules, then d/u tends to 1/5 as x →→ 1. Determining d/u 1. Determining d/u experimentally would therefore lead to important insights into texperimentally would therefore lead to important insights into the mechanisms responsible he mechanisms responsible for spinfor spin--flavor symmetry breaking. flavor symmetry breaking.


Because of the 4:1 weighting of the squared quark charges betweeBecause of the 4:1 weighting of the squared quark charges between the up and downn the up and downquarks, data on the proton structure function, Fquarks, data on the proton structure function, F22

pp , provide strong constraints on the u quark, provide strong constraints on the u quarkdistribution at large x:distribution at large x:

( ) ( ) ( )( ) ( ) ( )⎟⎠⎞

⎜⎝⎛ +≈+= ∑ xdxuxxqxqexxF

qq

p

91

942

2

The determination of the d quark distribution, on the other handThe determination of the d quark distribution, on the other hand, requires in addition the , requires in addition the measurement of the neutron structure function, Fmeasurement of the neutron structure function, F22

n.n. In particular, the d/u ratio can beIn particular, the d/u ratio can bedetermined from the ratio of neutron to proton structure functiodetermined from the ratio of neutron to proton structure functions:ns:

udud

FF

p

n

+

+≈

4

41

2

2


For, x > 0.4, so that the sea For, x > 0.4, so that the sea quarks can be neglected.quarks can be neglected.



Proton Structure Function FProton Structure Function F22pp measured very accurately. measured very accurately.

Neutron Structure Function FNeutron Structure Function F22nn have been extracted from inclusive scattering off have been extracted from inclusive scattering off

deuterium. deuterium.

Theoretical uncertainties in the treatment Theoretical uncertainties in the treatment

of nuclear corrections (Fermi motion, nucleon of nuclear corrections (Fermi motion, nucleon

offoff--shell correction) can lead to values for shell correction) can lead to values for

FF22nn/F/F22

pp which differ by 50% at x=0.75, and which differ by 50% at x=0.75, and

by a factor ~2by a factor ~2--3 at x=0.85.3 at x=0.85.

udud

FF

p

n

+

+≈

4

41

2

2 For, x > 0.4, so that For, x > 0.4, so that the sea quarks can the sea quarks can be neglected.be neglected.

So, the measurements of the Neutron So, the measurements of the Neutron Structure Function FStructure Function F22

nn will eliminate the will eliminate the uncertainties from nuclear models !!!uncertainties from nuclear models !!!


e-

p

?

np

e-

before

Spectator proton

after

The BoNuS Approach: An Effective Free The BoNuS Approach: An Effective Free Neutron target from DeuteriumNeutron target from Deuterium



The Proton is DetectedThe Proton is Detected



n

ep n

e

p

<-- ambiguous -->proton target neutron target

e

p

nneutron target !

If the proton is going If the proton is going backwardsbackwards in the lab framein the lab frame, it is almost , it is almost guaranteed to be only a spectator.guaranteed to be only a spectator.

Measurement of the Measurement of the structure Function Fstructure Function F22

nn on on nearly free neutrons in the nearly free neutrons in the reaction reaction ee--dd →→ ee--pXpX by by measuring the slowly measuring the slowly backward moving recoil backward moving recoil proton with the momentum proton with the momentum below 100 below 100 MeV/cMeV/c..


Backgrounds (Choice of Spectator Momentum and Angle)Backgrounds (Choice of Spectator Momentum and Angle)

0.5

1.0

1.5

2.0

0 2 0 4 0 6 0 8 0 100 120

p = 0.3

p = 0.4

p = 0.5

(PW

IA +

T.F

.) / P

WIA

θpq

(degrees)

Q2 = 4 (GeV/c)2

x = 0.6

Target fragmentation negligible for θpq> 90

PWIA PWIA -- plane wave impulse plane wave impulse approximation (PWIA)approximation (PWIA)

0 30 60 90 120 150 180

0.2

0.4

0.6

0.8

1.0

1.2

1.4

SFSI /S

PWIA

θ [degr]

ps = 0

ps = 0.1

ps = 0.2

0 30 60 90 120 150 180

0.2

0.4

0.6

0.8

1.0

1.2

1.4

SFSI /S

PWIA

θ [degr]

ps = 0

ps = 0.1

ps = 0.2

0 100 200 300 4000.8

0.85

0.9

0.95

1

1.05

|p| (MeV/c)

x=0.3

x=0.6

Rn

0.4

0.5

Ratio of Bound / free neutron structure Functions O (1%)

Another possible source of Another possible source of uncertainty arises from final uncertainty arises from final state interaction (FSI) state interaction (FSI) effects, or effects, or rescatteringrescattering of the of the spectator proton by the deep spectator proton by the deep inelastic remnants, X, of the inelastic remnants, X, of the scattered neutron.scattered neutron.

Final state Final state interactions interactions OO(5%)(5%)


Experimental SetupExperimental Setup

Hall B CLAS spectrometer Hall B CLAS spectrometer for electron detectionfor electron detection

Thin deuterium target (7.5 Thin deuterium target (7.5 atmatm gas)gas)

Radial Time Projection Radial Time Projection Chamber (RTPC) for Chamber (RTPC) for spectator proton detectionspectator proton detection

DVCS solenoid to contain DVCS solenoid to contain MollerMoller backgroundbackground


Nearly 4Nearly 4ππ AcceptanceAcceptance

Beam ~10 Beam ~10 nAnA

CerenkovCerenkov CountersCounters

Drift ChambersDrift Chambers

Forward CalorimetersForward Calorimeters

Main Main TorusTorus MagnetMagnet

LargeLarge--Angle Angle CalorimetersCalorimeters

Data AcquisitionData Acquisition

TimeTime--ofof--Flight SystemFlight System

CCEBAF EBAF LLarge arge AAcceptance cceptance SSpectrometer (CLAS)pectrometer (CLAS)

The Location of the Pads (strips) The Location of the Pads (strips) provides position information provides position information ((AzimuthalAzimuthal angle angle ψψ and the distance and the distance zz along the beam direction) for the along the beam direction) for the collected drift electrons, and the collected drift electrons, and the times of their arrivals provide a times of their arrivals provide a measure of the radius (measure of the radius (rr) at which ) at which they were produced. By recording they were produced. By recording the amount of charge produced the amount of charge produced along the track one can estimate along the track one can estimate dE/dxdE/dx and and therebaytherebay constrain the constrain the mass of the particle that produces it.mass of the particle that produces it.


70 MeV/c

80 MeV/c

90 MeV/c

100 MeV/c

110 MeV/c

120 MeV/c

5 mm D2 gas50 μm KaptonHe... Field PlaneRTPC GasGEMs, readout, etc.

Energy Deposited in each layer of materialas initial spectator momentum is varied.

D k He Cu k Cu

GEANT modelGEANT model

Will measure 70 < pproton < 200 MeV/c

60 MeV/c

RTPC PenetrationRTPC Penetration


Very Important ProtonsVery Important Protons

10-9

10-8

10-7

10-6

0 20 40 60 80 100 120 140 160 180 200

Deuteron ~ free proton + free Deuteron ~ free proton + free neutron at small nucleon neutron at small nucleon momentamomenta

30% of momentum distribution 30% of momentum distribution is in chosen is in chosen ppss rangerange


■■■■■■

■

■

■

■

■

■

■

■■

■■

■■■■■■■■■■■■■●●●●●●

●

●

●

●

●●●●●●●●●●●●●●●●●●●●▲▲▲▲▲▲▲

▲

▲▲

▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲0.0x100

1.0x105

2.0x105

3.0x105

4.0x105

5.0x105

6.0x105

7.0x105

0 0.05 0.1 0.15 0.2 0.25 0.3

■Counts(Cut1)

●Counts(Cut2)

▲Counts(Cut3)

Ps [GeV/c]

Co

un

ts in

20

day

s

Theta (qps) [degrees]

■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■

■■■■■■

■

■

■

■

■■■

■

■

■■■■■■■■■■■■

■■■■

■■■■■■■■■■■■■■■■■■■■■■■■■●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲

▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲0.0x100

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

1.2x105

1.4x105

0 20 40 60 80 100 120 140 160 180

Cut 1: Electron in CLAS, Cut 1: Electron in CLAS, ppss > 60 > 60 MeV/cMeV/c

Cut 2: Cut 1 plus Cut 2: Cut 1 plus ppss < 100 < 100 MeV/cMeV/c, , QQpqpq > 110> 110oo

Cut 3: Cut 2 plus spectator in acceptance of recoil detectorCut 3: Cut 2 plus spectator in acceptance of recoil detector

VIPs at 6 VIPs at 6 GeVGeV


x

F2n

/F2p

RR

••

••

••

•

••

••

••

••

••

••

••

•••

••

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

• Q = 1.8 GeV

• Q = 2.2 GeV

• Q = 2.6 GeV

• Q = 3 GeV

• Q = 3.6 GeV

• Q = 4.4 GeV

• Q = 5.2 GeV

Naive SU(6) Quark Modeld/u = 1/2

Helicityconservation d/u = 1/5

1-gluon exchanged/u = 0

2 2

2 2

2 2

2 2

2 2

2 2

2 2

Yellow shaded area Yellow shaded area represents current represents current theoretical uncertaintytheoretical uncertainty

RR data begin the RR data begin the Resonance RegionResonance Region

(W(W22 > 3 GeV> 3 GeV22, Q, Q22 ~ 5)~ 5)

Gray shaded areas Gray shaded areas represent systematic represent systematic uncertaintyuncertainty

Light = totalLight = total

Dark = normalized, Dark = normalized, pointpoint--toto--pointpoint

FF22nn / F/ F22

pp ((d/ud/u) Ratio at Large x ) Ratio at Large x –– Projected ResultsProjected Results

Preamplifier cardsPreamplifier cards

Extended volumeExtended volume

BoNuS CloseBoNuS Close--upup

•••• zz

Inside RTPC

Extended volumeWindows

Gas inlet

Kapton tube holdingtarget gas

He gas surrounds target.

The Target CellThe Target Cell

Installing BoNuS into CLASInstalling BoNuS into CLAS


Event in BoNuS

Tracks from BoNuSTracks from BoNuS


Distributions Distributions …………………………

0

0.2

0.4

0.6

0.8

1

-15 -10 -5 0 5 10 15

Z(CLAS)-Z(BoNuS) (cm)N

um

ber

of

Eve

nts

Mean = -0.31Sigma = 1.00

NEWNEW OLDOLD

1.1 1.1 GeVGeV Hydrogen Hydrogen

θθ CLAS CLAS –– θθ BoNuS (radians)BoNuS (radians)ΨΨ CLAS CLAS –– ψψ BoNuS in (radians)BoNuS in (radians)

En

trie

sE

ntr

ies

Proton scattering angle; crossProton scattering angle; cross--check with CLAScheck with CLAS


SummarySummary

☺☺Elastic form factors Elastic form factors

☺☺Resonance structureResonance structureTransition form factorsTransition form factors

QuarkQuark--hadronhadron dualityduality

☺☺Data over a Data over a rangerange of Qof Q22, x , x Structure function momentsStructure function moments

Large x nucleon structureLarge x nucleon structure

Experiment is finishedExperiment is finished…………


Physics Motivation (Neutron Resonance Structure)Physics Motivation (Neutron Resonance Structure)

Almost nothing is known about the Almost nothing is known about the nature of the resonance excitations of nature of the resonance excitations of the neutron !!!the neutron !!!

The extracted neutron The extracted neutron -- ΔΔ00 transition form factor appears transition form factor appears to be consistent with that of the proton to be consistent with that of the proton -- ΔΔ++ within the within the rather large uncertainties, and should therefore exhibit rather large uncertainties, and should therefore exhibit the same anomalous behavior seen in the proton data. the same anomalous behavior seen in the proton data. Indeed, this would be expected for a pure Indeed, this would be expected for a pure ΔΔ resonance resonance contribution (and in fact for any isospin I = 3/2 contribution (and in fact for any isospin I = 3/2 excitation) in the limit of zero width, as isospin excitation) in the limit of zero width, as isospin conservation constrains I = 3/2 amplitudes for the proton conservation constrains I = 3/2 amplitudes for the proton and neutron to be identical. In practice, however, a finite and neutron to be identical. In practice, however, a finite width together with tails from other resonances give rise width together with tails from other resonances give rise to a nonto a non--resonant background, and even though it is resonant background, and even though it is smaller for the smaller for the ΔΔ(1232) than for higher mass resonances, (1232) than for higher mass resonances, it will differ for the proton and neutron. A difference it will differ for the proton and neutron. A difference between p between p →→ ΔΔ++ and n and n →→ΔΔ00 transition form factors would transition form factors would therefore provide the first hints about the isospin therefore provide the first hints about the isospin structure of the nonstructure of the non--resonant background. For I = 1/2 resonant background. For I = 1/2 transitions, on the other hand, such as to the Roper transitions, on the other hand, such as to the Roper resonance or the negative parity Sresonance or the negative parity S1111(1535), measurement (1535), measurement of the electroof the electro--excitation of the neutron would allow the excitation of the neutron would allow the first determination of the isospin dependence of first determination of the isospin dependence of resonance production. resonance production.

Documents

Measurements of the Neutron Structure Functions...measurement of the neutron structure function, F 2 n.n. In particular, the d/u ratio can be determined from the ratio of neutron to