Inclusive Scattering from Nuclei at x>1 and High Q2 with a 5.75 GeV Beam

Nadia Fomin

University of Virginia

Momentum distributions of nucleons inside nucleiShort range correlations (the NN force)

2-Nucleon and 3-Nucleon correlations

Comparison of heavy nuclei to 2H and 3He

Scaling (x, y) at large Q2

Structure Function Q2 dependence

Constraints on the high momentum tail of the nuclear wave function

Physics topics we can study at x>1

Quasielastic scattering: an example (Deuterium)

At low ν (energy transfer), the cross-section is dominated by quasi-elastic scattering

As the energy transfer increases, the inelastic contribution begins to dominate

Electron scattering and x ranges

Scattering from a free nucleon: 0<x<1 : x=1 (elastic) x<1 (inelastic)

x > 1:momentum is shared between nucleons, so 0<x<A probing the effect of nuclear medium on quark distributions kinematics determine whether the electron scatters from quarks or hadrons

Regions being probed: Low Q2 – entire nucleus (elastic) Intermediate Q2 – single nucleon (Quasielastic Scattering – QES)

Higher Q2 – DIS (“superfast” quarks at x>1) x>1 probes the QES and DIS regions

pM

Qx

2

2

Inelastic Cross Section and x-scaling

)]2/(cos),()2/(sin),(2['4

'22

222

14

223

QWQW

Q

E

ddE

d

The struck nucleon can be excited into a resonance state or be broken up

Inclusive Scattering -> only the electron is detected, so the final hadronic state is unknown

For unpolarized electron scattering from a charged particle with internal structure, the cross-section can be written as:

For the case of inelastic electron-proton scattering, W1 and W2 are the proton structure functions

If the reaction time is much less that the hadronization time, the reaction should look like scattering from a quasi-free quark

(x.1)

x-scaling (continued)

The cross section for elastic scattering from a free, spin ½ fermion with no internal structure is

)2

1(1

)]2/(cos)2/(sin2

['4

'

222

2

2

4

223

qq m

Q

m

Q

Q

E

ddE

d

(x.2)

In the DIS limit, the structure functions from Eq.x.1 simplify and we are able to extract the following expressions:

So, in this limit, the structure functions

simplify to functions of , instead of

functions of Q2 and ν independently.

)2

1(2

222

1

qqq m

Q

m

QWm

)2

1(2

2

qm

QW qm

Q

2

2

x-scaling (continued again)

For confined quarks, the δ-function is replaced by the momentum distribution of the quarks.

The structure functions are usually expressed in terms of the Bjorken x variable, defined as:

, where M is the nucleon mass.

In the limit of ν,Q2 , x is the fraction of the nucleon momentum carried by the struck quark, and the structure function in the scaling limit represents the momentum distribution of quarks inside the nucleon.

M

Qxbjorken 2

2

∞

More scaling: ξ-scaling

Another variable, in addition to x, is often used to examine scaling behavior in inelastic e-p scattering is the Nachtmann variable ξ.

)4

11(

2

2

22

QxM

x

As Q2 ∞, ξ x, so the scaling of structure functions should also be seen in ξ, if we look in the deep inelastic region.

However, the approach at finite Q2 will be different.

It’s been observed that in electron scattering from nuclei, the structure function νW2, scales at the largest measured values of Q2 for all values of ξ, including low ξ (DIS) and high ξ (QES).

ξ-scaling (continued)

Scaling is observed only at low values of x (x<0.4)

Onset of scaling occurs at higher Q2 for increasing values of ξ, but the structure function appears to approach a universal curve

Iron data from the NE3 experiment at SLAC

ξ-scaling : Competing Explanations

One explanation for ξ-scaling is that it’s a consequence of the Bloom-Gilman duality in e-p scattering

An alternative explanation proposed by Benhar and Liuti explains the observed scaling at high ξ-values in terms of y-scaling of the quasi-elastic cross-section.

A third explanation proposed by Sick and Day explains the apparent scaling by the approximate compensation between the contribution from the QE cross-section and the failure of the resonance and DIS contributions at large ξ and Q2.

Proton Resonance structure functions vs. the deep inelastic limit. Data is from SLAC experiment E133 and the scaling limit is from L.W. Whitlow

Bloom and Gilman examined the structure function in the resonance region as a function of ω’=1/x+M2/Q2 and Q2

They observed that the resonance form factors have the same Q2 behavior as the structure functions

The scaling limit of the inelastic structure functions can be generated by averaging over the resonance peaks seen at low Q2

If the same is true of a nucleon inside a nucleus, then the momentum distribution of the nucleons may cause this averaging of the resonances and the elastic peak.

The idea is that the Q2-dependence arises from looking at ξ, rather than y, is cancelled by the Q2-dependence of the final state interactions

y-scaling: From cross sections to momentum distributions

Inclusive electron scattering by nuclei at high Q2 is analyzed in the impulse approximation with fully relativistic kinematics. The nucleon cross-section is an incoherent sum over the individual nucleons

))()((),(),( 2/122*1

2/122

1''

2

kMpMMEkPdEdkddE

dq AAiei

A

iee

k and p=k+q are the initial and final momenta of the struck nucleon

Pi(k,E) is the spectral function

MA is the nucleon mass

E=M*A-1+M-MA is the separation energy

M*A-1 is the mass of the residual nucleon system

σei is the fully relativistic off-shell cross section for electron scattering from a nucleon of momentum k.

(1)

Using the delta function to do the angular integral and the constraints of energy and momentum conservation as well as requiring the final state particles to be on mass-shell, we arrive at

eii

A

i

E

E

EK

EK k

wEkPkdkdEq

_1

||1

)(

)(

||),(2),(max

min

max

min

2

0

__

2

1),,,( dEkq eieiei

(2)

,where φ is the polar angle of k with respect to q.

Next, we introduce a function F:

And y is defined using the delta function from eq.1

||),()(),(

),(

kyqSZAyqZS

qF

enep

2/1221

2/122 )())(( yMyqMM AA

(3)

(4)

)|,|,,(),( min)(

_

)( EyqyqS nepnep ,where

F is a function of q and y only and at large q for a fixed value of y, F has an asymptotic value -> it scales in y.

As q->∞, the dependence on q is weak, so F=F(y) at large momentum transfer and can be expressed as

n(k) is the nucleon momentum distribution, obtained by integrating the spectral function over energy.

Summary:

Scaling : the dependence of the reaction on a single new variable (y), rather than momentum transfer and energy

F(y) is defined as ratio of the measured cross-section to the off-shell electron-nucleon cross-section times a kinematic factor

y is the momentum of the struck nucleon parallel to the momentum transfer.

||

)(2)(y

dkkknyF

22

2

)()(

1)(

qyMNZdd

dyF

np

q

Y-Scaling (Example: 3He)

y is the momentum of the struck nucleon parallel to the momentum transfer.

0.1<Q2<3.9 (GeV2)

Slide provided by John Arrington with plots from Donal Day

Slide provided by John Arrington with plots from Donal Day

New Frontiers

Existing dataExisting He data

Improved 3He coverage: another perspective

E02-019 Details

E02-019 running is completedE02-019 is an extension of E89-008, but with

higher E (5.75 GeV) and Q2.Cryogenic Targets: H,2H, 3He, 4HeSolid Targets: Be, C, Cu, Au.Spectrometers: HMS and SOS (mostly HMS)

Experimental Setup in Hall C

SOSHMS

Scattering ChamberBeam Line

High Momentum Spectrometer Superconducting magnets in a QQQD configuration Maximum central momentum of 6.0 GeV/c with

0.1% resolution and a momentum bite of ±10% Solid angle of 6.7 msr Detectors

2 sets of Drift chambers2 sets of x-y hodoscopesGas Čerenkov detectorLead glass shower counter

Pion Rejection of ~75,000 using the Čerenkov and the Lead Glass Shower Counter

High Momentum Spectrometer

Short Orbit Spectrometer

For E02-019, the SOS is primarily used to estimate the charge symmetric background.

Has a solid angle of 7 msr and a large momentum bite (±20%)

Maximum central momentum of 1.75 GeV/c QDD magnet configuration (non-superconducting): Pion Rejection of ~10,000 using the Čerenkov and

the Lead Glass Shower Counter Detector Package is very similar to that of HMS

Newer Data is better Data

Xbj

Cro

ss-s

ecti

on (

cm2 /

MeV

·sr)

y(x=0.94) = -.01GeV

3He online spectrum

E=5.75 GeV

Phms=5.1 GeV/c

θhms=18°

All events past xbj=3y(x=2.32) = -0.58GeV

3He and Au coverage at 40°

Overlap regions look good

Status

All the data have been taken This experiment will provide data over an extended

kinematic range and significantly improve the 3He and 4He data sets

The positron background has been measured and is small for E02-019

Detector calibrations are currently being performed

Summary

The hard work is now beginning

Immediate goals:

Extraction of cross-sections, including acceptance, bin-centering, and radiating corrections

Extraction of scaling and structure functions, and comparison with theory

E02-019 Collaboration

J. Arrington (spokesperson), L. El Fassi, K. Hafidi, R. Holt, D.H.

Potterveld, P.E. Reimer, E. Schulte, X. Zheng

Argonne National Laboratory, Argonne, IL

B. Boillat, J. Jourdan, M. Kotulla, T. Mertens, D. Rohe, G. Testa, R. Trojer

Basel University, Basel, Switzerland

B. Filippone (spokesperson)

California Institute of Technology, Pasadena, CA

C. Perdrisat

College of William and Mary, Williamsburg, VA

D. Dutta, H. Gao, X. Qian

Duke University, Durham, NC

W. Boeglin

Florida International University, Miami, FL

M.E. Christy, C.E. Keppel, S. Malace, E. Segbefia, L. Tang,

V. Tvaskis, L. Yuan

Hampton University, Hampton, VA

G. Niculescu, I. Niculescu

James Madison University, Harrisonburg, VA

P. Bosted, A. Bruell, V. Dharmawardane, R. Ent, H. Fenker, D. Gaskell, M.K. Jones, A.F. Lung (spokesperson), D.G. Meekins, J. Roche, G. Smith, W.F. Vulcan, S.A. Wood

Jefferson Laboratory, Newport News, VA

B. Clasie, J. Seely

Massachusetts Institute of Technology, Cambridge, MA

J. Dunne

Mississippi State University, Jackson, MS

V. Punjabi

Norfolk State University, Norfolk, VA

A.K. Opper

Ohio University, Athens, OH

F. Benmokhtar

Rutgers University, Piscataway, NJ

H. Nomura

Tohoku University, Sendai, Japan

M. Bukhari, A. Daniel, N. Kalantarians, Y. Okayasu, V. Rodriguez

University of Houston, Houston, TX

T. Horn, Fatiha Benmokhtar

University of Maryland, College Park, MD

D. Day (spokesperson), N. Fomin, C. Hill, R. Lindgren, P. McKee, O. Rondon, K. Slifer, S. Tajima, F. Wesselmann, J. Wright

University of Virginia, Charlottesville, VA

R. Asaturyan, H. Mkrtchyan, T. Navasardyan, V. Tadevosyan

Yerevan Physics Institute, Armenia

S. Connell, M. Dalton, C. Gray

University of the Witwatersrand, Johannesburg, South Africa