Hall C Spin-Averaged Structure Functions

Program: Status and Outlook

S. Malace (JLab)

Outline

electron-nucleon inclusive scattering: from observables to model parameters, the structure functions

status of FL measurements & the Rosenbluth LT separation technique

Hall C unpolarized structure functions program (will not cover the the EMC effect and x > 1 program): FL measurements on proton in the resonance region Moments of the proton FL structure function and comparison to QCD fits FL on deuteron in the resonance region and extraction of non-singlet moments for F2, FL

RD – RH at low Q2

RA – RD in the resonance region status of RA – RD measurements in DIS implications of RA RD for the physics interpretation of sA/sD

Plans for future PR12-13-001: measurements of Rp, RA-RD, F2, F1, FL in a model-independent fashion in DIS

Structure Functions

s 221 4/),( TMKQxF purely transverse

)4

1(4/)(),(22

222

2xM

QKQxF TL ss combination of L & T

Probe the quark structure of the nucleon: electron deep inelastic scattering off nucleon targets

12

22

2

'22'

2

)2

tan)4

1(21(1

1

2

s

xM

Q

E

E

Q

K)εσ+Γ(σ=

dEd

dLT

e

e

p M

W QED + QCD

Virtual photon: longitudinally /transversely

polarized

Observables – cross sections:

'

2

dEd

d

s),( 2QxTs ),( 2QxLs

Model Parameters – Structure Functions:

T

LRs

s

purely longitudinal

s2

2

4

2),( L

L

xKMQxF

Structure Functions: QCD

Extraction of SFs from cross section measurements useful for a detailed understanding of QCD

xP (1-x)P

e e

Infinite Momentum Frame (IMF) Naïve QPM: Q2 scaling (Bjorken scaling)

i

ii xfexF )(2

1)(

21 1

22 2)()( xFxfexxF

i

ii

if longitudinal momentum distribution of parton i

In IFM FL R sL = 0, no transverse momentum

QCD-improved QPM: Q2 scaling violations

In QCD FL R sL 0, longitudinal & transverse momentum (gluon radiation)

FL directly connected to gluons

gluon radiation

Structure Functions: F2

F2 has been precisely mapped in both x and Q2

Scaling violations measured over orders of magnitude in x and Q2 well described by a universal set of parton distribution functions (PDFs) within pQCD

R

R

Q

K

dEd

dF

s

1

1

)/1(4 222'

2

2

Most experiments that provided the wealth of data on F2 did not measure R in a model-independent fashion

Structure Functions: FL

FL has NOT been precisely mapped in both x and Q2

L/T Separations: Rosenbluth Technique

= transverse flux = relative longitudinal flux

Why fewer data on FL?

)εσ+(σ=dEd

dLT'

21

s ),( 2QxTs

intercept ),( 2QxLs

slo

pe

The L & T contributions are separated by performing a fit of the reduced cross section dependence with at fixed x and Q2

Requirements for precise L/T extractions:

As many points as possible spanning a large interval from 0 to 1 as many (E, E’, ) settings as possible Very good control of point-to-point systematics 1-2 % on the reduced cross section translates into 10-15 % on FL

To date the most precise, model-independent L/T extractions come from SLAC and JLab

Hall C Program: Structure Functions

year experiment type targets physics

1999 E94-110 L/T H F1, FL, F2

2000 E99-118 L/T H, D, nuclei F1, FL, F2

2003 E00-002 L/T H, D F1, FL, F2

2003 E00-116 No L/T H, D F2

2005 E02-109 L/T D F1, FL, F2

2007 E06-009 L/T D F1, FL, F2

2005(7) E04-001 L/T C, Al, Fe/Cu F1, FL, F2

nucl-exp/0410027

PRL98:14301

publ. drafted

PRC80:035207 PRL104:102001

finalizing analysis

drafting publ.

drafting publ./finalizing analysis

year experiment type targets physics

2015 E12-10-002 No L/T H, D F2

? PR12-13-001 L/T H, D, Be, C, Cu, Ag, Au

F1, FL, F2, RA - RD

E94-110: Proton FL & R in RES Region

Alekhin

MRST2004+TM MRST2004

~ 200 individual L/T separations

one of the most precise ever performed (< 2 % point-to-point uncertainties at the cross section level)

the resonance structure clearly observed in FL

first observation of quark-hadron duality in FL

data have been since included in global fits of F1, FL, R, F2 and used for FL moments calculations

Y. Liang, Ph.D. Thesis, Hampton 2002

Moments of Proton FL Inclusion of high-precision E94-110 data

results in small uncertainties at Q2 < 4 GeV2 P. Monaghan et al., arXiv:1209.4542

Nachtmann moments of the proton FL extracted for Q2: (0.75 - 45) GeV2 and compared to C-N moments extracted from QCD calculations

Careful study of uncertainties for x intervals where lack of measurements lead to use of model

Conclusions:

Neglecting HT or HO terms in the PDF fits may lead to an overestimation of the PDFs at large x

PDF fits should include large-x F2 and FL data

E06-009: Deuterium FL in RES Region

Extend high-precision RES region L/T separations to deuteron

Allow non-singlet moment extractions for F2 ,F1 (and FL) and compare to lattice predictions at Q2 = 4 GeV2 experimental test of QCD predictions of the nucleon valence structure

Extract FLn from FL

d and FLp and

allow study of quark-hadron duality for neutron in both transverse and longitudinal structure

I. Albayrak, Ph.D. Thesis, Hampton 2011

Construct FLp and FL

d (FLn) moments and compare to those extracted

from theory to test pQCD calculations

preliminary

E06-009

Preliminary, do not quote

E06-009: Non-Singlet Moments of F2 FL I. Albayrak, Ph.D. Thesis, Hampton 2011

Cornwall-Norton Moments before Fermi corrections

Cornwall-Norton Moments after Fermi corrections

Extract non-singlet moments: 2Mp – Md

(corr.)

Use existing Mp (Monaghan et al.) For D, extract QE contribution from measurements, add world data to populate the entire x range (SLAC), apply Fermi corrections

Calculate the Md(corr.) moment

Q2 (GeV2) ML2(NS) ML

4(NS)

2 0.0068 (65) 0.0025 (12)

3 0.0042 (92) 0.0023 (9)

4 0.0020 (161) 0.0009 (13)

n Hall C (prev.) E06-009 Hall B LQCD1 LQCD2 LQCD3

2 0.049 (17) 0.045 (3) 0.050 (9) 0.059 (8) 0.091 (8) 0.082 (3)

4 0.015 (3) 0.0090 (4) 0.0094 (16) 0.009 (3) 0.030 (16) 0.023 (7)

F2 non-singlet moments

E00-116: Q-H Duality in F2p and F2

n

S. Malace, Ph.D. Thesis, Hampton 2006 Phys. Rev. C 80, 035207 2009

Region Wmin Wmax

1st 1.3 1.9 2nd 1.9 2.5 3rd 2.5 3.1 4th 3.1 3.9 DIS 3.9 4.5

Calculate:

)( 2222 MQWQx

max

min

max

min

22

x

x

pQCDx

x

data dxFdxF

To what extent the resonance region data average to the QCD curve?

Good agreement between RES data and QCD fit on average; averaged RES data could be used to constrain PDFs at large x

E00-116: Q-H Duality in F2p and F2

n

)(~

)()()(~

22

)()(

222 xFxFFxFxF pdshelloffQEddn

data

data

S. Malace, Ph.D. Thesis, Hampton 2006

The inelastic contribution to the neutron F2

n structure function is extracted from measurements of F2

d and F2

p in a model-dependent fashion (off-shell corrections included; FSI, MEC not included but expected to be quite small)

The extraction agrees to F2n from

BoNUS

Y. Kahn, W. Melnitchouk, S.A. Kulagin, Phys. Rev. C 79, 035205 (2009)

S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)

N. Baillie et al., Phys. Rev. Lett. 108 199902 (2012)

E00-116: Q-H Duality in F2p and F2

n

S. Malace, Ph.D. Thesis, Hampton 2006

W2 : (1.3-1.9) GeV2

W2 : (1.9-2.5) GeV2

W2 : (2.5-3.1) GeV2

Confirmation of duality in both proton and neutron => phenomenon not accidental but a general property of nucleon structure functions => use it to access the large-x region

S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)

E99-118/E00-002: RD – RH at low Q2 V. Tvaskis, Ph.D. Thesis, Vrije 2004 (E99-118)

V. Tvaskis, A. Tvaskis, I. Niculescu, G. Niculescu (E00-002)

Precision L/T separations on proton and deuteron at low Q2

preliminary, do not quote

E99-118: first hint of RD RH

V. Tvaskis et al., PRL 98 142301 (2007)

029.0054.0 HD RR

E00-002: confirmation of systematic negative value of RD RH

018.0042.0 HD RR

To be submitted for publication soon: preliminary, do not quote

The difference amounts to ~20% effect in this kinematic range

E04-001/E06-009: RA - RD

w2

)](1

1[ DAD

TD

TA

D

A RRR

s

s

s

s

V. Mamyan, Ph.D. Thesis, UVA (2011)

preliminary, do not quote

preliminary, do not quote

Precision L/T separations on deuteron, carbon, aluminum and copper in RES region mostly

Extract RA – RD from fitting the dependence of the nuclear to deuterium cross section ratio with

DR

1

,

Preliminary results indicate a negative value for RA – RD for all targets studied

RA – RD in DIS: Experimental Status

Summary by D. Gaskell

Present data lack in precision and kinematic coverage thus failing to set a tight constraint on the nuclear dependence of R

RA – RD = ? in DIS: Implications Why do we care to test WITH HIGH PRECISION if RA different than RD?

It can affect the physics interpretation of modifications of the nucleus to deuteron cross section ratio sA/sD

])1)(1(

)1(1[

),(

),(2

2

22

DDD

A

D

A

RR

R

QxF

QxF

s

s

]

)1(1[

),(

),(2

1

21

DD

A

D

A

R

R

QxF

QxF

s

s

antishadowing EMC effect

antishadowing

EMC effect

Seen in DIS but NOT in Drell-Yan nor in neutrino scattering

Small effect: few percent

Independent of A

In the leading twist formalism connected to enhancements in the valence quark and gluon distributions

If we cannot equate the cross section ratio to the F2 (or F1) ratio, then the direct connection to modifications of the quark distributions cannot be easily made

RA – RD = ? in DIS: Implications for the Antishadowing Region

“Moderate to low precision” data leave room for various assumptions regarding limits on RA - RD

NMC:

NMC data taken at large Q2, R is small in absolute value presumably harder to spot small differences between RA and RD

V. Guzey et al., PRC 86 045201 (2012)

“Since the nuclear dependence of R has not as yet been systematically measured, we shall test two assumptions for ∆R…”

1) (Absolute) RA – RD = 0.04

2) (Relative) (RA – RD)/RN = 30%

(RA – RD)NMC = 0.04 (RA – RD)/RN = 22 - 120%

Implications for the Antishadowing Region

])1)(1(

)1(1[

),(

),(2

2

22

DDD

A

D

A

RR

R

QxF

QxF

s

s

])1(

1[),(

),(2

1

21

DD

A

D

A

R

R

QxF

QxF

s

s

EMC, BCDMS, NMC: close to unity

regardless of the assumption made

for R ),(

),(2

2

22

QxF

QxFD

A

D

A s

s

On the other hand: D

A

D

A

QxF

QxF

s

s

),(

),(2

1

21

In fact, the few percent enhancement in the cross section ratio is significantly reduced or disappears altogether in the F1 structure function ratio if a positive small variation of R around zero is assumed

RA – RD = ? in DIS: Implications for the Antishadowing Region

])1)(1(

)1(1[

),(

),(2

2

22

DDD

A

D

A

RR

R

QxF

QxF

s

s

])1(

1[),(

),(2

1

21

DD

A

D

A

R

R

QxF

QxF

s

s

SLAC E140, E139: NOT close to unity but mid-range or smaller

positive R translates into

),(

),(

),(

),(2

2

22

21

21

QxF

QxF

QxF

QxFD

A

D

A

D

A

s

s

and in the reduction or disappearance of the antishadowing effect in F1 structure function

Could the antishadowing effect observed in DIS nuclear to deuteron cross section ratios be due to the FL contribution mostly?

needs experimental verification

RA – RD = ? in DIS: the EMC Effect Region

Slight disagreement between SLAC and JLab data for large A targets (good agreement for small A ones) could this be due to RA being different than RD?

E139 data mostly at large ε

JLab data at small ε if RA ≠ RD, this might explain the difference

Motivated the Hall C Nuclear Structure Functions Collaboration to re-examine earlier experiments that measured the nuclear dependence of R

)](1

1[ DAD

TD

TA

D

A RRR

s

s

s

s

RA – RD = ? in DIS: the EMC Effect Region

SLAC E140 measurements of dependence of cross section ratio sA/sD for x = 0.2, 0.35, 0.5 and Q2 = 1, 1.5, 2.5 and 5 GeV2 on Fe and Au targets

E140, Phys. Rev. D 49 5641 (1993)

With NO Coulomb corrections applied RA – RD consistent with zero within uncertainties

Reanalysis of SLAC E140 by Solvignon and collaborators including Coulomb corrections calculated in the Effective Momentum Approximation

With Coulomb corrections applied RA – RD 2 standard deviations away from zero

Rp, RA – RD = ? in DIS: PR12-13-001 We propose to measure in Hall C with unprecedented statistical precision inclusive inelastic electron-nucleon and electron-nucleus cross sections in DIS to perform high-precision Rosenbluth separations and extract Rp, RA – RD, F1, FL, F2 in a model-independent fashion

Projected statistics: 0.2 – 0.5% in a W2 bin of 0.1 GeV2

Systematic: we assumed 1.8 % for individual cross sections and 1.1 % for the cross section ratios (mostly based on the 6 GeV performance)

We will use SHMS and HMS

We will use: H, D, Be, C, Cu, Ag, Au targets

PR12-13-001: Projections

We use a LT fit to calculate the reduced cross section at the proposed kinematics which is then randomized according to the point-to-point syst. uncertainty the randomized reduced cross section is then fitted with epsilon and to R and its uncertainty

We estimate the projected precision of our proposed data assuming that we will match the precision of the 6 GeV LT experiments

Rp in DIS: PR12-13-001 Projections for the Rp extraction in DIS

The large acceptance of SHMS ensures a very good coverage from low (~0.1) to high (~0.8) x; we would considerably improve the FL

p mapping (could be used in PDF fits to constrain the gluon especially at small x)

RA – RD = ? in DIS: PR12-13-001 Projections for the RA - RD extraction in DIS

Similar precision as SLAC but much better kinematic coverage in x and Q2 and a wide variety of targets

We will precisely map F1A/F1

D , FLA/FL

D and F2A/F2

D in the antishadowing region and for part of the EMC effect region

PR12-13-001: Summary We would provide one of the largest Rosenbluth LT data set on proton and on a variety of nuclear targets (Be, C, Cu, Ag, Au) with a kinematic coverage in x from 0.1 to 0.6 and in Q2 from 1 to 5 GeV2

These measurements would help address some of the questions that arose recently regarding:

the FL vs F1 contribution to the

nuclear to deuteron cross section ratio in the antishadowing region

slight disagreement between JLab (low ) and SLAC (large ) data in the EMC effect region

FL data: provide constraints on the

gluon especially at low x, where the gluon contribution to FL is quite large

Summary

Acknowledgements: E. Christy, D. Gaskell, I. Albayrak, V. Mamyan, V. Tvaskis, I. & G. Niculescu, R. Ent, C. Keppel, P. Solvignon, Hall C staff

Hall C unpolarized structure functions program: we are probing the quark and gluon structure of the nucleon

one of the best calibrated high-precision spectrometers: HMS

allows us to access observables that require high experimental precision in their extraction (R) but whose detailed knowledge is essential to constrain the physics interpretation of well know quantities like sA/sD

perfectly suited to provide experimental constraints at moderate/large x &

moderate Q2 (low W) to improve knowledge of quark distributions in the valence region our data provide constraints for the newer generation PDF fits (CJ, ABKM) that venture and seek experimental constraints into the large x & moderate Q2 region where non-perturbative effects are non-negligible