Simona Malace University of South Carolina Users Group Workshop and Annual Meeting, June 7–9 2010, JLAB

Nucleon Structure at

Large Bjorken x Simona Malace

University of South Carolina

Users Group Workshop and Annual Meeting, June 7–9 2010, JLAB

Outline

QCD calculations and Parton Distribution Functions (PDFs)

pQCD Leading Twist (LT) and standard PDFs extraction

how far pQCD LT can take us? (PDFs uncertainties)

efforts to push PDFs extraction at larger x

- CTEQ6X and Alekhin et al.: PDFs at large x (from high W2 DIS to low W2 DIS)

- PDFs extraction into the Resonance Region? (quark-hadron duality)

- plans for future

DIS

First results from famous SLAC-MIT experiments: presented in 1968 in Vienna by Panofsky, published in 1969

Deep inelastic scattering (DIS)

region

resonance region

“… theoretical speculations are focused on the possibility that these data might give evidence on the behavior of point-like, charged structures within the nucleon”

Quarks inside the Nucleon?

PD

F

Decades of accumulated data + sophisticated QCD analyses => mapping of PDFs over a large kinematic range

Quarks inside the Nucleon

PDFs connect hadron-parton processes universal: many processes calculated with same set of PDFs information as to the underlying structure of hadrons

Distribution of quarks and gluons (PDFs) inside the nucleon: fundamental characterization of its structure in QCD

Q: How precisely?A: It depends…

Two ideas of QCD + data:

+

x dependence obtained from global fits to

data

Data: DIS ( ), neutrino DIS dimuon production, vector boson production, hadronic jet production,…

NNdlpl ,,,

input (PDF)

perturbative

Factorization:

Gffi

pisip Q

y

xQydyCQxF

,,

1

0

2/

22

22 ),())(,(),(

perturbative

Gffj x

pjijs

ijpi Qy

xyP

QyP

y

dyQx

dQ

dQ

,,

121

202

22 ),(...))(

2

)()((),(

Evolution:LO

NLO+

Standard PDF extraction in QCD

1) pQCD, LT (leading twist) calculation cannot use data from kinematic regions which require corrections beyond LT

2) data coverage not uniform across x knowledge of PDFs not uniform across x

PDFs Uncertainties

small

larg

e

W2 >

12.2

5

Q2 > 4

example: CTEQ6

data n

ot use

ddata

use

d

No data at large x large uncertainties for PDFs at large x

RES. r

egio

n

W2 >

12.2

5

W2 >

3

stage 1

stage 2

stage 3?

Extraction of PDFs in QCD Stage 1 (last few decades): LT calculations PDFs

constrained up to x ~ 0.7 (CTEQ, MRST(MSTW), GRV, etc.)

Stage 2 (last decade): calculations beyond LT PDFs constrained up to x ~ 0.8-0.9 Alekhin et al. S. Alekhin, Phys. Rev. D 63, 094022 (2001) ….

S. Alekhin, J. Blumlein, S. Klein, S. Moch, Phys. Rev. D 81, 014032 (2010)

CTEQ6XAccardi, Christy, Keppel, Melnitchouk, Monaghan, Morfín, Owens, Phys. Rev. D 81, 034016 (2010)

Accardi et al., in preparation

CTEQ6X: future?

Stage 3 (future):

Corrections beyond Leading Twist

1

0 ,..8,62

2)(

2

2)(42)(

22

222)(

2 ,...8,6,))(())((

))((),()(

nQ

QA

Q

QAQAQxFxdxQM s

ns

n

snnn

Operator Product Expansion:leading twist (LT)

beyond LT: higher twist (HT)

To extend to large x and low->intermediate Q2:1) higher twist2) target mass corrections (TMC)3) nuclear corrections

4) quark-hadron duality5) jet mass corrections (JMC) 6) Heavy quark mass corrections7) Large x resummation8) Large x DGLAP evolution9) parton recombination at large x10) perturbative stability at low Q211) …

2/Q222 /QMx N

22 /Qm j22 /QmQ

List from A. Accardi (talk at INT09)

least

PDFs Extraction: Calculations beyond LT

LT+TMC

)1()(

);)(

1)(,(),(

31

22

22

2

2 xcxcxC

Q

xCQxFQxF

c

LT

residual power

corrections (HT)

NLO global fit to proton and deuteron data with Q2 > 1.69 GeV2 and W2 > 3 GeV2: DIS from SLAC, JLab, FNAL Drell-Yan, W asymmetry data at higher x

(Hall C E00-116)

cut 0: Q2 > 4 GeV2, W2 > 12.25 GeV2 (standard)

cut 1: Q2 > 3 GeV2, W2 > 8 GeV2

cut 2: Q2 > 2 GeV2, W2 > 4 GeV2

cut 3: Q2 > 1.69 GeV2, W2 > 3 GeV2

CTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016 (2010)

TMC via colinear factorization (CF) method HT: applied multiplicatively; same for proton as for neutron

no direct constraints from data

stronger suppression of d-quark PDF at large x (sensitive to the treatment of nuclear corrections) greatly reduced experimental errors: 10-20% for x < 0.6 and up to 40-60% at larger x

u and d ~ stable with respect to choice of TMC if flexible enough param. of HT is used

PDFs Extraction: Calculations beyond LTCTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016

(2010)

PDFs Extraction: Calculations beyond LTCTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016

(2010) d-quark constrained by Deuterium data:

2

2241

Q

xMF x Q dy f y F

xyQA N A N

x

M M

N p n

A

22

0 22( , ) ( , ) ,//

,

smearing function

d-quark extraction sensitive to the treatment of nuclear corrections no nuclear corrections: strong enhancement of d-quark compared to ref.

nuclear corrections: strong suppression of d-quark compared to ref.

nuclear corrections (DMC): strongenhancement of d-quark compared to ref.

Accardi et al., in preparation

PDFs Extraction: Calculations beyond LT

222,

22

2

)(),(),(

Q

xHQxFQxF TMCLT

TMC: via “Georgi and Politzer” (OPE) [CTEQ6X: TMC via CF]

HT: applied additively; HT(proton) different from HT(neutron) [CTEQ6X: HT applied multiplicatively; HT(proton) same as HT(neutron)]

nuclear corrections + off-shell via Kulagin-Petti (K-P) [CTEQ6X(standard) = nuclear corrections, no off-shell corrections]

S. Alekhin, J. Blumlein, S. Klein, S. Moch, Phys. Rev. D 81, 014032 (2010) NNLO global fit to data with W2 > 3.4 GeV2

S. Alekhin, Phys. Rev. D 63, 094022 (2001)…

CTEQ6X vs ALEKHIN et al.

F2p (direct constraints from

data): very good agreement within 5% up to x = 0.8 within 15% at x = 0.9

F2d (direct constraints from

data): very good agreement within 5% up to x = 0.8

F2n: good agreement

within 15% up to x = 0.7 within 20-25% at x = 0.8

CTEQ6X(standard)/ALEKHIN

sensitive to nuclear corrections

on-shell off-shell (K-P)Comparisons of full calculations

CTEQ6X vs ALEKHIN et al.

CTEQ6X(K-P off-shell)/ALEKHINComparisons of full calculations

F2p comparisons (direct

constraints from data): mostly insensitive to off-shell corrections in CTEQ6X (x < 0.9) F2

d comparisons (direct constraints from data): mostly insensitive to off-shell corrections in CTEQ6X (x < 0.8)

F2n comparisons: ~ 15-20%

change; CTEQ6X(K-P off-shell)/ALEKHIN closer to unity

CTEQ6X vs ALEKHIN et al.Compare: relative contributions of various effects (HT)

TMC contributions same for both calculations (OPE) nuclear corrections: similar treatment

HT contributions differ: more for F2

n than F2p

Difference in HT for F2n

correlated to difference in LT?

resonances

W2 >

12.2

5

W2 >

3

stage 1

stage 2

stage 3?

2nd res. Region: Q2 = 2 GeV2

2nd res. Region: Q2 = 5 GeV2

PDFs extraction: into the Res. Region?

Use quark-hadron duality to access even larger x and provide goodQ2 coverage at large x for PDF studies

Need good (& extended) Q2 coverage from data at fixed x for a thorough study of PDFs extraction at large x

Quark-Hadron Duality: experimental observation which could be a working hypothesis for extending PDFs at large x

=> needs to be verified and quantified

Quark-Hadron Duality Duality between quark and hadron descriptions of observables in electron-hadron scattering

observed by Bloom and Gilman in proton F2 (1969)

firmly established for proton F2 and FL (JLAB)

studied in spin-dependent in semi-inclusive scattering (JLAB)

recently acknowledged in neutron F2 (JLAB)

interpreted in OPE as cancellations of dynamical HT

…

Random facts about quark-hadron duality

dxQxFdxQxFIM

m

M

m

x

x

paramx

x

data ),(),( 22

22 Calculate:

1st 2st 2nd

2st 3rd

4th

DIS

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

)( 2222 MQWQx

Quantifing Quark-Hadron Duality

To what extent the resonance region data average to the QCD

curve?

Quark-Hadron Duality in F2p

To what extent the resonance region data average to a (stage 2) QCD curve (Alekhin03)?

dxQxFdxQxFM

m

M

m

x

x

parampx

x

datap ),(),( 2,2

2,2

Within 10% : globally, low W DIS, 4th, 3rd, 2nd

S.P. Malace et al., Phys. Rev. C 80, 035207 (2009)

1st : special case some models predict stronger violations of duality

calculation based on handbag diagram may break at low W

at the largest x where QCD curves poorly constrained => difficult to test duality

Impulse Approximation – virtual photon scatters incoherently from individual nucleons

New method : employs iterative procedure of solving integral convolution equations

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

F x Q dy f y FxyQA N A N

x

M M

N p n

A

22

0 22( , ) ( , ) ,//

,

nuclear F2 nucleon F2

smearing function

2

2241

Q

xM

Quark-Hadron Duality in F2n

Some arguments: quark-hadron duality in F2p could be the result

of accidental cancellations between quark charges (do not occur for F2

n)…

Is quark-hadron duality an accident?Verify quark-hadron duality in F2n

Need F2n in the resonance region…

quasielastic peak

Use proton and deuteron data at fixed Q2 (matched kinematics)

)(~

)()()(~

22)()(

222 xFxFFxFxF pdshelloffQEddn

data

data

Data: SLAC at Q2 = 0.6, 0.9, 1.7, 2.4 GeV2 + data from Jlab (Hall C E00-116) at Q2 = 4.5, 5, 5.5, 6.2, 6.4 GeV2

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

Extraction of F2n from Data

model model

QE extracted from data using model (form factors + same smearing function as for extraction) Off-shell corrections: upper limit from model(MST) ~1.5%; assign 100% uncertainty to correction => contributes < 2% to total uncertainty on F2

n

F2n in resonance region: 3 resonant enhancements (fall with Q2

at ~ rate as for F2p)

F2n in the Resonance Region


F2n in resonance region appears to average to F2

n from Alekhin09

S.P. Malace, Y. Kahn, W. Melnitchouk, in preparation

2nd and 3rd RES regions: agreement within 15-20%, on average

1st RES region: agreement worsens at the highest Q2 (corresponds to the largest x)

globally remarkable agreement: within 10%

W2 : (1.3-1.9) GeV2

W2 : (1.9-2.5) GeV2

W2 : (2.5-3.1) GeV2

Quark-Hadron Duality in F2n


To what extent the resonance region data average to a (stage 2) QCD curve (Alekhin09)?

dxQxFdxQxFM

m

M

m

x

x

paramnx

x

datan ),(),( 2,2

2,2

Plans for Future: Quark-Hadron Duality

A. Accardi, S.P. Malace, in preparation

preliminary

Study sensitivity of quark-hadron duality ratios to various prescriptions for inclusion of:

HT: additive vs multiplicative; HT(proton) same/different than HT(neutron)

TMC: OPE, CF…

etc.

dxQxFdxQxFM

m

M

m

x

x

parampx

x

datap ),(),( 2,2

2,2

(in preparation for) Stage 3…



prel

imin

ary

prel

imin

ary

Study applicability of QCD calculation at low values of W; criterion: separation between target jet and current jet,


y

3y 4y



prel

imin

ary

dxQxFdxQxFM

m

M

m

x

x

parampx

x

datap ),(),( 2,2

2,2 Extend studies to larger Q2


E12-10-002 (Hall C): approved by PAC35 Will extend proton and deuteron F2 precision measurements to larger x and Q2 by measuring H(e,e’) and D(e,e’) cross sections in the resonance region and beyond up to Q2 ~ 17 GeV2 and x ~ 0.99

Plans for Future: E12-10-002 @ 12 GeVSpokespeople: S.P. Malace (contact person), I.M. Niculescu, C.

Keppel

We aim for similar precision as for the lower energy run E00-116

Plans for Future: E12-10-002 @ 12 GeV Expected kinematic coverage in the ratio deuteron to

proton truncated moments from E12-10-002dxQxFM

M

m

x

x

),( 222

Plans for Future: E12-10-002 @ 12 GeV Expected kinematic coverage in the ratio deuteron to

proton truncated moments from E12-10-002dxQxFM

M

m

x

x

),( 222

The 3rd International Workshop on Nucleon Structure at Large Bjorken x (HiX2010)

This workshop will continue a series of meetings held previously at Temple University, Philadelphia (2000) and CPPM, Marseille (2004).

We will have ~36 speakers (30 minutes talks); 30 speakers already confirmed

Proceedings

We can offer travel support for students

Plans for Future

http://conferences.jlab.org/HiX2010/

Plans for Future: Py in 4He(e,e’p)3HNo connection to what I discussed up to this point…

E03-104 in Hall A: search for medium modifications of the proton structure in 4He(e,e’p)3H

Hz

x

Hez

x

P

P

P

P

'

'

'

'

4

Induced polarization Py: my primary responsibility in the project

http://www.jlab.org/intralab/calendar/phys_seminar/2010/Malace_talk.pdf

S.P. Malace, M. Paolone, S. Strauch et al., in preparation

Mike Paolone (Ph.D. in Dec. 2008): M. Paolone, S. Malace, S. Strauch et al., accepted for publication to Phys. Rev. Lett.

Documents

Simona Malace University of South Carolina Users Group Workshop and Annual Meeting, June 7–9 2010, JLAB