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

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 W 2 DIS to low W 2 DIS)
- PDFs extraction into the Resonance Region? (quark-hadron duality)
- plans for future

 First results from famous SLAC-MIT experiments: presented in 1968 in Vienna by Panofsky , published in 1969 resonance region
DIS
Deep inelastic scattering (DIS) 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 ”


Distribution of quarks and gluons ( PDFs ) inside the nucleon: fundamental characterization of its structure in QCD
PDFs
 connect hadron-parton processes
 universal: many processes calculated with same set of PDFs
 information as to the underlying structure of hadrons
 Decades of accumulated data
+ sophisticated QCD analyses =>
mapping of PDFs over a large kinematic range
Q: How precisely?
A: It depends…

 Two ideas of QCD + data :
 perturbative
Factorization:
F
2
 p
( x , Q
2
)
 i
 f
  f , , G
1
0 dyC
2
 i
( y ,
 s
( Q
2
))
  i / p
( x
, Q
2 y input (PDF)
)
NLO x dependence obtained from global fits to data
Evolution:
Q
2 d dQ
2
 i p
( x , Q
2
)
 j

  f , f , G
1 x dy y
LO
( P ij
0
( y )


( Q s
2

2
)
P ij
1
( y )

...)
  j p
( x y
, Q
2
)
 perturbative
Data: DIS ( ), neutrino DIS dimuon production, vector boson production, hadronic jet production,…
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

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

 Stage 1 (last few decades): LT calculations  PDFs constrained up to x ~ 0.7 ( CTEQ , MRST(MSTW) , GRV , etc.) stage 1 stage 2 stage 3?
 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)
 CTEQ6X
Accardi, Christy, Keppel, Melnitchouk,
Monaghan, Morfín, Owens, Phys. Rev. D 81,
034016 (2010)
Accardi et al., in preparation

Stage 3 (future):
 CTEQ6X: future?

 Operator Product Expansion: beyond LT: higher twist (HT) leading twist (LT)
M
2
( n )
( Q
2
)

1

0 dx x n

2
F
2
( x , Q
2
)

A
2
( n )
(
 s
( Q
2
))

A
(
4 n )
(
 s
( Q
2
))
Q
2

 
6


, 8 ,..
A

( n )
(

Q
 s
(

2
Q
2
))
, n

6 , 8 ,...
 To extend to large x and low->intermediate Q 2 :
1) higher twist  
/ Q
3) nuclear corrections
2
2) target mass corrections (TMC)  x
2
M
2
N
/ Q
2
4) quark-hadron duality
5) jet mass corrections (JMC) 
6) Heavy quark mass corrections
7) Large x resummation
8) Large x DGLAP evolution
9) parton recombination at large x m
 j
2
/ Q m
2
Q
2
/ Q
2
10) perturbative stability at low Q2
11) …
List from A. Accardi (talk at INT09)

CTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016 (2010)
LT+TMC residual power corrections ( HT )
(Hall C E00-116)
F
2
( x , Q
2
)

F
2
LT
( x , Q
2
)( 1

C (
Q
2 x )
);
C ( x )
 c
1 x c
2 ( 1
 c
3 x )
 TMC via colinear factorization ( CF ) method
 HT : applied multiplicatively ; same for proton as for neutron
 NLO global fit to proton and deuteron data with Q 2 > 1.69 GeV 2 and W 2 > 3
GeV 2 : DIS from SLAC, JLab, FNAL
Drell-Yan, W asymmetry data at higher x cut 0: Q 2 > 4 GeV 2 , W 2 > 12.25 GeV 2
(standard) cut 1: Q 2 > 3 GeV 2 , W 2 > 8 GeV 2 cut 2: Q 2 > 2 GeV 2 , W 2 > 4 GeV 2 cut 3: Q 2 > 1.69 GeV 2 , W 2 > 3 GeV 2

CTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016 (2010)
 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 no direct constraints from data
 u and d ~ stable with respect to choice of TMC if flexible enough param. of
HT is used

CTEQ6X: A. Accardi et al., Phys. Rev. D 81, 034016 (2010)
 d-quark constrained by Deuterium data:
F
2
A
( ,
2
)
   x
M
A
/ M dy f
0

F
2
N

 smearing function x y
, Q
2


 
1

4 M
2 x
2
Q
2
 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 ): strong enhancement of d-quark compared to ref.
Accardi et al., in preparation

S. Alekhin, Phys. Rev. D 63, 094022 (2001)
…
S. Alekhin, J. Blumlein, S. Klein, S. Moch, Phys. Rev. D 81, 014032 (2010)

NNLO global fit to data with W 2 > 3.4 GeV 2
F
2
( x , Q
2
)

F
2
LT , TMC
( x , Q
2
)

H
2
( x )
Q
2
 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]

Comparisons of full calculations on-shell off-shell (K-P)
CTEQ6X(standard)/ALEKHIN

F
2 p (direct constraints from data): very good agreement

 within 5% up to x = 0.8
within 15% at x = 0.9


F
2 d (direct constraints from data): very good agreement within 5% up to x = 0.8


F

2 n : good agreement within 15% up to x = 0.7
within 20-25% at x = 0.8
sensitive to nuclear corrections

Comparisons of full calculations

F
2 p comparisons (direct constraints from data): mostly insensitive to off-shell corrections in CTEQ6X (x < 0.9)

F
2 d comparisons (direct constraints from data): mostly insensitive to off-shell corrections in CTEQ6X (x < 0.8)
CTEQ6X(K-P off-shell)/ALEKHIN

F
2 n comparisons : ~ 15-20% change;
CTEQ6X(K-P off-shell)/ALEKHIN closer to unity

Compare: relative contributions of various effects ( HT )


TMC contributions same for both calculations (OPE) nuclear corrections: similar treatment

F
2 n
HT contributions differ : more for than F
2 p

Difference in HT for F
2 n correlated to difference in LT ?

 Need good (& extended) Q 2 coverage from data at fixed x for a thorough study of PDFs extraction at large x stage 1 stage 2 stage 3?
 Use quark-hadron duality to access even larger x and provide good
Q 2 coverage at large x for PDF studies
2 nd res. Region: Q 2 = 2 GeV 2
2 nd res. Region: Q 2 = 5 GeV 2

 Duality between quark and hadron descriptions of observables in electron-hadron scattering
Random facts about quark-hadron duality
 observed by Bloom and Gilman in proton F
2
(1969)
 firmly established for proton F
2 and F
L
(JLAB)
 studied in spin-dependent in semi-inclusive scattering (JLAB)
 recently acknowledged in neutron F
2
(JLAB)
 interpreted in OPE as cancellations of dynamical HT

…
Quark-Hadron Duality: experimental observation which could be a working hypothesis for extending PDFs at large x => needs to be verified and quantified

Region W min
1 st
W max
1.3 1.9
2 nd
3 rd
4 th
1.9 2.5
2.5 3.1
3.1 3.9
DIS 3.9 4.5 x

Q
2
DIS
( W
2 
Q
2 
M
2
)
4 th
3 rd
2 nd
1 st
To what extent the resonance region data
average to the QCD
curve?
Calculate:
I
  x x
M m
F
2 data
( x , Q
2
) dx
 x x
M m
F
2 param
( x , Q
2
) dx


To what extent the resonance region data average to a ( stage 2 )
QCD curve ( Alekhin03 )?
 x x
M m
F
2 p , data
( x , Q
2
) dx
 x
M x m
F
2 p , param
( x , Q
2
) dx

Within 10% : globally , low
W DIS, 4 th , 3 rd , 2 nd

1 st : 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
S.P. Malace et al., Phys. Rev. C 80, 035207 (2009)

 Some arguments: quark-hadron duality in F
2 p could be the result of accidental cancellations between quark charges (do not occur for F
2 n )…
Is quark-hadron duality an accident?
Verify quark-hadron duality in F
2 n
Need F
2 n in the resonance region…
New method : employs iterative procedure of solving integral convolution equations
Y. Kahn, W. Melnitchouk, S.A. Kulagin, Phys. Rev. C 79, 035205 (2009)
 Impulse Approximation – virtual photon scatters incoherently from individual nucleons
2
A
F x Q
2
( , )
   x
M
A
/ M dy f
0

F
2
N

 x y
, Q
2


 
1

4 M
2 x
2
Q
2 nuclear F
2 smearing function nucleon F
2

 Use proton and deuteron data at fixed Q 2
~
F
2 n
( x )

F
2 d
( x )

F
2 d ( QE )  
( off
 shell )
F
2 d
( x
(matched kinematics)
)

~
F
2 p
( x ) data data model model
 Data: SLAC at Q
GeV 2 at Q 2
2 = 0.6, 0.9, 1.7, 2.4
+ data from Jlab (Hall C E00-116 )
= 4.5, 5, 5.5, 6.2, 6.4 GeV 2
 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 F
2 n quasielastic peak
S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)

 F
2 n rate as for F
 F
2 n in resonance region : 3 resonant enhancements (fall with Q 2
2 p ) in resonance region appears to average to F at ~
2 n from Alekhin09
S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)
S.P. Malace, Y. Kahn, W. Melnitchouk, in preparation


To what extent the resonance region data average to a ( stage 2 )
QCD curve ( Alekhin09 )?
 x x
M m
F
2 n , data
( x , Q
2
) dx
 x x
M m
F
2 n , param
( x , Q
2
) dx W 2 : (1.3-1.9) GeV 2
 1 st RES region: agreement worsens at the highest Q 2 (corresponds to the largest x)
 2 nd and 3 rd RES regions: agreement within 15-20% , on average
W 2 : (1.9-2.5) GeV 2
W 2 : (2.5-3.1) GeV 2
 globally remarkable agreement: within 10%
S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)

(in preparation for) Stage 3…
A. Accardi, S.P. Malace, in preparation
 x x
M m
F
2 p , data
( x , Q
2
) dx
 x x
M m
F
2 p , param
( x , Q
2
) dx

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.

(in preparation for) Stage 3…
A. Accardi, S.P. Malace, in preparation
 Study applicability of QCD calculation at low values of W; criterion: separation between target jet and current jet,  y
 y

3
 y

4

(in preparation for) Stage 3…
A. Accardi, S.P. Malace, in preparation

Extend studies to larger Q 2 x
M  x m
F
2 p , data
( x , Q
2
) dx
 x x
M m
F
2 p , param
( x , Q
2
) dx

Spokespeople : S.P. Malace (contact person), I.M. Niculescu, C. Keppel
E12-10-002 (Hall C) : approved by PAC35
Will extend proton and deuteron F
2 precision measurements to larger x and Q 2 by measuring H(e,e’) and D(e,e’) cross sections in the resonance region and beyond up to Q 2 ~ 17 GeV 2 and x ~ 0.99
We aim for similar precision as for the lower energy run E00-116


Expected kinematic coverage in the ratio deuteron to proton
truncated moments from E12-10-002
M x
M
( x , Q
2
) dx
2

F
2 m
 x


Expected kinematic coverage in the ratio deuteron to proton
truncated moments from E12-10-002
M x
M
( x , Q
2
) dx
2

F
2 m
 x

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

No connection to what I discussed up to this point…

E03-104 in Hall A : search for medium modifications of the proton structure in 4 He(e,e’p) 3 H



P x
'
P z
'


4
He


P x
'
P z
'


H
Mike Paolone (Ph.D. in Dec. 2008):
M. Paolone, S. Malace, S. Strauch et al., accepted for publication to Phys. Rev. Lett.
 Induced polarization P y
: 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