simona malace university of south carolina users group workshop and annual meeting, june 7–9 2010,...
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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
S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)
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
S.P. Malace, Y. Kahn, W. Melnitchouk, C. Keppel, Phys. Rev. Lett. 104 102001 (2010)
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…
A. Accardi, S.P. Malace, in preparation
Plans for Future: Quark-Hadron Duality
prel
imin
ary
prel
imin
ary
Study applicability of QCD calculation at low values of W; criterion: separation between target jet and current jet,
(in preparation for) Stage 3…
y
3y 4y
A. Accardi, S.P. Malace, in preparation
Plans for Future: Quark-Hadron Duality
prel
imin
ary
dxQxFdxQxFM
m
M
m
x
x
parampx
x
datap ),(),( 2,2
2,2 Extend studies to larger Q2
(in preparation for) Stage 3…
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.