Post on 04-Jan-2016
Simona MalaceUniversity of South Carolina
Overview
Standard pQCD fits and their limitations (example => CTEQ6)
Another kind of QCD fits: extension of fits at larger x in the nonperturbative region (example => Alekhin)
Can we go even further? Quark-hadron duality: => experimental observation & working hypothesis for PDFs extension at large x => recent results from Jlab on quark-hadron duality in the F2
p,d structure function => Quark-hadron duality in F2
n
Plans for future
Complete picture(or closer to …)
Naive picture
Operator Product Expansion in pQCD:
leading-twist higher-twist
The quark and gluon structure of the Proton in QCD
1 ( ) 2( ) 2 2 22 2 2
2,4,..0
( ( ))( ) ( , ) , 2, 4,6,..
nn n sA Q
M Q dx x F x Q nQ
q
xqxexF )(22
q
Qxqxqxe
QxF22
22
,
,
perturbative ln(Q2) corrections
nonperturbative corrections
1 (2) 2(2) 2 2 2 42 2
0
( )( ) ( ( , ) ( , )) ...q
q
A QM Q e dx x q x Q q x Q
Q
How does it compare to data?
Very good, where only the leading twist is expected to contribute
Most cases, parton distribution functions (PDFs) are extracted from data from “safe kinematic regions”, only (no nonperturbative effects) What is the price to pay? A: Unconstrained PDFs outside the “safe kinematic regions”
Let’s see why….Let’s see why….
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PDFs Extraction in pQCD
Two basic ideas of QCD:
Factorization: separate the long-distance from short-distance dependence
Gffj x
pjsijpi QQx
Pd
QxdQ
dQ
,,
1222
22 ),())(,(),(
),())(,(, 222
,,
1
0
22 QQ
xCdQxF pis
i
Gffi
p
perturbative
nonperturbative input (PDF)
Evolution: knowledge of implies knowledge of ……………at all Q2 > (<) Q2
0, where a perturbative expansion is still appropriate => DGLAP equations
),( 20Qxpi
),( 2Qxpi
splitting functions
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PDFs Extraction in pQCD: Recap Three basic quantities needed for pQCD calculation of F2 : ))(,( 2
2 Qx
C si
))(,( 2Qx
P sij
Computed perturbatively as power series in s
Examples of parameterizations for nonperturbative input: Only requirements: flexible enough to accommodate small/large x behavior + obey the sum rules
Q2 evolution of PDF calculated via DGLAP equationsx dependence of PDF assumed and constrained by data
),( 2Qxpi
CTEQ6:
MSTW:
Alekhin:
54321 )1()1(),( 02
0AAxAAA xeexxAQxx
)1()1(),( 2120 xxxAxQxx
)1()1(2
),( 20 xxx
NQxx ba
To constrain the x dependence is evolved to all Q2 where data exist in the “safe kinematic regions”
),( 20Qx
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Standard pQCD fits: PDFs from CTEQ6
CTEQ6: pQCD fit to hard scattering and DIS data with Q2 > 4 GeV2 and W2 > 12.25 GeV2; the x dependence of PDFs parameterized at Q2 = 1.3 GeV2; evolution up to NLO
JHEP 0207:012, 2002
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CTEQ6: Comparison to Data
Good fit to data in the “safe kinematic regions” but beyond …
/ndf = 1.1 /ndf = 1.52
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CTEQ6: Large Uncertainties at Large x
Large x region important for (see Alberto’s talk): - study the mechanism of spin-flavor symmetry breaking in valence …..quark distributions - determining high-energy cross sections at collider energies - quantification of quark-hadron duality, etc.
but what’s involved in extending PDFs validity to larger x?
Large uncertainties where there are no constraints from data
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Complete picture
1 (2) 2(2) 2 2 2 42 2
0
( )( ) ( ( , ) ( , )) ...q
q
A QM Q e dx x q x Q q x Q
Q
Corrections beyond leading twist
PDFs at Large x and low Q2
))(~
)(2
1()( 2)2(
42)2(
,422)2(
4 QAQAMQA TMC
1) Higher-Twists: kinematic and dynamical
Kinematic HT – associated to twist-2 operator => no additional information on the quark dynamics
Dynamical HT – contains information about the valence quarks dynamics (confinament)
2) Large-x resummation
3) Nuclear Corrections – for the neutron
Messy but needs to be done to achieve exhaustive knowledge of the dynamic of the nucleon!
4) …
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Stepping out of the “safe kinematic region” => inclusion of nonperturbative effects (TMC, HT)
(and nuclear effects for nuclear targets)
Example: PDFs from ALEKHIN
22,
22
)(
Q
xHFF TMCLT
Phys. Rev. D 68, 014002 (2003); JETP Lett. 82, 628 (2005) Extension of PDF fits to larger x: kinematic cuts
(W2,Q2,x,) are relaxed to provide more constraints from data
ALEKHIN
CTEQ6
The x dependence of PDFs parameterized at Q2 = 9 GeV2; evolution up to NNLO
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Uncertainties: Alekhin vs CTEQ6 Result: smaller uncertainties at large x
Relative experimental uncertainties of PDFs at a Q2 of 9 GeV2:
full = Alekhin; dotted = CTEQ6
Redu
ctio
n by
~
10 o
f d
unce
rtai
nty
at
larg
e x
Redu
ctio
n by
~ 4
of u
unc
erta
inty
at la
rge
x
Phys. Rev. D 68, 014002 (2003)
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Dynamical Higher Twist Interplay of Higher-Order QCD corrections and dynamical Higher Twists
Decrease of magnitude of HT with increase of pQCD order but HT don’t vanish in NNLO
HT contribution to F2: at most ~10% of Leading Twist (maximal at x~0.6 and Q2 = 5 GeV2)
order S
LO 0.1301 +/- 0.0026
NLO 0.1171 +/- 0.0015
NNLO 0.1143 +/- 0.0014
From extrapolation: HT not expected to vanish in NNNLO either
Phys. Rev. D 68, 014002 (2003)
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How about extending PDFs to even large x?
2nd resonance region at Q2 = 2 GeV2
2nd resonance region at Q2 = 5 GeV2
Q2 = 2 GeV2
Q2 = 5 GeV2
Extending to larger x at finite Q2 => encounter the resonance region Resonances are basically “made” of higher twists
The contribution of higher-twist terms in the resonance region would be expected to be large…
Or is it?
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Bloom-Gilman Duality The resonance region data: - oscillate around the scaling curve - are on average equivalent to the scaling curve. - “slide” along the deep inelastic curve with increasing Q2
222
1 20
222
,2 QmM mm
dWdQWQ
M
Quantitatively: comparing the lhs to the rhs, relative difference 10% for Q2=1 GeV2 to <2% for Q2=2 GeV2.
Phys. Rev. Lett. 25, 1140 (1970)
“… resonances are not a separate entity but are an intrinsic part of the scaling behavior of W2 …”
Yes, but not on average
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Duality in QCD
W2
W2
W2
Q2 = 1 GeV2
Q2 = 3 GeV2
Q2 = 5 GeV2
data
pQCD
De Rujula, Georgi, Politzer:
“The most intriguing aspects of SLAC data on inclusive electroproduction are precocious scaling and local duality ”
Phys. Lett. B 64, 428 (1976)
Duality = higher-twists are either small or cancel on average (on average, the interactions between the valence quarks are suppressed)
Operator product expansion:
1
2''2
''1
'1
5
4
4
22'
2'
4
3
2
22
23
22
2'
),(12),(6),(),(
QFddk
x
Q
mQFd
k
x
Q
mQF
k
xxQW SSS
Mellin transform of twist-2
pQCD calculation of W2
1
0 1
220
22 )()()(),(k
nkk
nn QBQMnQAdQF
twist-2
On average, the resonance region data mimic the twist-2 pQCD calculation
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Quark-Hadron Duality in F2: Recent Experiments at JLab
Jefferson Lab
Electron-beam acceleratorAs of now, beam energies up to 6 GeVAs of now, three experimental halls: A, B, C
Two spectrometers: HMS & SOS
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1996 JLab-96 (I. Niculescu): duality dedicated experiment; measures H(e,e’) & D(e,e’) cross sections
1998 E94-110 (Y. Liang): performs Rosenbluth separation (measures R = L/T); measures H(e,e’) cross sections
2003 E00-116 (S. Malace): duality dedicated experiment, push to larger x and Q2;
measures H(e,e’) & D(e,e’) cross sections
Inclusive Resonance Region Measurements in Hall C
Among other, three experiments: JLab-96, E94-110, E00-116
Kinematics covered: x between ~0.3 and 0.9, Q2 up to 7 GeV2, in the resonance region (mainly)
JLab-96E94-110E00-116
CTEQ6ALEKHIN
2
3
4
1111
)('' AdEdNN
BGNdEd
d
temeasured
Procedure for F2 extraction Differential one-photon exchange (Born) cross section
background BG
acceptancedetector A
detectionforefficiencytotal
F2 extraction requires the knowledge of cross section and R
2222
21
11
41
1),(
Q
K
R
R
Edd
dQxF
E94-110: measured RJLab-96: used R from E94-110E00-116: used R from R1998 (R < 0.2 @ E00-116 kinematics)
Experimental natural variables: momentum and angle of scattered electron
+ energy of incoming electron
x, Q2, W2
crap
crap
crap
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Physics Results from JLab-96 Verifying quark-hadron duality “a la Bloom-Gilman”
NMC fit to DIS data at the same but higher W2, Q2 than RES data
The new precision data display the signature oscillation around the DIS curve (the agreement, on average, better than 10%)
JLab-96 conclusively verifies the observations of Bloom and Gilman
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Physics Results from JLab-96 Verifying quark-hadron duality in a pQCD framework: analysis in fixed W2 bins
Averaged RES data
pQCD(NLO) pQCD(NLO)+TMC
larg
e-x
resu
mm
ati
on:
bri
ngs
pQ
CD
ca
lcula
tion in b
ett
er
agre
em
ent
wit
h
data
TMC significant effect: pQCD calculation in better agreement with data LxR: resummation on ln(1-z) in x space => Q2 scale replaced by Q2(1-z)/z HT: in RES region similar to those for W2> 10, with exception of
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Physics Results from E94-110 More precise data from JLab: the resonances average to pQCD+TMC calculations from CTEQ and MRST The resonance data slide with increasing Q2 to higher x always following the pQCD curves
The ratio of F2 integrals data to pQCD better than 5% at Q2 = 0.5 GeV2 but ~ 18% at Q2 = 3.5 GeV2 ?!? Violation of duality, unconstrained PDFs at large x, something else ?
inegrals over
entire RES region
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Physics Results from E00-116
1st 2st 2nd
2st 3rd
4th
DIS
Verify quark-hadron duality at higher Q2
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
dxQxF
dxQxF
IM
m
M
m
x
x
param
x
x
data
),(
),(
22
22
Calculate:
Define:
Data from E00-116, E94-110, JLab-96 and SLAC; parametrizations from CTEQ6, MRST, ALEKHIN
Compare:
Larg
e d
iscrep
an
cies in
the
descrip
tion
of F
2 at la
rge
x
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Physics Results from E00-116 Comparison: data [H(e,e’)] to CTEQ6M (NLO) + TMComparison: data [H(e,e’)] to CTEQ6M (NLO) + TM
I ~ 1 at Q2 ~ 1.5 GeV2 then rises with increasing Q2 and reaches a plateau at ~ 4 GeV2; above this value Q2 dependence saturates
This behavior displayed when integrating globally and locally except for first resonance.
Not a failure of pQCD in describing the Q2 evolution but a paucity in the strength of PDFs at large x I becomes constant at different value for each RES region
Related to growing uncertainty of PDFs strength at large x
Phys. Rev. C 80, 035207 2009
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Physics Results from E00-116 Comparison: data [H(e,e’)] to MRST04 (NNLO) + Comparison: data [H(e,e’)] to MRST04 (NNLO) + TMTM The observed Q2 dependence of I
yields similar conclusions as drawn from the CTEQ6
Not surprising: the extraction procedure (and kinematic cuts) of PDFs similar for MRST04 and CTEQ6
Differences:Differences: MRST04 undershoots the data by an even larger amount and I saturates at a larger value of Q2
than for CTEQ6
Possibly results from the difference in modeling the x dependence of PDFs (?) Phys. Rev. C 80, 035207
2009
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Physics Results from E00-116 Comparison: data [H(e,e’)] to ALEKHIN (NNLO) + HT + Comparison: data [H(e,e’)] to ALEKHIN (NNLO) + HT + TMTM Due to cuts employed for data
selection, Alekhin’s fits far better constrained at large x
For the 4th RES region and DIS, I very close to 1 for entire Q2 range analyzed
Good agreement for 3rd and 2nd RES regions: I deviates from 1 by about 5%
HT in RES region, on average, differ by at most 5% from those extracted by Alekhin 1st resonance in disagreement
with Alekhin’s fit: the validity of the fit questionable at these kinematics Averaged RES data could be used to constrain PDF fits
Phys. Rev. C 80, 035207 2009
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Physics Results from E00-116
Good description at Q2= 3,5 GeV2 (except for largest x regime: 1st RES) Q2= 7 GeV2 : probing the largest x regime (ALEKHIN least constrained) => growing discrepancy Q2= 1 GeV2 : discrepancy as x grows reached limits of applicability
ALEKHINALEKHIN
CTEQ6CTEQ6 Fails to describe x dependence of data
Better data description by ALEKHIN than CTEQ6
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Physics Results from E00-116 Comparison: data [D(e,e’)] to CTEQ6 and ALEKHINComparison: data [D(e,e’)] to CTEQ6 and ALEKHIN
F2d(ALEKHIN,CTEQ6) = F2
p(ALEKHIN,CTEQ6) * d/p (from empirical fit)
The Q2 dependence of I: similar characteristics as in the study of H(e,e’) ALEKHIN offers better description of averaged RES data than CTEQ6
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Is Quark-Hadron Duality Verified in the Proton? Duality is an experimental observation and could be a working hypothesis for extending PDFs at large x => needs to be verified and quantified
It has been observed to work better 5% down to a Q2 as low as 1 GeV2 when compared to pQCD fits from MRST: E94-110
Surprisingly, it has been observed that the violation of duality becomes more pronounced as x and Q2 increase
Our studies indicate that this increasing violation of duality with Q2 is very likely only APPARENT: duality studies involve extrapolations of pQCD fits (unconstrained at large x)
The unconstrained PDFs at large x pose problems for quantifying how well duality holds in this kinematic regime (and that’s not good)
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Extraction of the Neutron Structure Function F2n
F x Q dy f y Fxy
QA N A N
x
M M
N p n
A
22
0 22( , ) ( , ) ,//
,
smearing functions (can be calculated from nuclear wave function)
Impulse Approximation (IA) – virtual photon scatters incoherently from individual nucleons
Beyond IA: nuclear shadowing, MEC, FSI, relativistic effects, off-shell corrections (most not addressed in present analysis)
New method of extracting neutron SF from inclusive SFs of New method of extracting neutron SF from inclusive SFs of nucleinuclei: employs iterative procedure of solving integral convolution equations (Phys. Rev. C 79, 035205 2009)
Can write the nuclear structure functions as convolutions of nucleon structure functions
Present analysis does not attempt to provide a complete Present analysis does not attempt to provide a complete description of nuclear SFs (yet)description of nuclear SFs (yet)
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Extraction of F2n
( )( ) ( , ) / )/
f x dy f y x yx
M MA F F (
NdNNdoffnpd FfFFFFF 2/
22)(
222
~,
~~
In the Weak Bound Approximation (WKA): the deuteron SF is sum of smeared proton and neutron SF and an additive term to account for modifications of SF off-shell
The effective smeared neutron SF:
pdoffQEddn FFFFF 22)()(
222
~~ Need to solve equation:
nn FfF 22
~ MethodMethod- Parameterize the nuclear corrections by an additive term )(
~22 Nn FF
- F2n extracted using an iterative
procedure which gives after first iteration)
~(
1 )0(22
)0(2
)1(2
nnnn FfFFF
assumed
Study sensitivity of extraction to: number of iterations, first guess for neutron SF etc.
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Results from E00-116: Extraction of F2n
The resonances are obvious in the extracted F2
n
After only two iterations F2d
reconstructed from F2p data
and extracted neutron F2n
agrees well with the F2d
data
The extracted F2n yields
similar results after two iterations when different inputs are used [F2
n(0) = F2p
& F2n(0) = F2
p/2]
Both F2p and F2
n average to the QCD fit from Alekhin suggesting the onset of duality How well?
Application of method to data (Application of method to data (Phys. Rev. Lett., xx, to be submittedPhys. Rev. Lett., xx, to be submitted))
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Quark-Hadron Duality in F2n
Compare integrals of neutron “data” to integrals of Alekhin’s newest fit (arXiv:0908.2766, August 2009) Without HT: agreement at the level of 10-15% for Q2 < 3 GeV2 (except for )
covers the highest x regime (the fit least constrained)
The discrepancy increases with increasing Q2 (unconstrained PDFs at larger x?, …) … sounds familiar?
With HT: good agreement; deviation less than 10% in most cases
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Neutron/Proton vs Q2 & x
Good agreement between data and pQCD fits, except for region which is somehow underestimated
The agreement slightly worsens as we go to larger Q2 and x
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Need more data at large x and “low” Q2?
We can help …
To be proposed at the next PAC in January 2010:
CTEQ6ALEKHIN
Measurements at 11 GeV @ JLab
Extend RES region and low W2 DIS region measurements at even higher x and Q2 at JLab
Systematic study of quark-hadron duality; extraction of dynamical HT (interesting in their own right); additional constraints for PDFs at large x; extract the neutron SF at even larger x (and maybe constrain the d quarks distribution better) …