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Tagged Structure Functionsin Global PDF Analysis
High Energy Nuclear Physics with Spectator TaggingOld Dominion University
March 9, 2015
Wally Melnitchouk
CTEQ-JLab (CJ) collaboration: http://www.jlab.org/CJ (with A. Accardi, E. Christy, C. Keppel, P. Monaghan, J. Owens, N. Sato)
1
Inclusive particle production
σAB→CX(pA, pB) =�
a,b
�dxa dxb fa/A(xa, µ) fb/B(xb, µ)
�
n
αns (µ) σ̂
(n)ab→CX (xapA, xbpB , Q/µ)
AB → C X
A B
C
a bσ̂
X
universal functions characterize internal structure of bound state A
fa/A
xa xb
Parton distributions in nucleons
2
PDFs extracted in global QCD analyses of data fromdeep-inelastic l-h scattering; lepton-pair, weak boson& jet production in h-h scattering, ...
~ 4,000 spin-averaged data points over large range of x and Q2
(more if include A > 2 nuclear data)
Parton distributions in nucleons
3
Needed to understand basic structure of QCD bound states - and for backgrounds in searches for physics beyond the Standard Model at high-energy colliders
Q evolution feeds low x, high Q from high x, low Q 2 22
In modern fits, PDFs typically parametrized asxf(x, µ) = Nxα(1− x)β P (x)
with polynomial e.g. P (x) = 1 + �√x+ η x
PDFs extracted in global QCD analyses of data fromdeep-inelastic l-h scattering; lepton-pair, weak boson& jet production in h-h scattering, ...
Parton distributions in nucleons
4
Several groups dedicated to global PDF analysis
MSTW (Martin-Stirling-Thorne-Watt) LHC focus, strong data cuts
CTEQ (Coordinate Theoretical-Experimental Project on QCD)- CT (CTEQ-Tung et al.) LHC focus
- CJ (CTEQ-JLab) includes high x, low Q- nCTEQ nuclear PDFs
2
ABM (Alekhin-Bluemlein-Moch) LHC focus, some lower Q
JR (Jimenez-Delgado-Reya) dynamically generated from low Q 2
NNPDF “neural networks”, strong data cuts
HERAPDF only H1 & ZEUS data
most use NLO, some use NNLO (partially known)
2
Parton distributions in nucleons
5
10-4 10-3 10-2 10-1 100x
0
0.2
0.4
0.6
0.8
1
1.2
1.4
x f (
x,Q
2 )
gCJ12mid
Q2 = 10 GeV2d_
+u_
d_−u
_
d
u
s
/10
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
gCJ12mid
Q2 = 10 GeV2
d_
+u_
d_−u_
d
u
s
Example of recent PDFs, from CJ12 analysis
Owens, Accardi, WMPRD 87, 094012 (2013)
Parton distributions in nucleons
6
CTEQ-JLab PDFsHigh-x region requires use of data at lower W & Q2
weak cut:Q > 1.3 GeV , W > 1.73 GeV
strong cut:Q > 2 GeV, W > 3.5 GeV
factor 2 increase in # of DIS data points when relaxstrong cut (excludes most SLAC, all JLab data) weak cut
W 2 = M2 +Q2 (1− x)
x
7
significant error reduction when cuts extended to low-W region
x x
High-x region requires use of data at lower W & Q2
cut0: strong cutcut3: weak cut
CTEQ-JLab PDFs
W 2 = M2 +Q2 (1− x)
x
8
higher twists usually parametrized phenomenologically
Low-Q data requires higher twist & target mass corrections2
F2(x, Q2) = FLT2 (x,Q2)
�1 +
C(x)Q2
�polynomialC(x)
x x
(no TMC ornuc.corr.)
different TMCprescriptions
significant at high-x
CTEQ-JLab PDFs
9
deuterium as “effective neutron” target,but need to correct for nuclear effects
u-quark PDF well constrained by proton data;d-quark PDF requires neutron data
Arrington, Rubin, WMPRL 108, 252001 (2012)
SU(6)
hard gluons
S=0 diquarksdifferent modelsof deuteron
CTEQ-JLab PDFs
10
Effect of nuclear corrections & statistics
0 0.2 0.4 0.6 0.8 1x
0.7
0.8
0.9
1
1.1
1.2
1.3
u / u
ref
no deuteronPDF + nuclear errorPDF error only
0 0.2 0.4 0.6 0.8 1x
00.20.40.60.81
1.21.4
1.61.82
d / d
ref
no deuteronPDF + nuclear errorPDF error only
significant uncertainties in u for x > 0.8, d for x > 0.6
CTEQ-JLab PDFs
11
0 0.2 0.4 0.6 0.8 1x
0.7
0.8
0.9
1
1.1
1.2
1.3
u / u
ref
CJ12midCT10MSTW08ABKM09
Q2 = 100 GeV2
increase in PDF error from more realistictreatment of nuclear corrections
reduction of error from larger database
CTEQ-JLab PDFs
0 0.2 0.4 0.6 0.8 1x
0.4
0.6
0.8
1
1.2
1.4
1.6
d / d
ref
CJ12midCT10MSTW08ABKM09
Q2 = 100 GeV2
Effect of nuclear corrections & statistics
12
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
d / u
CJ12midCT10MSTW08ABKM09
• with same functionalform for u & d, most PDF fits assume either0 or for limitx → 1∞
CTEQ-JLab PDFsEffect of nuclear corrections & statistics
13
flexible parametrizationfor behaviorx → 1
CJ12min: WJC-1 + mild off-shell (0.3% nucleon swelling)CJ12mid: AV18 + medium off-shell (1.2% swelling)CJ12max: CD-Bonn + large off-shell (2.1% swelling)
*
allows finite, nonzerox = 1 limit
•
•
d/u → 0.22
± 0.20 (PDF)
± 0.10 (nucl)
. d → d + a xb u
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
d / u
CJ12minCJ12midCJ12max
*
CTEQ-JLab PDFsEffect of nuclear corrections & statistics
Owens, Accardi, WMPRD 87, 094012 (2013)
14
Large-x PDF uncertainties have implications for colliders
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4
A W
yW
LHCCJ (min nuclear)CJ (max nuclear)
0
0.2
0.4
0.6
0.8
1
0 1 2 3yW
TevatronCDF Data
pp,√s = 7 TeV
pp,√s ≈ 2 TeV
Brady, Accardi, WM, OwensJHEP 1206, 019 (2012)
e.g. asymmetryW±
rapidity y =1
2ln
�E + pzE − pz
�
15
sensitive tod at high x
Large-x PDF uncertainties have implications for colliders
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4
A W
yW
LHCCJ (min nuclear)CJ (max nuclear)
0
0.2
0.4
0.6
0.8
1
0 1 2 3yW
TevatronCDF Data
pp,√s = 7 TeV
pp,√s ≈ 2 TeV
Brady, Accardi, WM, OwensJHEP 1206, 019 (2012)
e.g. asymmetryW±
rapidity y =1
2ln
�E + pzE − pz
�
favors smalleroff-shell effect
16
CJ15 PDFsNew CJ15 analysis includes several new theoretical developments (better treatment of heavy quarks; off-shell corrections to valence and sea distributions; improved d / u parametrization)and new data sets (D0 W asymmetries; BONuS )
_ _
Fn2 /F
d2
Explore whether new data can constrain PDFs,and nuclear corrections, at large x
Kulagin, Petti, NPA 765, 126 (2006)Owens et al., PRD 87, 094012 (2013)
vary off-shell “rescaling” parameterwithin “spectator diquark” model
λ = ∂ logΛ2
∂p2
minimize as a function of χ2 λ
17
CJ15 PDFsMinimum total for different deuteron wave functionand off-shell models
χ2
models 2-15: λ = {−0.9%,−0.8%, ...,+0.4%}
minimum total χ2
18
CJ15 PDFsNuclear EMC effect in the deuteron for differentnuclear models
} spectatoroff-shellmodel
larger off-shell effects for larger , and for KP modelλ
enhancement at x ~ 0.2 in KP model
19
CJ15 PDFsSLAC deuteron data favor smaller off-shell corrections,disfavor (hardest) WJC-1 wave function
λ = −0.9% λ = +0.4%
20
deuteronwave function
LC momentum distribution(“smearing function”)
21
0 0.5 1 1.5 2 2.5 3yW
0
0.2
0.4
0.6
0.8
1A W
D0CJ15CJ15 (KP off-shell)
CJ15 PDFs
PRL 112, 151803 (2014)
D0 W-asymmetry data disfavor large nucleonoff-shell corrections at high x
larger asymmetry at high rapidity corresponds tosmaller d-quark PDF (smaller EMC effect) at high x
σW+ − σW−σW+ + σW−
∼ 1− d/u
1 + d/u
22
CJ15 PDFs
λ = −0.9% λ = +0.4%
PRL 112, 151803 (2014)
D0 W-asymmetry data disfavor large nucleonoff-shell corrections at high x
23
CJ15 PDFsBONuS data favor larger nucleon off-shellcorrections (and harder deuteron wave function)
Fn2 /F
d2
improvement in with KP model� 5% χ2
24
CJ15 PDFsIs improvement from specific kinematics?χ2
calculated larger at high x with KP modelFn2 /F
d2
25
CJ15 PDFs
calculated larger at high x with KP modelFn2 /F
d2
Is improvement from specific kinematics?χ2
26
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ (no-BONuS fit)
Q2 = 4.0 GeV2
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ15 (no-BONuS fit)
Q2 = 3.4 GeV2
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ15 (no-BONuS fit)
Q2 = 2.9 GeV2
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ15 (no-BONuS fit)
Q2 = 2.4 GeV2
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ15 (no-BONuS fit)
Q2 = 2.0 GeV2
3 4 5 6
W 2 (GeV2)
0
0.2
0.4
0.6
0.8
F 2n / F
2d
BONuSCJ15CJ15 (no-BONuS fit)
Q2 = 1.7 GeV2
CJ15 PDFsCD-Bonn & λ=−0.7%
slightly larger neutron (hence d-quark) with BONuSF2
27
Outlook“BONuS6” data demonstrated how spectator taggingcan be used to constrain PDFs; impact not dramatic... “BONuS12” promises to extend range to x ~ 0.85 with reduced experimental & minimal nuclear uncertainties
28
OutlookParallel effort in global analysis of spin-dependent PDFs Jefferson Lab Angular Momentum (JAM) Collaboration (Nobuo Sato, A. Accardi, J. Ethier)
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8
x
xΔu+
xΔd+
ref.+ smear+ TMC+ HT
-1-0.8-0.6-0.4-0.2
0 0.2 0.4 0.6 0.8
1
0.1 0.2 0.3 0.4 0.5 0.6 0.7
x
Δu+/u+
Δd+/d+
Q2 = 1 GeV2
Jimenez-Delgado, Accardi, WMPRD 89, 034025 (2014)
currently assessing impact of new JLab6 data(eg1b, eg1-DVCS, d2n, ...)
full JAM15 analysis will include SIDIS & RHIC-spin data
29
0
0.1
0.2
0.3
0.4
0.5
0.2 0.4 0.6 0.8
x
Δd+ Q2 = 1 GeV2
0
0.05
0.1
0.15
0.2
0.25
0.2 0.4 0.6 0.8
rela
tive
erro
r
x
Δu+
JAM +12 GeV
Upcoming 12 GeV experiments will measure inclusiveand semi-inclusive polarization asymmetries up to x ~ 0.8
will significantly reduce PDF uncertainties at large x(~ 70% for x ~ 0.6-0.8)
Outlook
30
The End
31