Recent developments in the CTEQ-TEA global analysis
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Recent developments in the CTEQ-TEA
global analysis
Tie-Jiun Hou
Northeastern University
November 23, 2019
The 2nd Workshop of Southern Nuclear Science Computing
Center, Guangzhou
1 / 32
CTEQ-TEA group
‚ CTEQ – Tung et al. (TEA)
in memory of Prof. Wu-Ki Tung, who established CTEQ
Collaboration in early 90’s.
‚ Current members:
Tie-Jiun Hou (Northeastern U.)
Sayipjamal Dulat, Ibrahim Sitiwaldi (Xinjiang U.)
Jun Gao (Shanghai Jiaotong U.)
Marco Guzzi (Kennesaw State U.)
Timothy Hobbs, Pavel Nadolsky, Boting Wang, Keping Xie
(Southern Methodist U.)
Joey Huston, Jon Pumplin, Carl Schmidt, Dan Stump, Jan
Winter, C.-P. Yuan (Michigan State U.)
2 / 32
CT18 in a nutshell
‚ Start with CT14-HERAII (HERAII combined data released after publication
of CT14)
‚ Examine a wide range of non-perturbative PDF parameterizations
‚ Use as much relevant LHC data as possible; using applgrid/fastNLO
interfaces to data sets, with NNLO/NLO K-factors, or fastNNLO tables in the
case of top pair (single and double differential) data
Good agreement between PDFSense, ePump results and global fit
‚ Implement a parallelization of the global PDF fitting to allow for faster
turn-around time
‚ Use diverse statistical techniques (PDFSense, ePump, Gaussian variables,
Lagrange Multiplier scans) to examine agreement between experiments
3 / 32
LHC data sets included in CT18
245 1505.07024 LHCb Z (W) muon rapidity at 7 TeV(applgrid)
246 1503.00963 LHCb 8 TeV Z rapidity (applgrid);
249 1603.01803 CMS W lepton asymmetry at 8 TeV (applgrid)
250 1511.08039 LHCb Z (W) muon rapidity at 8 TeV(applgrid)
253 1512.02192 ATLAS 7 TeV Z pT (applgrid)
542 1406.0324 CMS incl. jet at 7 TeV with R=0.7 (fastNLO)
544 1410.8857 ATLAS incl. jet at 7 TeV with R=0.6 (applgrid)
545 1609.05331 CMS incl. jet at 8 TeV with R=0.7 (fastNLO)
573 1703.01630 CMS 8 TeV tt (pT , yt) double diff. distributions (fastNNLO)
580 1511.04716 ATLAS 8 TeV tt pT and mtt diff. distributions (fastNNLO)
248 1612.03016 ATLAS 7 TeV Z and W rapidity (applgrid) Ñ CT18Z
4 / 32
5 / 32
De-correlation for incl. jetD
ata
/ T
heor
y
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
|y| < 0.5
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
Dat
a /
The
ory
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
0.5 < |y| < 1.0
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
Dat
a /
The
ory
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
1.0 < |y| < 1.5
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
Dat
a /
The
ory
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
1.5 < |y| < 2.0
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
Dat
a /
The
ory
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
2.0 < |y| < 2.5
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
Dat
a /
The
ory
PT [GeV]
ATLAS, √s=7 TeV, L=4.5 [fb]-1, R=0.6
2.5 < |y| < 3.0
Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
100 1000
‚ The corr. error ”jes16” and ”jes62” of ATLAS 7 TeV incl. jet data are
decorrelated according to Table 6 of 1706.03192. Its χ2{Npts reduces from
2.34 to 1.68 for CT14HERA2NNLO.
6 / 32
Selected Top Quark Pair Observables from ATLASand CMS
‚ Modest effect observed if t-tbar data are included together with the Tevatron
and LHC jet production data.
‚ Its impact on gluon PDF is consistent with jet data, though jet data provide
stronger constraint.
‚ For ATLAS 8 TeV, select the pT and mtt distributions that directly probes
large-x region; statistical correlations are included in order to fit pT and mtt
simultaneously; fully correlated for experimental systematics except for
decorrelation of PS sys. error.
χ2{Npts nominal w/o PS decorrelation w/o statistical correlation
(with CT18 PDFs)
ATLAS 8 TeV abs.
dσ{dpT and dσ{dmtt 0.62 3.55 0.51
(Npts=15)
CMS 8 TeV nor.
dσ{dpTdyt 1.18 - -
(Npts=16)7 / 32
Theory calculations @NNLO
‚ Studies of QCD scale dependence and other theory uncertainties for DIS,
high-pT Z, jet production
‚ An uncorrelated error of 0.5% is included for:
ATLAS 7 TeV and CMS 7/8 TeV jet production, and
ATLAS 8 TeV high-pT Z production to account for numerical uncertainties in
the MC integration of NNLO cross sections.
‚ Alternative renormalization/factorization scale choices were examined in
high-pT Z production, do not significantly alter the conclusions.8 / 32
NLO QCD calculation interface
‚ Direct QCD NLO/NNLO calculation need weeks/months CPU-time, which is
not suitable for global analysis at all.
‚ Traditionally, NLO/NNLO calculation are done by using LO * K-factor (bin
by bin) in global analysis, which is not precise enough for the era of LHC.
‚ Upgrade approch: fast interfaces to NLO calculations; NLO QCD prediction
can be done by PDF convolution the grid files. NNLO QCD prediction is
done by NLO QCD prediction times K-factor.
‚ Applgrid: interface to MCFM and NLOjet++‚ fastNLO: interface to NLOjet++
‚ Limitation of the fast interface.
‚ limited processes to be storaged in grids‚ Only QCD calculation without EQ correct.‚ Only fixed order calculation.
9 / 32
Explore various non-perturbative parametrizationforms of PDFs
Rat
io to
CT
18N
NL
O
x
g(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
0.0
0.5
1.0
1.5
2.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
18N
NL
Ox
u(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
18N
NL
O
x
d(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
18N
NL
O
x
s(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
18N
NL
O
x
–u(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
0.4
0.6
0.8
1.0
1.2
1.4
1.6
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
18N
NL
O
x
–d(x,Q) at Q =1.3 GeV 90%C.L.CT18NNLOCT18par
0.4
0.6
0.8
1.0
1.2
1.4
1.6
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
‚ CT18 – sample result of exploring various non-perturbative parametrization
forms.
‚ There is no data to constrain very large or very small x region.
10 / 32
gpx,Qq upx,Qq dpx,Qq
spx,Qq upx,Qq dpx,Qq
Fitting code parallelization with multi-threads
Typical 3-layer structure of the
CT18 global analysis, from
various scans to global
minimization, then to the chi2
calculations upgrade to a
parallelized version of the fitting
code, two-layer parallelization:
‚ LY1, through rearrangement of the minimization algorithm, a factor of 4 5
improvement on speed;
‚ LY2, via redistribution of the data sets, further improved by a factor of 2
11 / 32
Preview of CT18 PDFs(g-PDF)
Rat
io to
CT
14H
ER
A2N
NL
O
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
‚ Smaller gluon for x „ 0.3, but no significant change in small x region.
‚ Detail competition among data should be checked by Lagrange multiplier
method.
12 / 32
gluon PDF of CT18PD
F R
atio
to C
T14
HE
RA
2NN
LO
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
∆χ2 e
g(x = 3E-1, Q = 125 GeV)
CT18χ2
totCMS7jetATLAS8ZpTATLAS7jetCMS8jetHERAI+IICMS8ttbpTtytLHCb7ZWE866ppBCDMS F2dCDHSW F2
-10
0
10
20
30
0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38
Lagrange Multiplier Scans
‚ At x around 0.3, competing with the CDHSW F2 and Tevatron jet data, which
prefer larger gluon, the ATLAS7 jet, CMS7 jet and ATLAS8 Z pT data prefer
a smaller gluon; some tension found in CMS7 and CMS8 jet data.
‚ tt production data(CMS8ttbpTtyt) has minor impact to the gluon PDF.
‚ The gluon PDF as x Ñ 1 is parametrization form dependent.
13 / 32
gluon PDF of CT18∆χ
2 e
g(x = 1E-2, Q = 125 GeV)
CT18χ2
totHERAI+IICMS8jetATLAS7jetCCFR F2D02jetBCDMS F2dCMS7jetHERA cCMS8ttbpTtytCDF2jetATLAS8ZpTNuTv NubE866pp
-10
0
10
20
30
770 780 790 800 810 820 830 840
Rat
io to
CT
14H
ER
A2N
NL
O
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Lagrange Multiplier Scans for gluon at x around 0.01:
‚ ATLAS 8 TeV Z pT data prefer a slightly larger gluon PDF.
‚ ATLAS 7 TeV and CMS 8TeV incl. jet data prefer a slightly smaller gluon
PDF.
‚ HERA I+II data prefer a slightly smaller gluon PDF.
‚ Including all the contribution in global analysis, the reduction of PDF
uncertainty for gg Ñ h production reduced by 5% comparing to CT14.
14 / 32
Impact of top-quark pair production on CT14HERA2PD
F R
atio
to C
T14
HE
RA
2.54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pCMS8NpT
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pCMS8Nya
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pCMS8Nmtt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pCMS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8pT
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8ya
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8mtt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8ytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8NpT
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8Nya
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8Nmtt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
‚ No significant impact on the uncertainty of PDFs.
‚ Minor impact on gluon in large x region.
PoS DIS2019 (2019) 017
15 / 32
Err
or b
ands
of
g(x,
Q)
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2.
54
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2.54CT14HERA2pATLAS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Err
or b
ands
of
g(x,
Q)
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2mjetCT14HERA2mjetpCMS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2m
jet
x
g(x,Q) at Q =100.0 GeV 90%C.L.CT14HERA2mjetCT14HERA2mjetpCMS8Nytt
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Impact from
ATLAS 8TeV
norm. ytt tt data on
CT14HERA2
Impact from CMS
8TeV norm. ytt tt
data on
CT14HERA2mjet
‚ CT14HERA2mjet: CT14HERA2 without all the jet data
included.
‚ Without the jet data included in global analysis, tt data have
rather obvious impact on both central predictions and error
bands of PDFs.
16 / 32
u-PDF of CT18
Err
or b
ands
of
u(x,
Q)
x
u(x,Q) at Q =100.0 GeV 90%C.L.
u(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2N
NL
O
x
u(x,Q) at Q =100.0 GeV 90%C.L.
u(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
∆χ2 e
u(x = 2E-3, Q = 100 GeV)
CT18χ2
totHERAI+IILHCb8WZCMS8W Aµ
chLHCb8ZE866ppNuTeV νNMC Fdeu
2 /Fpro2
ATLAS7ZWLHCb7ZW
NuTeV –ν
-10
0
10
20
30
600 610 620 630 640 650 660 670
∆χ2 e
u(x = 3E-1, Q = 100 GeV)
CT18χ2
totCDHSW F2CDHSW F3E866ppLHCb8ZWLHCb7ZWBCDMS Fpro
2NMC Fdeu
2 /Fpro2
E605BCDMS Fdeu
2CDF2jetHERAI+II
-20
-10
0
10
20
30
1.1 1.12 1.14 1.16 1.18
‚ For small x region, the LHC 8TeV data and CMS 8TeV W asymmetry data
compete with the E866 data, and drop the u-PDF down.
‚ At large x region, new data has minor impact compare to HERA1+2 data,
CDHSW data and E866 data, and has minor impact to u-PDF.17 / 32
d-PDF of CT18
Err
or b
ands
of
d(x,
Q)
x
d(x,Q) at Q =100.0 GeV 90%C.L.
d(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2N
NL
O
x
d(x,Q) at Q =100.0 GeV 90%C.L.
d(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
∆χ2 e
d(x = 2E-3, Q = 100 GeV)
CT18χ2
totE866BCDMS Fdeu
2NMC Fdeu
2 /Fpro2
HERAI+IILHCb8ZWATLAS7ZWCMS8W Aµ
ch
-10
0
10
20
30
570 580 590 600 610 620 630 640
∆χ2 e
d(x = 3E-1, Q = 100 GeV)
CT18χ2
totBCDMS Fdeu
2D02W Ae
chCCFR F3
NMC Fdeu2 /Fpro
2CDHSW F2
BCDMS Fpro2
LHCb8ZWHERAI+IICMS8W Aµ
chLHCb7ZW
-10
0
10
20
30
0.4 0.41 0.42 0.43 0.44 0.45 0.46
‚ At small x region, the CMS 8TeV W asymmetry data drive the d-PDF up.
‚ At large x region, the LHCb 7TeV ZW data stongly prefer a larger d-PDF.
18 / 32
u-PDF and d-PDF of CT18
Rat
io to
CT
14H
ER
A2N
NL
O
x
–u(x,Q) at Q =100.0 GeV 90%C.L.
–u(x,Q)
CT14HERA2NNLOCT18
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2N
NL
O
x
–d(x,Q) at Q =100.0 GeV 90%C.L.
–d(x,Q)
CT14HERA2NNLOCT18
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
∆χ2 e
–u(x = 3E-1, Q = 100 GeV)/1E3
CT18χ2
totE605E866E866ppNMC Fdeu
2 /Fpro2
CDHSW F2LHCb7ZWHERAI+IICDHSW F3
-10
0
10
20
30
0.02 0.025 0.03 0.035 0.04∆χ
2 e
–d(x = 3E-1, Q = 100 GeV)
CT18χ2
totE605E866LHCb7ZWCDHSW F2NMC Fdeu
2 /Fpro2
CCFR F3E866ppCDHSW F3
-10
0
10
20
30
0.025 0.03 0.035 0.04 0.045 0.05
‚ Minor changes on ubar and dbar PDFs at small x region mainly come from
LHCb W and Z rapidity data, at 7 and 8 TeV.
‚ The LHCb 7TeV ZW data drive the u and d PDFs down at large x region.
‚ The behavior of ubar and dbar PDFs, as x Ñ 1, is parametrization form
dependent.19 / 32
LHCb 8 TeV W and Z data in CT18 fitD
ata
/ T
heor
y
ηµ
LHCb, √s=8TeV, L=2.0[fb]-1 dσ(W+→µ+ν) / dηµpµ
T > 20GeV
W+Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
2 2.5 3 3.5 4 4.5
Dat
a /
The
ory
ηµ
LHCb, √s=8TeV, L=2.0[fb]-1 dσ(W-→µ-–ν) / dηµ
W-Unshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
2 2.5 3 3.5 4 4.5
Dat
a /
The
ory
yZ
LHCb, √s=8TeV, L=2.0[fb]-1 dσ(Z→µ+µ-) / dyZ
ZUnshifted dataCT18, 68% C.L.Shifted data for CT18
0.8
0.9
1.0
1.1
1.2
2 2.5 3 3.5 4 4.5
arXiv:1511.08039
‚ Z data dominate the fit.
‚ Not able to fit some large Z rapidity
‚ Show slight tension with CCFR F2 and CMS 7 TeV W-lepton asymmetry data
20 / 32
Study of αspMzq through global analysis
∆χ2 e
αs
CT18 NNLO
αs = 0.1164 +- 0.0026
HERAI+IIBCDMS Fp
2CMS 8 TeV incl. jetCDF II incl. jetCDHSW Fp
2E866 DY, Q3d2σpp /(dQdxF)CMS 7 TeV incl. jetATLAS 7 TeV incl. jetD0 II incl. jetLHCb 8 TeV W/ZATLAS 8 TeV t–t dpT(t) and mt–tATLAS 8 TeV Z pT∆χ2
tot-20
-10
0
10
20
30
40
50
60
0.112 0.114 0.116 0.118 0.12
‚ The global fitting of αspMzq value need to change all the αspMzq value at the
same time.
‚ The fixed target F2 data and HERA DIS data prefer smaller αs value.
‚ The ATLAS 8TeV Z pT , ATLAS 7 TeV incl. jet data,
bring the central value of αspMzq from 0.115`0.006´0.004 (CT14) to
0.1164 ˘ 0.0026 (CT18).
21 / 32
σpgg Ñ Hq CT18 v.s. CT14
Err
or b
ands
of
g(x,
Q)
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2N
NL
O
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Err
or B
ands
Mx [GeV]
Lgg at Ecm=13.0TeV, 68%C.L., |y|<5.0
g-g Lumi
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
14H
ER
A2N
NL
O
Mx [GeV]
Lgg at Ecm=13.0TeV, 68%C.L., |y|<5.0
g-g Lumi
CT14HERA2NNLOCT18
0.8
0.9
1.0
1.1
1.2
101 102 103
σpgg Ñ hq 7TeV
CT14 14.67 ˘0.46
CT18 14.57 ˘0.44
σpgg Ñ hq 8TeV
CT14 18.70 ˘0.57
CT18 18.45 ˘0.55
σpgg Ñ hq 13TeV
CT14 42.78 ˘1.32
CT18 42.43 ˘1.26
σpgg Ñ hq 14TeV
CT14 48.23 ˘1.50
CT18 47.91 ˘1.42
‚ PDF induced errors (at 90%C.L.) are reduced by about 5% as compared to
CT14 predictions.
22 / 32
PDF Luminosities at 13 TeV LHCCT18, MMHT14 and NNPDF3.1
Rat
io to
CT
18N
NL
O
Mx [GeV]
Lgg at Ecm=13.0TeV, 68%C.L., |y|<5.0
CT18NNLOMMHT2014nnloNNPDF31nnloas01181000
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
18N
NL
O
Mx [GeV]
Lgq at Ecm=13.0TeV, 68%C.L., |y|<5.0
CT18NNLOMMHT2014nnloNNPDF31nnloas01181000
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
18N
NL
O
Mx [GeV]
Lqq at Ecm=13.0TeV, 68%C.L., |y|<5.0
CT18NNLOMMHT2014nnloNNPDF31nnloas01181000
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
18N
NL
O
Mx [GeV]
LqQ at Ecm=13.0TeV, 68%C.L., |y|<5.0
CT18NNLOMMHT2014nnloNNPDF31nnloas01181000
0.8
0.9
1.0
1.1
1.2
101 102 103
23 / 32
ATLAS 7 TeV WZ production
0 0.5 1 1.5 2 2.5
| [p
b]
lη/d
|σ
d
450
500
550
600
650
Uncorr. uncertainty
Total uncertainty
1.8%)±luminosity excluded (
Data
ABM12
CT14
HERAPDF2.0
JR14
MMHT2014
NNPDF3.0
-1 = 7 TeV, 4.6 fbs
ν + l→ +W > 25 GeV
T,lp
> 25 GeVνT,
p
> 40 GeVTm
ATLAS
|l
η|0 0.5 1 1.5 2 2.5
Th
eo
ry/D
ata
0.951
1.05 0 0.5 1 1.5 2 2.5
| [p
b]
lη/d
|σ
d
300
320
340
360
380
400
420
440
460
480
Uncorr. uncertainty
Total uncertainty
1.8%)±luminosity excluded (
Data
ABM12
CT14
HERAPDF2.0
JR14
MMHT2014
NNPDF3.0
-1 = 7 TeV, 4.6 fbsν
- l→
-W
> 25 GeVT,l
p
> 25 GeVνT,
p
> 40 GeVTm
ATLAS
|l
η|0 0.5 1 1.5 2 2.5
Th
eo
ry/D
ata
0.951
1.05
0 0.5 1 1.5 2 2.5
lA
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Uncorr. uncertainty
Total uncertainty
Data
ABM12
CT14
HERAPDF2.0
JR14
MMHT2014
NNPDF3.0
-1 = 7 TeV, 4.6 fbs
- - W
+WLepton Asymmetry
> 25 GeVT,l
p
> 25 GeVνT,
p
> 40 GeVTm
ATLAS
|l
η|0 0.5 1 1.5 2 2.5
Th
eo
ry/D
ata
0.951
1.05 0 0.5 1 1.5 2
| [p
b]
ll/d
|yσ
d
20
40
60
80
100
120
140
160
Uncorr. uncertainty
Total uncertainty
1.8%)±luminosity excluded (
Data
ABM12
CT14
HERAPDF2.0
JR14
MMHT2014
NNPDF3.0
-1 = 7 TeV, 4.6 fbs
-l+ l→* γZ/
< 116 GeVll66 < m
> 20 GeVT,l
p
| < 2.5l
η|
ATLAS
|ll
|y0 0.5 1 1.5 2
Th
eo
ry/D
ata
0.951
1.05
The statistical error
of measurment is
about 1%, while the
uncertainty from
PDF is about
5% „ 7%.
EPJC77 (2017) no.6, 367
24 / 32
CT18ZLHC data treatment
‚ Start with CT18 data set
‚ Add in ATLAS 7 TeV W and Z rapidity data (arXiv:1612.03016; 4.6fb´1);
large χ2{d.o.f „ 2.1 Ñ CT18A
‚ Remove CDHSW data
‚ Use a special x-dependent factorization scale mDIS, x at NNLO calculation
Ñ CT18X
‚ CT18Z uses a combination of mDIS,x (preferred by DIS) and an increased
mpolec “ 1.4 GeV (preferred by LHC vector boson production, disfavored by
DIS)
25 / 32
PDF uncertainty bandsCT18 vs. CT18Z
x*f(
x,Q
)
x
CT18 at 1.4GeV s–d–uudg/5
0.0
0.2
0.4
0.6
0.8
1.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
x*f(
x,Q
)
x
CT18Z at 1.4GeV s–d–ug/5ud
0.0
0.2
0.4
0.6
0.8
1.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
CT18Z has enhanced gluon, u-, d- and s-PDFs at x „ 10´4 , and
reduced g-PDFs at x ą 10´2 . The CT18Z fit is performed so as to
maximize the differences from CT18 PDFs, while preserving about
the same goodness-of-fit as for CT18 analysis.
26 / 32
CT18Z vs.CT18 PDFsPD
F R
atio
to C
T14
HE
RA
2
x
g(x,Q) at Q =100.0 GeV 90%C.L.
g(x,Q)
CT14HERA2CT18CT18Z
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2
x
u(x,Q) at Q =100.0 GeV 90%C.L.
u(x,Q)
CT14HERA2CT18CT18Z
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2
x
d(x,Q) at Q =100.0 GeV 90%C.L.
d(x,Q)
CT14HERA2CT18CT18Z
0.8
0.9
1.0
1.1
1.2
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2
x
s(x,Q) at Q =100.0 GeV 90%C.L.
s(x,Q)
CT14HERA2CT18CT18Z
0.0
0.5
1.0
1.5
2.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2
x
–u(x,Q) at Q =100.0 GeV 90%C.L.
–u(x,Q)
CT14HERA2CT18CT18Z
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Rat
io to
CT
14H
ER
A2
x
–d(x,Q) at Q =100.0 GeV 90%C.L.
–d(x,Q)
CT14HERA2CT18CT18Z
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
‚ G increases at small-x, and decreases at x „ 0.010.3
‚ u and d increase at small-x
‚ d increases at x „ 0.2 ´ 0.3
‚ s increases at small-x
27 / 32
CT18Z vs.CT18 PDFs
Flav
or R
atio
x
d(x,Q)/u(x,Q) at Q =100.0 GeV 90%C.L.
d(x,Q)/u(x,Q)
CT14HERA2CT18CT18Z
0.0
0.5
1.0
1.5
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
Flav
or R
atio
x
–d(x,Q)/–u(x,Q) at Q =100.0 GeV 90%C.L.
–d(x,Q)/–u(x,Q)
CT14HERA2CT18CT18Z
0.0
0.5
1.0
1.5
2.0
2.5
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9Fl
avor
Rat
io
x
(s+–s)/(–u+–d) at Q =100.0 GeV 90%C.L.
(s+–s)/(–u+–d)
CT14HERA2CT18CT18Z
0.0
0.5
1.0
1.5
2.0
10-6 10-4 10-3 10-2 10-1 0.2 0.5 0.9
‚ d{u decreases at large-x
‚ rs increases at small-x
28 / 32
PDF Luminosities at 13 TeV LHCCT14HERA2, CT18 and CT18Z
Rat
io to
CT
14H
ER
A2N
NL
O
Mx [GeV]
Lgg at Ecm=14.0TeV, 90%C.L., |y|<5.0
CT14HERA2NNLOCT18NNLOCT18ZNNLO
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
14H
ER
A2N
NL
O
Mx [GeV]
Lgq at Ecm=14.0TeV, 90%C.L., |y|<5.0
CT14HERA2NNLOCT18NNLOCT18ZNNLO
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
14H
ER
A2N
NL
O
Mx [GeV]
Lqq at Ecm=14.0TeV, 90%C.L., |y|<5.0
CT14HERA2NNLOCT18NNLOCT18ZNNLO
0.8
0.9
1.0
1.1
1.2
101 102 103
Rat
io to
CT
14H
ER
A2N
NL
O
Mx [GeV]
LqQ at Ecm=14.0TeV, 90%C.L., |y|<5.0
CT14HERA2NNLOCT18NNLOCT18ZNNLO
0.8
0.9
1.0
1.1
1.2
101 102 103
29 / 32
Mild reduction in nominal PDF error bands and crosssection uncertainties
Err
or B
ands
Mx [GeV]
LqQ at Ecm=14.0TeV, 90%C.L., |y|<5.0
q-Q Lumi
CT14HERA2NNLOCT18CT18Z
0.8
0.9
1.0
1.1
1.2
101 102 103
Err
or B
ands
Mx [GeV]
Lgg at Ecm=14.0TeV, 90%C.L., |y|<5.0
g-g Lumi
CT14HERA2NNLOCT18CT18Z
0.8
0.9
1.0
1.1
1.2
101 102 103
σ t– t 1
4 T
eV [
pb]
σ(gg -> h) 14 TeV [pb]
CT14HERA2CT18CT18Z
910
920
930
940
950
960
970
980
990
1000
1010
46 46.5 47 47.5 48 48.5 49 49.5
30 / 32
31 / 32
Summary
‚ A new CT18 PDF global analysis is release to public.
‚ The CT18 PDF uncertainty is mildly reduced at NNLO compared to the CT14
PDF uncertainty.
‚ 700+ data points from 12 new LHC data sets. The LHC constraints on the
CT18 PDFs are weaken by some inconsistencies between the LHC data sets
and the pre-LHC data sets.
‚ HERA DIS and fixed-target experiments deliver key constraints on CT18
PDFs.
‚ We observe some impact on PDFs from ATLAS and CMS incl. jet data,
ATLAS, CMS, LHCb W/Z data and ATLAS 8 TeV Z pT data. LHC top quark
pair data provides a similar impact to g-PDF as incl. jet data, but cannot
reduce g-PDF errors as strong as incl. jet data due to its much smaller number
of data points.
‚ ATLAS 7 TeV W and Z rapidity data, associate with x-dependent factorization
scale for NNLO DIS cross section, are included in the CT18Z PDF analysis.
32 / 32
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