Recent developments in the CTEQ-TEA global analysis

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


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


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


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


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


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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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)

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

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

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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


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

PDF

Rat

io to

CT

14H

ER

A2.

54

x


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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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

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

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


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


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


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


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


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

PDF

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

PDF

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

PDF

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

PDF

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

PDF

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


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


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


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

Recent developments in the CTEQ-TEA global analysis

Documents