L2 Sensitivities: PDF pulls of experiments in the CT18 global analysis

On this webpage, we collect calculations of the L2 sensitivities for the experiments fitted in the CT18 global QCD analysis [arXiv:1912.10053]. The L2 sensitivity reliably approximates the variation in χ² for a given experiment when the parton distribution function (PDF), f(x,Q), for a particular parton flavor, f, is increased by one PDF uncertainty (defined at the 90% C.L.) at a specific value of (x,Q). This method can be used for both Hessian and Monte Carlo PDF error sets, and can be computed very quickly, unlike the complementary Lagrange Multiplier (LM) scans, which are computationally expensive. The L2 sensitivities can therefore be evaluated for many PDF flavors and combinations across a wide range of (x,Q) values. This can be done for all fitted experiments in a way that delivers a comprehensive view of the experimental pulls on the PDFs, as well as possible tensions among them. These tensions are realized in the L2 sensitivity plots shown below as peaks in opposing directions (i.e., ±Δχ²) at similar values of x and Q.

We present two families of L2 sensitivity plots, for the CT18 and CT18Z PDF analyses. For each of these, we show the sensitivities for various PDF flavors experiment-by-experiment, as well as the pulls of the most sensitive experiments on specific PDF flavors and combinations.

Citation policy

If you use the results from this website, please kindly cite:

1. Charting the coming synergy between lattice QCD and high-energy phenomenology
   T. J. Hobbs, Bo-Ting Wang, Pavel Nadolsky, and Fredrick I. Olness,
   Phys. Rev. D100 (2019) no.9, 094040
2. New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
   Tie-Jiun Hou and others, [arXiv:1912.10053].

Website development: Tim Hobbs, Pavel Nadolsky

Figures

• CT18: Pulls on parton luminosities and on PDFs by PDF flavors and combinations, by experiments
• CT18Z: Pulls on parton luminosities and on PDFs by PDF flavors and combinations, by experiments

We plot the L2 sensitivities in each case above for a wide range of parton fractions, 5×10^-5 < x < 0.8, and at two scale choices, Q=2, 100 GeV.
 
Click on the link "[pdf]" or the image itself to download a high-resolution image in the Adobe PDF or PNG formats.

CT18, Pulls on parton luminosities

Here we show the L2 sensitivities for parton luminosities computed with CT18 NNLO PDFs, for a pp collider with energy 14 TeV, for massive states produced in the rapidity interval |y| < 2.5.

Glue-glue: [pdf]	Quark-glue: [pdf]
Quark-antquark: [pdf]	Quark-quark: [pdf]

CT18, Pulls on PDFs and their combinations

Here we show the L2 sensitivities for the CT18 NNLO PDFs and some of their common ratios and combinations.

CT18, Q=2 GeV

g(x,Q=2 GeV): [pdf]	u(x,Q=2 GeV): [pdf]	ub(x,Q=2 GeV): [pdf]
d(x,Q=2 GeV): [pdf]	db(x,Q=2 GeV): [pdf]	s(x,Q=2 GeV): [pdf]
c(x,Q=2 GeV): [pdf]	uval(x,Q=2 GeV): [pdf]	dval(x,Q=2 GeV): [pdf]
d/u(x,Q=2 GeV): [pdf]	db/ub(x,Q=2 GeV): [pdf]	(s+sb)/(ub+db)(x,Q=2 GeV): [pdf]
(s+sb)/(2db)(x,Q=2 GeV): [pdf]	(c+cb)/(ub+db)(x,Q=2 GeV): [pdf]	(u*db)/(d*ub)(x,Q=2 GeV): [pdf]
(u+ub-d-db)(x,Q=2 GeV): [pdf]

CT18, Q=100 GeV

g(x,Q=100 GeV): [pdf]	u(x,Q=100 GeV): [pdf]	ub(x,Q=100 GeV): [pdf]
d(x,Q=100 GeV): [pdf]	db(x,Q=100 GeV): [pdf]	s(x,Q=100 GeV): [pdf]
c(x,Q=100 GeV): [pdf]	uval(x,Q=100 GeV): [pdf]	dval(x,Q=100 GeV): [pdf]
d/u(x,Q=100 GeV): [pdf]	db/ub(x,Q=100 GeV): [pdf]	(s+sb)/(ub+db)(x,Q=100 GeV): [pdf]
(s+sb)/(2db)(x,Q=100 GeV): [pdf]	(c+cb)/(ub+db)(x,Q=100 GeV): [pdf]	(u*db)/(d*ub)(x,Q=100 GeV): [pdf]

CT18, Pulls on PDFs by experiments

We plot the pulls on the PDFs and their combinations experiment-by-experiment.

CT18, Q=2 GeV

BCDMS F2p: [pdf1] [pdf2]	BCDMS F2d: [pdf1] [pdf2]	NMC F2d/F2p ratio: [pdf1] [pdf2]	CDHSW F2: [pdf1] [pdf2]
CDHSW F3: [pdf1] [pdf2]	CCFR F2: [pdf1] [pdf2]	CCFR F3: [pdf1] [pdf2]	NuTeV dimuon nu: [pdf1] [pdf2]
NuTeV dimuon nubar: [pdf1] [pdf2]	CCFR dimuon nu: [pdf1] [pdf2]	CCFR dimuon nubar: [pdf1] [pdf2]	HERA b production: [pdf1] [pdf2]
HERA c production: [pdf1] [pdf2]	HERA I+II DIS: [pdf1] [pdf2]	HERA FL: [pdf1] [pdf2]	E605 Drell-Yan: [pdf1] [pdf2]
E866 sigma_d/(2*sigma_p) ratio: [pdf1] [pdf2]	E866 Drell-Yan pp: [pdf1] [pdf2]	CDF Run-1 W asymmetry: [pdf1] [pdf2]	CDF Run-2 W asymmetry: [pdf1] [pdf2]
D0 Run-2 Muon W asymmetry: [pdf1] [pdf2]	LHCb 7 TeV Z/W rapidity: [pdf1] [pdf2]	LHCb 8 TeV Z ele rapidity: [pdf1] [pdf2]	CMS 8 TeV W asymmetry: [pdf1] [pdf2]
LHCb 8 TeV W/Z rapidity: [pdf1] [pdf2]	ATLAS 8 TeV Z pT: [pdf1] [pdf2]	D0 Run-2 Z rapidity: [pdf1] [pdf2]	CDF Run-2 Z rapidity: [pdf1] [pdf2]
CMS 7 TeV Muon W asymmetry: [pdf1] [pdf2]	CMS 7 TeV Electron W asymmetry: [pdf1] [pdf2]	ATLAS 7 TeV Z/W total cross sections(35/pb): [pdf1] [pdf2]	D0 Run-2 electron W asymmetry: [pdf1] [pdf2]
CDF Run-2 jets: [pdf1] [pdf2]	D0 Run-2 jets: [pdf1] [pdf2]	CMS 7 TeV jets: [pdf1] [pdf2]	ATLAS 7 TeV jets: [pdf1] [pdf2]
CMS 8 TeV jets: [pdf1] [pdf2]	CMS 8 TeV ttbar pTt,yt: [pdf1] [pdf2]	ATLAS 8 TeV ttbar pt,Mtt: [pdf1] [pdf2]

CT18, Q=100 GeV

BCDMS F2p: [pdf1] [pdf2]	BCDMS F2d: [pdf1] [pdf2]	NMC F2d/F2p ratio: [pdf1] [pdf2]	CDHSW F2: [pdf1] [pdf2]
CDHSW F3: [pdf1] [pdf2]	CCFR F2: [pdf1] [pdf2]	CCFR F3: [pdf1] [pdf2]	NuTeV dimuon nu: [pdf1] [pdf2]
NuTeV dimuon nubar: [pdf1] [pdf2]	CCFR dimuon nu: [pdf1] [pdf2]	CCFR dimuon nubar: [pdf1] [pdf2]	HERA b production: [pdf1] [pdf2]
HERA c production: [pdf1] [pdf2]	HERA I+II DIS: [pdf1] [pdf2]	HERA FL: [pdf1] [pdf2]	E605 Drell-Yan: [pdf1] [pdf2]
E866 sigma_d/(2*sigma_p) ratio: [pdf1] [pdf2]	E866 Drell-Yan pp: [pdf1] [pdf2]	CDF Run-1 W asymmetry: [pdf1] [pdf2]	CDF Run-2 W asymmetry: [pdf1] [pdf2]
D0 Run-2 Muon W asymmetry: [pdf1] [pdf2]	LHCb 7 TeV Z/W rapidity: [pdf1]	LHCb 8 TeV Z ele rapidity: [pdf1]	CMS 8 TeV W asymmetry: [pdf1]
LHCb 8 TeV W/Z rapidity: [pdf1]	ATLAS 8 TeV Z pT: [pdf1] [pdf2]	D0 Run-2 Z rapidity: [pdf1] [pdf2]	CDF Run-2 Z rapidity: [pdf1] [pdf2]
CMS 7 TeV Muon W asymmetry: [pdf1] [pdf2]	CMS 7 TeV Electron W asymmetry: [pdf1] [pdf2]	ATLAS 7 TeV Z/W total cross sections(35/pb): [pdf1] [pdf2]	D0 Run-2 electron W asymmetry: [pdf1] [pdf2]
CDF Run-2 jets: [pdf1] [pdf2]	D0 Run-2 jets: [pdf1] [pdf2]	CMS 7 TeV jets: [pdf1] [pdf2]	ATLAS 7 TeV jets: [pdf1] [pdf2]
CMS 8 TeV jets: [pdf1] [pdf2]	CMS 8 TeV ttbar pTt,yt: [pdf1] [pdf2]	ATLAS 8 TeV ttbar pt,Mtt: [pdf1] [pdf2]

CT18Z, Pulls on parton luminosities

Here we show the L2 sensitivities for parton luminosities computed with CT18Z NNLO PDFs, for a pp collider with energy 14 TeV, for massive states produced in the rapidity interval |y| < 2.5.

Glue-glue: [pdf]	Quark-glue: [pdf]
Quark-antquark: [pdf]	Quark-quark: [pdf]

CT18Z, Pulls on PDFs and their combinations

Here we show the L2 sensitivities for the CT18Z NNLO PDFs and some of their common ratios and combinations.

CT18Z, Q=2 GeV

g(x,Q=2 GeV): [pdf]	u(x,Q=2 GeV): [pdf]	ub(x,Q=2 GeV): [pdf]
d(x,Q=2 GeV): [pdf]	db(x,Q=2 GeV): [pdf]	s(x,Q=2 GeV): [pdf]
c(x,Q=2 GeV): [pdf]	uval(x,Q=2 GeV): [pdf]	dval(x,Q=2 GeV): [pdf]
d/u(x,Q=2 GeV): [pdf]	db/ub(x,Q=2 GeV): [pdf]	(s+sb)/(ub+db)(x,Q=2 GeV): [pdf]
(s+sb)/(2db)(x,Q=2 GeV): [pdf]	(c+cb)/(ub+db)(x,Q=2 GeV): [pdf]	(u*db)/(d*ub)(x,Q=2 GeV): [pdf]
(u+ub-d-db)(x,Q=2 GeV): [pdf]

CT18Z, Q=100 GeV

g(x,Q=100 GeV): [pdf]	u(x,Q=100 GeV): [pdf]	ub(x,Q=100 GeV): [pdf]
d(x,Q=100 GeV): [pdf]	db(x,Q=100 GeV): [pdf]	s(x,Q=100 GeV): [pdf]
c(x,Q=100 GeV): [pdf]	uval(x,Q=100 GeV): [pdf]	dval(x,Q=100 GeV): [pdf]
d/u(x,Q=100 GeV): [pdf]	db/ub(x,Q=100 GeV): [pdf]	(s+sb)/(ub+db)(x,Q=100 GeV): [pdf]
(s+sb)/(2db)(x,Q=100 GeV): [pdf]	(c+cb)/(ub+db)(x,Q=100 GeV): [pdf]	(u*db)/(d*ub)(x,Q=100 GeV): [pdf]

CT18Z, Pulls on PDFs by experiments

We plot the pulls on the PDFs and their combinations experiment-by-experiment.

CT18Z, Q=2 GeV

BCDMS F2p: [pdf1] [pdf2]	BCDMS F2d: [pdf1] [pdf2]	NMC F2d/F2p ratio: [pdf1] [pdf2]
CCFR F2: [pdf1] [pdf2]	CCFR F3: [pdf1] [pdf2]	NuTeV dimuon nu: [pdf1] [pdf2]
NuTeV dimuon nubar: [pdf1] [pdf2]	CCFR dimuon nu: [pdf1] [pdf2]	CCFR dimuon nubar: [pdf1] [pdf2]	HERA b production: [pdf1] [pdf2]
HERA c production: [pdf1] [pdf2]	HERA I+II DIS: [pdf1] [pdf2]	HERA FL: [pdf1] [pdf2]	E605 Drell-Yan: [pdf1] [pdf2]
E866 sigma_d/(2*sigma_p) ratio: [pdf1] [pdf2]	E866 Drell-Yan pp: [pdf1] [pdf2]	CDF Run-1 W asymmetry: [pdf1] [pdf2]	CDF Run-2 W asymmetry: [pdf1] [pdf2]
D0 Run-2 Muon W asymmetry: [pdf1] [pdf2]	LHCb 7 TeV Z/W rapidity: [pdf1] [pdf2]	LHCb 8 TeV Z ele rapidity: [pdf1] [pdf2]	CMS 8 TeV W asymmetry: [pdf1] [pdf2]
LHCb 8 TeV W/Z rapidity: [pdf1] [pdf2]	ATLAS 8 TeV Z pT: [pdf1] [pdf2]	D0 Run-2 Z rapidity: [pdf1] [pdf2]	CDF Run-2 Z rapidity: [pdf1] [pdf2]
CMS 7 TeV Muon W asymmetry: [pdf1] [pdf2]	CMS 7 TeV Electron W asymmetry: [pdf1] [pdf2]	D0 Run-2 electron W asymmetry: [pdf1] [pdf2]
CDF Run-2 jets: [pdf1] [pdf2]	D0 Run-2 jets: [pdf1] [pdf2]	CMS 7 TeV jets: [pdf1] [pdf2]	ATLAS 7 TeV jets: [pdf1] [pdf2]
CMS 8 TeV jets: [pdf1] [pdf2]	CMS 8 TeV ttbar pTt,yt: [pdf1] [pdf2]	ATLAS 8 TeV ttbar pt,Mtt: [pdf1] [pdf2]

CT18Z, Q=100 GeV

BCDMS F2p: [pdf1] [pdf2]	BCDMS F2d: [pdf1] [pdf2]	NMC F2d/F2p ratio: [pdf1] [pdf2]
CCFR F2: [pdf1] [pdf2]	CCFR F3: [pdf1] [pdf2]	NuTeV dimuon nu: [pdf1] [pdf2]
NuTeV dimuon nubar: [pdf1] [pdf2]	CCFR dimuon nu: [pdf1] [pdf2]	CCFR dimuon nubar: [pdf1] [pdf2]	HERA b production: [pdf1] [pdf2]
HERA c production: [pdf1] [pdf2]	HERA I+II DIS: [pdf1] [pdf2]	HERA FL: [pdf1] [pdf2]	E605 Drell-Yan: [pdf1] [pdf2]
E866 sigma_d/(2*sigma_p) ratio: [pdf1] [pdf2]	E866 Drell-Yan pp: [pdf1] [pdf2]	CDF Run-1 W asymmetry: [pdf1] [pdf2]	CDF Run-2 W asymmetry: [pdf1] [pdf2]
D0 Run-2 Muon W asymmetry: [pdf1] [pdf2]	LHCb 7 TeV Z/W rapidity: [pdf1] [pdf2]	LHCb 8 TeV Z ele rapidity: [pdf1] [pdf2]	CMS 8 TeV W asymmetry: [pdf1] [pdf2]
LHCb 8 TeV W/Z rapidity: [pdf1] [pdf2]	ATLAS 8 TeV Z pT: [pdf1] [pdf2]	D0 Run-2 Z rapidity: [pdf1] [pdf2]	CDF Run-2 Z rapidity: [pdf1] [pdf2]
CMS 7 TeV Muon W asymmetry: [pdf1] [pdf2]	CMS 7 TeV Electron W asymmetry: [pdf1] [pdf2]	D0 Run-2 electron W asymmetry: [pdf1] [pdf2]
CDF Run-2 jets: [pdf1] [pdf2]	D0 Run-2 jets: [pdf1] [pdf2]	CMS 7 TeV jets: [pdf1] [pdf2]	ATLAS 7 TeV jets: [pdf1] [pdf2]
CMS 8 TeV jets: [pdf1] [pdf2]	CMS 8 TeV ttbar pTt,yt: [pdf1] [pdf2]	ATLAS 8 TeV ttbar pt,Mtt: [pdf1] [pdf2]