NNPDFPDFS:
FROM RUN II TO RUN III
STEFANO FORTEUNIVERSITA DI MILANO & INFN
CMS SM MEETING FEBRUARY 25, 2020
MOTIVATIONS: PRECISIONPDF4LHC PDFS (2014) NNPDF3.0 NNLO
GLUON SINGLET FLAVORS
• GLUON BETTER KNOWN AT SMALL x, VALENCE QUARKS AT LARGE x, SEA QUARKS IN BETWEEN
• TYPICAL UNCERTAINTIES IN DATA REGION ∼ 3− 5%
• SWEET SPOT: VALENCE Q - G; DOWN TO 1%
• UP BETTER KNOWN THAN DOWN; FLAVOR SINGLET BETTER THAN INDIVIDUAL FLAVORS
MOTIVATIONS: PRECISIONCURRENT PDFS (2017) NNPDF3.1 NNLO
GLUON SINGLET FLAVORS
• GLUON BETTER KNOWN AT SMALL x, VALENCE QUARKS AT LARGE x, SEA QUARKS IN BETWEEN
• TYPICAL UNCERTAINTIES IN DATA REGION ∼ 1− 3%
• SWEET SPOT: VALENCE Q - G; 1% OR BELOW
• UP BETTER KNOWN THAN DOWN; FLAVOR SINGLET BETTER THAN INDIVIDUAL FLAVORS
MOTIVATIONS: ACCURACYIMPACT OF ATLAS W/Z 7TEV DATA
CT18 NNPDF3.1
• CT18: PDF SETS RELEASED WITH/WITHOUT ATLAS W/Z DATA INCLUDED
• NNPDF3.1: CONSISTENCY OF ALL DATASETS INCLUDED
SUMMARY
TOWARDS NNPDF4.0 (2020)
DATA• THE NNPDF4.0 DATASET
• TOP PAIRS
• SINGLE TOP
• JETS
THEORY• ELECTROWEAK CORRECTIONS
• REGULARIZED COVARIANCE MATRICES
• THEORY UNCERTAINTIES
(METHODOLOGY)
DATA
DATASET WIDENINGNNPDF3.0 VS NNPDF3.1 (CT14 VS. CT18: SIMILAR)
NEW DATA: (BLACK EDGE)
• HERA COMBINED F b2• D0 W LEPTON ASYMMETRY
• ATLAS W,Z 2011, HIGH& LOW MASS DY 2011;CMS W± RAPIDITY 8TEVLHCB W,Z 7TEV & 8TEV
• ATLAS 7TEV JETS 2011,CMS 2.76TEV JETS
• ATLAS & CMS TOPDIFFERENTIAL RAPIDITY
• ATLAS Z pT DIFFERENTIALRAPIDITY & INVARIANT MASS8TEV,CMS Z pT DIFFERENTIALRAPIDITY 8TEV
DATASET WIDENINGNNPDF4.0 SUMMARY (EXPECTED IN 2020)
1. OLD DATASETS WITH IMPROVED TREATMENT
• ASSORTED DEBUGGING
• CORRELATIONS IN ATLAS TOP DISTRIBUTIONS AT 8 TEV• CHOICE OF SCALE AND CORRELATION MODELS FOR SINGLE-JET DATA
• MASSIVE CORRECTIONS TO NEUTRINO DIS DIMUON CROSS SECTIONS AT NNLO• NUCLEAR UNCERTAINTIES IN FIXED-TARGET DIS AND DY
2. NEW DATASETS FOR OLD PROCESSES
• DIS c AND b PRODUCTION (HERA COMBINED)• SINGLE JET PRODUCTION (ATLAS, CMS)• TOP PAIR PRODUCTION (ATLAS, CMS)• COLLIDER DY/INCLUSIVE VECTOR BOSON PRODUCTION (ATLAS, CMS, LHCB)• COLLIDER VECTOR BOSON PRODUCTION IS ASSOCIATION WITH CHARM (CMS)
3. NEW DATASETS FOR NEW PROCESSES
• ISOLATED PHOTON PRODUCTION (ATLAS)• SINGLE TOP PRODUCTION (ATLAS, CMS)• COLLIDER DIJET PRODUCTION (ATLAS, CMS)• DIS+JET(S) PRODUCTION (H1, ZEUS)• COLLIDER VECTOR BOSON PRODUCTION IS ASSOCIATION WITH JETS (ATLAS, CMS)
O(50) NEW/REVISED DATASETS
DISCUSSED IN THIS TALK
NEW DATASETS FOR OLD PROCESSES• DIS c AND b PRODUCTION
HERA COMBINED REDUCED CROSS SECTIONS (REPLACES H1 AND ZEUS DATA SETS)
• SINGLE-INCLUSIVE JETSATLAS 8 TEV DOUBLE DIFFERENTIAL DISTRIBUTIONS (R=0.4; R=0.6) (IMPLEMENT CORRELATION MODELS)CMS 8 TEV DOUBLE DIFFERENTIAL DISTRIBUTIONS (R=0.7)(IMPLEMENT CORRELATION MODELS)
• TOP PAIR PRODUCTIONATLAS 8 TEV DIFFERENTIAL ABS. AND NORM. DISTRIBUTIONS; DILEPTON; mtt; yttCMS 8 TEV DOUBLE DIFFERENTIAL NORM. DISTRIBUTIONS; DILEPTON; (ptT , yt); (mtt, yt); (mtt, ytt)CMS 13 TEV DIFFERENTIAL ABS. AND NORM. DISTRIBUTIONS; DILEPTON; ptT ; yt; ytt; mtt
CMS 13 TEV DIFFERENTIAL ABS. AND NORM. DISTRIBUTIONS; LEPTON+JET; ptT ; yt; ytt; mtt
CMS 5.02 TEV TOTAL CROSS SECTION
• COLLIDER DY/INCLUSIVE VECTOR BOSON PRODUCTION OR IN ASSOCIATION WITH CHARMATLAS 13 TEV W+, W− AND Z TOTAL CROSS SECTIONS (INCLUDING CORRELATIONS)ATLAS 7 TEV W+, W− AND Z RAPIDITY DISTRIBUTIONS (INCLUDIG OFF-PEAK AND FORWARD)ATLAS 8 TEV DOUBLE-DIFFERENTIAL HIGH-MASS DY DISTRIBUTIONS (TO BE CHECKED)ATLAS 8 TEV TRIPLE DIFFERENTIAL DY DISTRIBUTIONCMS 8 TEV DOUBLE-DIFFERENTIAL DY DISTRIBUTIONCMS 13 TEV DY DIFFERENTIAL CROSS-SECTIONS (VARIOUS DISTRIBUTIONS, AMONG WHICH ZpT )CMS 13 TEV W + c DIFFERENTIAL DISTRIBUTIONSLHCB 8 TEV W AND Z RAPIDITY DISTRIBUTIONS, ELECTRON CHANNELLHCB 13 TEV Z RAPIDITY DISTRIBUTIONS, DIELECTRON AND DIMUON CHANNELS
ALREADY IMPLEMENTED; ONGOING IMPLEMENTATION; TO DO
NEW DATA SETS FOR NEW PROCESSES• ISOLATED PHOTON PRODUCTION
ATLAS 8 TEV DIFFERENTIAL DISTRIBUTIONS, INCLUDING CORRELATIONSATLAS 13 TEV DIFFERENTIAL DISTRIBUTIONS
• SINGLE TOP PRODUCTION, t-CHANNELATLAS TOP TO ANTITOP RATIO, 7, 8 AND 13 TEVATLAS TOP AND ANTITOP ABS. AND NORM. DIFFERENTIAL DISTRIBUTIONS, 7 TEV, pT ; yATLAS TOP AND ANTITOP ABS. AND NORM. DIFFERENTIAL DISTRIBUTIONS, 8 TEV, pT ; yCMS TOP AND ANTITOP TOTAL CROSS SECTION, 7 TEVCMS TOP TO ANTITOP RATIO, 8 AND 13 TEV
• COLLIDER DI-JET PRODUCTIONATLAS 7 TEV DIJET DOUBLE DIFFERENTIAL DISTRIBUTIONS (R=0.4; R=0.6)CMS 5.02 TEV DIJET DOUBLE DIFFERENTIAL DISTRIBUTIONSCMS 7 TEV DIJET DOUBLE DIFFERENTIAL DISTRIBUTIONS (R=0.7)CMS 8 TEV DIJET TRIPLE DIFFERENTIAL DISTRIBUTIONS (R=0.7)
• DIS+JET(S) PRODUCTIONH1 SINGLE- AND DI-JET DIFFERENTIAL DISTRIBUTIONSZEUS SINGLE- AND DI-JET DIFFERENTIAL DISTRIBUTIONS
• COLLIDER VECTOR BOSON PRODUCTION IN ASSOCIATION WITH JETSATLAS 8 TEV W+JET DIFFERENTIAL DISTRIBUTIONS
ALREADY IMPLEMENTED; ONGOING IMPLEMENTATION; TO DO
TOP PAIR PRODUCTION(PAST RESULTS)
CONSISTENCY OF DIFFERENT OBSERVABLESTOP PRODUCTION AND THE GLUON
INCLUSION OF ATLAS TOP DATA IN HERA+TOP FIT (XFITTER)HQ PAIR RAPIDITY DISTN INVARIANT MASS DISTN.
INCONSISTENCY?
TOP PAIR PRODUCTION(PAST RESULTS)
TOP PRODUCTION AND THE GLUONINCLUSION OF ATLAS TOP DATA IN NNPDF3.1-LIKE FIT
ATLAS ONLY
0.1 0.2 0.3 0.4 0.5 0.6 0.7 x
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
g (
x, Q
) /
g (
x, Q
) [r
ef]
Baseline no-top+ ATLAS ytt+ ATLAS mtt+ ATLAS yt
det), Q = 100 GeVSαNNPDF3.1NNLO (ATLAS+CMS
0.1 0.2 0.3 0.4 0.5 0.6 0.7 x
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
g (
x, Q
) /
g (
x, Q
) [r
ef]
Baseline no-top
+ ATLAS+CMS ytt
+ ATLAS+CMS mtt
+ ATLAS+CMS yt
det), Q = 100 GeVSαNNPDF3.1NNLO (
• FOR ATLAS mtt & y DISTRIBUTIONS PULL IN OPPOSITE DIRECTION⇒ COMPATIBLE WITHIN UNCERTAINTIES
• mtt HAS MUCH LESS PULL
• FOR CMS, BOTH mtt & y PULL IN THE SAME DIRECTION
CONSISTENCY!
ASIDE: THE CHARM PDF FROM DATAIMPACT ON LIGHT QUARK PDFS
• TRADITIONALLY CHARM PERTURBATIVELY GENERATEDFROM (LOW-ORDER) MATCHING CONDITIONS
• NNPDF3.1: CHARM FITTED
FITTED VS. PERTURBATIVE CHARMQQBAR LUMI
( GeV )XM10 210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2 fitted charm
perturbative charm
LHC 13 TeV, NNLOANTIDOWN PDF
x 4−10 3−10 2−10 1−10
) [r
ef]
2 (
x, Q
d)
/ 2
( x
, Qd
0.9
0.95
1
1.05
1.1
1.15 Fitted charm
Perturbative charm
NNPDF3.1 NNLO, Q = 100 GeV W+/W− XSECT RATIO
1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33σW+/σW−
ATLAS 13 TeV
Heavy: NNLO QCD + NLO EWLight: NNLO QCD
Ratio of W+ to W− boson
NNPDF3.1
NNPDF3.0
CT14
MMHT14
ABMP16
data ± total uncertainty
• QUARK (ESPECIALLY QUARK-ANTIQUARK) LUMI AFFECTED
• FLAVOR DECOMPOSITION ALTERED
• NECESSARY FOR AGREEMENT OF 13TeV PREDICTED CROSS-SECTIONS
TOP PAIR PRODUCTION(NEW RESULTS)
(S.F., E. Nocera, J. Rojo, subm. to Les Houches 2019)
• WHAT IF WE FIT ALL DISTRIBUTIONS AT ONCE?CORRELATIONS ⇒ NOW POSSIBLE
• NORMALIZED VS. ABSOLUTE DISTRIBUTIONS?
• FITTING CHARM? (NEEDED FOR GOOD FIT TO ATLAS W/Z IN NNPDF3.1)
t RAPIDITY VS. ALL ALL NORM. VS. ABSOLUTE ALL NORM FIT. VS. PERT. CHARM
TOP PAIR PRODUCTION(NEW RESULTS)
(S.F., E. Nocera, J. Rojo, subm. to Les Houches 2019)
• WHAT IF WE FIT ALL DISTRIBUTIONS AT ONCE? ⇒ NO EFFECT!CORRELATIONS ⇒ NOW POSSIBLE
• NORMALIZED VS. ABSOLUTE DISTRIBUTIONS? ⇒ BIG EFFECT!
• FITTING CHARM? ⇒ SIZABLE EFFECT!t RAPIDITY VS. ALL ALL NORM. VS. ABSOLUTE ALL NORM FIT. VS. PERT. CHARM
• DIFFERENT DISTRIBUTIONS CONSISTENT (BUT pt BAD FIT)
• ABSOLUTE PATHOLOGICAL (BAD FIT, INCONSISTENT GLUON)
• FITTED CHARM NEEDED FOR CONSISTENCY WITH GLOBAL DATASET
SINGLE TOP PRODUCTION (t-CHANNEL)
(E. Nocera, M. Ubiali, C. Voisey, arXiv:1912.09543)
• CANNOT USE MULTIPLE OBSERVABLES (NO CORRELATION)
• OPTIMAL SET⇒ XSECT RATIOS (ATLAS, CMS), TOTAL XSECT (CMS) + NORMALIZED RAPIDITYDISTRIBUTION (ATLAS)
• SEVERAL PROBLEMATIC DATA: pT DISTRIBUTIONS, ATLAS XSECT RATIOS
UP DOWN U/D RATIO
• CENTRAL VALUES UNCHANGED
• SLIGHT REDUCTION OF UNCERTAINTY ON LIGHT QUARKS
SINGLE TOP PRODUCTION(t-CHANNEL)IMPACT ON PHENOMENOLOGY
• MOST PRECISE REGION FOR qq LUMI SOMEWHAT EXTENDED
• UNCERTAINTY ON W+/W− HARDLY REDUCED
QUARK-ANTIQUARK LUMINOSITYBASELINE
4 2 0 2 4y
101
102
103
104
MX (
GeV)
Relative uncertainty for qq-luminosityBaseline (Fit 1) - s = 13000 GeV
1
5
10
25
50
Rela
tive
unce
rtain
ty (%
)
BASELINE+SINGLE TOP
4 2 0 2 4y
101
102
103
104
MX (
GeV)
Relative uncertainty for qq-luminosityOptimal fit - s = 13000 GeV
1
5
10
25
50
Rela
tive
unce
rtain
ty (%
)
W+/W− RATIO
3.3 3.4 3.5 3.6 3.7W [fb] ×106
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
W+
[fb]
×106 W± (NNLO)BaselineOptimal fit
• WHAT’S WRONG WITH THE ATLAS 8TEV XSECT RATIO?
• WHAT’S WRONG WITH THE pT DISTRIBUTIONS?
• CORRELATIONS BETWEEN OBSERVABLES?
JETS:SINGLE-INCLUSIVE: NNPDF3.1 DATASET
NNPDF+NNLOJET++, in preparation
• IMPACT ON GLUON UNCERTAINTY AT LARGE x
• SERIOUS ISSUES WITH THE ATLAS 7 TEV COVARIANCE MATRIX
• HT BETTER FIT AT NLO VS pT , NO DIFFERENCE AT NNLO
• MODERATE IMPACT OF EW CORRNS ON PDFS, BUT BETTER FIT
IMPACT ON THE GLUONNLO
0.1 0.2 0.3 0.4 0.5 x
0.8
0.9
1
1.1
1.2
1.3
) [r
ef]
2)
/ g (
x, Q
2g
( x,
Q
Baseline (no jet data)
)jet
T=pµ+ 7 TeV InclJets (
)T
H=µ+ 7 TeV InclJets (
NNPDF3.1 NLO, Q = 100 GeVNNLO UNCERTAINTY
0.1 0.2 0.3 0.4 0.5 x
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
)2R
elE
rr o
n g
( x,
Q
Baseline (no jet data)
)jet
={T}µ+ 7 TeV InclJets (
)T
H=µ+ 7 TeV InclJets (
NNPDF3.1 NNLO, Q = 100 GeV
NNLO
0.1 0.2 0.3 0.4 0.5 x
0.8
0.9
1
1.1
1.2
1.3
) [r
ef]
2)
/ g (
x, Q
2g
( x,
Q
Baseline (no jet data)
)jet
={T}µ+ 7 TeV InclJets (
)T
H=µ+ 7 TeV InclJets (
NNPDF3.1 NNLO, Q = 100 GeVEW CORRECTIONS
0.1 0.2 0.3 0.4 0.5 x
0.8
0.9
1
1.1
1.2
1.3
) [r
ef]
2)
/ g (
x, Q
2g
( x,
Q
Baseline (no jet data)
+ 7 TeV InclJets (QCD)
+ 7 TeV InclJets (QCD+EW)
NNPDF3.1 NNLO, Q = 100 GeV
JETSSINGLE-INCLUSIVE: FULL DATASET
NNPDF+NNLOJET++, in preparation
• CMS, ATLAS, 7, 8 TEV DATSETS CONSISTENT ⇒ UNCERTAINTY REDUCTION
• 8 TEV DATA ⇒ LARGE x GLUON AFFECTED
IMPACT ON THE NNLO GLUONPDF
10 2 10 1
x
0.85
0.90
0.95
1.00
1.05
1.10
1.15
Ratio
to B
asel
ine
(no
jet d
ata)
g at 100.0 GeVBaseline (no jet data) (68 c.l.+1 )Baseline + ATLAS and CMS single jets 7 TeV (68 c.l.+1 )Baseline + all single-jet data (68 c.l.+1 )
UNCERTAINTY
10 2 10 1
x
0.02
0.04
0.06
0.08
0.10
(Rat
io to
Bas
elin
e (n
o je
t dat
a))
g at 100.0 GeVBaseline (no jet data)Baseline + ATLAS and CMS single jets 7 TeVBaseline + all single-jet data
JETS:SINGLE-INCLUSIVE VS. DIJETS
NNPDF+NNLOJET++, in preparation
• CANNOT USE BOTH BECAUSE OF MISSING CORRELATIONS
• DIJETS BETTER FIT QUALITY
IMPACT ON THE GLUONPDF
10 2 10 1
x
0.85
0.90
0.95
1.00
1.05
1.10
1.15
Ratio
to B
asel
ine
(no
jet d
ata)
g at 100.0 GeVBaseline (no jet data) (68 c.l.+1 )Baseline + all single-jet data (68 c.l.+1 )Baseline + all di-jet data (68 c.l.+1 )
UNCERTAINTY
10 2 10 1
x
0.02
0.04
0.06
0.08
0.10
0.12
0.14
(Rat
io to
Bas
elin
e (n
o je
t dat
a))
g at 100.0 GeVBaseline (no jet data)Baseline + all single-jet dataBaseline + all di-jet data
• SMILAR IMPACT OF EITHER OBSERVABLE
• SINGLE-INCLUSIVE ⇒ SMALLER UNCERTAINTY (BUT MORE DATA)
• DIJETS ⇒ (MORE) LARGE x ENHANCEMENT
• NEED FULL DATASET TO FIGURE OUT THE FINAL PRECISE PDF SHAPE
THEORY
ELECTROWEAK CORRECTIONSEXAMPLE: TOP PAIR PRODUCTION
NNPDF3.1
ELECTROWEAK CORRECTIONSEXAMPLE: TOP PAIR PRODUCTION
NNPDF4.X
S. Carrazza, E. Nocera, C. Schwan, M. Zaro, in preparation
ELECTROWEAK CORRECTIONSEXAMPLE: TOP PAIR PRODUCTION
NNPDF4.X
S. Carrazza, E. Nocera, C. Schwan, M. Zaro, in preparation
• TOOLCHAIN BASED ON mg5 aMC, aMCblast, APPLgridEW INTERFACED TO NNPDFTHROUGH APFELcomb
• GRIDS COMPUTED AND TEST FITS PERFORMED FOR SELECTED PROCESSES
EXAMPLE: GLUON-GLUON GRID FOR tt 8 TeV
010203040ya
0
10
20
30
40
y bδgg→tt(xa(ya), xb(yb), Q
2 = m2t)
−10.0
−7.5
−5.0
−2.5
0.0
2.5
5.0
7.5
10.0
• ∆ = O(ααs )/O(α2s); yi(x) = − lnxi + 5(1− xi)
• CORRECTION TYPICALLY ∼ 5%
ELECTROWEAK CORRECTIONSTHE DOUBLE-COUNTING PROBLEM
CONTRIBUTIONS SOMETIMES SUBTRACTED BY EXPERIMENTEXAMPLE: ATLAS 7 TeV HIGH-MASS DY IN Z, γ → e+e− CHANNEL
• PHOTON-INDUCED SUBTRACTED AT LO (BUT NOT PHOTON-QUARK)
• THREE DATASETS DEFINED:– BORN LEPTONS: NO FINAL-STATE RADIATION (OK FOR QCD)– BARE LEPTONS: FINAL-STATE RADIATION
– DRESSED LEPTONS: FINAL-STATE RADIATION + RECOMBINATION WITHINGIVEN RADIUS (OK FOR QCD+EW)
DESIDERATA
• NEED DATASETS BOTH AT THE BARE & DRESSED LEVEL 4• PLEASE DO NOT SUBTRACT PHOTON INDUCED! (WHY WOULD YOU?) 7
THE COVARIANCE MATRIX PROBLEM• FOR SEVERAL DATSETS, FULL CORRELATED χ2 POOR
EXAMPLES:
• ATLAS 8 TeV tt ABSOLUTE DISTRIBUTIONS: χ2/Ndat ∼ 6,DECORRELATING OBSERVABLES χ2/Ndat ∼ 2
• ATLAS 2011 7 TeV SINGLE-INCLUSIVE JETS: χ2/Ndat ∼ 2.5,DECORRELATING RAPIDITY BINS χ2/Ndat ∼ 1 ⇔ IF ONLY ONE BIN FITTED, ALL BINS
PREDICTED WITH χ2/Ndat ∼ 1
• ATLAS W/Z 2011 7 TEV: χ2/Ndat ∼ 2
THE COVARIANCE MATRIX PROBLEMEXAMPLE: THE ATLAS JETS
• ONLY CENTRAL RAPIDITY BIN ⇒ χ2 ∼ 1, ALL BINS χ2 ∼ 2.5
• BUT PDFS UNCHANGED!
PDFS: CENTRAL BIN VS ALL BINSGLUON QUARK SINGLET
10 5 10 4 10 3 10 2 10 1 100
x
0.900
0.925
0.950
0.975
1.000
1.025
1.050
1.075
1.100
Ratio
to C
urre
nt F
it
at 1.7 GeVCurrent Fit (68 c.l.+1 )Reference Fit (68 c.l.+1 )
THE COVARIANCE MATRIX PROBLEMATLAS W/Z 2011 7 TEV CORRELATION MATRIX
• POORLY CONDITIONED MATRIX: ONE (OR MORE) VERY SMALL EIGENVALUES
• GENERIC SITUATION WITH SMALL UNCORRELATED UNCERTAINTIES AND ONE ALMOSTFULLY CORRELATED UNCERTAINTY
REGULARIZING ⇔ DECORRELATINGZ. Kassabov, E. Nocera, M. Wilson, in preparation
• PERFORM SINGULAR-VALUE DECOMPOSITION
• REPLACE SMALLEST EIGENVALUES WITH CUTOFF 1/δ
ATLAS W/Z 2011 7 TEV CORRELATION MATRIX
• EFFECTIVELY ADDS 1/δ TO DIAGONAL OF COVARIANCE MATRIX
• CORRELATION MATRIX ALMOST UNCHANGED
REGULARIZED FITZ. Kassabov, E. Nocera, M. Wilson, in preparation
• APPLY REGULARIZATION TO FULL NNPDF3.1 DATASET
• REFIT
RATIO OF REGULARIZED TO DEFAULT
• χ2 DOWN FROM 1.16 TO 1.0 FOR ∼ 4000 DATAPOINTS
• PDFS UNCHANGED
THE MISSING HIGHER ORDER UNCERTAINTY ON PDFS
NLO-NNLO SHIFT VS. NLO PDF UNCERTAINTY (NNPDF3.1)ANTIDOWN
x 4−10 3−10 2−10 1−10
)2 (
x, Q
d ∆
0.9
0.95
1
1.05
1.1
1.15
NLO PDF uncertainties
TH error (NLO => NNLO shift)
NNPDF3.1, Q = 100 GeVGLUON
x 4−10 3−10 2−10 1−10
)2 g
( x
, Q∆
0.9
0.95
1
1.05
1.1
1.15
NLO PDF uncertainties
TH error (NLO => NNLO shift)
NNPDF3.1, Q = 100 GeV
• NEVER INCLUDED IN CURRENT PDF SETS
• TODAY: NLO PDF & MHOU UNCERTAINTIES COMPARABLE
• NEAR FUTURE: SHOULD WE WORRY ABOUT NNLO MHOU?
THE THEORY COVARIANCE MATRIX FROM SCALE VARIATION
NNPDF, 2019
• INDEPENDENT NUISANCE PARAMETERS ⇒ TH. AND EXP. ERRORS COMBINE IN QUADRATURE
χ2 =∑Ndat
i,j=1
(Di − T
(0)i
)[S + C]−1
ij
(Di − T
(0)i
)• REN. SCALE ⇒ CORRELATIONS INDUCED BETWEEN
EXPERIMENTALLY UNRELATED MEASUREMENTS OF SAME PROCESS
• FACT. SCALE ⇒ CORRELATIONS INDUCED BETWEEN DIFFERENT PROCESSES
THE COVARIANCE MATRIXEXPERIMENT
DIS NCDIS CC DY JETSTOP
DIS NC
DIS CC
DY
JETSTOP
Experimental Covariance Matrix
102101
10010 1
10 2
0
10 210 1
100101
102
% o
f dat
a
THEORY (9 PT)
DIS NCDIS CC DY JETSTOP
DIS NC
DIS CC
DY
JETSTOP
Theory Covariance matrix (9 pt)
101
100
10 1
10 2
0
10 2
10 1
100
101
% o
f dat
a
PDFS WITH THEORY UNCERTAINTIESGLUON
5−10 4−10 3−10 2−10 1−10 x
0.8
0.9
1
1.1
1.2
1.3
) [r
ef]
2)
/ g (
x, Q
2g
( x,
Q
NNPDF3.1 Global, Q = 10 GeV
NLO, CNLO, C+S(9pt)NNLO, C
NNPDF3.1 Global, Q = 10 GeVANTIDOWN
5−10 4−10 3−10 2−10 1−10 x
0.8
0.9
1
1.1
1.2
1.3
) [r
ef]
2 (
x, Q
d)
/ 2
( x
, Qd
NNPDF3.1 Global, Q = 10 GeV
NLO, CNLO, C+S(9pt)NNLO, C
NNPDF3.1 Global, Q = 10 GeV
C C + S(9pt)
χ2 1.139 1.109φ 0.314 0.415
• FIT QUALITY χ2 IMPROVES
• RELATIVE ERROR φ ON PREDICTION MILDLY INCREASED
• CENTRAL VALUE MOVES TOWARDS KNOWN NNLO
EQUALLY PRECISE BUT MORE ACCURATE RESULT!
PHENOMENOLOGY (LHC 13)HIGGS GG
NLO NNLO N3LO
30
35
40
45
50
σ[p
b]
light: scale uncertainty
dark: PDF uncertainty
left: C
right: C+S (9pt)
Higgs production: gluon fusion
NNLO PDFs
HIGGS VBF
NLO NNLO N3LO
3.88
3.90
3.92
3.94
3.96
3.98
4.00
4.02
4.04
σ[p
b]
light: scale uncertainty
dark: PDF uncertainty
left: C
right: C+S (9pt)
Higgs production: Vector Boson Fusion
NNLO PDFs
TOP PAIRS
NLO NNLO
650
700
750
800
850
σ[p
b]
light: scale uncertainty
dark: PDF uncertainty
left: C
right: C+S
pp→ tt, LHC 13 TeV, global NLO PDFs at all orders
NNLO PDFs
USAGE: JUST COMPUTE PDF ERROR AS USUAL &COMBINE WITH MHOU ON HARD MATRIX ELEMENT COMPUTED WITH YOUR PREFERRED RECIPE
• GLUON FUSION, TOP
– NO EFFECT ON CENTRAL VALUE
– VISIBLE INCREASE OF UNCERTAINTIE
• VBF– MODERATE EFFECT ON UNCERTAINTIES
– VISIBLE SHIFT OF CENTRAL VALUES
• ALL: TRUE NNLO NOW WITHIN NLO ERROR BAND
METHODOLOGY
NNPDF4.0: N3FITS. Carrazza, J. Cruz-Martinez, NNPDF, 2020
• FIRST PDF SET BASED ON DEEP LEARNING MODELS:HYPEROPTIMIZED METHODOLOGY
• CLOSURE TESTED
• “FUTURE” TESTED
PREDICTED VS TRUE GLUONONLY PRE-HERA DATA USED
NNPDF4.X HIGHLIGHTS
• BASED ON DEEP-LEARNING & CLOSURE TESTED
• VERY LARGE DATASET: ∼ 50 NEW DATA, SEVERAL NEW PROCESSES
• THEORY UNCERTAINTIES ACCOUNTED FOR
• ELECTROWEAK CORRECTIONS INCLUDED UP TO NLO
THE WORK OF MANY PEOPLE
NNPDF collaboration and N3PDF team meeting,
Varenna, Italy, September 2019