parton distributions for lhc run ii · 2015-07-03 · parton distributions for lhc run ii stefano...
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PARTON DISTRIBUTIONS
FOR LHC RUN II
STEFANO FORTE
UNIVERSITA DI MILANO & INFN
LAL ORSAY, JULY 3, 2015
PROLOGUEPDFS FOR LHC RUN I
WHY WORRY ABOUT PDFS?HIGGS PRODUCTION
(J. Campbell, HCP2012)
PDF UNCERTAINTY EITHER DOMINANT, OR VERY LARGE, OR BOTH
. . . AND NOT ONLY FOR THE HIGGS!(W MASS DETERMINATION, NEW PHYSICS SEARCHES FOR HEAVY STATES,. . . )
PDFS FOR LHC RUN IσX(s,M2
X) =∑
a,b
∫ 1
xmindx1 dx2 fa/h1
(x1)fb/h2(x2)σqaqb→X
(
x1x2s,M2X
)
x-610 -510 -410 -310 -210 -110 1
]2
[ G
eV2 T
/ p
2 /
M2
Q
1
10
210
310
410
510
610
710NMCPD
NMC
SLAC
BCDMS
HERA1AV
CHORUS
FLH108
NTVDMN
ZEUSH2
ZEUSF2C
H1F2C
DYE886
DYE605
CDFWASY
CDFZRAP
D0ZRAP
ATLASWZRAP
D0R2CON
CDFR2KT
ATLASR04JETS
CMSWEASY
LHCBW
NNPDF2.3 Dataset
LHC KINEMATICS
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
100
101
102
103
104
105
106
107
108
109
fixedtarget
HERA
x1,2
= (M/14 TeV) exp(±y)Q = M
LHC parton kinematics
M = 10 GeV
M = 100 GeV
M = 1 TeV
M = 10 TeV
66y = 40 224
Q2
(GeV
2 )
x
MSTW08 CT10 NNPDF2.3 HERAPDF1.5 ABM11/12 JR09
HERA DIS ✔ ✔ ✔ ✔ ✔ ✔
FIXEDTARGET DIS ✔ ✔ ✔ ✗ ✔ ✔
FIXEDTARGET DY ✔ ✔ ✔ ✗ ✔ ✔
TEVATRON W+Z+JETS ✔ ✔ ✔ ✗ ✗ ✗
LHC W+Z+JETS ✗ ✗ ✔ ✗ some, approx. ✗
RUN I PDF SETS: THE APPROACH
METHODOLOGY
• STATISTICAL TREATMENT: CTEQ, MSTW HESSIAN WITH DYNAMICAL TOLERANCE;
HERAPDF, STANDARD HESSIAN+PARM. ERROR ANALYSIS; GJR, HESSIAN WITH FIXED
TOLERANCE; ABKM STANDARD HESSIAN; NNPDF MONTE CARLO (ALSO STUDIED BY
HERAPDF, MSTW)
• PARTON PARAMETRIZATION: CTEQ, MSTW, HERAPDF xα(1− x)β× POLYNOMIALS;
GJR: DITTO + VALENCELIKE ASSUMPTION; NNPDF NEURAL NETS; CHEBYSHEV POLYNOMIALS
STUDIED BY HERAPDF, MSTW;
• COVARIANCE MATRIX, NORMALIZATION UNCERTAINTIES, OUTLIERS, THEORETICAL UNCERTAINTIES . . .
THEORY
• αs VALUE: CTEQ: EXTERNAL PARAMETER, SEVERAL VALUES AVAILABLE; NNPDF:
EXTERNAL PARAMETER, SEVERAL VALUES AVAILABLE, BESTFIT DETERMINED; MSTW: FITTED,
BUT ALSO VARIABLE AS EXT.PARAMETER; ABKM: FITTED, VARIABLE AS EXT.PARAMETER (ONLY
CENTRAL VALUE); GJR: FITTED, NOT VARIABLE AS EXT. PARAMETER;
• HEAVY QUARKS: CTEQ: GMVFN (SACOTχ SCHEME); MSTW: GMVFN (ACOT+TR’
SCHEME); NNPDF: GMVFN (FONLL SCHEME); ABKM: FFN (Nf = 3, 4 MATCHED WITH
BMSN SCHEME); GJR: FFN (Nf = 3)
• NUCLEAR CORRECTIONS, HIGHER TWISTS, KINEMATIC CUTS, “INITIAL SCALE”, . . .
MSTW08 CT10 NNPDF2.3 HERAPDF1.5 ABM11/12 JR09
NO. OF PDFS 7 6 7 5 6 5STATISTICS HESS.+DT HESS.+DT MC HESS.+MODEL+PARM. HESS. HESS.+TPDF PARMS. 20+8 25 259 14 24 12HEAVY QUARKS VFN TR VFN ACOT VFN FONLL VFN TR FFN FFN
LHC EW STANDARD CANDLESW+
) [p
b]ν
) B
(l+
(Wσ
6.6
6.8
7
7.2
7.4
7.6
7.8 = 0.118Sα) - VRAP NNLO - +(WσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
W−
) [p
b]ν
) B
(l-
(Wσ
4.7
4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
= 0.118Sα) - VRAP NNLO - -(WσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
Z
) [p
b]- l+
) B
(l0
(Zσ
1.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22
1.24
1.26 = 0.118Sα) - VRAP NNLO - 0(ZσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
• AGREEMENT/DISAGREEMENT DRIVEN
BY DATA
• DISONLY FIT (HERAPDF) SAFE, BUT
LARGE UNCERTAINTY
• FITS WITH SMALLER DATASETS PRONE
TO TH. BIAS
PARTON LUMINOSITIES: QUARK SECTOR (qq)
GLOBAL PDF SETS
(ratio to NNPDF2.3)
XM210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
OTHER PDF SETS
(ratio to NNPDF2.3)
XM210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
ABM11 NNLO
HERAPDF1.5 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
• CROSSSECTIONS REFLECT UNDERLYING LUMINOSITIES
FEWER DATA → LARGER UNCERTAINTIES (OR SYSTEMATIC BIAS)
• GLOBAL SETS: GOOD AGREEMENT IN THE REGION OF THE EW SCALE
• UNCERTAINTIES BLOW UP FOR LARGEMASS FINAL STATES
PARTON LUMINOSITIES: GLUON SECTOR
GLOBAL PDF SETS
(ratio to NNPDF2.3)
XM210 310
Glu
on -
Glu
on L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
OTHER PDF SETS
(ratio to NNPDF2.3)
XM210 310
Glu
on -
Glu
on L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
ABM11 NNLO
HERAPDF1.5 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
• FEWER DATA → LARGER UNCERTAINTIES (OR SYSTEMATIC BIAS)
• GLOBAL SETS: NOT SO GOOD AGREEMENT IN THE REGION OF THE EWSCALE
• UNCERTAINTIES BLOW UP FOR LARGEMASS FINAL STATES
ISSUESHIGGS IN GLUON FUSION
(H)
[pb]
σ
17.5
18
18.5
19
19.5
20
20.5=0.117, 0.119sα =0.117, 0.119sα =0.117, 0.119sα
uncertaintiesSαLHC 8 TeV - iHixs 1.3 NNLO - PDF+
NNPDF2.3
MSTW08
CT10
• DISCREPANCY NOT UNDERSTOOD DESPITE INTENSIVE BENCHMARKING
• CONSERVATIVE WAY OUT: TAKE THE ENVELOPE OF RESULTS
(PDF4LHC PRESCRIPTION)
KNOWN ISSUES: METHODOLOGYEXAMPLE: THE d/u RATIO
THE d/u RATIO
x0.1 0.2 0.3 0.4 0.5 0.6 0.7
)2 0
d /
u (
x ,
Q
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Ratio to NNPDF2.0
NNPDF2.0
CT10
MSTW08
Ratio to NNPDF2.0
THE CMS W ASYMMETRY
• LONGSTANDING DISCREPANCY IN THE d/u RATIO BETWEEN MSTW AND
OTHER GLOBAL FITS
• RESOLVED BY W ASYMMETRY DATA
• EXPLAINED BY INSUFFICIENTLY FLEXIBLE PDF PARAMETRIZATION
⇒ NEW MSTW08DEUT SET
KNOWN ISSUES: METHODOLOGYPARAMETRIZATION
MSTW08 DEUT VS DEFAULT
(MSTW, 2013)
CTX PDF SET
(P.Nadolsky, PDF4LHC, Nov.3, 2014)
• IMPROVED PARAMETRIZATION (MORE PARAMETERS)
• ⇒ MORE REALISTIC SHAPE
• MORE DATA ⇒ BIGGER UNCERTAINTY
KNOWN ISSUESTHEORY AND DATA
FFN, DIS VS DEFAULT
(tt)
[pb]
σ
220
230
240
250
260
270
= 0.119S
α(tt) - top++v2.0 NNLO+NNLL - σLHC 8 TeV
Global DIS FFN DIS+FFN Deut HT(p=1)
NNPDF2.3 ABM11 CT10 MSTW
TOP PRODUCTION
(CMS, 2014)
• FFN SCHEME NOT ADEQUATE FOR HIGHENERGY DATA
• DIS DATA ⇒ ’RUNAWAY’ DIRECTION TOWARDS SMALL GLUON, SMALL αs
• ⇒ CANNOT FIT TOP DATA
GETTING READY FOR RUN II:NNPDF3.0
THE NNPDF COLLABORATION: R. D. BALL, V. BERTONE, S. CARRAZZA, C. D. DEANS,
L. DEL DEBBIO, A. GUFFANTI, M. P. HARTLAND, Z. KASSABOV, P. GROTHMERRILD,
J. I. LATORRE, J. ROJO AND M. UBIALI
SUMMARY
THE NNPDF METHODOLOGY ADDRESSES IN A
QUANTITATIVE & SYSTEMATIC WAY ISSUES OF
• METHODOLOGY: CLOSURE TESTS
• THEORY CONSISTENCY: BENCHMARKS
CASE STUDY I: JETS AND NNLO
• DATA: COMPATIBILITY & IMPACT ANALYSIS TOOLS
CASE STUDY II: THE STRANGE PDF
CASE STUDY III: CONSERVATIVE PARTONS
CASE STUDY IV: ASSESSING DATA IMPACT
THE NNPDF METHODOLOGYA BRIEF SUMMARY
MONTE CARLO APPROACH
• PSEUDODATA REPLICAS ARE GENERATED USING
FULL INFO ON CORRELATED SYSTEMATICS
⇒ MONTECARLO REPRESENTATION OF COVARIANCE MATRIX
• A PDF REPLICA SET IS FITTED TO EACH PSEUDODATA REPLICA
• THE SET OF PDF REPLICAS CAN BE USED TO COMPUTE ANY SET OF OBSERVABLES
CENTRA VALUES (MEANS), UNCERTAINTIES (VARIANCES),CORRELATIONS (COVARIANCES), CONFIDENCE LEVELS. . .
Experimental Data
MC generation
NN parametrization
Fi i=1,...,Ndata
NMC,BCDMS,SLAC,HERA,CHORUS...
Fi(1) Fi(2) Fi(N)Fi(N-1)
q0net(1) q0net(2) q0net(N-1) q0net(N)
REPRESENTATION OF
PROBABILITY DENSITY
EVOLUTION
TRAINING
NEURAL NETWORK PARAMETRIZATION
• EACH PDF IS PARAMETRIZED BY A NEURAL NETWORK
37 PARAMETERS WITH DEFAULT 2− 5− 3− 1 ARCHITECTURE
• MINIMIZATION IS PERFORMED USING GENETIC ALGORITHMS
• BESTFIT IS NOT MINIMUM OF χ2 (WOULD BE FITTING NOISE) ⇒CROSSVALIDATION
DIVIDE DATA IN TWO SETS, FIT TRAINING SET, MONITOR VALIDATION SET, STOP
WHEN VALIDATION χ2STARTS RISING
THE NNPDF3.0 DATASETA BRIEF SUMMARY
NEW IN NNPDF3.0
• COMBINED HERA CHARM PRODUCTION (55D.P)
• HERA II ZEUS+H1 STRUCTURE FUNCTIONS
(778 D.P.)
• ATLAS 2.76TEV JETS (59 D.P.)
• ATLAS HIGHMASS DRELLYAN (5 D.P.)
• ATLAS W pT (9 D.P.)
• CMS W MUON ASYMMETRY (11 D.P.)
• CMS DOUBLEDIFFERENTIAL DRELLYAN
(110 D.P.)
• CMS JETS (133 D.P.)
• CMS W + c (10 D.P.)
• LHCB Z RAPIDITY (9 D.P.)
• ATLAS & CMS TOP TOTAL XSECT (3+3 D.P.)
• TOTAL DATASET:
4276/4078 (NLO/NNLO)
x-610 -510 -410 -310 -210 -110 1
]2
[ G
eV2 T
/ p
2 /
M2
Q
1
10
210
310
410
510
610
710 FT DIS
HERA1
FT DY
TEV EW
TEV JET
ATLAS EW
LHCB EW
LHC JETS
HERA2
ATLAS JETS 2.76TEV
ATLAS HIGH MASS
ATLAS WpT
CMS W ASY
CMS JETS
CMS WC TOT
CMS WC RAT
LHCB Z
TTBAR
NNPDF3.0 NLO dataset
NNPDF3.0 THEORY AND METHODOLOGYA BRIEF SUMMARY
NEW IN NNPDF3.0
• UNCERTAINTIES: ALL CAN BE ADDITIVE OR MULTIPLICATIVE
• EW CORRECTIONS INCLUDED
• FULL MIGRATION OF CODE TO C++
• PDF PARAMETRIZATION SCALE (Q2 = 1 GeV) & BASIS (EVOLUTION EIGENSTATES)
• PREPROCESSING: BASIS INDEPENDENT, SELFCONSISTENTLY DETERMINED
• GENETIC ALGORITHM: NODAL MUTATION
• IMPLEMENTATION OF CROSSVALIDATION: LOOKBACK STOPPING
METHODOLOGY:CLOSURE TESTING
CLOSURE TESTS:
THE BASIC IDEA
• ASSUME PDFS KNOWN: GENERATE FAKE EXPERIMENTAL DATA
• CAN DECIDE DATA UNCERTAINTY (ZERO, OR AS IN REAL DATA, OR . . . )
• FIT PDFS TO FAKE DATA
• CHECK WHETHER FIT REPRODUCES UNDERLYING “TRUTH”:
– CHECK WHETHER TRUE VALUE GAUSSIANLY DISTRIBUTED ABOUT FIT
– CHECK WHETHER UNCERTAINTIES FAITHFUL
– CHECK STABILITY
(INDEP. OF METHODOLOGICAL DETAILS)
LEVEL0 CLOSURE TESTS• ASSUME VANISHING
EXPERIMENTAL UNCERTAINTY
• MUST BE ABLE TO GET χ2 = 0
• UNCERTAINTY AT DATA POINTS TENDS TO ZERO
(NOT NECESSARILY ON PDF!)
DEFINE φ ≡√
〈χ2rep〉 − χ2,
EQUALS FIT UNCERTAINTY/DATA UNCERTAINTY; CHECK
φ → 0
• BEST FIT ON TOP OF “TRUTH” IN DATA REGION
THE GLUON
x-510 -410 -310 -210 -110 1
)2xg
(x,Q
-2
-1
0
1
2
3
4
5
6
7
Level 0 closure test vs. MSTW
Level 0 Closure Test Fit
MSTW2008nlo68cl
Level 0 closure test vs. MSTW
χ2VS TRAINING LENGTH
Number of Generations310 410 510
2 χ
-410
-310
-210
-110Old (2.3) genetic algorithm
New genetic algorithm
Effectiveness of Genetic Algorithm in Level 0 Closure Tests
FRACTIONAL UNCERTAINTY VS TRAINING LENGTH
Number of GA Generations310 410 510
] ]
fit [
T [f
ϕ
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Effectiveness of Genetic Algorithms in Level 0 Closure Tests
NNPDF3.0 GA settings
NNPDF2.3 GA settings
Effectiveness of Genetic Algorithms in Level 0 Closure Tests
LEVEL0, LEVEL1 AND LEVEL2
• LEVEL 0: FAKE DATA GENERATED WITH NO UNCERTAINTY→ INTERPOLATION AND EXTRAPOLATION UNCERTAINTY
• LEVEL 12: FAKE DATA GENERATED WITH SAME UNCERTAINTY AS REALDATA (INCLUDING CORRELATIONS)
• LEVEL 1: NO PSEUDODATA REPLICAS:⇒ REPLICAS FITTED TO SAME DATA OVER AND OVER AGAIN→ FUNCTIONAL UNCERTAINTY DUE TO INFINITY OF EQUIVALENT MINIMA
• LEVEL 2: STANDARD NNPDF METHODOLOGY⇒ REPLICAS FITTED TO PSEUDODATA REPLICAS→ DATA UNCERTAINTY
• THREE SOURCES OF UNCERTAINTY COMPARABLE IN DATA REGION
THE GLUON: LEVEL 0, LEVEL 1 AND LEVEL 2
x-510 -410 -310 -210 -110 1
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Ratios of gluon at different closure test levels
Lvl0 Closure FitLvl1 Closure FitLvl2 Closure Fit
Ratios of gluon at different closure test levels
x0 0.2 0.4 0.6 0.8 1
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Lvl0 Closure FitLvl1 Closure FitLvl2 Closure Fit
Ratios of gluon at different closure test levels
LEVEL2: CENTRAL VALUES AND UNCERTAINTIESTHE GLUON: FITTED/”TRUE”
x0 0.2 0.4 0.6 0.8 1
)2(x
,QM
ST
W)
/ g2
(x,Q
CT
g
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Ratio of Closure Test g to MSTW2008• CENTRAL VALUES:
COMPARE FITTED VS. “TRUE” χ2
BOTH FOR INDIVIDUAL EXPERIMENTS& TOTAL DATASET
FOR TOTAL ∆χ2 = 0.001± 0.003
• UNCERTAINTIES: DISTRIBUTION OF DEVIATIONS BETWEEN FITTED AND “TRUE” PDFSSAMPLED AT 20 POINTS BETWEEN 10−5 AND 1FIND 0.699% FOR ONESIGMA,0.948% FOR TWOSIGMA C.L.
LEVEL2 FITTED χ2 VS “TRUE”
Experiments
NMC SLACBCDMS
CHORUSNTVDMN
HERA1AVZEUSHERA2
H1HERA2HERAF2CHARM
DYE886DYE605
CDF D0 ATLASCMS LHCB
TOP
2 χ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
for experiments2χDistribution of
2χClosure test 2χMSTW2008nlo
2χClosure test central 2χMSTW2008nlo central
for experiments2χDistribution of
NORM. DISTRIBUTION OF DEVIATIONS
)σDifference to theory (-5 -4 -3 -2 -1 0 1 2 3 4 5
Ent
ries
0
20
40
60
80
100
120
140
160
180
200 Replica distribution
Gaussian distribution
Distribution of single replica fits in level 2 uncertainties
LEVEL2 STABILITY TESTS
• CHANGE UNDERLYING PDF SET (CT10, NNPDF2.3)
• INCREASE MAXIMUM GA TRAINING LENGTH TO 80KTESTS EFFICIENCY OF CROSSVALIDATION
• INCREASE NN ARCHITECTURE TO 220151NUMBER OF FREE PARAMETRES INCREASE BY MORE THAT 10×
• CHANGE PDF PARAMETRIZATION BASISOLD: ISOTRIPLET, u− d, s+ s, s− s;NEW: ISOTRIPLET, SU(3)OCTET, BOTH TOTAL (q + q) & VALENCE (q − q)
STATISTICAL EQUIVALENCE!
DISTANCES BETWEEN REF. AND NEW FIT:difference in unites of standard deviation of the mean
30K GENS VS 80K GENS 2.3 BASIS VS 3.0 BASIS 300 VS 37 PARMS
THEORY BENCHMARKING
CORRECTIONS AND CUTS
• PDFS PROVIDED AT LO, NLO, NNLO IN αs
• NNLO QCD CORRNS BENCHMARKED
BETWEEN CODES:FOR DY MCFM VS FEWZ AT NLO; FEWZ& DYNNLO FOR NNLO;
• SIZE OF NNLO MONITORED: IN NLO FIT,DISCARD IF ≫ THAN EXPT UNCERTAINTIES
LOWEST Q2 BIN OF CMS 2DDY DISCARDED
• VIRTUAL PURE EW CORRECTIONS INCLUDED;FSRCORRECTED DATA USED;QED CORRECTIONS MONITORED
HIGHEST Q2 BIN OF CMS 2DDY DISCARDED
NLO, NNLO & EW CORRNS
ATLAS AND CMS
HIGH MASS DY
0.9
0.95
1
1.05
1.1
150 200 300 400 600 800 1200
C-f
acto
rs
M(ll)
0.9
0.95
1
1.05
1.1
150 200 300 400 600 800 1200
C-f
acto
rs
M(ll)
EWNNLO
10-6
10-5
10-4
10-3
10-2
10-1
150 200 300 400 600 800 1200
dσ/d
M(ll
) pe
r bi
n [p
b]
ATLAS pp→Z→l+l- at LHC 7 TeV
NNPDF23 NNLO
NLONNLO
NLO+EWdata
0.9
0.95
1
1.05
1.1
0 0.5 1 1.5 2
C-f
acto
rs
Y(ll)
0.9
0.95
1
1.05
1.1
0 0.5 1 1.5 2
C-f
acto
rs
Y(ll)
EWNNLO
5
10
15
20
25
0 0.5 1 1.5 2
dσ/d
M(ll
)/dY
(ll)
per
bin
[pb]
CMS pp→Z→l+l- at LHC 7 TeV
20 GeV < Mll< 30 GeV, NNPDF23 NNLO
NLONNLO
NLO+EWdata
JET DATA AT NLO AND NNLOPERCENTAGE ACCURACY OF THRESHOLD APP.
IN GLUON CHANNEL
-410
-310
-210
-110
1
10
210
(GeV)T
p200 400 600 800 1000 1200 1400 1600 1800 2000
|y|
0
0.5
1
1.5
2
2.5
| for gg-channelδCMS 2011 - | | for gg-channelδCMS 2011 - |
-410
-310
-210
-110
1
10
210
(GeV)T
p200 400 600 800 1000 1200 1400
|y|
0
0.5
1
1.5
2
2.5
3
3.5
4
| for gg-channelδATLAS 7 TeV - | | for gg-channelδATLAS 7 TeV - |
-410
-310
-210
-110
1
10
210
(GeV)T
p50 100 150 200 250 300 350 400 450 500
|y|
0
0.5
1
1.5
2
2.5
3
3.5
4
| for gg-channelδATLAS 2.76 TeV - | | for gg-channelδATLAS 2.76 TeV - |
-410
-310
-210
-110
1
10
210
(GeV)T
p100 200 300 400 500 600 700
|y|
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
| for gg-channelδCDF - | | for gg-channelδCDF - |
IMPACT OF THE JET DATA:
NLO&NNLO
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)2x
g (
x, Q
0
0.2
0.4
0.6
0.8
1
2 = 2 GeV2 = 0.118, QSαNNPDF3.0 NLO,
Global
No Jet Data
2 = 2 GeV2 = 0.118, QSαNNPDF3.0 NLO,
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)2x
g (
x, Q
0
0.2
0.4
0.6
0.8
1
2 = 2 GeV2 = 0.118, QSαNNPDF3.0 NNLO,
Global
No Jet Data
2 = 2 GeV2 = 0.118, QSαNNPDF3.0 NNLO,
• EXACT NNLO CORRECTIONS NOW KNOWN IN GLUON CHANNEL (GEHRMANN, GLOVER,DE RIDDER, PIRES, 2014)
• THRESHOLD APPROX AVAILABLE IN ALL CHANNELS (DE FLORIAN ET AL, 2014)
• ONLY ACCURATE AT HIGH pT , CENTRAL RAPIDITY, LARGER JET RADIUS
(CARRAZZA & PIRES, 2014)
• AT NNLO RETAIN ONLY BINS SUCH THAT ACCURACY BETTER THAN 10%CORRECTION THERE SMALLER THAN 15% ⇒ ATLAS (R = 0.4) MOSTLY CUT OUT
• IMPACT OF JET DATA STILL SIZABLE
DATA CONSISTENCY& IMPACT ANALYSIS
NUCLEON STRANGENESS
χ2exp
GLOBAL NO NEUTRINO NO W+c NO NEUTRINO/W+c
CHORUS 1.13 3.87 1.09 3.45NUTEV 0.62 4.31 0.66 6.45
ATLAS W, Z 2010 1.21 1.05 1.24 1.08CMS W+c 2011 0.86 0.50 0.90 0.61
STRANGENESS RATIO
AT LOW & HIGH SCALE
x -310 -210 -110
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2 = 2 GeV2 = 0.118, QSαNNLO,
Global Fit
no Neutrino Data
no W+c Data
no Neutrino, W+c Data
2 = 2 GeV2 = 0.118, QSαNNLO,
x -410 -310 -210 -110
0.4
0.6
0.8
1
1.2
1.4
1.6
2 GeV4 = 102 = 0.118, QSαNNLO,
Global Fit
no Neutrino Data
no W+c Data
no Neutrino, W+c Data
2 GeV4 = 102 = 0.118, QSαNNLO,
• IN GLOBAL FITS, STRANGENESS DETERMINED IN EQUAL
PROPORTION BY NEUTRINO & W/Z PRODUCTION DATA
• NOW SPECIFIC INFORMATION FROM W + cBUT ONLY 10 CMS DATAPOINTS;ATLAS NOT YET INCLUDED BECAUSE DATA ARE HADRONLEVEL
• DEFINE STRANGENESS RATIO r(x,Q2) = s+su+d
• ALL DETERMINATIONS CONSISTENTWITHIN UNCERTAINTIES
• AT PRESENT NEUTRINO DATA CONTROL BOTHCENTRAL VALUE & UNCERTAINTY
• W/Z PRODUCTION DATA FAVOR LARGER rBUT WITH MUCH LARGER UNCERTAINTY
• CMS W + c DATA HAVE VERY LITTLE IMPACT,ON GLOBAL FIT OR ON FIT W/O NEUTRINO DATA
(PERHAPS FAVOR HIGHER r)
CONSERVATIVE PARTONS
• RESCALE ALL UNCERTAINTIES σ → ασ: χ2→ χ2/α2
FOR A GIVEN EXPERIMENT
• DETERMINE PROBABILITY DISTRIBUTION P (α) (USING BAYES)
• DISCARD ALL EXPERIMENT FOR WHICH P (α) PEAKS WELL ABOVE ONE
TWO OUT OF MEDIAN, MODE, MEAN, GREATER THAN αthreshold
• χ2 = 1.29 FOR NNLO GOBAL, BECOMES χ2 = 1.16 FOR αthreshold = 1.3,χ2 = 1.10 FOR αthreshold = 1.2, χ2 = 1.01 FOR αthreshold = 1.1, BUT
CONSIDERABLE DETERIORATION OF UNCERTAINTIES
CONSERV. VS. DEFAULT
GLUON AND VALENCE
x -510 -410 -310 -210 -110
)2x
g (
x, Q
-1
0
1
2
3
4
5
2 = 2 GeV2 = 0.118, QSαNNLO,
Global
=1.1maxαConservative,
=1.2maxαConservative,
2 = 2 GeV2 = 0.118, QSαNNLO,
x -510 -410 -310 -210 -110
)2x
V (
x, Q
0
0.5
1
1.5
2
2 = 2 GeV2 = 0.118, QSαNNLO,
Global
=1.1maxαConservative,
=1.2maxαConservative,
2 = 2 GeV2 = 0.118, QSαNNLO,
α PEAK FOR EXPERIMENTS DISCARDED IN CONS. FIT
WHEN INCLUDED OR EXCLUDED FROM FITNNLO global fit NNLO cons. fit αmax = 1.1
Experiment mean mode median mean mode median
NMC σNC,p 1.27 1.26 1.27 1.50 1.45 1.48SLAC 1.13 1.09 1.12 1.61 1.37 1.48
BCDMS 1.20 1.19 1.20 2.02 1.86 1.92CHORUS 1.10 1.09 1.09 2.55 1.69 2.32
ZEUS HERA-II 1.25 1.24 1.25 1.38 1.33 1.36H1 HERA-II 1.35 1.34 1.34 1.51 1.47 1.49HERA σc
NC1.14 1.11 1.13 1.13 1.09 1.12
E886 p 1.15 1.14 1.15 2.18 1.62 2.03CDF Z rapidity 1.39 1.32 1.36 1.56 1.40 1.50
CDF Run-II kt jets 1.15 1.12 1.14 1.25 1.18 1.22ATLAS W, Z 2010 1.17 1.12 1.15 1.38 1.25 1.32
ATLAS high-mass DY 1.00 1.34 1.63 1.63 1.19 1.45CMS W muon asy 1.60 1.40 1.53 2.90 2.48 2.81CMS W+c total 1.50 1.09 1.33 1.85 1.37 1.67CMS W+c ratio 2.00 1.39 1.69 2.12 1.58 1.94CMS 2D DY 2011 1.28 1.27 1.28 1.29 1.28 1.29
LHCb 1.20 1.12 1.17 1.58 1.22 1.48
THE IMPACT OF LHC (AND HERA) DATA• OVERALL MEASURE OF IMPACT:
φ ⇒ FIT UNCERTAINTY/DATA UNCERTAINTY
• HERAII IMPACT SIZABLE
• IMPACT OF LHC DATA MODERATE BUT VISIBLE
• IMPACT OF CMS OR ATLAS COMPARABLE TO (MODERATE) IMPACT OF NONLHC, NONHERA DATA
FRACTIONAL UNCERTAINTYDataset ϕ
χ2 NLO ϕχ2 NNLO
Global 0.291 0.302HERA-I 0.453 0.439HERA all 0.375 0.343HERA+ATLAS 0.391 0.318HERA+CMS 0.315 0.345Conservative 0.422 0.478no LHC 0.312 0.316
GLOBAL VS NO LHC: g& d
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / g
( x
, Q2
g (
x, Q
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
2 GeV4 = 102 = 0.118, QSαNNLO,
Global Fit
No LHC data
2 GeV4 = 102 = 0.118, QSαNNLO,
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / d
( x
, Q2
d (
x, Q
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
2 GeV4 = 102 = 0.118, QSαNNLO,
Global Fit
No LHC data
2 GeV4 = 102 = 0.118, QSαNNLO,
GLOBAL VS HERA+ATLAS: g& d
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / g
( x
, Q2
g (
x, Q
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
2 GeV4 = 102 = 0.118, QSαNNLO,
HERA-only
HERA + ATLASGlobal fit
2 GeV4 = 102 = 0.118, QSαNNLO,
x -410 -310 -210 -110
) [r
ef]
2 (
x, Q
d)
[new
] /
2 (
x, Q
d
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
2 GeV4 = 102 = 0.118, QSαNNLO,
HERA-only
HERA + ATLASGlobal fit
2 GeV4 = 102 = 0.118, QSαNNLO,
GLOBAL VS HERA+CMS: g& d
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / g
( x
, Q2
g (
x, Q
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
2 GeV4 = 102 = 0.118, QSαNNLO,
HERA-onlyHERA + CMSGlobal fit
2 GeV4 = 102 = 0.118, QSαNNLO,
x -410 -310 -210 -110
) [r
ef]
2 (
x, Q
d)
[new
] /
2 (
x, Q
d
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
2 GeV4 = 102 = 0.118, QSαNNLO,
HERA-onlyHERA + CMSGlobal fit
2 GeV4 = 102 = 0.118, QSαNNLO,
IMPACT OF THE COMBINED HERA DATA
• REPLACE ALL HERA DATA WITH NEW COMBINED SET
• φ OF HERA2 NONCOMBINEDCDATA QUITE SMALL ⇒ SMALL IMPACT
• φ OF COMBINED HERA1 & TOTAL COMBINED HERA QUITE SIMILAR ⇒ IMPACT OF
COMBINATION SMALL
• DATA: WHERE LIES THE PROMISE
• CAN USE α & φ INDICATORS TO ASSESS OBJECTIVELY
WHICH DATA COULD HAVE BIGGER IMPACT
• LARGE α MODE ⇒ MUST IMPROVE COMPATIBILITY
• SMALL φ ⇒ MUST REDUCE UNCERTAINTY
P (α) MODE & φ
Experiments
NMC SLACBCDMS
CHORUSNTVDMN
HERA1AVZEUSHERA2
H1HERA2HERAF2CHARM
DYE886DYE605
CDF D0 ATLASCMS LHCB
TOP
Val
ue
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
) for experimentsα and mode P(φDistribution of
φ)αMode P(
NNPDF3.0 NLO NNLO global fitExperiment Ndat P (α) mode φ
ATLAS W, Z 2010 30 1.12 0.32ATLAS 7 TeV jets 2010 90 0.92 0.25ATLAS 2.76 TeV jets 59 0.57 0.34ATLAS high-mass DY 5 1.34 0.11CMS W electron asy 11 0.87 0.29CMS W muon asy 11 1.40 0.51
CMS jets 2011 133 1.07 0.37CMS W+c total 5 1.09 0.24CMS W+c ratio 5 1.39 0.39CMS 2D DY 2011 88 1.27 0.13
LHCb W, Z rapidity 19 1.12 0.24σ(tt) 6 0.75 0.35
SOME PRELIMINARY INDICATIONS...
• 2.76TEV JET DATA SEEEM TO HAVE OVERESTIMATED UNCERTAINTIES,POTENTIALLY HIGH IMPACT
• TOP DATA: SUPRISINGLY HIGH IMPACT GIVEN SMALL DATA SAMPLE
• HIGHMASS DY ⇒ CONSISTENCY PROBLEM
OUTLOOKWHAT LIES BEHIND THE
CORNER
SUMMARY
ALL GLOBAL FITTING GROUPS HAVE PUBLISHED MAJOR UPDATESFOR LHC RUN II:
• METHODOLOGY AND DATA IMPROVEMENT → IMPROVED AGREEMENT
• TOWARDS A NEW PDF4LHC PRESCRIPTION: COMBINED PDF SETS
• NEW ANALYSIS TOOLS: CMC, META/MC2H AND SM PDFS
GLOBAL FITS: PROGRESS
• MMHT (SUCCESSOR OF MSTW08) DECEMBER 2014
• CT14 JUNE 2015
• FOR ALL, PROGRESS IN METHODOLOGY & DATASET
METHODOLOGY
NNPDF3.0 MMHT14 CT14NO. OF FITTED PDFS 7 7 6
PARAMETRIZATION NEURAL NETS xa(1 − x)b× CHEBYSCHEV xa(1 − x)b×BERNSTEIN
FREE PARAMETERS 259 37 3035UNCERTAINTIES REPLICAS HESSIAN HESSIAN
TOLERANCE NONE DYNAMICAL DYNAMICAL
CLOSURE TEST ✔ ✗ ✗
REWEIGHTING REPLICAS EIGENVECTORS EIGENVECTORS
• MMHT, CT10 LARGER # OF PARMS., ORTHOGONAL POLYNOMIALS
• NNPDF CLOSURE TEST
DATASETNNPDF3.0 MMHT14 CT14(PREL)
SLAC P,D DIS ✔ ✔ ✗
BCDMS P,D DIS ✔ ✔ ✔
NMC P,D DIS ✔ ✔ ✔
E665 P,D DIS ✗ ✔ ✗
CDHSW NUDIS ✗ ✗ ✔
CCFR NUDIS ✗ ✔ ✔
CHORUS NUDIS ✔ ✔ ✗
CCFR DIMUON ✗ ✔ ✔
NUTEV DIMUON ✔ ✔ ✔
HERA I NC,CC ✔ ✔ ✔
HERA I CHARM ✔ ✔ ✔
H1,ZEUS JETS ✗ ✔ ✗
H1 HERA II ✔ ✗ ✗
ZEUS HERA II ✔ ✗ ✗
E605 & E866 FT DY ✔ ✔ ✔
CDF & D0 W ASYM ✗ ✔ ✔
CDF & D0 Z RAP ✔ ✔ ✔
CDF RUNII JETS ✔ ✔ ✔
D0 RUNII JETS ✗ ✔ ✔
ATLAS HIGHMASS DY ✔ ✔ ✔
CMS 2D DY ✔ ✔ ✗
ATLAS W,Z RAP ✔ ✔ ✔
ATLAS W PT ✔ ✔ ✗
CMS W ASY ✔ ✔ ✔
CMS W +C ✔ ✗ ✗
LHCB W,Z RAP ✔ ✔ ✔
ATLAS JETS ✔ ✔ ✔
CMS JETS ✔ ✔ ✔
TTBAR TOT XSEC ✔ ✔ ✗
TOTAL NLO 4276 2996 3248TOTAL NNLO 4078 2663 3045
PROGRESS...PARTON LUMINOSITIES: IMPROVED AGREEMENT
QUARKQUARK
2012
XM210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO - 2015
[GeV]XM210 310
Rat
io
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
Quark-Quark, luminosity
nnpdf3.0nnlommhtnnloct14nnlo
= 8.00e+03 GeVS
Gen
erat
ed w
ith
AP
FE
L 2
.4.0
Web
GLUONGLUON
XM210 310
Glu
on -
Glu
on L
umin
osity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.118sαLHC 8 TeV - Ratio to NNPDF2.3 NNLO -
[GeV]XM210 310
Rat
io
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
Gluon-Gluon, luminosity
nnpdf3.0nnlommhtnnloct14nnlo
= 8.00e+03 GeVS
Gen
erat
ed w
ith
AP
FE
L 2
.4.0
Web
PROGRESS: STANDARD CANDLES & HIGGS• PDF UNCERTAINTY ON HIGGS PRODUCTION DOWN TO ABOUT 2%
• CONSERVATIVE ENVELOPE NO LONGER NEEDED
• STATISTICAL COMBINATION ADEQUATE
HIGGS IN GLUON FUSION
Cro
ss-S
ectio
n (p
b)
41
41.5
42
42.5
43
43.5
44
44.5
45
=0.118sαggH, ggHiggs NNLO, LHC 13 TeV,
NNPDF3.0MMHT14CT14pCMCPDFEnvelope
=0.118sαggH, ggHiggs NNLO, LHC 13 TeV, W+ PRODUCTION
Cro
ss-S
ectio
n (n
b)5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
=0.118sα, VRAP NNLO, LHC 13 TeV, -W
NNPDF3.0MMHT14CT14pCMCPDFEnvelope
=0.118sα, VRAP NNLO, LHC 13 TeV, -W
(Carrazza, Latorre, Rojo, Watt, 2015)
TOWARDS A NEW PDF4LHC PRESCRIPTION
• PERFORM MONTE CARLO COMBINATION OF UNDERLYING PDF SETS
• SETS ENTERING THE COMBINATION MUST SATISFY COMMON REQUIREMENTS
• DELIVER A SINGLE COMBINED PDF SET THROUGH SUITABLE TOOLS
MONTE CARLO COMBINATION(Watt, S.F., 2010-2013)
• CONVERT ALL SETS INTO MONTE CARLO
• HESSIAN SETS CAN BE CONVERTED BY PERFORMING MONTE CARLO IN PARAMETER
SPACE (Watt, Thorne, 2012)
• COMBINE MONTE CARLO REPLICAS INTO SINGLE SET
COMBINED MC SETS FOR ANTIDOWN & STRANGE
(Carrazza, Latorre, Rojo, Watt, 2015)
CMC PDFS AND NONGAUSSIAN BEHAVIOURDEVIATION FROM GAUSSIANITY OBSERVEDE.G. AT LARGE x, DUE TO LARGE UNCERTAINTY & POSITIVITY BOUNDS
(MAY BE RELEVANT FOR SEARCHES)
MONTE CARLO COMPARED TO HESSIANCMS W + c production LHCb electrons
• MONTE CARLO PDFS REPRODUCE NONGAUSSIAN, HESSIAN FAIL
• PROBLEM DOES NOT ARISE FOR BULK OF DATA ⇒ HESSIAN ADEQUATE!
TOOLS FOR DELIVERY
• COMBINED MC SET IS LARGE (300 REPLICAS)
• HESSIAN DELIVERY OFTEN DESIRABLE (PDF UNCERTAINTIES AS NUISANCE
PARAMETERS)
• CMC: GA COMPRESSION OF MC SET TO A SMALLER SET WITH MINIMALINFORMATION LOSS (300 → 40 REPLICAS)
• METAPDFS OR MCH PDFS: HESSIAN REPRESENTATION OBTAINED BYREFITTING MC REPLICAS WITH FUNCTIONAL FORM (META), OR
REPRESENTING THEM ON LINEAR BASIS OF REPLICAS (MCH)
• VALIDATION AND BENCHMARKING SUCCESFUL
GLUONGLUON CORRELATIONSTARTING COMBINED SET COMPRESSED MC SET METAPDF SET
(PDF4LHC: preliminary, 2015)
THE MC2H IDEA:• NONGAUSSIAN EFFECTS NOT VERY IMPORTANT FOR BULK OF DATA
• HESSIAN DELIVERY OFTEN ADVANTAGEOUS FOR ANALYSIS
• CAN WE CONVERT MC TO HESSIAN (GAUSSIAN)?
A: USE REPLICAS AS BASIS FUNCTIONS (CONTINUITY, SUM RULES, DGLAPAUTOMATICALLY IMPLEMENTED)
(Carrazza, S.F., Rojo, Kassabov 2015)
MC2HGA
• SINGLE OUT GAUSSIAN REGION (ONE SIGMA = 68% C.L.)
• OPTIMIZE UNCERTAINTIES VIA GENETIC ALGORITHM
MC2HPCA
• REPRODUCE COVARIANCE MATRIX ON VERY FINE SET OF GRID POINTS
• REPRESENT IT BY SINGULARVALUE DECOMPOSITION ON REPLICAS
• PICK LARGEST CONTRIBUTIONS (PRINCIPAL COMPONENT ANALYSIS)
⇒ COVARIANCE MATRIX PERFECTLY REPRODUCED; NO CHOICES: NO BIAS
MC2HPCA• PRIOR COMBINATION OF CT14, MMHT, NNPDF3.0: MC900 OR META300
• MC2H=PCA: SETS OF 100 OR 120 HESSIAN EIGENVECTORS
• METAPDFS: V2 SETS OF 2*30 AND 2*50 EIGENVECTORS
THE CORRELATION MATRIX:PRIORFINAL (HIGH RESOLUTION)
MC2H
MC2H ACHIEVES PERCENT ACCURACY
MINIMAL SETS: SMPDFS• GIVEN ONE OR MORE PROCESSS (“SIGNAL”), SELECT EIGENVECTORS WHICH
PROVIDE THE DOMINANT CONTRIBUTION:– DETERMINE SUBSET OF GRID POINTS WHICH HAVE THE HIGHEST CORRELATION TO THE
PROCESS
– PERFORM PCA ANALYSIS ON THE CORRESPONDING SUBMATRIX
– NOTE USAGE OF SUBGRID GUARANTEES STABILITY: SIMILAR PROCESSES WILL ALSO BE
WELL REPRODUCED (EXAMPLE: TOP VS HIGGS)
• .
• .
HIGGS
13 eigenvectorsHIGGS pT DISTRIBUTION IN GLUON FUSION
MINIMAL SETS: SMPDFS• GIVEN ONE OR MORE PROCESSS (“SIGNAL”), SELECT EIGENVECTORS WHICH
PROVIDE THE DOMINANT CONTRIBUTION:– DETERMINE SUBSET OF GRID POINTS WHICH HAVE THE HIGHEST CORRELATION TO THE
PROCESS
– PERFORM PCA ANALYSIS ON THE CORRESPONDING SUBMATRIX
– NOTE USAGE OF SUBGRID GUARANTEES STABILITY: SIMILAR PROCESSES WILL ALSO BE
WELL REPRODUCED (EXAMPLE: TOP VS HIGGS)
• ADD ONE OR MORE PROCESSES (“BACKGROUND”): REPEAT ANALYSIS & PICKFURTHER EIGENVECTORS
• .
HIGGS+TOP
14 eigenvectorsTOP INVARIANT MASS DISTRIBUTION
MINIMAL SETS: SMPDFS• GIVEN ONE OR MORE PROCESSS (“SIGNAL”), SELECT EIGENVECTORS WHICH
PROVIDE THE DOMINANT CONTRIBUTION:– DETERMINE SUBSET OF GRID POINTS WHICH HAVE THE HIGHEST CORRELATION TO THE
PROCESS
– PERFORM PCA ANALYSIS ON THE CORRESPONDING SUBMATRIX
– NOTE USAGE OF SUBGRID GUARANTEES STABILITY: SIMILAR PROCESSES WILL ALSO BE
WELL REPRODUCED (EXAMPLE: TOP VS HIGGS)
• ADD ONE OR MORE PROCESSES (“BACKGROUND”): REPEAT ANALYSIS & PICKFURTHER EIGENVECTORS
• CAN ITERATE AT WILL ⇒ EVENTUALLY RECOVER FULL EIGENVECTOR SET
HIGGS+TOP+Z+W15 eigenvectors
W pT DISTRIBUTION
OUTLOOK: NNPDF3.1NEW DATA (MINIMAL SET)
• HERAII COMBINED DATA arxiv:1506.06042
• D0 W ASYMMETRY arXiv:1412.2862
• ATLAS LOWMASS DY arXiv:1404.1212
• ATLAS PROMPT PHOTON arXiv:1311.1440
• ATLAS W + c arXiv:1402.6263
• ATLAS Z pt arXiv:1406.3660
• ATLAS tt RAPIDITY arXiv:1407.0371
• ATLAS INCLUSIVE JETS 7 TEV 5 FB−1
arXiv:1410.8857
• CMS DOUBLEDIFFERENTIAL 8 TEV arXiv:1412.1115
• CMS Z pt arXiv:1504.03511
• LHCB W → µν RAP. arxiv:1408.4354
NNPDF3.1 AND BEYOND
• RESUMMED PDFS
– SMALL x AND EVOLUTION
– THRESHOLD RESUMMATION AND NEW PHYSICS SEARCHES
• HEAVY QUARKS
– RUNNING QUARK MASSES & QUARK MASS STUDIES
– FITTED (“INTRISIC”) CHARM
• THEORY UNCERTAINTY ON PDFS
– SCALE VARIATION
– PERTURBATIVE SERIES: CACCIARIHOUDEAU
• MORE CLOSURE TESTS:
– INCONSISTENT DATA
– QUANTITATIVE MODELS OF FUNCTIONAL UNCERTAINTY
– TOLERANCE & ∆χ2RULE
• QED PDF SET
– MIXED QCDQED EFFECTS
– DETERMINATION OF PHOTON FROM WW PRODUCTION
• MONTE CARLO PDFS
PDFS: PLUMBING OR PRECISION PHYSICS?
EXTRAS
TREATMENT OF αsNEW SIMPLIFIED PDF4LHC PRESCRIPTION
• SEPARATE αs UNCERTAINTY FROM PDF UNCERTAINTY:DETERMINE EACH SEPARATELY AND COMBINE IN QUADRATURE IF NEEDED
PROVEN TO BE EQUIVALENT TO CORRELATED DETERMINATION, UP TO NONLINEAR TERMS
• AGREE ON A CENTRAL VALUE AND AN UNCERTAINTY ON αs (SEE BELOW)
• FOR THE DETERMINATION OF THE PDF UNCERTAINTY,USE PDFS AT THE (FIXED) CENTRAL VALUE OF αs
• FOR THE DETERMINATION OF THE αs UNCERTAINTY,
– COMPUTE OBSERVABLES WITH αs SHIFTED BY ONE σ, WITH PDFS
CORRESPONDING TO THE GIVEN FIXED VALUE
– TAKE RESULT AS ONEσ αs UNCERTAINTY ON OBSERVABLE
THE VALUE OF αs
PDG VALUE (AUGUST 2014): αs(MZ) = 0.1185± 0.0006
COMMENTS• LATTICE UNCERTAINTY CURRENTLY ESTIMATED
BY FLAG (arXiv:1310.8555) TO BE TWICE THE
PDG VALUE (±0.0012)• IT IS AN AN AVERAGE OF AVERAGES
• SOME SUBAVERAGES (E.G. DIS) INCLUDE MUTUALLY INCONSISTENT/INCOMPATIBLE
DATA/EXTRACTIONS
• SOME SUBAVERAGES (E.G. τ OR JETS) INCLUDE DETERMINATIONS WHICH DIFFERFROM EACH OTHER BY EVEN FOURFIVE σ
• AVERAGING THE TWO MOST RELIABLE VALUES (GLOBAL EW FIT & τ , BOTH N3LO,NO DEP. ON HADRON STRUCTURE) GIVES
αs = 0.1196± 0.0010
NEW PDF4LHC AGREEMENT
• PDG UNCERTAINTY CONSERVATIVELY MULTIPLIED BY 2
• CENTRAL VALUE & UNCERTAINTY ROUNDED:PDF SETS USUALLY GIVEN IN STEPS OF ∆αs(Mz) = 0.001
αs(MZ) = 0.118± 0.001
THE NNPDF APPROACH:THE NEURAL MONTE CARLO
BASIC IDEA: MONTE CARLO SAMPLINGOF THE PROBABILITY MEASURE IN THE (FUNCTION) SPACE OF PDFS
• START FROM MONTE CARLO SAMPLING OF DATASPACE
• SPACE OF FUNCTIONS HUGE
5 BINS FOR 10 PTS× 7 FCTNS → 570 ∼ 1049BINS
• IMPORTANCE SAMPLING: DATA TELL US WHICHBINS ARE POPULATED
replica averagesvs. central values
0.001
0.01
0.1
1
10
100
0.001 0.01 0.1 1 10 100
Mon
te C
arlo
rep
licas
Experimental data
NNPDF1.2 - Central values
Nrep=10 Nrep=100
Nrep=1000
replica standard dev.vs. uncertainties
0.0001
0.001
0.01
0.1
1
10
100
0.0001 0.001 0.01 0.1 1 10
Mon
te C
arlo
rep
licas
Experimental data
NNPDF1.2 - Errors
Nrep=10 Nrep=100
Nrep=1000
10 REPLICAS ENOUGH FOR CENTRAL VALS, 100 FOR
UNCERTAINTIES, 1000 FOR CORRELNS
Experimental Data
MC generation
NN parametrization
Fi i=1,...,Ndata
NMC,BCDMS,SLAC,HERA,CHORUS...
Fi(1) Fi(2) Fi(N)Fi(N-1)
q0net(1) q0net(2) q0net(N-1) q0net(N)
REPRESENTATION OF
PROBABILITY DENSITY
EVOLUTION
TRAINING
DATA MONTE CARLO ⇒ PDF MONTE CARLONEURAL NETWORK PARM+ CROSSVALIDATION METHOD
• EACH PDF↔ NEURAL NETWORKPARAMETRIZED BY 37 PARAMETERS
• NNPDF1.2: 37⊗7 = 259 PARMS
(RECALL MSTW, CTEQ → 20FREE PARAMETERS)“INFINITE” NUMBER OF PARAMETERS⇒ CAN REPRESENT ANYFUNCTION
• COMPLEX SHAPES (LARGE NO.OF
PARAMETERS) REQUIRE LONGERFITTING
• FIT STOPS WHEN QUALITY OFFIT TO RANDOMLY SELECTED“VALIDATION” DATA (NOT FITTED)STOPS IMPROVING
• CAN OBTAIN A FIT WITH χ2LOWER
THAN BEST FIT (“OVERLEARNING”)
Experimental Data
MC generation
NN parametrization
Fi i=1,...,Ndata
NMC,BCDMS,SLAC,HERA,CHORUS...
Fi(1) Fi(2) Fi(N)Fi(N-1)
q0net(1) q0net(2) q0net(N-1) q0net(N)
REPRESENTATION OF
PROBABILITY DENSITY
EVOLUTION
TRAINING
DATA MONTE CARLO ⇒ PDF MONTE CARLOCROSSVALIDATION
• REPLICAS ARE FITTED TO A DATA SUBSET
• A DIFFERENT SUBSET OF DATA USE FOR EACH REPLICA
• OPTIMAL FIT WHEN FIT TO VALIDATION (CONTROL) DATA STOPS IMPROVING
•
OPTIMAL FITTING
χ2 FIT TO DATA
DATA MONTE CARLO ⇒ PDF MONTE CARLOCROSSVALIDATION
• REPLICAS ARE FITTED TO A DATA SUBSET
• A DIFFERENT SUBSET OF DATA USE FOR EACH REPLICA
• OPTIMAL FIT WHEN FIT TO VALIDATION (CONTROL) DATA STOPS IMPROVING
• THE BEST FIT IS NOT AT THE MINIMUM OF THE χ2
OVERFITTING
χ2 FIT TO DATA
LOOKBACK CROSSVALIDATION
• IN PREVIOUS NNPDF RELEASES, “INCREASING” AND “DECREASING”TRAINING AND VALIDATION χ2 DEFINED IN TERMS OF THRESHOLD VALUES
δtr AND δval:INCREASE: χ2
val(Ngen +∆) > χ2(Ngen +∆) + δval
• IN NNPDF3.0 USE LOOKBACK:FIT IS RUN UP TO SOME LARGE # OF GA GENERATIONS
THEN ONE “LOOKS BACK” FOR ABSOLUTE MIN. OF VALIDATION χ2
• CHECK THAT RESULTS ARE INDEPENDENT OF THE LARGE # OF GA GENS
• CHECK THAT RESULTS ARE INDEPENDENT OF FLUCTUATIONS IN VALUE OF
ABSOLUTE MINIMUM
DIFFERENT STOPPING POINTS, BUT INDISTINGUISHABLE PDFS
LEVEL 1 VS. LEVEL 2DO WE NEED THE PSEUDODATA REPLICAS?
TRUTHFIT: LEVEL 1 VS. LEVEL 2
)σDifference to theory (-5 -4 -3 -2 -1 0 1 2 3 4 5
Ent
ries
0
20
40
60
80
100
120
140
160
180
200 Replica distribution
Gaussian distribution
Distribution of single replica fits in level 1 uncertainties
)σDifference to theory (-5 -4 -3 -2 -1 0 1 2 3 4 5
Ent
ries
0
20
40
60
80
100
120
140
160
180
200 Replica distribution
Gaussian distribution
Distribution of single replica fits in level 2 uncertainties
• LEVEL 1 UNDERESTIMATES
UNCERTAINTIES
• LEVEL 0 TRUTHFIT DISTN.WIDER THAN PREDICTED
• REWEIGHT VS. REFIT: X
STAT. EQUIVALENCE FOR LEVEL 2
• REWEIGHT VS. REFIT: REFITTED
SIGMA TOO SMALL
FOR LEVEL 1REWEIGHT VS REFIT:
LEVEL 1 VS. LEVEL 2
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6)2xg(x,Q
Level 1 Reweighted
Level 1 Fitted
)2xg(x,Q
x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6)2xg(x,Q
Level 2 Reweighted
Level 2 Fitted
)2xg(x,Q
REWEIGHTREFIT
(LEVEL 2)
x0 1 2 3 4 5 6 7 8 9 10
Ent
ries
0
0.1
0.2
0.3
0.4
0.5
0.6 LVL2 reweighted vs refit
Distribution for 1 DOF2χ
Distribution of distance for Central Values
ASYMPTOTIC EXPONENTSLEVEL 0 TEST
x-610 -510 -410 -310 -210
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
uv alpha effective exponent
ClosureTest_MSTW_lvl0_100k_fl, 68% c.l.
MSTW2008nlo68cl, central value
ClosureTest_MSTW_lvl0_100k_fl, 68% c.l.
MSTW2008nlo68cl, central value
uv alpha effective exponent
x0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
0
0.5
1
1.5
2
2.5
3
3.5
4
uv beta effective exponent
ClosureTest_MSTW_lvl0_100k_fl, 68% c.l.
MSTW2008nlo68cl, central value
ClosureTest_MSTW_lvl0_100k_fl, 68% c.l.
MSTW2008nlo68cl, central value
uv beta effective exponent
• AS x → 0, PDF GOES AS xα, AS x → 1, PDF GOES AS (1− x)β
• DEFINE EFFECTIVE EXPONENTS αeff,i(x) ≡ ln fi(x)
ln 1/x, βeff,i
(x) ≡ ln fi(x)ln(1−x)
• COMPARE VALUES FROM FIT WITH VALUES OBTAINED FROM UNDERLYING “TRUE”(MSTW08) FORM
PREPROCESSING
x0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
0
1
2
3
4
5
6
Large-x Effective Exponent for Gluon
x-610 -510 -410 -310 -210
1
1.05
1.1
1.15
1.2
1.25
Small-x effective exponent for the Singlet
• PDFS ARE PARAMETRIZED WITH NEURAL NETWORKS TIMES
PREPROCESSING FUNCTION: fi(x) = xαi(1− x)βiNN(x)
• GOAL IS TO SPEED UP TRAINING WITHOUT BIASING RESULT
• αi, βi RANDOM REPLICA BY REPLICA WITH UNIFORM DISTRIBUTION IN RANGE
• CHECK THAT THE RANGE IS WIDER THAN THE 90% C.L. OF EFFECTIVE EXPONENTS
NNPDF3.0 VS CT10 & MSTW08PARTON LUMINOSITIES
( GeV )XM210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF3.0
CT10
MSTW2008
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Qua
rk -
Qua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF3.0
CT10
MSTW2008
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Qua
rk -
Glu
on L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF3.0
CT10
MSTW2008
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Glu
on -
Glu
on L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF3.0
CT10
MSTW2008
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3 VS NNPDF3.0PARTON LUMINOSITIES
( GeV )XM210 310
Qua
rk -
Ant
iqua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3
NNPDF3.0
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Qua
rk -
Qua
rk L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3
NNPDF3.0
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Qua
rk -
Glu
on L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3
NNPDF3.0
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
( GeV )XM210 310
Glu
on -
Glu
on L
umin
osity
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3
NNPDF3.0
)=0.118 - Ratio to NNPDF2.3Z
(MSαLHC 13 TeV, NNLO,
NNPDF2.3 VS NNPDF3.0METHODOLOGY VS. DATANNLO 2.3 VS 3.0: GLUON & VALENCE
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / g
( x
, Q2
g (
x, Q
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
2 GeV4 = 102 = 0.118, QSαNNLO,
NNPDF2.3 NNLO
NNPDF3.0 NNLO
2 GeV4 = 102 = 0.118, QSαNNLO,
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / V
( x
, Q2
V (
x, Q
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
2 GeV4 = 102 = 0.118, QSαNNLO,
NNPDF2.3 NNLO
NNPDF3.0 NNLO
2 GeV4 = 102 = 0.118, QSαNNLO,
3.0 DEFAULT VS 2.3LIKE DATASET: GLUON & ANTIDOWN
x -410 -310 -210 -110
) [r
ef]
2)
[new
] / g
( x
, Q2
g (
x, Q
0.9
0.95
1
1.05
1.1
1.15
1.2
2 GeV4 = 102 = 0.118, QSαNNLO,
Global Fit
2.3 Dataset
2 GeV4 = 102 = 0.118, QSαNNLO,
x -410 -310 -210 -110
) [r
ef]
2 (
x, Q
d)
[new
] /
2 (
x, Q
d
0.9
0.95
1
1.05
1.1
1.15
1.2
2 GeV4 = 102 = 0.118, QSαNNLO,
Global Fit
2.3 Dataset
2 GeV4 = 102 = 0.118, QSαNNLO,
PERTURBATIVE STABILITYLO, NLO, NNLO: GLUON & VALENCE
x -510 -410 -310 -210 -110
)2x
g (
x, Q
-2
-1
0
1
2
3
4
5
6
7
2 = 2 GeV2 = 0.118, QSαNNPDF3.0,
LO
NLO
NNLO
2 = 2 GeV2 = 0.118, QSαNNPDF3.0,
x -510 -410 -310 -210 -110
)2x
V (
x, Q
0
0.5
1
1.5
2
2 = 2 GeV2 = 0.118, QSαNNPDF3.0,
LO
NLO
NNLO
2 = 2 GeV2 = 0.118, QSαNNPDF3.0,
NLO, NNLO PDF UNC. & NLO TH. UNC.
x -410 -310 -210 -110
) 2)
) / g
( x
, Q2
( g
( x,
Q∆
-0.2
-0.1
0
0.1
0.2
0.3
0.4
2 GeV4 = 102 = 0.118, QSαNNPDF3.0,
NLO 1-sigma PDF uncertainty
NNLO 1-sigma PDF uncertainty
( NNLO - NLO ) / NNLO
2 GeV4 = 102 = 0.118, QSαNNPDF3.0,
x -410 -310 -210 -110
)2)
) / V
( x
, Q2
( V
( x
, Q∆
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
2 GeV4 = 102 = 0.118, QSαNNPDF3.0,
NLO 1-sigma PDF uncertainty
NNLO 1-sigma PDF uncertainty
( NNLO - NLO ) / NNLO
2 GeV4 = 102 = 0.118, QSαNNPDF3.0,
MULTIPLICATIVE VS. ADDITIVE UNCERTAINTIES
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)2x
g (
x, Q
0
0.5
1
1.5
2
2=2 GeV2=0.118, QsαNNPDF3.0 NNLO,
Baseline
Additive
2=2 GeV2=0.118, QsαNNPDF3.0 NNLO,
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)2 (
x, Q
Σx
0
0.2
0.4
0.6
0.8
1
1.2
1.4
2=2 GeV2=0.118, QsαNNPDF3.0 NNLO,
Baseline
Additive
2=2 GeV2=0.118, QsαNNPDF3.0 NNLO,
• NORMALIZATION UNCERTAINTY PROPORTIONAL TO MEASURED VALUE ⇒
MULTIPLICATIVE
• WHAT ABOUT OTHER UNCERTAINTIES?IN COLLIDER MOSTLY MULTIPLICATIVE (A. Glazov)
• IN NNPDF3.0 DEFAULT ALL UNCERTAINTIES MULTPLICATIVE
FOR HERA, TEVATRON, LHC
• REPEAT FIT WITH ALL UNCERTAINTIES ADDITIVE (AS IN NNPDF2.3)
• t0 METHOD USED FOR MULTIPLICATIVE UNCERTAINTIES
• NEGLIGIBLE CHANGE SEEN
REQUIREMENTS FOR INCLUSION
PDFS TO BE INCLUDED IN THE COMBINATION MUST SATISFY REQUIREMENTS
WHICH MAKE THEM COMPATIBLE
DOCUMENT IN PDF4LHC APRIL 2015 INDICO
SOME LISTED HERE (SEE DOCUMENT FOR FULL LIST):
• PROVIDE RESULTS AT NLO AND NNLO, WITH NNLO αs, EVOLUTION
BENCHMARKED AGAINST HOPPET OR QCDNUM
• SEPARATE TREATMENT OF αs AS DISCUSSED
• USE A GENERALMASS VARIABLE FLAVOR NUMBER SCHEME WITH UP TO 5FLAVORS
• CURRENT TECHNOLOGY: FITS MUST BE BASED ON APPROXIMATELY
COMMON, GLOBAL SET OF DATA
REQUEST TO RELAX THIS (HERAPDF)