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)