PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC S TEFANO F ORTE U - - PowerPoint PPT Presentation

SLIDE 1

PARTON DISTRIBUTIONS AT THE DAWN OF THE LHC

STEFANO FORTE UNIVERSIT`

A DI MILANO & INFN

CTEQ-MCNET SUMMER SCHOOL LAUTERBAD, JULY 30, 2010

SLIDE 2

SUMMARY

LECTURE II: ISSUES AND RECENT DEVELOPMENTS

PDF UNCERTAINTIES { MONTE CARLO VS HESSIAN: GAUSSIAN UNCERTAINTIES { TOLERANCE { PARTON PARAMETRIZATION THEORETICAL ISSUES { HEAVY QUARKS { HIGHER ORDERS THE STATE OF THE ART { LHC STANDARD CANDLES { THEORETICAL UNCERTAINTIES?

SLIDE 3

PDF UNCERTAINTIES

SLIDE 4

WHAT IS A ONE- UNCERTAINTY?

MSTW/CTEQ: THE SPREAD OF PDFS WITHIN AN ACCEPTABLE TOLERANCE

STANDARD

• 2

= 1 BANDS TOO NARROW ) LARGE DISCREPANCIES FOR INDIVIDUAL

EXPERIMENTS

• )
• )

MINIMUM

• 2

i

VS GLOBAL

• 2

Collins, Pumplin 2001

SLIDE 5

WHAT IS A ONE- UNCERTAINTY?

MSTW/CTEQ: THE SPREAD OF PDFS WITHIN AN ACCEPTABLE TOLERANCE CTEQ TOLERANCE CRITERION &

STANDARD

• 2

= 1 BANDS TOO NARROW ) LARGE DISCREPANCIES FOR INDIVIDUAL

EXPERIMENTS

TOLERANCE ) ENVELOPE OF UNCERTAINTIES OF EXPERIMENTS

• )

MINIMUM

• 2

i

VS GLOBAL

• 2

Collins, Pumplin 2001

CTEQ TOLERANCE PLOT FOR 4TH EIGENVEC.

30 20 10 10 20 30 40 distance Eigenvector 4 BCDMSp BCDMSd H1a H1b ZEUS NMCp NMCr CCFR2 CCFR3 E605 CDFw E866 D0jet CDFjet

SLIDE 6

WHAT IS A ONE- UNCERTAINTY?

MSTW/CTEQ: THE SPREAD OF PDFS WITHIN AN ACCEPTABLE TOLERANCE CTEQ TOLERANCE CRITERION & MSTW DYNAMICAL TOLERANCE

STANDARD

• 2

= 1 BANDS TOO NARROW ) LARGE DISCREPANCIES FOR INDIVIDUAL

EXPERIMENTS

TOLERANCE ) ENVELOPE OF UNCERTAINTIES OF EXPERIMENTS DYNAMICAL ) SEPARATELY DETERMINED FOR EACH HESSIAN EIGENVECTOR

MINIMUM

• 2

i

VS GLOBAL

• 2

Collins, Pumplin 2001

CTEQ TOLERANCE PLOT FOR 4TH EIGENVEC.

30 20 10 10 20 30 40 distance Eigenvector 4 BCDMSp BCDMSd H1a H1b ZEUS NMCp NMCr CCFR2 CCFR3 E605 CDFw E866 D0jet CDFjet

MSTW TOLERANCE PLOT FOR 13TH EIGENVEC.

2 p F µ BCDMS 2 d F µ BCDMS 2 p F µ NMC 2 d F µ NMC p µ n/ µ NMC 2 p F µ E665 2 d F µ E665 2 SLAC ep F 2 SLAC ed F L NMC/BCDMS/SLAC F E866/NuSea pp DY E866/NuSea pd/pp DY 2 N F ν NuTeV 2 N F ν CHORUS 3 N xF ν NuTeV 3 N xF ν CHORUS X µ µ → N ν CCFR X µ µ → N ν NuTeV NC r σ H1 ep 97-00 NC r σ ZEUS ep 95-00 CC r σ H1 ep 99-00 CC r σ ZEUS ep 99-00 charm 2 H1/ZEUS ep F H1 ep 99-00 incl. jets ZEUS ep 96-00 incl. jets

• incl. jets

p II p ∅ D

• incl. jets

p CDF II p asym. ν l → II W ∅ D asym. ν l → CDF II W II Z rap. ∅ D CDF II Z rap. 2 p F µ BCDMS 2 d F µ BCDMS 2 p F µ NMC 2 d F µ NMC p µ n/ µ NMC 2 p F µ E665 2 d F µ E665 2 SLAC ep F 2 SLAC ed F L NMC/BCDMS/SLAC F E866/NuSea pp DY E866/NuSea pd/pp DY 2 N F ν NuTeV 2 N F ν CHORUS 3 N xF ν NuTeV 3 N xF ν CHORUS X µ µ → N ν CCFR X µ µ → N ν NuTeV NC r σ H1 ep 97-00 NC r σ ZEUS ep 95-00 CC r σ H1 ep 99-00 CC r σ ZEUS ep 99-00 charm 2 H1/ZEUS ep F H1 ep 99-00 incl. jets ZEUS ep 96-00 incl. jets

• incl. jets

p II p ∅ D

• incl. jets

p CDF II p asym. ν l → II W ∅ D asym. ν l → CDF II W II Z rap. ∅ D CDF II Z rap.

global 2

χ ∆ Distance =

• 20
• 15
• 10
• 5

5 10 15 20

68% C.L. 68% C.L. 90% C.L. 90% C.L.

MSTW 2008 NLO PDF fit

Eigenvector number 13 GLOBAL MSTW TOLERANCE Eigenvector number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

global 2

χ ∆ Tolerance T =

• 20
• 15
• 10
• 5

5 10 15 20

(MRST) 50 + (MRST) 50

• (CTEQ)

100 + (CTEQ) 100

• NC

r σ H1 ep 97-00 NC r σ H1 ep 97-00 2 d F µ NMC X µ µ → N ν NuTeV X µ µ → N ν NuTeV X µ µ → N ν CCFR E866/NuSea pd/pp DY E866/NuSea pd/pp DY X µ µ → N ν NuTeV 3 N xF ν NuTeV X µ µ → N ν NuTeV X µ µ → N ν NuTeV asym. ν l → II W ∅ D 2 d F µ BCDMS 2 d F µ BCDMS 2 p F µ BCDMS NC r σ H1 ep 97-00 NC r σ ZEUS ep 95-00 2 d F µ BCDMS 2 SLAC ed F NC r σ H1 ep 97-00 NC r σ ZEUS ep 95-00 E866/NuSea pd/pp DY E866/NuSea pd/pp DY E866/NuSea pp DY 3 N xF ν NuTeV 2 d F µ NMC asym. ν l → II W ∅ D NC r σ H1 ep 97-00 2 N F ν NuTeV X µ µ → N ν CCFR E866/NuSea pd/pp DY X µ µ → N ν NuTeV X µ µ → N ν CCFR asym. ν l → II W ∅ D E866/NuSea pd/pp DY NC r σ H1 ep 97-00 NC r σ H1 ep 97-00 3 N xF ν NuTeV X µ µ → N ν NuTeV

MSTW 2008 NLO PDF fit

SLIDE 7

WHAT IS A ONE- UNCERTAINTY?

NNPDF: THE CENTRAL 68% OF THE MC DISTRIBUTION OF PDFS

Example: the gluon distribution in the NNPDF1.0 set

• 2
• 1

1 2 3 4 1e-05 0.0001 0.001 0.01 0.1 1 xg(x,Q0

2)

x

Nrep=25

• 2
• 1

1 2 3 4 1e-05 0.0001 0.001 0.01 0.1 1 xg(x,Q0

2)

x

Nrep=100

ENSEMBLE OF REPLICAS $ PROBABILITY DISTRIBUTION OF PDFS EXPECTED CENTRAL VALUE $ MEAN; UNCERTAINTY $ STANDARD DEVIATION ANY FEATURES OF DISTRIBUTION CAN BE DETERMINED

(C.L. INTERVALS, CORRELATIONS...)

SLIDE 8

WHERE IS THE UNCERTAINTY COMING FROM?

WHY DOES ONE NEED LARGE TOLERANCES? DATA INCOMPATIBILITY

(Pumplin, 2009) CAN “REDIAGONALIZE”:

DIAGONALIZE SIMULTANEOUSLY

• 2 FOR

TOTAL AND

i–TH EXPT ) COMPATIBILITY OF EACH EXPT WITH

GLOBAL FIT

STUDY DISTRIBUTION OF DISCREPANCIES APPROX.

GAUSSIAN WITH UNCERTAINTIES RESCALED BY

2

)

• 2
• 10 FOR 90%C.L.

(Pumplin, 2009)

• 2
• 2

= 10

SLIDE 9

WHERE IS THE UNCERTAINTY COMING FROM?

WHY DOES ONE NEED LARGE TOLERANCES? DATA INCOMPATIBILITY

(Pumplin, 2009) CAN “REDIAGONALIZE”:

DIAGONALIZE SIMULTANEOUSLY

• 2 FOR

TOTAL AND

i–TH EXPT ) COMPATIBILITY OF EACH EXPT WITH

GLOBAL FIT

STUDY DISTRIBUTION OF DISCREPANCIES APPROX.

GAUSSIAN WITH UNCERTAINTIES RESCALED BY

2

)

• 2
• 10 FOR 90%C.L.

FUNCTIONAL BIAS

(Pumplin, 2009) IF PARM. NOT GENERAL ENOUGH, GLOBAL MIN.

IS NOT TRUE MIN.

ONE- VARIATION ABOUT FAKE MIN CORRESP.

TO LARGE

• 2 VARIATION

USE OF CHEBYSHEV POLYNOMIALS SUGGESTS

“MOST GENERAL” PARM. WITHIN

• 2

= 10 OF

CTEQ6.6 PARM.

SLIDE 10

PARAMETRIZATION UNCERTAINTIES?

NONGAUSSIAN BEHAVIOUR?

LOGNORMAL VS. GAUSSIAN

• 1
• 0.5

0.5 1 1.5 2 2.5 3

• 1
• 0.5

0.5 1 1.5 2 2.5 3

THE HERALHC BENCHMARK

(F eltesse, Glazo v, Rades u + NNPDF 2008) TRY EXPERIMENTAL SYSTEMATICS GIVEN BY EITHER GAUS-

SIAN OR LOGNORMAL DISTRIBUTION

REPEAT

(BENCHMARK) HERAPDF,

WITH MONTECARLO LOGNORMAL OR GAUSSIAN, IN EITHER CASE DETERMINE UN- CERTAINTY EITHER WITH HESSIAN OR MONTECARLO

• LOGNORMAL: HESS. VS MC

Fit vs H1PDF2000, Q2 = 4. GeV2

1 2 3 4 5 6 7 8 9 10 10

• 4

10

• 3

10

• 2

10

• 1

1

x xG(x)

GAUSSIAN: HESS. VS MC Fit vs H1PDF2000, Q2 = 4. GeV2 1 2 3 4 5 6 7 8 9 10 10

• 4

10

• 3

10

• 2

10

• 1

1

x xG(x)

NO DIFFERENCE BETWEEN LOGNORMAL, GAUSSIAN, MC, HESSIAN

SLIDE 11

PARAMETRIZATION UNCERTAINTIES?

NONGAUSSIAN BEHAVIOUR?

LOGNORMAL VS. GAUSSIAN

• 1
• 0.5

0.5 1 1.5 2 2.5 3

• 1
• 0.5

0.5 1 1.5 2 2.5 3

THE HERALHC BENCHMARK

(F eltesse, Glazo v, Rades u + NNPDF 2008) TRY EXPERIMENTAL SYSTEMATICS GIVEN BY EITHER GAUS-

SIAN OR LOGNORMAL DISTRIBUTION

REPEAT

(BENCHMARK) HERAPDF,

WITH MONTECARLO LOGNORMAL OR GAUSSIAN, IN EITHER CASE DETERMINE UN- CERTAINTY EITHER WITH HESSIAN OR MONTECARLO

COMPARE TO NNPDF FIT TO SAME DATA

LOGNORMAL: HESS. VS MC Fit vs H1PDF2000, Q2 = 4. GeV2 1 2 3 4 5 6 7 8 9 10 10

• 4

10

• 3

10

• 2

10

• 1

1

x xG(x)

GAUSSIAN: HESS. VS MC Fit vs H1PDF2000, Q2 = 4. GeV2 1 2 3 4 5 6 7 8 9 10 10

• 4

10

• 3

10

• 2

10

• 1

1

x xG(x) NNPDF

x

• 4

10

• 3

10

• 2

10

• 1

10 1 )

2

= 4 GeV

2

x g (x, Q 2 4 6 8 10

NO DIFFERENCE BETWEEN LOGNORMAL, GAUSSIAN, MC, HESSIAN SIZABLE DIFFERENCE WR TO FLEXIBLE NNPDF PARAMETRIZATION

SLIDE 12

PARAMETRIZATION UNCERTAINTIES?

EXPLORING THE SPACE OF PARAMETERS: HESSIAN APPROACH

IN HESSIAN APPROACH CAN VARY THE FUNCTIONAL FORM,

ASSUMPTIONS, STARTING SCALE

DONE

IN THE

HERAPDF1.0

FIT: VARIATION OF STRANGENESS FRACTION, LARGE

x BEHAVIOUR, HIGHER

ORDER POLYNOMIAL TERMS

NO TOLERANCE ( 2 = 1), UNCERTAINTY

DOUBLED

ORTHOGONAL POLYNOMIALS

OLD IDEA (PARISI, SOURLAS, 1978; ZOMER 1996):

EXPAND PDFS OVER BASIS OF ORTHOGONAL POLYNOMIALS

GLAZOV, RADESCU, 2009: COUPLED TO MONTE CARLO METHOD LENGTH PENALTY TO STABILIZE THE FIT (Glazo v, Rades u, 2009)

SLIDE 13

PARAMETRIZATION UNCERTAINTIES?

EXPLORING THE SPACE OF PARAMETERS: NNPDF APPROACH

CENTRAL VALUES: VARYING PARTITION VS FIXED PARTITION REPLICAS CENTRAL VALUE FIXED PARTITION

• 2

1.32 1.32

1.3 h 2 i rep 2:79

• 0:24

1:65

• 0:20
• 1:6
• 0:2

h dat i

0.039 0.035

0.03 xed partition results

• btained

a v eraging

• v

er 5 dieren t hoi es

• f

partition (100 repli as ea h); more partitions needed for a urate results QUALITY OF FIT UNCHANGED

• h

2 i rep UNCHANGED ) CENTRAL FIT UNCHANGED UNCERTAINTY ON PREDICTION (I.E. ON PDFS) REDUCED

• h

dat i = 0:03

• h

dat i = 0:005 h dat i = 0:009

GLUE

x

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 ) 2 xg (x, Q

• 2
• 1

1 2 3 4 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

VALENCE

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q T xV

• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

TRIPLET

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q 3 xT 0.1 0.2 0.3 0.4 0.5 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

STRANGE

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q + xs 0.05 0.1 0.15 0.2 0.25 0.3 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

SLIDE 14

PARAMETRIZATION UNCERTAINTIES?

EXPLORING THE SPACE OF PARAMETERS: NNPDF APPROACH

CENTRAL VALUES: VARYING PARTITION VS FIXED PARTITION REPLICAS CENTRAL VALUE FIXED PARTITION

• 2

1.32 1.32

1.3 h 2 i rep 2:79

• 0:24

1:65

• 0:20
• 1:6
• 0:2

h dat i

0.039 0.035

0.03 xed partition results

• btained

a v eraging

• v

er 5 dieren t hoi es

• f

partition (100 repli as ea h); more partitions needed for a urate results QUALITY OF FIT UNCHANGED

• h

2 i rep UNCHANGED ) CENTRAL FIT UNCHANGED UNCERTAINTY ON PREDICTION (I.E. ON PDFS) REDUCED

FUNCTIONAL UNCERTAINTY

MORE THAN HALF OF UNCERTAINTY DUE TO “FUNCTIONAL

FORM”:

h dat i = 0:03

SMALLER FOR HERA DATA

REMAINING UNCERTAINTY ROUGHLY SCALES WITH DATA UN-

CERTAINTY:

h dat i = 0:005 CENT.; h dat i = 0:009 REP.

GLUE

x

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 ) 2 xg (x, Q

• 2
• 1

1 2 3 4 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

VALENCE

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q T xV

• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

TRIPLET

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q 3 xT 0.1 0.2 0.3 0.4 0.5 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

STRANGE

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q + xs 0.05 0.1 0.15 0.2 0.25 0.3 CTEQ6.6 MRST2001E NNPDF1.2 Current fit

SLIDE 15

DATA INCOMPATIBILITY?

DIS VS. HADRONIC DATA

A SENSITIVE TEST: IS THE IMPACT OF A DATASET INDEP. OF THE DATA IT IS ADDED TO? ADDING JET DATA. . .

. . . TO DIS DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xg (x, Q

• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 NNPDF2.0 DIS NNPDF2.0 DIS+JET x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS NNPDF2.0 DIS+JET

. . . TO DIS+DY DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xg (x, Q

• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 NNPDF2.0 NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 NNPDF2.0 DIS+DY

ADDING DRELL-YAN DATA. . .

. . . TO DIS DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q 3 xT 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q S ∆ x

• 0.02

0.02 0.04 0.06 0.08 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q

• xs
• 0.02
• 0.01

0.01 0.02 0.03 0.04 NNPDF2.0 DIS NNPDF2.0 DIS+DY

. . . TO DIS+JET DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q 3 xT 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q S ∆ x 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q

• xs
• 0.02
• 0.01

0.01 0.02 0.03 0.04 NNPDF2.0 DIS+JET NNPDF2.0 )

SLIDE 16

DATA INCOMPATIBILITY?

DIS VS. HADRONIC DATA

A SENSITIVE TEST: IS THE IMPACT OF A DATASET INDEP. OF THE DATA IT IS ADDED TO? ADDING JET DATA. . .

. . . TO DIS DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xg (x, Q

• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 NNPDF2.0 DIS NNPDF2.0 DIS+JET x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS NNPDF2.0 DIS+JET

. . . TO DIS+DY DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xg (x, Q

• 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 NNPDF2.0 NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 NNPDF2.0 DIS+DY

ADDING DRELL-YAN DATA. . .

. . . TO DIS DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q 3 xT 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q S ∆ x

• 0.02

0.02 0.04 0.06 0.08 NNPDF2.0 DIS NNPDF2.0 DIS+DY x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ) 2 (x, Q

• xs
• 0.02
• 0.01

0.01 0.02 0.03 0.04 NNPDF2.0 DIS NNPDF2.0 DIS+DY

. . . TO DIS+JET DATA

x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q 3 xT 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 xV (x, Q 0.2 0.4 0.6 0.8 1 1.2 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q S ∆ x 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 NNPDF2.0 DIS+JET NNPDF2.0 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 (x, Q

• xs
• 0.02
• 0.01

0.01 0.02 0.03 0.04 NNPDF2.0 DIS+JET NNPDF2.0

FITS COMMUTE

) GOOD COMPATIBILITY!

SLIDE 17

DATA INCOMPATIBILITY?

FIT QUALITY: DIS DATA AND HADRONIC DATA

NNPDF2.0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

for sets

2

χ Distribution of

N M C

• p

d N M C S L A C p S L A C d B C D M S p B C D M S d H E R A 1

• N

C e p H E R A 1

• N

C e m H E R A 1

• C

C e p H E R A 1

• C

C e m C H O R U S n u C H O R U S n b F L H 1 8 N T V n u D M N N T V n b D M N Z 6 N C Z 6 C C D Y E 6 5 D Y E 8 8 6 p D Y E 8 8 6 r C D F W A S Y C D F Z R A P D Z R A P C D F R 2 K T D R 2 C O N

for sets

2

χ Distribution of

NO OBVIOUS MUTUAL TENSION BETWEEN DIS AND HADRONIC DATA CLEAR SIGN OF INTERNAL DATA INCONSISTENCIES

(NMC DIS DATA, CDF

Z AND W RAPIDITY DISTRIBUTIONS)

SLIDE 18

THEORETICAL ISSUES

SLIDE 19

HEAVY QUARKS IN DIS

IN MS SCHEME, n f = 6 IN LOOPS,

• s RUNNING AND DGLAP EQNS AT ALL SCALES

) FOR Q 2 >> m 2 q, NEGLECT THE MASS WHEN Q 2 << m 2 q A DECOUPLING SCHEME MORE CONVENIENT: LOOPS

SUBTRACTED AT ZERO MOMENTUM,

n f = n l IN

• s RUNNING AND DGLAP EQNS

) FOR Q 2 >> m 2 q, NEGLECT THE HEAVY QUARK WHAT HAPPENS WHEN Q 2

• m

2 q?

MATCHED SCHEMES: ACOT

(Aiv azis, Collins, Olness, T ung, 1988, 1994) m 6= 0, LO harm radiation m = 0, LO harm radiation m = harm p df

γ∗

c c c

• c

X( )

γ∗

c c

X

• c

G

c

• c

X

γ∗

G

• +

USE MS FOR Q 2 > m 2 q

WITH FULL MASS DEP. RETAINED

KEEP ALL FLAVOURS IN

RUNNING, DGLAP

SUBTRACT

DOUBLE COUNTING SIMPLIFIED SACOT: EVEN IN MASSIVE CONTRIBUTION, NEGLECT

m q IN FINAL STATE

SLIDE 20

MATCHED SCHEMES: TR

(Thorne, Rob erts, 1998, 2008) SWITCH OFF HQ FOR Q 2 < m 2 q USE MASSLESS APPROX FOR Q 2 > m 2 q ADD MASSIVE TERMS AND ENFORCE CONTINUITY AT THRESHOLD VIA SUBL. TERMS

MATCHED SCHEMES: FONLL

(Ca iari, Gre o, Nason, 1998; for DIS s.f., Laenen, Ro jo, Nason, 2010) USE MS (MASSLESS) PARTONS COMPUTE MASSIVE CONTRIBUTIONS IN THE DECOUPLING SCHEME, BUT EXPRESS

EVERYTHING IN TERMS OF

MS PARTONS ADD MASSIVE EXPRESSION TO THE MASSLESS ONE, SUBTRACT DOUBLE COUNTING

(TRIVIAL, AS EVERYTHING EXPRESSED IN SAME SCHEME)

F (n l ) (x; Q 2 ) = x R 1 x dy y P i=q ;

• q

;g B i

• x

y ; Q 2 m 2 ;

• (n

l +1) s (Q 2 )

• f

(n l +1) i (y ; Q 2 ); F (n l ; 0) (x; Q 2 )

• x

Z 1 x dy y X i=q ;

• q

;g B (0) i

• x

y ; Q 2 m 2 ;

• (n

l +1) s (Q 2 )

• f

(n l +1) i (y ; Q 2 ); lim m!0 h B i (x; Q 2 m 2 )B (0) i

• x;

Q 2 m 2

• i

= F F ONLL (x; Q 2 )

• F

(d) (x; Q 2 ) + F (n l ) (x; Q 2 ); F (d) (x; Q 2 )

• F

(n l +1) (x; Q 2 )

• F

(n l ; 0) (x; Q 2 )

SLIDE 21

THE PROBLEM OF DAMPING TERMS

IN ANY SCHEME, DGLAP RESUMMATION PRODUCES

TERMS

• s

(Q 2 ) ln Q 2 m 2 q TO ALL ORDERS IN

• s

(Q 2 ) MASS CORRECTIONS TO SUCH TERMS ARE PROVIDED AT LOW ORDERS IN

• s

(Q 2 ),

BUT NOT TO HIGHER ORDERS

THESE TERMS ARE COMPLETELY INACCURATE WHEN Q 2 IS JUST ABOVE m 2 q AND

CAN BE NON–NEGLIGIBLE IN PRACTICE

SOLUTION: KILL THESE TERMS WITH A SUITABLE DAMPING PRESCRIPTION

SLIDE 22

THE IMPACT ON PHENOMENOLOGY

MANY FITS (CTEQ<6, NNPDF, ALEKHIN<09) TREAT CHARM

AS MASSLESS ABOVE THRESHOLD

) “ZMVFN” SCHEME TR/TR’ PROCEDURE IMPLEMENTED SINCE ’98 IN MRST

• !
• W

(Nadolsky et al., 2008) (Ro jo et al., 2010)

• O

( s ) O ( 2 s (m )) Q 2

SLIDE 23

THE IMPACT ON PHENOMENOLOGY

MANY FITS (CTEQ<6, NNPDF, ALEKHIN<09) TREAT CHARM

AS MASSLESS ABOVE THRESHOLD

) “ZMVFN” SCHEME TR/TR’ PROCEDURE IMPLEMENTED SINCE ’98 IN MRST WHEN CTEQ IMPLEMENTED ACOT IN 2008, SURPRISING

CHANGE CTEQ61 !CTEQ6.5 IN

• W , & AGREEMENT WITH

MRST SPOILED (LATER RESTORED)

0.9 1 1.1 1.2 1.3 W+ W- Z0 W+h0H 120L W-h0H 120L tt

• H

171L ggfi h0H 120L h+H 200L s–dsPDF in units of sH CTEQ66ML LHC,NLO CTEQ6.6 CTEQ6.1 IC-Sea

KNNLO

(Nadolsky et al., 2008) (Ro jo et al., 2010)

• O

( s ) O ( 2 s (m )) Q 2

SLIDE 24

THE IMPACT ON PHENOMENOLOGY

MANY FITS (CTEQ<6, NNPDF, ALEKHIN<09) TREAT CHARM

AS MASSLESS ABOVE THRESHOLD

) “ZMVFN” SCHEME TR/TR’ PROCEDURE IMPLEMENTED SINCE ’98 IN MRST WHEN CTEQ IMPLEMENTED ACOT IN 2008, SURPRISING

CHANGE CTEQ61 !CTEQ6.5 IN

• W , & AGREEMENT WITH

MRST SPOILED (LATER RESTORED)

0.9 1 1.1 1.2 1.3 W+ W- Z0 W+h0H 120L W-h0H 120L tt

• H

171L ggfi h0H 120L h+H 200L s–dsPDF in units of sH CTEQ66ML LHC,NLO CTEQ6.6 CTEQ6.1 IC-Sea

KNNLO

(Nadolsky et al., 2008)

RECENT PROGRESS: THE LES HOUCHES 2009 BENCHMARKS

(Ro jo et al., 2010) TR, FONLL AND ACOT FOR DIS BENCHMARKED AT NLO

AND NNLO

• O

( s ) FONLL, ACOT COINCIDE EXACTLY, TR’ DIFFERS BY

SUBLEADING

O ( 2 s (m )) Q 2–INDEP. TERM DIFFERENCES BETWEEN DAMPING PRESCRIPTIONS SIZABLE

SLIDE 25

THE PROBLEM OF DAMPING TERMS:

PHENOMENOLOGY

IMPACT OF SUBLEADING TERMS SIZABLE CLOSE TO THRESH-

OLD

DIFFERENCE BETWEEN DIFFERENT PRESCRIPTIONS (ACOT- –SCALING,

FONLL-DAMPING, MSTW-MATCHING)

AS LARGE AS DIFFERENCE BETWEEN FFN (NO DGLAP RESUM- MATION FOR CHARM) AND ZMVFN (NO CHARM MASS)

• s
• O

( 2 s ) O ( s ) ) (s.f., Laenen, Nason, Ro jo 2010)

• O

( 3 ) (Bieren baum, Bl

• umlein,

Klein, 2009)

SLIDE 26

THE PROBLEM OF DAMPING TERMS:

PHENOMENOLOGY

IMPACT OF SUBLEADING TERMS SIZABLE CLOSE TO THRESH-

OLD

DIFFERENCE BETWEEN DIFFERENT PRESCRIPTIONS (ACOT- –SCALING,

FONLL-DAMPING, MSTW-MATCHING)

AS LARGE AS DIFFERENCE BETWEEN FFN (NO DGLAP RESUM- MATION FOR CHARM) AND ZMVFN (NO CHARM MASS)

THE SOLUTION: GO UP ONE ORDER

IF EVERYTHING AT ONE EXTRA ORDER IN

• s, DIFFERENCES

MINOR

IN FONLL, CAN COMBINE O ( 2 s ) TREATMENT OF HQ WITH

STANDARD NLO

O ( s ) TREATMENT OF LIGHT QUARKS )

EXCELLENT APPROX TO FULL RESULT

(s.f., Laenen, Nason, Ro jo 2010) RECENT PROGRESS: O ( 3 ) MASSLESS LIMIT OF HQ PRO-

DUCTION COEFF. FCTNS. COMPUTED

(Bieren baum, Bl

• umlein,

Klein, 2009)

SLIDE 27

NNLO CORRECTIONS: THE W CHARGE ASYMMETRY

Catani, F errera, Grazzini, 2010 NNLO CORRECTIONS VISIBLY IMPROVE AGREEMENT WITH DATA EFFECT ON MATRIX ELEMENT COMPARABLE TO EFFECT ON PDFS,

BUT IN DIFFERENT REGIONS

NNLO NEEDED FOR STANDARD CANDLES!

SLIDE 28

NNLO PARTON DISTRIBUTIONS?

E-605 (Y=0) 0.05 0.1 0.15 0.2 0.25 0.3 0.2 0.25 0.3 0.35 0.4 M5dσ/d(M)/d(Y)/(1-x1)2.5 (nbGeV4) NNLO (±1σ) NLO 0.1 0.2 0.3 0.4 0.5 0.2 0.25 0.3 0.35 0.4 0.45 x2 x1 Q2=9 GeV2 10

• 3

10

• 2

10

• 1

0.1 0.2 0.3 0.4 0.5 0.6 DIS(±1σ) DIS/DY(±1σ) x x(u

• +d
• )/2

Alekhin, Melnik

• v,

P etriello, 2006 CURRENT GLOBAL PDF FITS ARE NLO MSTW08 NNLO TREATS DIS AT NNLO, JETS AT NLO, DRELL-YAN AT

LO+ K–FACTORS

HERAPDF+ALEKHIN-SERIES FITS GENUINELY NNLO, BUT SMALLER

DATASET

BUT IMPACT NOT NEGLIGIBLE...

SLIDE 29

PROGRESS

Q: WHY IS NNLO NOT INCLUDED IN PARTON FITS?

• !
• $
• !
• R

1 x 0;1 dx 1 R 1 x 0;2 dx 2 f a (x 1 )f b (x 2 )C ab (x 1 ; x 2 ) ! P N x ; =1 f a (x 1; )f b (x 2; ) R 1 x 0;1 dx 1 R 1 x 0;2 dx 2 I (; ) (x 1 ; x 2 )C ab (x 1 ; x 2 )

SLIDE 30

PROGRESS

Q: WHY IS NNLO NOT INCLUDED IN PARTON FITS? A: CONVOLUTIONS ARE HARD!

TOWARDS A SOLUTION: GRID–BASED METHODS

ORIGINAL IDEA

EXPANSION OF PDFS ON BASES OF POLYNOMIALS (PASCAUD, ZOMER, 2001

PRECOMPUTE

CONVOLUTION WITH BASIS FUNCTIONS

EXPAND PDF OVER BASIS CONVOLUTIONS REDUCED TO LINEAR COM-

BINATIONS

! MATRIX MULTIPLICATION

THE GRID IDEA

(CARLI, SALAM, SIEGERT 2005)

REPRESENT PDFS ON INTERPOLATED GRID BASIS FCTNS $ INTERPOLATING FCTNS DO CONVOLUTIONS OVER BASIS FUNCTIONS

(IF MONTE CARLO USED, BASIS FCTNS

!

WEIGHTS FOR MC INTEGRAL)

GRID CAN BE OPTIMIZED R 1 x 0;1 dx 1 R 1 x 0;2 dx 2 f a (x 1 )f b (x 2 )C ab (x 1 ; x 2 ) ! P N x ; =1 f a (x 1; )f b (x 2; ) R 1 x 0;1 dx 1 R 1 x 0;2 dx 2 I (; ) (x 1 ; x 2 )C ab (x 1 ; x 2 )

SLIDE 31

GRID–BASED METHODS

SOME RECENT NLO IMPLEMENTATIONS:

FASTNLO: FAST INTERFACE FOR JET CROSS SECTIONS (Kluge, Rabb ertz, W

• bis

h 2006) FASTKERNEL: GRID METHOD INTERFACED TO N-SPACE COMPUTATION OF GLAP

GREEN FUNCTIONS, INTERFACED TO FASTNLO FOR JETS AND TO SUITABLE FAST-DY

(NNPDF, 2010) APPLGRID: OPTIMIZED GRID, POTENTIALLY UNIVERSAL INTERFACE, IMPLEMENTED

FOR JETS, W AND Z PRODUCTION

(Carli et al., 2010)

FASTKERNEL PERC. ACCURACY

0.5 1 1.5 2 2.5

y

0.00001 10ˉ⁴ 10ˉ³ 10ˉ² 0.1

E605 E886p E886r Wasy Zrap

!"#$%&'(&)*+,-./0

APPLGRID REL. ACCURACY

(GeV)

positron T

p 50 100 150 200 250 300 350 400 450 500

standard

σ /

grid

σ 0.9988 0.999 0.9992 0.9994 0.9996 0.9998 1 1.0002 1.0004 1.0006

= 0

PDF

=25, Int.: (5, 5, 0); a = 2; W

bins

N = 0

PDF

=25, Int.: (5, 5, 0); a = 3; W

bins

N = 0

PDF

=25, Int.: (5, 5, 0); a = 4; W

bins

N = 0

PDF

=25, Int.: (5, 5, 0); a = 5; W

bins

N |<0.5

positron

η |

SLIDE 32

THE STATE OF THE ART

SLIDE 33

PDFS: TOWARDS LHC PHYSICS

THE HIGGS CROSS SECTION

FIRST PDFS WITH UNCERTAINTIES

Alekhin CTEQ MRST

√s = 14 TeV

σ(gg → H) [pb]

MH [GeV] 1000 100 100 10 1 0.1 1000 100 1.1 1.05 1 0.95 0.9

(Djouadi, F errag, 2004)

PDFS WITH ERROR (2002-2003)

CTEQ, MRST (global); Alekhin (DIS) WIDELY

DIFFERENT UNCERTAINTY ESTIMATES

UNSATISFACTORY

AGREEMENT WITHIN UNCERTAINTIES

• 2

= 100 (CTEQ); 50 (MRST); 1 (ALEKHIN)

CURRENT GLOBAL PDF SETS

gluon luminosities

0.9 0.95 1 1.05 1.1 100 150 200 250 300 350 400 450 500 PDF uncertainty - Ratio to MSTW08 MH [GeV] GG luminosity S = (7 TeV)2 MSTW08 NNPDF2.0 CTEQ6.6 0.9 0.95 1 1.05 1.1 100 150 200 250 300 350 400 450 500 PDF uncertainty - Ratio to MSTW08 MH [GeV] GG luminosity S = (14 TeV)2 MSTW08 NNPDF2.0 CTEQ6.6

gg!H ross se tion (Demartin et al., 2010) THREE

GLOBAL (DIS+HADRONIC)

PDF SETS AVAILABLE

REASONABLE AGREEMENT OF CEN-

TRAL VALUES & UNCERTAINTIES

SLIDE 34

AN ONGOING EFFORT

HERALHC (2004-2008): A WORKSHOP TO TRANSFER KNOWN-HOW FROM

HERA TO THE LHC COMMUNITY

{ t w

• sessions

(2004-2005; 2006-2007), four plenary meetings, v e mid-term and w

• rking

group meetings { t w

• CERN/DESY

rep

• rts

(y ello w b

• ks):

HEP-PH/0601012-HEP-PH/0601013

; ARXIV:0903.3861. PDF4LHC (2008 - ONGOING): A PERMANENT WORKING GROUP TO PROVIDE

GUIDANCE ON PDF TO LHC EXPERIMENTS AND PHENOMENOLOGY

{ quarterly meetings, 10 sin e in eption in F ebruary 2008 { w ebsite http://www.hep.u l.a .uk/pdf4lh / and wiki https://wiki.teras ale.de/index.php?title=PDF4LHC WIKI resour es a v ailable { fruitful in tera tions with the LHC Higgs Cross Se tion W G

SLIDE 35

CURRENT PDF SETS

• X

(s; M 2 X ) = P a;b R 1 x min dx 1 dx 2 f a=h 1 (x 1 )f b=h 2 (x 2 ) ^

• q

a q b !X

• x

1 x 2 s; M 2 X

• data

for a global t (NNPDF2.0)

x

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 ]

2

[ GeV

2 T

/ p

2

/ M

2

Q 1 10

2

10

3

10

4

10

5

10

6

10

NMC-pd NMC SLAC BCDMS HERAI-AV CHORUS FLH108 NTVDMN ZEUS-H2 DYE605 DYE886 CDFWASY CDFZRAP D0ZRAP CDFR2KT D0R2CON

NNPDF2.0 dataset

LHC kinemati s

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 10 10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

fixed target 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 6 6 y = 4 2 2 4

Q

2 (GeV 2)

x

CTEQ6.6: GLOBAL, NLO, VFN WITH HQ MASS, SEVERAL

• s VALUES

MSTW08: GLOBAL, NLO & NNLO, VFN WITH HQ MASS, SEVERAL

• s VALUES

NNPDF2.0: GLOBAL, NLO, VFN WITHOUT HQ MASS, SEVERAL

• s VALUES

ALEKHIN ABKM: DIS+SOME DY, NLO & NNLO, BMSN (FFN), SINGLE

• s VALUE

HERAPDF1.0: ONLY HERA DATA, NLO, VFN WITH HQ MASS, SEVERAL

• s VALS.

SETS BASED ON MODEL ASSUMPTIONS (GRV/GJR, STATISTICAL PDFS,...)

SLIDE 36

FEATURES, TRADEOFFS AND CHOICES

DATASET:CTEQ, MSTW, NNPDF FIXED TARGET AND COLLIDER, eP AND

• P

P

DATA; ABKM, GJR GLOBAL DIS+ FIXET-TARGET DY; HERAPDF: HERA ONLY

STATISTICAL TREATMENT: CTEQ HESSIAN WITH TOLERANCE; MSTW HESSIAN

WITH DYNAMICAL TOLERANCE; HERAPDF, ABKM, GJR, STANDARD HESSIAN;

NNPDF MONTE CARLO (ALSO STUDIED BY HERAPDF)

PARTON PARAMETRIZATION:CTEQ, MSTW, HERAPDF x

• (1
• x)
• POLYNOMIALS; GJR: DITTO + VALENCELIKE ASSUMPTION; NNPDF NEURAL NETS;

CHEBYSHEV POLYNOMIALS STUDIED BY HERAPDF;

HEAVY QUARKS:CTEQ: GM-VFN (SACOT- SCHEME); MSTW: GM-VFN

(ACOT+TR’ SCHEME); NNPDF: ZM-VFN, ORELIM: GM-VFN (FONLL-A

SCHEME); ABKM: FFN (N

f = 3; 4 MATCHED WITH BMSN SCHEME); GJR: FFN

( N

f = 3) PERTURBATIVE ORDER:CTEQ: NLO, BUT DY LO WITH K-FACTORS; MSTW:

NNLO, BUT DY LO WITH K-FACTORS; NNPDF FULL NLO; ABKM, GJR: FULL NNLO

• s VALUE:CTEQ, NNPDF: EXTERNAL PARAMETER, SEVERAL VALUES AVAILABLE;

MSTW: FITTED, BUT ALSO VARIABLE AS EXT.PARAMETER; ABKM, GJR: FITTED,

NOT VARIABLE AS EXT. PARAMETER

THE PDF4LHC RECOMMENDATION

AT NLO, ENVELOPE OF CTEQ, MSTW, NNPDF AT NNLO, MSTW WITH UNCERTAINTY RESCALED MY MSTWNLO/NLO ENVELOPE

SLIDE 37

WHERE DO WE STAND?

LHC STANDARD CANDLES

W + W

• TOP

Z (G. W att, 2010) GLOBAL FITS IN GOOD MUTUAL AGREEMENT CHOICE OF

• s VALUE IMPORTANT

SLIDE 38

WHERE DO WE STAND?

PARTON LUMINOSITIES

GLUON-GLUON QUARK-QUARK

THE HIGGS CROSS SECTION

m H = 120 GEV: DIFFERENT GROUPS

THE PDF4LHC RECIPE

0.85 0.9 0.95 1 1.05 1.1 100 150 200 250 300 350 400 450 500 R mH (GeV) LHC 7 TeV normalized to MSTW2008 pdf+αs 68% C.L. different values of αs(mZ) exact pdf+αs uncertainties NNPDF2.0 CTEQ6.6 MSTW2008nlo PDF4LHC recipe

(G. W att, 2010)

ENVELOPE TAKES CARE OF POORLY UNDERSTOOD DISAGREEMENTS

SLIDE 39

WHERE ARE WE GOING?

THEORETICAL UNCERTAINTIES

• s UNCERTAINTIES: CAN BE COMBINED IN QUADRATURE WITH PDF UNCERTAINTIES

(Lai et al, CTEQ, 2010); AVAILABLE FOR CTEQ, HERAPDF, MSTW, NNPDF

IN PROGRESS: DEPENDENCE ON

& b MASS m : MSTW08

x

• 4

10

• 3

10

• 2

10

• 1

10

Ratio to MSTW 2008 NLO

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

2

GeV

4

= 10

2

Charm quark distribution at Q

MSTW 2008 NLO (90% C.L.) = 1.30 GeV

c

m = 1.50 GeV

c

m

x

• 4

10

• 3

10

• 2

10

• 1

10

Ratio to MSTW 2008 NLO

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

m b: NNPDF, CTEQ

NEEDED:

ORDERS: RENORMALIZATION AND FACTORIZATION SCALE VARIATION HEAVY QUARKS: MATCHING SCHEME VARIATION RESUMMATION: SMALL x REGION AT HERA, LARGE REGION FOR

FIXED-TARGET DY

SLIDE 40

CONCLUSION

THIS IS JUST THE BEGINNING!

SLIDE 41

EXTRAS

SLIDE 42

PDF DEPENDENCE ON

• s

THE GLUON DISTRIBUTION

Q = 2 GEV

MSTW08

0.5 1 1.5 2 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x MSTW Q0 = 2 GeV pdf unc. αs = 0.120 αs = 0.110 αs = 0.113 αs = 0.116 αs = 0.119 αs = 0.121 αs = 0.123 αs = 0.125 αs = 0.128 αs = 0.130

CTEQ6.6

0.6 0.8 1 1.2 1.4 1.6 1.8 2 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x CTEQ6.6alphas Q0 = 2 GeV pdf unc. αs = 0.118 αs = 0.116 αs = 0.117 αs = 0.118 αs = 0.119 αs = 0.120

NNPDF1.2

0.5 1 1.5 2 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x NNPDF1.2 Q0 = 2 GeV pdf unc. αs = 0.119 αs = 0.110 αs = 0.113 αs = 0.116 αs = 0.119 αs = 0.121 αs = 0.123 αs = 0.125 αs = 0.128 αs = 0.130

Q = 100 GEV

MSTW08

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x MSTW Q0 = 100 GeV pdf unc. αs = 0.120 αs = 0.110 αs = 0.113 αs = 0.116 αs = 0.119 αs = 0.121 αs = 0.123 αs = 0.125 αs = 0.128 αs = 0.130

CTEQ6.6

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x CTEQ6.6alphas Q0 = 100 GeV pdf unc. αs = 0.118 αs = 0.116 αs = 0.117 αs = 0.118 αs = 0.119 αs = 0.120

NNPDF1.2

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1e-05 0.0001 0.001 0.01 0.1 1 g(x)/gbest(x) x NNPDF1.2 Q0 = 100 GeV pdf unc. αs = 0.119 αs = 0.110 αs = 0.113 αs = 0.116 αs = 0.119 αs = 0.121 αs = 0.123 αs = 0.125 αs = 0.128 αs = 0.130

SLIDE 43

WHERE IS THE MONTE CARLO UNCERTAINTY COMING FROM?

FIT TO REPLICAS VS RANDOM SUBSET OF CENTRAL VAL.S

REPLICAS CENTRAL V.

• 2

1.32 1.32

h 2 i rep 2:79

• 0:24

1:65

• 0:20

h dat i

0.039 0.035

GLUE

repli as . v als.

LIGHT QUARKS STRANGE

QUALITY OF FIT &PDFS UNCHANGED REDUCTION OF h 2 i rep BY FACTOR

• 2

) FLUCTUATIONS ABOUT TRUE VALUE HALVED UNCERTAINTY ON DATA ONLY REDUCED BY 1.1 ) EXPT. UNCERTAINTIES UNDERESTIMATED

OR UNDERLYING INCOMPRESSIBLE UNCERTAINTY

SLIDE 44

WHAT DETERMINES PDF UNCERTAINTIES?

UNCERTAINTIES IN MSTW/CTEQ FITS OFTEN GO UP WHEN DATA ARE ADDED, BECAUSE OF THE NEED TO ADD PARAMETERS Smaller high-x gluon (and slightly smaller αS) results in larger small-x gluon – now shown at NNLO.

x

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1

Ratio to MSTW 2008 NNLO

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

2

GeV

4

= 10

2

Gluon at Q

MSTW 2008 NNLO MRST 2006 NNLO

Larger small-x uncertainty due to extrat free parameter.

PDF4LHCMSTW 24

• R. THORNE, HERALHC2008

SLIDE 45

WHAT DETERMINES PDF UNCERTAINTIES?

THE PROBLEM OF BENCHMARK FITS (HERALHC 2005-2008)

PERFORM A MRST (MRSTBENCH) FIT TO A CONSISTENT SUBSET OF DATA, USE

• 2

= 1 ) RESULTS NOT CONSISTENT, UNCERTAINTY DOES NOT GROW AS DATASET DECREASES

• )

SLIDE 46

WHAT DETERMINES PDF UNCERTAINTIES?

THE PROBLEM OF BENCHMARK FITS (HERALHC 2005-2008)

PERFORM A MRST (MRSTBENCH) FIT TO A CONSISTENT SUBSET OF DATA, USE

• 2

= 1 ) RESULTS NOT CONSISTENT, UNCERTAINTY DOES NOT GROW AS DATASET DECREASES ...BUT MRST WAS DONE WITH TOLERANCE 50: REPEAT WITH DYNAMICAL TOLERANCE

(MSTW08BENCH)

IMPROVEMENT, BUT PROBLEM NOT SOLVED ) MUST TUNE PARAMETRIZATION AND STATISTICAL TREATMENT TO DATASET

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Up valence distribution

MSTW08 bench MRST01 global MSTW08 global

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

SLIDE 47

WHAT DETERMINES PDF UNCERTAINTIES?

THE NNPDF SOLUTION (HERALHC 2008) MRST/MSTW: BENCH VS REF

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Up valence distribution

MSTW08 bench MRST01 global MSTW08 global

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

NNPDF: BENCH VS REF

x

• 4

10

• 3

10

• 2

10

• 1

10 1

)

2

= 20 GeV

2

(x, Q

V

x u

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

NNPDF_bench_H-L NNPDF1.0

NNPDF BENCH VS MRST/MSTW

BENCH

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Up valence distribution

HERA-LHC bench NNPDF MRST01 MSTW08

x

• 4

10

• 3

10

• 2

10

• 1

10

)

2

= 20 GeV

2

(x, Q

v

xu

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

SINGLE PARAMETRIZATION AND STAT. TREATMENT CAN ACCOMMODATE DIFFERENT

DATASETS

IMPACT OF DATA CAN BE STUDIED INDEPENDENT OF THEORETICAL FRAMEWORK