STATUS & PROGRESS - NNPDF

PDF ISSUES

FOR HIGGS PHYSICS

STEFANO FORTE

UNIVERSITA DI MILANO & INFN

HIGGS WORKING GROUP BNL, MAY 5, 2011

SUMMARY

� PROGRESS

{ NLO STATUS

{ NLO PROGRESS

{ NNLO

� ISSUES

{ PDF UNCERTAINTIES

{ DATA CONSISTENCY

{ FIXEDTARGET DATA

{ �s

� OUTLOOK

{ PRACTICAL PRESCRIPTIONS

{ TOWARDS COLLIDERONLY FITS

STATUS & PROGRESS

CURRENT PDF SETS

�X(s;M

2X) =

Pa;b

R1

xmin

dx1 dx2 fa=h1(x1)fb=h2(x2)^�qaqb!X

�x1x2s;M

2X

�

data in global �ts

x-510 -410 -310 -210 -110 1

]2 [

GeV

2 T /

p2

/ M

2Q

1

10

210

310

410

510

610 NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2ZEUSF2CH1F2CDYE605DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KTD0R2CON

NNPDF2.1 dataset

LHC kinemati s

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

� CT10: GLOBAL, NLO, SEVERAL �s VALUES, VFN

� MSTW08: GLOBAL, NLO & NNLO, SEVERAL �s VALUES, VFN

� NNPDF2.1: GLOBAL, NLO, SEVERAL �s VALUES, VFN

� ALEKHIN ABKM: DIS+SOME DY, NLO & NNLO, SINGLE �s VALUE, FFN

� HERAPDF1.0: HERA DIS, NLO, SEVERAL �s VALS, VFN

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

FEATURES, TRADEOFFS AND CHOICES

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

DATA; ABKM, GJR GLOBAL DIS+ FIXETTARGET DY; HERAPDF: HERA DISONLY

� 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)

� PARTON PARAMETRIZATION: CTEQ, MSTW, HERAPDF x�(1� x)��

POLYNOMIALS; GJR: DITTO + VALENCELIKE ASSUMPTION; NNPDF NEURAL NETS;CHEBYSHEV POLYNOMIALS STUDIED BY HERAPDF;

� �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

� PERTURBATIVE ORDER: CTEQ: NLO, BUT DY LO WITH KFACTORS; MSTW:NNLO, BUT DY LO WITH KFACTORS; NNPDF FULL NLO, NNLO DIS; ABKM,HERAPDF, GJR: NNLO

� HEAVY QUARKS: CTEQ: GMVFN (SACOT� SCHEME); MSTW: GMVFN(ACOT+TR’ SCHEME); NNPDF: GMVFN (FONLL SCHEME); ABKM: FFN(Nf = 3; 4 MATCHED WITH BMSN SCHEME); GJR: FFN (Nf = 3)

STATUSLHC STANDARD CANDLES

W

+ W

�

TOP

Z

(G. Watt, 2011)

� FITS WITH WIDEST DATASET IN GOOD MUTUAL AGREEMENT

� CHOICE OF �s VALUE IMPORTANT

STATUSPARTON LUMINOSITIES

GLUONGLUON QUARKQUARK

(G. Watt, 2011)

QUARKGLUON

1/2 / S )S( -310 -210 -110

Q-Q

bar

Lum

i

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

LHC 7 TeV

NNPDF2.1NNPDF2.0

=0.119sαCT10 -

=0.119sαMSTW08 -

LHC 7 TeV

CHARMCHARM

1/2 / S )S( -310 -210 -110

C-C

bar

Lum

i

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

LHC 7 TeV

NNPDF2.1NNPDF2.0

=0.119sαCT10 -

=0.119sαMSTW08 -

LHC 7 TeV

(NNPDF, 2011)

PROGRESSSSINCE LAST WG MEETING

� NNPDF2.0 ! NNPDF2.1

{ INCLUSION OF HQ MASSES (FONLLA)

{ F

2

DATA INCLUDED

� CTEQ6.6 ! CT10

{ IMPROVED STATISTICS (SIMILAR TO DYNAMICAL TOLERANCE)

{ MORE FLEXIBLE dv, GLUON, STRANGENESS (BUT STILL s = �s)

{ COMBINED HERA DATA, RUN II JETS, W ASYM, Z RAPIDITY DISTN.

ANNOUNCED AND/OR PRESENTED IN PRELIMINARY FORM(BUT NOT YET ON LHAPDF)

� CTEQ: NNLO

� NNPDF: NNLO (& LO) (2.1); INCLUSION OF LHC W ASYM DATA (2.2)

� HERAPDF: NNLO (1.0); INCLUSION OF HERAII AND HERA JET DATA

(1.5)

� ABKM: INCLUSION OF JET DATA

PROGRESSPARTON LUMINOSITIES

GLUONGLUON

2010 2011

QUARKQUARK2010 2011

(G. Watt, 2011)

CONSIDERABLY IMPROVED AGREEMENT!

PROGRESSTHE HIGGS CROSS SECTION

mH = 120 GEV: 2010 mH = 120 GEV: 2011

(G. Watt)

[GeV]HM

100 150 200 250 300 350 400 450 500

R

0.85

0.9

0.95

1

1.05

1.1

1.15

LH

C H

IGG

S X

S W

G 2

010

LHC 7 TeV 68% C.L.sαPDF+

normalized to MSTW2008nlo

)Z

(msαdifferent values of uncertaintiessαexact PDF+

PDF4LHC recipe

NNPDF2.0

CTEQ6.6

MSTW08nlo

(Higgs WG)

(G. Watt)

� (SMALL) IMPROVEMENT, MOSTLY CTEQ AND @ LARGE MH

NNLO STATUSGLUONGLUON PARTON LUMINOSITY

MSTW NNLO/NLO

best �t �s

(G. Watt, 2011)

MSTW NNLO/NLO

�xed �s

(GeV) H M100 150 200 250 300 350 400 450 5000.9

0.95

1

1.05

1.1

1.15

1.2

PDF Uncertainty in Gluon-Gluon lumi - LHC 7 TeV - Ratio to MSTW08 NLO

=0.119S

αMSTW08 NNLO

=0.119S

αMSTW08 NLO

PDF Uncertainty in Gluon-Gluon lumi - LHC 7 TeV - Ratio to MSTW08 NLO

(J. Rojo, 2011)

LESS GLOBAL VS MSTW.

(G. Watt, 2011)

� NLO VS NNLO MSTW LUMINOSITIES QUITE CLOSE

. . . BUT PARTLY DUE TO LOWER NNLO �s (0.117 VS 0.120)

� DIFFERENCES AS DATASED VARIED MUCH LARGER

. . . BUT IN SOME CASE ALSO �s QUITE DIFFERENT (ABKM: 0.113)

NNLO PROGRESS

� CTEQ NNLO IN PREPARATION

� NNPDF NNLO PRESENTED IN PRELIM. FORM (DIS ONLY AT NNLO, FULL NNLOIN PREPARATION)

{ GLUON SIMILAR TO MSTW, BUT NO SMALL x INSTABILITY

{

GLUON PDF: NLO VS NNLONNPDF MSTW

NNLO PROGRESS

� CTEQ NNLO IN PREPARATION

� NNPDF NNLO PRESENTED IN PRELIM. FORM (DIS ONLY AT NNLO, FULL NNLOIN PREPARATION)

{ GLUON SIMILAR TO MSTW, BUT NO SMALL x INSTABILITY

{ LUMINOSITY & HIGGS XSECT QUITE CLOSE TO MSTW. . . PROVIDED SAME �s USED

GLUON LUMI & HIGGS XSECT: NNPDF VS MSTWGLUON LUMI

(GeV) H M100 150 200 250 300 350 400 450 5000.9

0.95

1

1.05

1.1

1.15

1.2

PDF Uncertainty in Gluon-Gluon lumi - LHC 7 TeV - Ratio to NNPDF2.1 NNLO

NNPDF2.1 NNLO (TMP)

=0.119sαMSTW08 NNLO-

PDF Uncertainty in Gluon-Gluon lumi - LHC 7 TeV - Ratio to NNPDF2.1 NNLO

HIGGS XSECT.

ISSUES

PDF UNCERTAINTIES:DO THEY HAVE A STATISTICAL MEANING?

SOMETIMES STATED THAT “PDF UNCERTAINTIES ARE THEORETICALUNCERTAINTIES” (THUS DEVOID OF STATISTICAL MEANING) IS IT TRUE?

)

hOinew

=

RO[f ℄Pnew(f)Df;= N�

RO[f ℄P(�2jf)Pold(f)Df;

hOinew

=

1

Nrep

PNrep

k=1

N�P(�2jfk)O[fk℄ =

1

Nrep

PNrep

k=1

wk O[fk℄ wk = N (�2k)

n=2�1e� 12�2k

)

(de Lorenzi, M Nulty, 2010-2011))

��

� )

PDF UNCERTAINTIES:DO THEY HAVE A STATISTICAL MEANING?

SOMETIMES STATED THAT “PDF UNCERTAINTIES ARE THEORETICALUNCERTAINTIES” (THUS DEVOID OF STATISTICAL MEANING) IS IT TRUE?

A WAY OF TESTING:NEW DATA ) BAYES’ THEOREM

hOinew

=

RO[f ℄Pnew(f)Df;= N�

RO[f ℄P(�2jf)Pold(f)Df;

IN A MONTE CARLO APPROACH...

hOinew

=

1

Nrep

PNrep

k=1

N�P(�2jfk)O[fk℄ =

1

Nrep

PNrep

k=1

wk O[fk℄, wk = N (�2k)

n=2�1e� 12�2k

) EFFECT OF NEW DATA IS ACCOUNTED FOR BYREWEIGHTING MONTE CARLO AVERAGES

(CAN ALSO BE IMPLEMENTED IN HESSIAN FRAMEWORK (de Lorenzi, M Nulty, 2010-2011))

� DETERMINE PDFS INCLUDING SOME DATA BY BAYES’ THEOREM(REWEIGHTING)

� DETERMINE PDFS BY ENLARGING THE DATASET TO THE NEW DATA(REFITTING)

� COMPARE RESULTS ) IF THEY AGREE, PDFS DO HAVE A STATISTICALINTERPRETATIONS ALRIGHT!

RUNNING THE TESTINCLUSION OF JET DATA: REWEIGHTING VS. REFITTING

NNPDF2.0DIS+DY VS. NNPDF2.0FULL

GLUON

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02xg

(x, Q

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7NNPDF2.0 (DIS+DYP)

NNPDF2.0 (DIS+DYP) + rw JET

NNPDF2.0

GLUON UNCERTAINTY

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02A

bs.e

r.(x

g) (

x, Q

0

0.05

0.1

0.15

0.2

0.25NNPDF2.0 (DIS+DYP)

NNPDF2.0 (DIS+DYP) + rw JET

NNPDF2.0

DISTANCES

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ q

(x,Q

02 ) ]

x

Distance between central values

NNPDF2.0 vs. NNPDF2.0 DIS+DYP + Jets(RW) (100)Σg

T3V

∆Ss+s-

0

1

2

3

4

5

6

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02 ) ]

x

Distance between central values


T3V

∆Ss+s-

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ σ

q(x,

Q02 )

]

x

Distance between PDF uncertainties


T3V

∆Ss+s-

0

1

2

3

4

5

6

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02 )

]

x

Distance between PDF uncertainties


T3V

∆Ss+s-

d � 1 ) STATISTICAL EQUIVALENCE

STATISTICAL INTERPRETATION VALIDATED

DATA CONSISTENCY: WHY WE NEED IT

� DIS ONLY FIT )

SIGNIFICANT LOSS IN

ACCURACY

FOR GLUON (& OTHER

PDFS)

� HERA ONLY

EVEN WORSE

� BUT COLLIDER ONLY

(HERA+TEVATRON)CLOSE TO GLOBAL FIT

(FOR GLUON,THOUGH NOT FOR VALENCE)

THE GLUON: GLOBAL VS DIS VS HERA

THE GLUON: GLOBAL VS COLLIDER ONLY

DATA CONSISTENCY: HOW TO TEST FOR IT

� INCONSISTENT DATA , UNDERESTIMATED UNCERTAINTIES

� RESCALE ALL UNCERTAINTIES IN A GIVEN EXPERIMENT BY SOME FACTOR �:

�

2� = �

2=� (TOLERANCE)

� DETERMINE PROBABILITY DISTRIBUTION OF � VALUES BY BAYES’ THEOREM

) REWEIGHTING: P(�) = N�

PNk=1

wkwk(�):

JETS

α0 1 2 3 4 5

)α

P(

0

0.01

0.02

0.03

0.04

0.05

0.06

)α|2χP(

)αP(

)α|2χP(D0 e INCLUSIVE

α0 1 2 3 4 5

)α

P(

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

)α|2χP(

)αP(

)α|2χP(

D0 e HIGH ET

α0 1 2 3 4 5

)α

P(

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

)α|2χP(

)αP(

)α|2χP(

� JETS: ) CONSISTENT DATA

� W

� CHARGE ASYMMETRIES, D0 INCLUSIVE e DATA )

UNCERTAINTIES UNDERESTIMATED BY � 30% (PROB. PEAKS AT � � 1:7)

� W

� CHARGE ASYMMETRIES, D0 e DATA WITH ET > 35 GEV ) INCONSISTENT DATA

NMC DATA: A PROBLEM?

� NMC PROTON AND DEUTERON DATA FOR DIS F2 STRUCTURE FUNCTION

� F2STRUCTURE FUNCTION DATA USED IN MSTW, CTEQ, NNPDF FITS,WOULD THE USE OF CROSS SECTION DATA MAKE A DIFFERENCE?

(Alekhin, Bl�umlein, Mo h, 2011)e�(x; y;Q2) = F2(x;Q

2)

�2� 2y + y2=[1 +R(x;Q

2)℄

�

(NLO: arXiv:1102.3182; NNLO: preliminary)

NMC DATA: A PROBLEM?

� NMC PROTON AND DEUTERON DATA FOR DIS F2 STRUCTURE FUNCTION

� F2STRUCTURE FUNCTION DATA USED IN MSTW, CTEQ, NNPDF FITS,WOULD THE USE OF CROSS SECTION DATA MAKE A DIFFERENCE?

(Alekhin, Bl�umlein, Mo h, 2011)e�(x; y;Q2) = F2(x;Q

2)

�2� 2y + y2=[1 +R(x;Q

2)℄

�NNPDF FIT REPEATED WITH NMC XSECT OR NO NMC

(NLO: arXiv:1102.3182; NNLO: preliminary)

EFFECT ON GLUON

x-410 -310 -210 -110

)]2R

[g (

x, Q

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

2 GeV4 = 102Ratio to NNPDF2.1, Q

NNPDF2.1

NNPDF2.1-NMCxsec

NNPDF2.1-noNMC

2 GeV4 = 102Ratio to NNPDF2.1, QEFFECT ON HIGGS XSECT

[ GeV ]HM100 120 140 160 180 200 220 240 260 280 300 320

( H

->

gg )

)σ

R (

0.9

0.95

1

1.05

1.1

1.15

NNLO gg->H production, Ratio to NNPDF2.5 (TMP)

NNPDF2.5 NNLO(TMP) NMC-XSEC

NNPDF2.5 NNLO(TMP) NMC SF

NNLO gg->H production, Ratio to NNPDF2.5 (TMP)

NO SIGNIFICANT CHANGE OBSERVED

NMC DATA: A PROBLEM?A CLOSER LOOK

� ALEKHIN ET AL. SEE LARGE SHIFT IN BESTFIT �s: FROM 0.1170 (NMC F2) TO0.1135 (NMC �s)

� HOW MUCH OF THEIR CHANGE IN HIGGS XSECT (� 8%) DUE TO CHANGE IN �s?

� BASED ON POWER COUNTING, EXPECT 2:8��s = 8% (!)

� EITHER REMOVE NMC DATA, OR CHANGE VALUE OF �s IN MSTW FIT

(Thorne, presented by Watt at PDF4LHC 2011):

{{ �s

{

�s = 0:113

NMC DATA: A PROBLEM?A CLOSER LOOK

� ALEKHIN ET AL. SEE LARGE SHIFT IN BESTFIT �s: FROM 0.1170 (NMC F2) TO0.1135 (NMC �s)

� HOW MUCH OF THEIR CHANGE IN HIGGS XSECT (� 8%) DUE TO CHANGE IN �s?

� BASED ON POWER COUNTING, EXPECT 2:8��s = 8% (!)

� EITHER REMOVE NMC DATA, OR CHANGE VALUE OF �s IN MSTW FIT

(Thorne, presented by Watt at PDF4LHC 2011):

{ IMPACT OF NMC DATA NEGLIGIBLE

{ IMPACT OF �s VALUE COMPARABLE (SOMEWHAT SMALLER) TO WHOLE ABKMEFFECT

{ MSTW AND ABKM RESULTS STILL QUITE DIFFERENT EVEN FOR SAME

�s = 0:113

THE VALUE OF �s

� DEDICATED MUNICH MEETING (FEB 2011):S. BETHKE PROPOSES TWO UPDATED VALUES:

{ (1) �s = 0:1174� 0:0011

{ (2) �s = 0:1187� 0:0006

{ BOTH INCLUDE NEW VALUE FROM � DECAYS �s = 0:1213� 0:0014

(WAS �s = 0:1197� 0:0016)

{ VALUE (1) ALSO INCLUDES NEW SCET VALUE FROM e+

e�

THRUST

(Abbate et al., 2010)

�s = 0:1135� 0:0010, BUT ALL UNCERTAINTIES RESCALED BY FACTOR 2

{ VALUE (2) EXCLUDES IT

� AVERAGING THE TWO MOST RELIABLE VALUES (GLOBAL EW FIT & � , BOTH

N3LO, NO DEP. ON HADRON STRUCTURE) GIVES

�s = 0:1209� 0:0013

� 0:002

THE VALUE OF �s

� DEDICATED MUNICH MEETING (FEB 2011):S. BETHKE PROPOSES TWO UPDATED VALUES:

{ (1) �s = 0:1174� 0:0011

{ (2) �s = 0:1187� 0:0006

{ BOTH INCLUDE NEW VALUE FROM � DECAYS �s = 0:1213� 0:0014

(WAS �s = 0:1197� 0:0016)

{ VALUE (1) ALSO INCLUDES NEW SCET VALUE FROM e+

e�

THRUST

(Abbate et al., 2010)

�s = 0:1135� 0:0010, BUT ALL UNCERTAINTIES RESCALED BY FACTOR 2

{ VALUE (2) EXCLUDES IT

� AVERAGING THE TWO MOST RELIABLE VALUES (GLOBAL EW FIT & � , BOTH

N3LO, NO DEP. ON HADRON STRUCTURE) GIVES

�s = 0:1209� 0:0013

� UNCERTAINTY LARGER THAN 0:002 QUITE UNLIKELY

OUTLOOK

PRACTICAL PRESCRIPTIONS

(no new PDF4LHC guidelines: my suggestion, to start dis ussion)

� ISSUES OF �s UNCERTAINTY & PDF UNCERTAINTY SHOULD NOT BE MIXED:AGREE ON REASONABLE CONSERVATIVE RANGE FOR EITHER

� �s UNCERTAINTY LARGER THAN ��s = 0:002 DOES NOT SEEM ADVISABLE;ANY OF ABOVE CENTRAL VALUES ACCEPTABLE WITH THIS UNCERTAINTY,BUT AGREE ON ONE

� EVEN AT FIXED �s, ENVELOPE INCLUDING PDFS W/O HADRONIC DATA NOT

ADVISABLE

� IDEALLY, WAIT FOR CTEQ+NNPDF NNLO AND/OR ABKM WITH

TEVATRON JETS & VARIOUS �s VALUES

� IF NOT, JUST UPDATE PDF4LHC NNLO WITH CT10 & NNPDF2.1

(res ale MSTW08 NNLO un ertainty by NLO MSTW/envelope un ertainty ratio)

MOTIVATION:

{ NNLO VS NLO DIFFERENCES SMALLER THAN DIFFERENCES BETWEEN SETS

{ DIFFERENCES BETWEEN PDFS BASED ON DIFFERENT DATASETS LIKELY TO

REFLECT MISSING INFORMATION

{ DIFFERENCES BETWEEN PDFS BASED ON WIDEST DATASET MAY REFLECT

GENUINE METHODOLOGICAL UNCERTAINTIES

EXTRAS

THE FUTURE: COLLIDERONLY PDFS

� LHC CAN PROVIDE US PRECISION INFORMATION ON PDFS

� TOWARDS A “COLLIDER ONLY” HERA+LHC PDF FIT

(TEVATRON DATA MIGHT BE SUPERFLUOUS)

{ MEDIUM & LARGE x GLUON

� PROMPT PHOTONS AVAILABLE

� (PRECISION) JETS IN PROGRESS

{ LIGHT FLAVORS AT MEDIUM @ SMALL x, FLAVOR SEPARATION @ SMALL x

� LOW–MASS DRELLYAN PRELIM.

� Z RAPIDITY DISTRIBUTIONS PRELIM.

� W ASYMMETRIES AVAILABLE

{ STRANGENES & HEAVY FLAVORS

� STRANGENESS ) W + FUTURE?

� CHARM ) Z + , + FUTURE?

� BOTTOM Z + b IN PROGRESS

BEYOND DGLAP?DISCOVERING A NEW QCD EFFECT IN HERA DATA

IDEA: (G�elis, 2008, ) Caola, s.f. ,Rojo 2010)

� CUT OUT DATA IN THE “DANGEROUS” (SMALL x)REGION

� DETERMINE PDFS IN THE “SAFE”(LARGE x AND Q

2) REGION

� EVOLVE BACKWARDS AND COMPARE TO DATA

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

�� x Q

2

� x Q

2

BEYOND DGLAP?DISCOVERING A NEW QCD EFFECT IN HERA DATA

IDEA: (G�elis, 2008, ) Caola, s.f. ,Rojo 2010)

� CUT OUT DATA IN THE “DANGEROUS” (SMALL x)REGION

� DETERMINE PDFS IN THE “SAFE”(LARGE x AND Q

2) REGION

� EVOLVE BACKWARDS AND COMPARE TO DATA

OLD HERA DATABACKWARD EV. VS DATA

x

-410

-310

-210

)2

=3

.5 G

eV

2(x

,Q2

F

0.2

0.4

0.6

0.8

1

1.2

1.4

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Fit without cutsxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

= 0.5cut

Fit with Axxxxxxxxxxxxxxxxxxxxxxxx

= 1.5cut

Fit with A

Data

DAT/TH DIST: NO CUT DAT/TH DIST: CUT

� BACKWARD EVOLVED FIT LIES SYSTEMATICALLY BELOW DATA

� DATA AT LOW x AND Q2

SHOW LESS EVOLUTION THAN PREDICTED BY NLO DGLAP

� IF LOW x AND Q2

DATA INCLUDED, THE FIT COMPENSATES READJUSTING PDFS

NEW COMBINED HERA DATABACKWARD EV. VS DATA

x

-410

-310

-210

)2

=3

.5 G

eV

2(x

,Q2

F

0.2

0.4

0.6

0.8

1

1.2

1.4

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Fit without cutsxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

= 0.5cut

Fit with Axxxxxxxxxxxxxxxxxxxxxxxx

= 1.5cut

Fit with A

Data

DAT/TH DIST: NO CUT DAT/TH DIST: CUT

� DATA AT LOW x AND Q2

SHOW LESS EVOLUTION THAN PREDICTED BY NLO DGLAP

� BACKWARD EVOLVED FIT LIES SYSTEMATICALLY BELOW DATA

� WITH MORE PRECISE DATA, THE FIT NO LONGER MANAGES TO COMPENSATE BY

READJUSTING THE PDFS: EVEN FULL FIT LIES BELOW DATA

DETERIORATION IN FIT QUALITY:

hd2i VS x SLICES

>2<d

0.5

1

1.5

2

2.5

3 = 1.5cutFit with A

Fit without cuts < 1.0 cutA

< 1.5cut1.0 < A

< 3.0cut1.5 < A

< 6.0 cut3.0 < A

> 6.0cutA

� QUALITY OF UNCUT FIT DETERIORATES IN LOW xREGIONS

� QUALITY OF CUT FIT INCREASINGLY POOR AS x

DECREASES

� DISTANCE RISES DESPITE HUGE INCREASE IN UNCERTAINTY

�

)

�2

x

1.0 1.5 3.0 6.0 6.0

fit

GeV

36 18 30 27 468

ranges

0.5

1.0

1.5

2.0

2.5

3.0

DETERIORATION IN FIT QUALITY:

hd2i VS x SLICES

>2<d

0.5

1

1.5

2

2.5

3 = 1.5cutFit with A

Fit without cuts < 1.0 cutA

< 1.5cut1.0 < A

< 3.0cut1.5 < A

< 6.0 cut3.0 < A

> 6.0cutA

� QUALITY OF UNCUT FIT DETERIORATES IN LOW xREGIONS

� QUALITY OF CUT FIT INCREASINGLY POOR AS x

DECREASES

� DISTANCE RISES DESPITE HUGE INCREASE IN UNCERTAINTY

� IN HESSIAN FIT (CTEQ) RESULTS DEPEND ON

PARAMETRIZATION ) EVIDENCE INCONCLUSIVE

�2

VS x SLICES FOR CT10

<1.0 1.0-1.5 1.5-3.0 3.0-6.0 >6.0

ææ

æ

ææ

à

à

à

àà

ì

ì

ì

ìì

CT10 fit

Fit 1 with Acut=1.5Fit 2 with Acut=1.5

Q > 2 GeV

N pts= 36 18 30 27 468Ags

ranges

0.5

1.0

1.5

2.0

2.5

3.0Χdata

2�Npts

NNPDF �s

NLO NNPDF2.1 GLOBAL DETERMINATION (ONLY STAT. ERROR KNOWN)

Nrep = 500 PER VALUE OF �s

�s(Mz) = 0:1191� 0:0006(stat:)� 0:0001(pro :)

3860

3880

3900

3920

3940

3960

3980

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

NNPDF2.1 Total Dataset

DataParabolic Fit

�

2=d:o:f: = 1:6 for the paraboli �t

THE RESULT: DIS ONLYDO DIS DATA PREFER A SMALLER VALUE?NLO NNPDF2.1 DEEPINELASTIC DATA

Nrep = 500 PER VALUE OF �s

�s(Mz) = 0:1177� 0:0009(stat:)� 0:0002(pro :)

3170

3180

3190

3200

3210

3220

3230

3240

3250

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

NNPDF2.1 - DIS data only

DataParabolic Fit

�

2=d:o:f: = 0:8 for the paraboli �t

� YES

� BUT NOT MUCH SMALLER & WITH LARGER UNCERTAINTY(COMPATIBLE WITHIN UNCERTAINTIES, AS IT OUGHT TO)

INDIVIDUAL EXPERIMENTS: WHAT’S GOING ON?

�2 PROFILE FOR INDIVIDUAL EXPERIMENTS IN GLOBAL & DIS FITS

110

115

120

125

130

135

140

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

NMCpd

NNPDF2.1NNPDF2.1-DIS

370

375

380

385

390

395

400

405

410

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

NMC


60

70

80

90

100

110

120

130

140

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

SLAC


690

700

710

720

730

740

750

760

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

BCDMS


610

615

620

625

630

635

640

645

650

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

HERA-I


900

920

940

960

980

1000

1020

1040

1060

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

CHORUS


30

35

40

45

50

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

NuTeV


160

162

164

166

168

170

172

174

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

ZEUS-H2


98

99

100

101

102

103

104

105

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

E605

NNPDF2.1

240

245

250

255

260

265

270

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

E866

NNPDF2.1

60

65

70

75

80

85

90

95

100

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

CDF jets

NNPDF2.1

88

90

92

94

96

98

100

102

104

0.113 0.115 0.117 0.119 0.121 0.123 0.125

αs(MZ)

D0 jets

NNPDF2.1

� BCDMS SIMILAR TO HERA, NMC PRETTY FLAT

� DIS EXPERIMENTS (BCDMS+HERA) IN DIS FIT HAVE A “RUNAWAY DIRECTION” AT

SMALL �s,ABSENT IN GLOBAL FIT

� JET EXPERIMENTS EXCLUDE SMALL �s

IS THERE A PROBLEM WITH DIS?

CONJECTURE

� IN DIS, GLUON DETERMINED BY SCALING VIOLATIONS ) CAN COMPENSATE SMALLER �s WITH LARGER GLUON (OR CONVERSELY)

) RUNAWAY DIRECTIONS POSSIBLE IN DIS FIT

� JET DATA ARE AT MUCH LARGER SCALE, IF �s TOO SMALL OR LARGE

HIGHSCALE GLUON WILL COME OUT WRONG

) RUNAWAY DIRECTION QUENCHED IN GLOBAL FIT x-510 -410 -310 -210 -110 1

]2 [

GeV

2 T /

p2

/ M

2Q

1

10

210

310

410

510

610 NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2ZEUSF2CH1F2CDYE605DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KTD0R2CON

NNPDF2.1 dataset

THE EVIDENCE

-1

-0.5

0

0.5

1

1.5

0.114 0.116 0.118 0.12 0.122 0.124

Cor

rela

tion

coef

ficie

nt

αs ( MZ )

NNPDF2.1 - Q2 = 2 GeV2 - Gluon - x=0.05

HERA-IBCDMSCDFjets

D0jetsE866

-1

-0.5

0

0.5

1

1.5

0.114 0.116 0.118 0.12 0.122 0.124

Cor

rela

tion

coef

ficie

nt

αs ( MZ )

NNPDF2.1 - Q2 = 2 GeV2 - Gluon - x=0.1

HERA-IBCDMSCDFjets

D0jetsE866

� COMPUTE THE CORRELATION BETWEEN �

2 & PDFS AT THE GLOBAL BEST FIT

LARGE (POSITIVE OR NEGATIVE) CORRN. , RUNAWAY DIRECTION

� OPPOSITE SIGN CORRELATIONS , DATA PULLING IN OPPOSITE DIRECTIONS

� AT LOW �s = 0:114 DIS FIT HAS A RUNAWAY DIRECTION STABILIZED BY JETS

� AT HIGH �s = 0:122 FIT IS GENERALLY STABLE,THOUGH STILL SOME PULL IN HERA LOW x

NNPDF2.1, MSTW08, CT10 COMPARISONSINGLET SECTOR

SINGLET

x-510 -410 -310 -210 -110

) 02 (

x, Q

Σx

0

1

2

3

4

5

6

NNPDF2.1

CT10

MSTW08

SINGLET

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

Σx

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

NNPDF2.1

CT10

MSTW08

GLUON

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

5

6

NNPDF2.1

CT10

MSTW08

GLUON

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

5

6

NNPDF2.1

CT10

MSTW08

NNPDF2.1, MSTW08, CT10 COMPARISONNONSINGLET SECTOR

TOTAL VALENCE

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xV

(x,

Q

0

0.2

0.4

0.6

0.8

1

1.2 NNPDF2.1

CT10

MSTW08

ISOSPIN TRIPLET

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02

(x,

Q3

xT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

NNPDF2.1

CT10

MSTW08

s+ �s

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

+xs

0

0.05

0.1

0.15

0.2

0.25

NNPDF2.1

CT10

MSTW08

s� �s

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

Q-

xs

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

NNPDF2.1

CT10

MSTW08

Documents

STATUS & PROGRESS - NNPDF