dynamical parton distribution functions...dynamical vs standard: gluon 0.1 1 10 100 10 xg(x,q 2) x 2...

DynamicalParton Distribution Functions

Pedro Jimenez-Delgado

Jefferson Lab Theory Seminar

DynamicalParton Distribution Functions

The dynamical approach to parton distributions

The longitudinal structure function

The dynamical determination of strange parton distributions

The treatment of heavy quarks: a brief critical review

Weak-gauge and Higgs boson production at hadron colliders

Jefferson Lab Theory Seminar 2/41

The dynamical approach to parton distributionsGlobal QCD analysisEstimation of uncertaintiesThe dynamical parametrizationBrief history of the dynamical PDFsThe new generationComparison with GRV98Dynamical vs standard: gluonDynamical vs standard: seaThe strong coupling constantComparing with other determinations

The longitudinal structure functionDIS reduced cross-sectionPerturbative stabilityConfronting results with data

The dynamical determination of strange partondistributions

Dimuon productionFitting the dataThe strangeness asymmetryThe NuTeV anomaly

The treatment of heavy quarks: a briefcritical review

FOPT heavy-quark contributionsMassive coefficient functionsPerturbative stability of the FFNSEffective heavy-quark PDFs: VFNSRelevance of the VFNSGeneral-mass VFNS’sPlausibility of the GM-VFNS’sPresent HQ treatments in DIS

Weak-gauge and Higgs bosonproduction at hadron colliders

Weak gauge boson production ratesNNLO benchmarks for W and ZHiggs boson production at LHCHiggs boson production at TevatronComparison of parton luminositiesNNLO benchmarks for Higgsproduction


Global QCD analysisDetermination of NP information: input distributions xf (x,Q2

0)

for light quarks + gluon: f = u, d, s, u, d, s and g (no heavy-quark PDFs!)

Selected experimental information + parametrizations

Nucleon DIS structure functions

Jets from Tevatron (up to NLO)

Drell-Yan pp + pn (or neutrino DIS)data needed for d 6= u

Not very sensitive to strange PDFs,⇒ input assumptions s= s(= 0)(or asymmetric, discussed later)

Chi-square method:

χ2(p)≡

N

∑i=1

(data(i)−theory(i,p)

error(i)

)210

-1

1

10

10 2

10 3

10 4

10 5

10 6

10-6

10-5

10-4

10-3

10-2

10-1

1x

Q2 (

GeV

2 )

[PDG Review]Jefferson Lab Theory Seminar 4/41

Estimation of uncertaintiesPropagation of experimental errors (only!) into the PDFs

Hessian method: quadratic expansion around the global minimum

∆χ2=χ

2−χ20 '

12

d

∑i,j=1

Hij(ai−a0i )(aj−a0

j )≤T2

Tolerance parameter: T2=T21σ

=√

2N/(1.65)2⇒ T'5

diagonalization of Hij −→ (rescaled) eigenvector matrix Mij

“Eigenvector sets”: a±ji = a0

i ±TMij

Calculation of a quantity X±∆X:

X=X(a0), ∆X =12

d

∑j=1

√(X(a+j)−X(a−j)

)2


The dynamical parametrizationSince we are free to (and have to) select an input scale for the RGE:

At low-enough Q2 only “valence” partons would be “resolved”⇒ structure at higher Q2 appears radiatively (i.e. due to QCD dynamics)

DYNAMICAL:

Q20<1GeV2 optimally determined

a>0 “valence-like”

“STANDARD”:

Q20 = 2GeV2 arbitrarily fixed

Unrestricted parameters

xf (x,Q20) = N xa(1− x)b(1+A

√x+Bx)

Positive definite input distributions

QCD predictions for x.10−2

More restrictive, less uncertainties

Arbitrary fine tunning (g <0!)

Extrapolations to unmeasured region

Less restrictive, marginally smaller χ2

Physical motivation for the CC of the DGLAP 6= NP structure of the nucleon

There are no extra theoretical assumptions involved in the dynamical approachwith respect to the “standard” one


Brief history of the dynamical PDFs

Dynamical assumption [Altarelli, Cabibbo, Maiani, Petronzio 74], [Parisi, Petronzio 76], [Novikov 76], [Gluck, Reya 77]

in connexion with the constituent quark model: only valence quarks

First dynamical determination of parton distributions [Gluck, Reya 77]

Used in the 80’s: e.g. for the discoveryof W and Z bosons (SPS, CERN)

Extended to include light sea [Gluck, Reya, Vogt 90]

and gluon [Gluck, Reya, Vogt 92] valence-like input−→ steep gluon and sea at small-x!!

Confirmed by first HERA F2(x,Q2) data[H1, ZEUS 93]

GRV95 and GRV98 contributed greatlyin the 90’s and beginning of the 00’sNew improved generation (GJR08, JR09):MS + DIS factorization schemes, NNLO, error analysis, FFNS+VFNS, new data


The new generation


Comparison with GRV98

00.20.40.60.8

11.21.4

10-5 10-4 10-3 10-2

xf

x

u + d

0

0.2

0.4

0.6

0.8

1

GJR08GRV98

0.1 0.3 0.5 0.7 0.9

g

uv

dv

d - u

0.6

0.8

1

1.2

1.4

0.05 0.1 1

dynN

LO/G

RV

98

x

uvdv

0.6

0.8

1

1.2

1.4

0.05 0.1 1

dynN

LO/G

RV

98

x

0.6

0.8

1

1.2

1.4

10-5 10-4 10-3 0.01 0.1 0.5

dynN

LO/G

RV

98

Q2 = 10 GeV2

- -

0.6

0.8

1

1.2

1.4

10-5 10-4 10-3 0.01 0.1 0.5

dynN

LO/G

RV

98

Q2 = 10 GeV2

- -

gu + d

Very similar to the previous dynamical (input) distributios GRV98 [up to NLO]

All quark distributions within error estimates (note the flat sea)

Similar gluon as well: peaks at slightly different x but within 2σ

Stable after evolution, less than 10−20% of “acceptable” (1σ ) difference


Dynamical vs standard: gluon

0.1

1

10

100

xg(x

,Q2 )

x

2 = Q2(GeV2)

(×0.5)

5

20

(×2)

dynNNLO

dynNLOstdNNLO

stdNLOAMP06

0.1

1

10

100

xg(x

,Q2 )

x

2 = Q2(GeV2)

(×0.5)

5

20

(×2)

10-5 10-4 10-3 0.01 0.1

Uncertainties decrease as Q2 increase: pQCD evolution

Valence-like input, i.e., larger “evolution distance”⇒ less uncertaintiesQ2

0 also play another role⇒ standard gluons fall below dynamical


Dynamical vs standard: sea

0.1

1

10

x(u

+ d)

(x,Q

2 )

x

2 = Q2(GeV2)(×0.5)

5

20

(×2)

10-5 10-4 10-3 0.01 0.1

dynNNLO

dynNLOstdNNLO

stdNLOAMP06

Rather flat input sea (au+d'0.15)⇒

equally increasing down to x' 10−2⇒ marginally smaller errors


The strong coupling constant

αs(µ2) and HQ masses are parameters which depend on the theoretical input

(order, scheme, scales, etc.)

It is desirable that their values come out of the global PDF fitsWe determine αs(M2

Z) together together with the distributions:

dynamical “standard”

NNLO 0.1124±0.0020 0.1158±0.0035

NLO 0.1145±0.0018 0.1178±0.0021

LO 0.1263±0.0015 0.1339±0.0030

Dynamical constraints reduce the uncertainty! (in particular at NNLO)

Dynamical results are smaller: larger “evolution distance” (Q20<1GeV2)


Comparing with other determinations

0.1

0.105

0.11

0.115

0.12

0.125

0.13

BBG06

BBG06

ABKM1

ABKM2

JR1

JR2

MSTW

09

ABM10

BB10

BB02

SMC98

ABFR98

αs(M

Z2)

[Blumlein 2010]

DIS data generally prefer lower values than LEP or hadron colliders:

Differences should be interpreted as uncertainties (not be “removed” by convention!)


DIS reduced cross-section

σNCr ≡

(2πα2

xyQ2 Y+

)−1d2σNC

dxdy = FNC2 −

y2

Y+FNC

L ∓Y−Y+

xFNC3

Usually dominated by Fγ

2

y = Q2

s1x

for fixed Q2 (and s)FL relevant withincreasing y (decreasing x)

→ turnover at small x

⇒ FL positive

1.0

1.5

σ r(x

,Q2 )

Q2 = 12 GeV2

Ep = 920 GeVEp = 575 GeVEp = 460 GeV

Q2 = 15 GeV2

1.0

1.5

x

Q2 = 25 GeV2

10-3 0.01

Q2 = 35 GeV2

10-3 0.01

gluon dominated in the small-x region ⇒ positive gluon (also beyond LO!)


Perturbative stability

0.0

0.1

0.2

0.3

0.4

0.5

F L(x

,Q2 )

Q2 = 2 GeV2

c

dynNNLO

dynNLOdynLO

Q2 = 4 GeV2

c

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-5 10-4 10-3 10-2 10-1

x

Q2 = 10 GeV2

c

10-5 10-4 10-3 10-2 10-1 100

Q2 = 100 GeV2

c (× 0.5)

0.0

0.1

0.2

0.3

0.4

0.5

F L(x

,Q2 )

Q2 = 2 GeV2

c

stdNNLO

stdNLOstdLO

Q2 = 4 GeV2

c

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10-5 10-4 10-3 10-2 10-1

x

Q2 = 10 GeV2

c

10-5 10-4 10-3 10-2 10-1 100

Q2 = 100 GeV2

c (× 0.5)

Observed [M(R)ST(W)] instabilities unphysical: artefact of negative gluons

Both dynamical and standard results manifestly positive at all orders

Dynamical predictions stable already at Q2&2 GeV2

Standard differ more but less distinguishable due to the larger error bands


Confronting results with data

0

0.2

0.4

0.6

0.8

1

10-5 10-4 10-3 10-2F L

(x,Q

2 )

Q2 (GeV2)

x

W = 276 GeV

1 10 100 103

dynNNLO

dynNLOstdNNLO

stdNLOprelim.

e+pe-p

[H1 2001+2003]

From our paper,preliminary data:[Lobodzinska 2004][Lastovicka 2004]

Positive and in complete agreement with measurements

Dynamical predictions more tightly constrained

Higher-twist effects may contribute for Q2≤2 GeV2


Confronting results with data

[H1 2010]

Positive and in complete agreement with measurements (confirmed!)

Greater precision achieved within the dynamical framework

Other results less precise and even turning negative at the lower Q2 values


Dimuon production

[NuTeV 2001]

Signature: Two muons of different sign

Directly related to charged currentcharm production ∝ s(x,Q2) (FFNS)

Sensitive to differences between s and s

Overall normalization proportional to Bc

dσ+

dxdy

(x,y,Eν(ν)

)=

G2FMEν(ν)

πBc A

(x,y,Eν(ν)

) dσν(ν)

dxdy

(x,y,Eν(ν)

)Acceptance corrections [Kretzer et al.] at NLO!

Nuclear corrections (iron) using FFNS NLO GRV98 [de Florian et al.]


Fitting the data

0.005

0.010

0.015y = 0.32, 0.56, 0.77

x

asymmetric

GJR08

Eν =

88,

π (G

F2 M E

ν)-1

dσ+

dxdy

( x,y

,Eν)

0.005

0.010

0.015

174,

0

0.005

0.010

0.015

0 0.1 0.2 0.3

0.1 0.2 0.3

0.1 0.2 0.3

247

GeV2

0.005

0.010y = 0.35, 0.58, 0.78

x

asymmetric

GJR08

E−ν =

78,

π (G

F2 M E

− ν)-1

dσ+

dxdy

(x,y

,E− ν)

0.005

0.010 144,

0

0.005

0.010

0.015

0 0.1 0.2

0.1 0.2

0.1 0.2

227

GeV2

Already well described by GJR08: χ2=65 for 90 data points (1σ )

⇒ radiatively generated strangeness plausible!: s(x,Q20)+ s(x,Q2

0) = 0

Introducing an asymmetry χ2 goes down to 60: s(x,Q20)− s(x,Q2

0) 6=0

Neutrino increases, antineutrino decreases⇒ “positive” asymmetry


The strangeness asymmetry

-0.01

-0.005

0

0.005

0.01

0.015

0.02

10-6 10-5 10-4 10-3 10-2

x(s - s)-

Q2 = 16 GeV2

x

0.1 0.2 0.3 0.4 0.5 0.6

asymmetric

MSTW2008

Compatible with previous determinations but smaller uncertainties

Very small effect (for most applications): S− ≡∫ 1

0 dx x(s− s) = 0.0008±0.0005

Important for dedicated experiments (e.g. NuTeV anomaly)Jefferson Lab Theory Seminar 22/41

The NuTeV anomalyExperimental methods(functionals): ∆s2

W =∫ 1

0 F[s2W ,δ

(−)q ; x]xδ

(−)q (x,Q2)dx

Total shift: ∆s2W |total=

=∆s2W |QED+∆s2

W |NP+∆s2W |strange

Isospin–symmetry violating PDFs:

NP mass effects: ∆s2W |NP [Londergan et al.]

radiative QED effects: ∆s2W |QED

Strange asymmetric PDFs: ∆s2W |strange

All effects combined remove the “anomaly” (within SM)!

Using R− ≡σνN

NC−σ νNNC

σνNCC−σ νN

CC

= R−PW +δR−I +δR−s overestimates the corrections (≈ 20%–40%)


FOPT heavy-quark contributions

Experiment: No (< 1%) intrinsic heavy-quark content in the nucleon

HQ generated in hard collisions, not collinearlly, short “lifetime” (6= parton)

⇒ Final state ≡ extrinsic heavy-quark content; fully massive calculations

⇒FOPT initiated by gluons and light (u,d,s) quarks ≡ FFNS (in this context)

Fhk=2,L(x,Q

2,m2) =αs(µ

2)Q2

4π2m2 ∑f=g,q,q

∫ 1

zth

dz f (z,µ2) Fhk=2,L(

xz ,µ

2,Q2,m2), zth = x(1+ 4m2

Q2 )

Gluon dominated (starts at LO), therefore “small-x”-dominated:about 80% originates in the region zth ≤ z≤ 3zth [A.Vogt 96]

⇒ threshold region is always important (irrespective of Q2)


Massive coefficient functions

Theoretical status:

The (inclusive) coefficient functions are known at LO [Witten 75, Gluck and Reya 79]

and NLO [Laenen,Riemersma,Smith,van Neerven 93]:

Fhk=2,L(

xz ,µ

2,Q2,m2) = e2hδfg c(0)k,g +4παs(µ

2)[e2

h

(c(1)k,f + c(1)k,f ln µ2

m2

)+ e2

f

(d(1)k,f + d(1)k,f ln µ2

m2

)]There is a fully exclusive NLO calculation [Harris and Smith 95]: HVQDIS,in which all the experimental analysis at HERA is based

At NNLO only the asymptotic (Q2�m2) coefficients [Bierenbaun,Blumlein,Klein 09] exist:

There is no complete NNLO (massive) calculation of HQ contributions in DIS

Some approximations can be made using small-x [Catani, Cialfoni, Hautmann 91]

and threshold [Laenen and Moch 99] resummations

The coefficient functions contain potentially large ln µ2

m2 ’s (not mass divergences):

Are these terms dangerous or is the FFNS stable for DIS phenomenology?


Perturbative stability of the FFNSIt should be clear since (again):

all the experimental analysis at HERA is based on the FFNS (HVQDIS)Nevertheless we can have a look at the (semi)inclusive calculation (used in the fits):

F 2c (x,Q

2 ) × 4i

Q2 (GeV2)1 10 100 103

0.01

0.1

1

10

100

103

104

105

H1 ,ZEUS

x = 0.00003 - 0.00007 (i = 9)

0.00013-0.0002 (8)

0.00035 (7)

0.0005 - 0.0008 (6)

0.001 (5)

0.002 (4)

0.003 (3)

0.005 - 0.006 (2)

0.012 (1)

0.03 (0)

dynNLO

dynLO

F 2c (x,Q

2 ) × 4i

Q2 (GeV2)1 10 100 103

0.01

0.1

1

10

100

103

104

105

H1 ,ZEUS

x = 0.00003 - 0.00007 (i = 9)

0.00013-0.0002 (8)

0.00035 (7)

0.0005 - 0.0008 (6)

0.001 (5)

0.002 (4)

0.003 (3)

0.005 - 0.006 (2)

0.012 (1)

0.03 (0)

0

1

2

3

4

5

6

7

8

9

10

1 10 100 1000

F 2,cNLO

/ F2,

cLO

+ i

Q2 (GeV2)

x = 0.00003 - 0.00007 (i = 9)

0.00013 - 0.0002 (8)

0.00035 (7)

0.0005 - 0.0008 (6)

0.001 (5)

0.002 (4)

0.003 (3)

0.005 - 0.006 (2)

0.012 (1)

0.03 (0)

FFNS gets trough all “stability tests”!!No need to resum supposedly “large logarithms”... why are there other schemes then?


Effective heavy-quark PDFs: VFNS

The only drawback of the FFNS is the calculational difficulty, for instance:

FFNS: gg→ bbH

b

h0

b

VFNS: bb→ H h0

b

b

We can construct effective heavy-quark PDFs from the the asymptotic limit ofthe massive calculation [Buza, Matiouine, Smith, van Neerven 98]:

HQ2�m2(Q2

µ2 ,µ2

m2 ) = A( µ2

m2 )⊗C(Q2

µ2 ) ⇒ f VFNSj = ∑

kAjk⊗ f FFNS

k

A’s=massive OME’s, process independent⇒ preserves universality!!C’s=light-parton coefficient functions

In practice: massless evolution with increasing nf at unphysical “thresholds” µ2'm2

This resums (RGE) the ln µ2

m2 ’s of the final-state contributions 6= intrinsic HQsThe effective VFNS HQ-PDFs are assumed to be correct asymptotically but:

Is this scheme relevant for DIS phenomenology?


Relevance of the VFNSF 2c (x

,Q2 ) ×

4i

Q2 (GeV2)1 10 100 103

0.01

0.1

1

10

100

103

104

105

H1 ,ZEUS

x = 0.00003 - 0.00007 (i = 9)

0.00013-0.0002 (8)

0.00035 (7)

0.0005 - 0.0008 (6)

0.001 (5)

0.002 (4)

0.003 (3)

0.005 - 0.006 (2)

0.012 (1)

0.03 (0)

FFNSVFNS

F 2c (x,Q

2 ) × 4

i

Q2 (GeV2)1 10 100 103

0.01

0.1

1

10

100

103

104

105

H1 ,ZEUS

x = 0.00003 - 0.00007 (i = 9)

0.00013-0.0002 (8)

0.00035 (7)

0.0005 - 0.0008 (6)

0.001 (5)

0.002 (4)

0.003 (3)

0.005 - 0.006 (2)

0.012 (1)

0.03 (0)

Even though W2� m2

c for all data:At small-x (small Q2): gross overestimateIt does better at larger x (larger Q2)

[Gluck,Reya,Stratmann 94]

It never reduces to the exact (FFNS) result(not even at very large Q2):

dropped terms (∝ m2

Q2 ) are always relevant

The VFNS should not be used for global analyses!! (this is well-known since a long time)


Relevance of the VFNSVFNS reliable for large invariant mass of the produced system: W2

th�m2

⇒ non-relativistic (β = |~p|E . 0.9) threshold effects supressed [Gluck,Reya,PJD 08]

For charm production in neutral-current DIS: Wthmc

= 2⇒ VFNS fails

For the previous example, Higgs-boson production in bb fusion:Wthmb

= 2mb+mHmb

' mHmb� 1⇒ VFNS should work

Note that we can generate VFNS PDFs from our FFNS PDFs (3-flavor input)

Input determined using DIS data and the FFNS!!

This combines the virtues of both FFNS + VFNS schemes

Typical scheme-choice uncertainties? Example, W production at LHC:

σNLO(pp→W++W−+X) =

{186.5±4.9pdf

+4.8−5.5 |scale nb (VFNS)

192.7±4.7pdf+3.8−4.8 |scale nb (FFNS)

VFNS sufficiently accurate (≈ 10%) for LHC and Tevatron energies.


General-mass VFNS’sPhenomenological models for HQ contributions in inclusive DIS; idea:

Interpolation between FFNS and VFNS

Constructed (as the VFNS) over the FFNS: no new information (e.g. no complete NNLO)

Often goes something like: FGM ≡ FFF +FZM−Fmodel with:Fmod→ FFF for Q2� m2

In the intermediate region there is a lot of “freedom” Fmod→ FZM for Q2 ' m2

[Thorne 10]

... and correspondingly many implementations:

ACOT [Aivazis,Collins,Olness,Tung] + variationsBMSN [Buza,Matiounine,Smith,van Neerven]

CSN [Chuvakin,Smith,van Neerven]

RT [Roberts,Thorne] + variationsFONNL [Forte,Laenen,Nason,Rojo]

(Although some of them are known “not to work” properly)

Scheme choices affect the PDFs and in turn the predictions for physical observables


Plausibility of the GM-VFNS’sIn GM-VFNS’s, DIS mass dependences are somewhat absorbed into the PDFs:

Process-dependent PDFs? What happened with universality?

GM-VFNS’s are unnecesary for HERA (FFNS) and for Tevatron or LHC (FF+VF):What is the advantage of interpolation models?

My opinion (other authors differ):We should not try to model HQ contributions, but stick toschemes unequivocally defined on solid theoretical grounds

Anyway, arguing about which is the best scheme is rather superfluous:How do the differences compare with the experimental errors?

We can compare Fh,FFNS−Fh,BMSN

with ∆Ftot2 [Alekhin,Blumlein,Klein,Moch 10]

⇒ generally effects are smaller(but in some regions in the limit)

∆F2

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

10 102

Q2 (GeV2)

x=0.00013

c-quark

b-quark

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

10 102

Q2 (GeV2)

x=0.0032

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

10 102

Q2 (GeV2)

x=0.032


Present HQ treatments in DIS

Traditionally the most “popular choice” for global fits was the VFNS,with the exception of the GRV group, which used the FFNS already for GRV95

This changed after the release of CTEQ6.5 (2007), where a GM-VFNS was usedand the effects of HQ masses in the predictions at hadron colliders were“re-discovered”: today their importance is generally recognized

Current choices of the (main) PDF groups are:

CTEQ: ACOT-like

MSTW and HERAPDF: TR-like

NNPDF: VFNS (switching to FONLL)

ABKM: both FFNS and BMSN

(G)JR: FFNS and VFNS (generated from the FFNS)

The experimental analyses use the FFNS (exclusive calculations needed)


Weak gauge boson production rates

0

5

10

15

20

25

30

0.6 0.8 1 1.2 1.4 1.6 1.8 2

σ (n

b)

√s (TeV)−

W+ + W-

Z0

NNLO NLO Alekhin NNLOAlekhin NLOUA1 UA2 D0 CDF

0

5

10

15

20

25

30

0.6 0.8 1 1.2 1.4 1.6 1.8 2

σ (n

b)

√s (TeV)−

W+ + W-

Z0

NNLO typically larger but stable; scale uncertainty greatly (%4) reduced

Our NNLO expectations for LHC (≈ 3% accuracy):

σ(pp→W++W−+X) = 190.2±5.6pdf+1.6−1.2|scale nb

σ(pp→ Z0 +X) = 55.7±1.5pdf+0.6−0.3|scale nb


NNLO benchmarks for W and Z

0.500 TeV 0.546 TeV 0.630 TeV 1.8 TeV 1.96 TeV

NNLO

ABM10

JR

HERAPDF

MSTW08

UA1

UA2

PHENIX W +

PHENIX W -

CDF

D0

W + + W

-

W + + W

-

Z 0

Z 0

σ(V

) /

nb

(a)

7 TeV 10 TeV 14 TeV

NNLO

ABM10

JR

HERAPDF

MSTW08

ATLAS

CMS

W + + W

-

W +

W -

Z 0

σ(V

) /

nb

(b)

Results from different groups agree within experimental uncertainty

Considering results from different groups accuracy better than ≈ 10% at LHC

A first inventigation points to differences in light-sea distributions


Higgs boson production at LHC

0

10

20

30

40

50

60

70

100 150 200 250 300

σ pp

→ H

X (p

b)

MH (GeV)

NNLO NNLO NLO

0

10

20

30

40

50

60

70

100 150 200 250 300

σ pp

→ H

X (p

b)

MH (GeV)

(NLO pdfs)

gluon fusion √s = 14 TeV−

NNLO rather (20%) larger than NLO but total uncertainty bands overlap

Not very dependent on PDF details. Our total errors at NNLO less than 10%


Higgs boson production at Tevatron

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

100 150 200 250 300

σ pp- →

H X

(pb)

MH (GeV)

NNLO NLO

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

100 150 200 250 300

σ pp- →

H X

(pb)

MH (GeV)

gluon fusion √s = 1.96 TeV−

Qualitatively similar features than at LHC but larger uncertainty bands

Briefly speaking uncertainties double at Tevatron (and also double at NLO)


Comparison of parton luminositiesDominant gluon fusion ∝ α2

s , and quadratic in the gluon (anticorrelated)

Obtained αs(M2Z) about 4(3)% smaller for JR(ABKM09) than for MSTW08

0.6

0.8

1

1.2

1.4

1.6

1.8

10-2

10-1

NNLO, Q2 = 4 GeV

2

ABKM09

JR

MSTW08

HERAPDF

x

xg(x,Q

2)/xg(x,Q

2) A

BKM

(a)0.6

0.8

1

1.2

1.4

1.6

1.8

10-2

10-1

NNLO, Q2 = 25600 GeV

2

ABKM09

JR

MSTW08

HERAPDF

x

xg(x,Q

2)/xg(x,Q

2) A

BKM

(b)

Differences of about 5% for < x >=√

x1x2 =MH√

S≈ 10−2 relevant for LHC

(For Tevatron 10-20% at < x >≈ 10−1)Jefferson Lab Theory Seminar 39/41

NNLO benchmarks for Higgs production

7 TeV 10 TeV 14 TeV

NNLO

ABM10

JR

HERAPDF

MSTW08

MH

120 GeV

150 GeV

180 GeV

σ(H

0)

/ pb

Differences due to αs(M2Z) and gluon distributions, largely understood

Considering the different NNLO results ≈ 10−20% accuracy at LHCJefferson Lab Theory Seminar 40/41

Summary and conclusions

Dynamical LO and NLO PDFs updated: Compatible with GRV98

Analyses extended: new data, NNLO, errors ...

Dynamical approach: more predictive and smaller uncertainties

Positive distributions and cross-sections (FL) in agreement with all data

Strangeness asymmetry precisely determined: small and positive

FFNS reliable: no need for heavy-quark distributions!

Effective (VFNS) “heavy”-quark distributions practical for hadron colliders

Total accuracy at LHC: ≈ 10% for gauge-boson production rates≈ 10−20% for Higgs production


dynamical parton distribution functions...dynamical vs standard: gluon 0.1 1 10 100 10 xg(x,q 2) x 2...

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