[PPT] - Topics related to MSTW PDFs Robert Thorne September 26th, 2012 PowerPoint Presentation

SLIDE 1

Topics related to MSTW PDFs

Robert Thorne September 26th, 2012 University College London IPPP Research Associate Together with Alan Martin, James Stirling, Graeme Watt and Arnold Mathijssen and Ben Watt

PDF4LHC IPPP – September 2012

SLIDE 2

Variety of topics - related in various ways.

Brief reminder of results from Monte Carlo approach using MSTW PDFs from

JHEP 1208 (2012) 052 (G. Watt and RT).

Some investigations using a 3-flavour FFNS fit - (RT to be in PRD).
Comparison of MSTW PDFs with LHC data and implications.
Investigation of parameterisation extension dependence.

Related to deuterium

corrections. Implication for LHC data.

PDF4LHC IPPP – September 2012 1

SLIDE 3

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

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

Up valence distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

x

5

10

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

Down valence distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

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

Study supported correctness

f

“dynamic tolerance” approach. Easiest in Hessian study with eigenvectors. However, can generate “random” PDF sets directly from parameters and variation from eigenvectors.

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

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

Up antiquark distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

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

Down antiquark distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

ai(Sk)=a0

i +n j=1eij

±t±

j

|Rjk|

(k = 1, . . . , Npdf). Or from eigenvectors directly (see LHCb study and De Lorenzi thesis). Far quicker.

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

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

Strange quark distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

2

GeV

4

= 10

2

Gluon distribution at Q

MSTW 2008 NLO (68% C.L.) Random params. (40) Random params. (40) Random PDFs (1000)

x

5

10

4

10

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

F( Sk)=F(S0) +

j
F(S±

j )−F(S0)

|Rjk|

Use in reweighting studies as NNPDF.

PDF4LHC IPPP – September 2012 2

SLIDE 4

Speed of convergence of prediction for Z cross section.

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.94 0.96 0.98 1 1.02 1.04 1.06

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross section at the LHC ( NLO Z

pdf

Same random numbers for each value of N

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.94 0.96 0.98 1 1.02 1.04 1.06

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross section at the LHC ( NLO Z

pdf

Different random numbers for each value of N

Left, add a new random set to existing ones sequentially. Right, increasing numbers

f independent random sets.

Very good with 40 sets. Excellent with 100 sets.

PDF4LHC IPPP – September 2012 3

SLIDE 5

Speed of convergence of prediction for W +/W − cross section ratio.

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.97 0.98 0.99 1 1.01 1.02 1.03

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross-section ratio at the LHC (

/W

+

NLO W

pdf

Same random numbers for each value of N

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.97 0.98 0.99 1 1.01 1.02 1.03

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross-section ratio at the LHC (

/W

+

NLO W

pdf

Different random numbers for each value of N

Left, add a new random set to existing ones sequentially. Right, increasing numbers

f independent random sets.

Very good with 40 sets. Excellent with 100 sets.

PDF4LHC IPPP – September 2012 4

SLIDE 6

Speed of convergence of prediction for t¯ t cross section.

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross section at the LHC ( t NLO t

pdf

Same random numbers for each value of N

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 7 TeV) s cross section at the LHC ( t NLO t

pdf

Different random numbers for each value of N

Left, add a new random set to existing ones sequentially. Right, increasing numbers

f independent random sets.

Very good with 40 sets. Excellent with 100 sets.

PDF4LHC IPPP – September 2012 5

SLIDE 7

Speed of convergence of prediction for H cross section.

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 120 GeV

H

= 7 TeV) for M s H at the LHC ( → NLO gg

pdf

Same random numbers for each value of N

pdf

Number of random predictions, N 10

2

10

3

10 Ratio to best-fit prediction 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

MSTW 2008 NLO PDFs (68% C.L.) predictions

pdf

Average and s.d. over N

= 120 GeV

H

= 7 TeV) for M s H at the LHC ( → NLO gg

pdf

Different random numbers for each value of N

Left, add a new random set to existing ones sequentially. Right, increasing numbers

f independent random sets.

Very good with 40 sets. Excellent with 100 sets.

PDF4LHC IPPP – September 2012 6

SLIDE 8

Can combine different PDF sets, e.g. comparison to PDF4LHC prescription. Smaller uncertainty and shifted central value if disagreement between individual

predictions. (Plots by G. Watt at http://mstwpdf.hepforge.org/random/).

PDF4LHC IPPP – September 2012 7

SLIDE 9

0.1 0.2 0.3 1 2 3 4 5 6 7 8 9

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 GMVFNSopt ZMVFNS FFNS

x=0.0001 Q2 Fc

2(x,Q2)

0.05 0.1 0.15 0.2 1 2 3 4 5 6 7 8 9

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 GMVFNSopt ZMVFNS FFNS

x=0.001 Q2 Fc

2(x,Q2)

Results using a FFNS Performed a fit to DIS

nly

data using the FFNS scheme. (At NLO since NNLO still requires potentially significant approximations). Do not include Drell-Yan or Tevatron jet data as FFNS calculations do not exist. As seen at higher Q2 charm structure function for FFNS always lower than any GM-VFNS. Fit a few tens of units worse than MSTW08 to same data (even without refitting). Slightly better for F c

2(x, Q2),

but flatter in Q2 for x ∼ 0.01 for inclusive structure function.

PDF4LHC IPPP – September 2012 8

SLIDE 10

0.9 0.95 1 1.05 1.1 10

5

10

4

10

3

10

2

10

1

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 ZMVFNS GMVFNSopt FFNS

GMVFNSa/2008 at NLO for g(x,Q2)

0.9 0.95 1 1.05 1.1 10

5

10

4

10

3

10

2

10

1

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 ZMVFNS GMVFNSopt FFNS

GMVFNSa/2008 at NLO for u(x,Q2)

PDFs evolved up to Q2 = 10, 000GeV2 (using variable flavour evolution for consistent comparison) different in form to MSTW08 and GM-VFNS variants. αS(M 2

Z) = 0.1187, a bit lower than

MSTW NLO value of 0.1202. PDFs do not automatically fit Tevatron jet data well at all, and are not good for CDF Z rapidity data.

PDF4LHC IPPP – September 2012 9

SLIDE 11

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ratio to MSTW 2008 NLO (90% C.L.)

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

2

GeV

4

= 10

2

Gluon distribution at Q

No Tevatron jets Fit only Run I jets II jets ∅ Fit CDFII(kT) + D /2

JET T

= p

F

µ =

R

µ Same with II jets ∅ Fit CDFII(Midpoint) + D II jets ∅ Fit Run I + CDFII(kT) + D

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ratio to MSTW 2008 NLO (90% C.L.)

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

In contrast in MSTW2008 fit central gluon hardly changed if Tevatron jet data left

ut, and only slight further rearrangement of quark flavours if Drell-Yan data left out

(actually improves CDF rapidity data). Main effect loss of tight constraint on αS(M 2

Z). Similar results from various other

groups. At NLO see qualitative effect from using FFNS as opposed to any GM-VFNS.

PDF4LHC IPPP – September 2012 10

SLIDE 12

Comparison to LHC data. Start with ATLAS jets. Use APPLGrid or FastNLO at NLO (Ben Watt) and correlated errors treated as in the formula, χ2 =

Npts.

i=1

ˆ Di − Ti σuncorr.

i

2 +

Ncorr.

k=1

r2

k,

where ˆ Di ≡ Di − Ncorr.

k=1 rk σcorr. k,i Di are the data points allowed to shift by the

systematic errors in order to give the best fit, and σcorr.

k,i

is a fractional uncertainty. Normalisation is treated as the other correlated uncertainties. MSTW fit very good (χ2 per point below left ), though numbers lower for inclusive

data. Always close to, if not best, particularly for R = 0.6. Not huge variation in

PDFs though.

Scale pT/2 pT 2pT Inclusive (R=0.4) 0.752 0.773 0.703 Inclusive (R=0.6) 0.845 0.790 0.721 Dijet (R=0.4) 2.53 2.24 2.20 Dijet (R=0.6) 2.44 2.04 1.74 |rk| < 1 1 < |rk| < 2 2 < |rk| < 3 3 < |rk| < 4 Inclusive (R=0.4) 85 2 1 Inclusive (R=0.6) 87 1 Dijet (R=0.4) 82 6 Dijet (R=0.6) 74 12 2

PDF4LHC IPPP – September 2012 11

SLIDE 13

Can see how fit varies across eigenvectors. Clearly no pull with present data. (Eigenvector χ2 variation lower than PDF variation.)

0.01
0.005

0.005 0.01 0.015 5 10 15 20 Χ2 per point Difference from Central (R=0.4) Χ2 per point for ATLAS Inclusive Jets

0.006
0.004
0.002

0.002 0.004 0.006 0.008 0.01 5 10 15 20 Χ2 per point Difference from Central (R=0.6) MSTW Eigenvector Number

PDF4LHC IPPP – September 2012 12

SLIDE 14

Can see effect of data on the gluon using reweighting technique, R = 0.6 (R = 0.4 similar). Clearly little pull with present data.

0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x g(x) at q2=10000 (GeV)2 Before Reweighting (Npdf=1000) After Reweighting (Neff=774)

PDF4LHC IPPP – September 2012 13

SLIDE 15

Comparison of MSTW2008 to total W, Z excellent.

PDF4LHC IPPP – September 2012 14

SLIDE 16

Also pretty good for inclusive distributions. Except some problems with asymmetry.

|

Z

|y 0.5 1 1.5 2 2.5 3 3.5 Theory/Data 0.9 1 1.1 0.5 1 1.5 2 2.5 3 3.5 | [pb]

Z

/d|y σ d 20 40 60 80 100 120 140 160

= 7 TeV) s Data 2010 ( MSTW08 HERAPDF1.5 ABKM09 JR09

1

L dt = 33-36 pb

∫

l

+

l → Z

Uncorr. uncertainty

Total uncertainty

ATLAS |

l

η | 0.5 1 1.5 2 2.5 Theory/Data 0.9 1 1.1 0.5 1 1.5 2 2.5 | [pb]

l

η /d| σ d 300 400 500 600 700 800

= 7 TeV) s Data 2010 ( MSTW08 HERAPDF1.5 ABKM09 JR09

1

L dt = 33-36 pb

∫

l

ν

+

l →

+

W

Uncorr. uncertainty

Total uncertainty

ATLAS |

l

η | 0.5 1 1.5 2 2.5 Theory/Data 0.9 1 1.1 0.5 1 1.5 2 2.5 | [pb]

l

η /d| σ d 100 200 300 400 500 600

= 7 TeV) s Data 2010 ( MSTW08 HERAPDF1.5 ABKM09 JR09

1

L dt = 33-36 pb

∫

l

ν

l

→

W
Uncorr. uncertainty

Total uncertainty

ATLAS |

l

η | 0.5 1 1.5 2 2.5

l

A 0.1 0.15 0.2 0.25 0.3 0.35

= 7 TeV) s Data 2010 ( MSTW08 HERAPDF1.5 ABKM09 JR09

1

L dt = 33-36 pb

∫

Stat. uncertainty

Total uncertainty

ATLAS

PDF4LHC IPPP – September 2012 15

SLIDE 17

Similar for CMS data (will return to this later), though depends on pT cut. Generally very good for LHCb.

µ

η 1 2 3 4

W

R 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x x x x

= 7 TeV s LHCb,

stat

Data MSTW08

tot

Data

x x x x

ABKM09 JR09 NNPDF21 HERA15 CTEQ6M (NLO)

> 20 GeV/c

µ T

p PDF4LHC IPPP – September 2012 16

SLIDE 18

Asymmetry used by Graeme Watt in reweighting, and moves uV − dV up around x = 0.01 - where parameterisation perhaps underestimates uncertainty. (ATLAS left, CMS pT > 25GeV right).

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

distribution at Q

v

d

v

u

MSTW08 (68% C.L.) = 1000)

pdf

MSTW08 (N = 264)

eff

MSTW08 (N

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

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

distribution at Q

v

d

v

u

MSTW08 (68% C.L.) = 1000)

pdf

MSTW08 (N = 485)

eff

MSTW08 (N

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

PDF4LHC IPPP – September 2012 17

SLIDE 19

Calculate χ2/N = 60/30 for ATLAS W, Z data again at NLO using APPLGrid. Not best, but fairly close to any other set except CT10 which is best. Again look at eigenvectors (Ben Watt). Fit improves markedly in one direction with eigenvector 9, gluon, which alters common shape and normalisation, and 14 and 18 which alter dV and uV , i.e. affect asymmetry. Not much variation in strange normalisation.

0.3
0.2
0.1

0.1 0.2 0.3 0.4 5 10 15 20 Χ2 per point Deviation From Central Value Eigenvector Number MSTW Eigenvectors for WZ Fit

PDF4LHC IPPP – September 2012 18

SLIDE 20

Can see effect of total rapidity data using reweighting. Fairly small effective number

f PDFs = 190.

Slightly smaller effect on uV − dV than asymmetry alone.

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x (uv-dv)(x) at q2=10000 (GeV)2 for W/Z Rapidity Distribution Before Reweighting (Npdf=1000) After Reweighting (Neff=190) PDF4LHC IPPP – September 2012 19

SLIDE 21

Can also see the effect on the gluon. Slight raise near x = 0.01 preferred. Improves

verall shape of rapidity distribution. After reweighting χ2 = 48/60.

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x g(x) at q2=10000 (GeV)2 Before Reweighting (Npdf=1000) After Reweighting (Neff=190) PDF4LHC IPPP – September 2012 20

SLIDE 22

Investigation of Parameterisation Issues - with A. Mathijssen. In the light of Monte Carlo studies investigate parameterisation dependence, initially concentrating on valence quarks. Decide to use Chebyshev polynomials (looked at other possibilities) xf(x, Q2

0) = A(1 − x)ηxδ(1 +

n

anTn(y)) i.e. keep high and low x limits. Choose y = 1 − 2√x.

0.001 0.01 0.1 1 x 0.5 0.0 0.5 1.0

Tiyx 1 2 x

0.001 0.01 0.1 1 x 0.5 0.0 0.5 1.0

Tiyx 1 2 x

0.001 0.01 0.1 1 x 0.5 0.0 0.5 1.0

Tiyx 1 2 x0.25

0.001 0.01 0.1 1 x 0.5 0.0 0.5 1.0

Tiyx cosΠ x

Same choice as in Pumplin study. Slightly different to Glazov, Moch and Radescu.

PDF4LHC IPPP – September 2012 21

SLIDE 23

Fit to 1000 pseudodata points for valence quark generated from very large order polynomial with smoothness constraints applied. Distributed evenly in ln(1/x) with percentage error constant down to x = 0.00001. Percent deviation for full function. Order increase across the visible spectrum (i.e. dark blue to red). 2 terms in polynomial mainly ≤ 2% deviation. 4 terms in polynomial ≤ 0.5 − 1% deviation except high x.

0.001 0.01 0.1 1 0.001 0.01 0.1 0.001 0.01 0.1 1 0.001 0.01 0.1

After on average ∼ 6 polynomials start fitting noise, i.e. χ2 lower than real function. Conclude 4 parameters fine.

PDF4LHC IPPP – September 2012 22

SLIDE 24

Deviations from true function for sea-like distribution.

0.001 0.01 0.1 1 x 0.001 0.01 0.1 1 Relative difference 0.001 0.01 0.1 1 x 0.001 0.01 0.1 1 Relative difference

A bit more difficult in this case. 4 terms in polynomial ≤ 2% deviation except high x. Note uncertainty in input MSTW2008 sea is ∼ 5 − 6% at best.

PDF4LHC IPPP – September 2012 23

SLIDE 25

Also to pseudodata for valence quark generated only between x = 0.01 and x = 0.7. Typically slightly more deviation again, especially with only two terms.

0.001 0.005 0.010 0.050 0.100 0.500 1.000 0.001 0.01 0.1 0.001 0.005 0.010 0.050 0.100 0.500 1.000 0.001 0.01 0.1

Look at χ2 distribution with increasing terms in polynomial.

0.02 0.05 0.10 0.20 0.50 1.00 0.001 0.1 10 0.02 0.05 0.10 0.20 0.50 1.00 0.01 0.1 1 10 0.02 0.05 0.10 0.20 0.50 1.00 104 0.01 1 0.02 0.05 0.10 0.20 0.50 1.00 105 0.001 0.1 10

Very good fits with 4 parameters. More tends to give over-fitting and peculiarities

utside of range of x fit.

PDF4LHC IPPP – September 2012 24

SLIDE 26

In this case see some variation with number of pseudodata points fit (not so clear in

ther cases), e.g. result for 100 points.

0.001 0.005 0.010 0.050 0.100 0.500 1.000 0.001 0.01 0.1

Lower no. points allows better fit with fewer parameters, but best possible fit less good match to true function, ∼ 1% deviations. General result that ∼ 4 terms is optimal unchanged.

PDF4LHC IPPP – September 2012 25

SLIDE 27

4 3 2 1 Log10,x 0.2 0.4 0.6 0.8 1.0 1.2

c4m05 Parton distributions at Q2 10 GeV2

4 3 2 1 Log10,x 0.2 0.4 0.6 0.8 1.0 1.2

c4m05 Parton distributions at Q2 104 GeV2

4 3 2 1 Log10,x 0.4 0.2 0.2 0.4 0.6

Fractional difference and Fractional uncertainty in xuv at Q2 1 GeV2

4 3 2 1 Log10,x 0.2 0.1 0.1 0.2

Fractional difference and Fractional uncertainty in xuv at Q2 104 GeV2

6 5 4 3 2 1 Log10,x 0.6 0.4 0.2 0.2 0.4 0.6

Fractional difference and Fractional uncertainty in xdv at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.3 0.2 0.1 0.1 0.2 0.3 0.4

Fractional difference and Fractional uncertainty in xdv at Q2 104 GeV2

6 5 4 3 2 1 Log10,x 0.3 0.2 0.1 0.1 0.2 0.3

Fractional difference and Fractional uncertainty in xS at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.10 0.05 0.05 0.10

Fractional difference and Fractional uncertainty in xS at Q2 104 GeV2

Fits to same data as MSTW2008 Just applying to valence quarks, 4 new parameters, ∆χ2 = −4. Significant change in uV (x), x ≤ 0.03 similar to earlier conclusion adding x2 term to parameterisation. Applying also to sea and gluon, 8 new parameters, ∆χ2 = −29 (mainly BCDMS and Drell Yan data). Still change significant

nly

for uV (x), x ≤ 0.03. Fits with requirement for fitting lepton asymmetry at LHC. − − − − valence, − − − − valence + sea

PDF4LHC IPPP – September 2012 26

SLIDE 28

6 5 4 3 2 1 Log10,x 3 2 1 1 2 3

Fractional difference and Fractional uncertainty in xg at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.10 0.05 0.05 0.10

Fractional difference and Fractional uncertainty in xg at Q2 104 GeV2

6 5 4 3 2 1 Log10,x 0.015 0.010 0.005 0.005 0.010

Absolute difference and uncertainty in xsv at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.010 0.005 0.005 0.010

Absolute difference and uncertainty in xsv at Q2 104 GeV2

6 5 4 3 2 1 Log10,x 1.0 0.5 0.5 1.0

Fractional difference and Fractional uncertainty in xssbar at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.15 0.10 0.05 0.05 0.10 0.15

Fractional difference and Fractional uncertainty in xssbarat Q2 104 GeV2

6 5 4 3 2 1 Log10,x 0.10 0.05 0.05 0.10

Absolute difference and uncertainty in x at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.06 0.04 0.02 0.02 0.04 0.06

Absolute difference and uncertainty in x at Q2 104 GeV2

Little change in other PDFs. Already 7 free parameters in the gluon. Sticking with two terms in Chebyshev polynomial leads to no change. Take this a default - MSTW2008Cp (preliminary), 6 new parameters - 34 in total. Prelim. study of uncertainties with 23 eigenvectors (one extra for valence quarks and sea). Little change except valence for x ≤ 0.03, where significant increase.

PDF4LHC IPPP – September 2012 27

SLIDE 29

Given previous relationship between Tevatron asymmetry and deuterium corrections where partial success was noted revisit with extended parameterisation. Default for MSTW some shadowing for x < 0.01. Previously big improvement in fit, but “unusual” corrections. Now improvement again but much more stable, and sensible for deuterium corrections. (No shadowing favoured though.)

PDF4LHC IPPP – September 2012 28

SLIDE 30

4 3 2 1 Log10,x 0.6 0.4 0.2 0.2 0.4 0.6

Fractional difference and Fractional uncertainty in xuv at Q2 1 GeV2

4 3 2 1 Log10,x 0.2 0.1 0.1 0.2 0.3

Fractional difference and Fractional uncertainty in xuv at Q2 104 GeV2

Now also get variation in dV (x) for higher x due to deuterium correction (seen before) and x ≤ 0.03 due to parameterization and corrections.

4 3 2 1 Log10,x 0.5 0.5 1.0

Fractional difference and Fractional uncertainty in xdv at Q2 1 GeV2

4 3 2 1 Log10,x 0.3 0.2 0.1 0.1 0.2 0.3

Fractional difference and Fractional uncertainty in xdv at Q2 104 GeV2

Prelim. MSTW2008Cpdeut PDFs.

Fit to ATLAS W, Z rapidity data at NLO improves to 49/30 for MSTWCp and 46/30 for MSTWCpeut.

6 5 4 3 2 1 Log10,x 0.3 0.2 0.1 0.1 0.2 0.3

Fractional difference and Fractional uncertainty in xS at Q2 1 GeV2

6 5 4 3 2 1 Log10,x 0.10 0.05 0.05 0.10

Fractional difference and Fractional uncertainty in xS at Q2 104 GeV2

− − − − CP, − − − − CPdeut

PDF4LHC IPPP – September 2012 29

SLIDE 31

Preliminary uncertainty sets have 23 eigenvectors (20 in MSTW2008). Main effect in uncertainty an increase in dV (x, Q2) due to deuterium correction uncertainties, and minor valence uncertainty increase from extra parameter. Shown is change in central value and uncertainty for uV (x) − dV (x) at Q2 = 10, 000 GeV2. Biggest effect at lower x than probed at the LHC (yet).

PDF4LHC IPPP – September 2012 30

SLIDE 32

1 2 3 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 35

lepton asymmetry, variable pTlep(min) MSTW2008 MSTW2008Cp MSTW2008Cpdeut

20 10 30

A+-(ylep) ylep

LHC 7 TeV MSTW2008 NLO

Increases lepton asymmetry, but very preferentially for high pT cut. (Curves made here with LO calculations). Most

f

the effect already

btained for parameterisation

extension, but some from deuterium study.

PDF4LHC IPPP – September 2012 31

SLIDE 33

|

l

η Lepton pseudorapidity, | 0.5 1 1.5 2 2.5 3 Lepton charge asymmetry 0.05 0.1 0.15 0.2 0.25 0.3

1

CMS (l = e), L = 840 pb

NLO PDFs (with NLO K-factors) /11 = 5.34

2

χ MSTW08 (68% C.L.), /11 = 1.53

2

χ MSTW08Cp (prel.), /11 = 0.95

2

χ MSTW08Cpdeut (prel.),

|

l

η Lepton pseudorapidity, | 0.5 1 1.5 2 2.5 3 Lepton charge asymmetry 0.05 0.1 0.15 0.2 0.25 0.3 > 35 GeV

l T

= 7 TeV) with p s at the LHC ( ν

±

l →

±

W

Prediction for pT > 35GeV CMS asymmetry data using MCFM (G. Watt). Note no change to data fit, just parameterisation and some from deuterium corrections. Main deuterium effect absence of shadowing in default fit.

PDF4LHC IPPP – September 2012 32

SLIDE 34

Can try reweighting approach and dependence on eigenvectors using modified MSTW2008 sets (B. Watt). No significant changes in fits to jet data at all. For W, Z rapidity data eigenvectors preferred mainly alter gluon shape and fine details

f uV and dV still. Small preference for eigenvectors with higher strange.

Effective number of sets now much higher, ∼ 500 out of 1000. After reweighting get χ2 = 39.5/30 and χ2 = 38.5/30. No noticeable pull on strange.

PDF4LHC IPPP – September 2012 33

SLIDE 35

Big change in high pT cut asymmetry, but very specifically sensitive to uV (x, Q2) − dV (x, Q2). What about other quantities? Other PDFs changed little. αS free but tiny change. Expect little variation. The % change in the cross sections (MH = 120GeV). MSTWCp MSTWCpdeut W Tev +0.6 +0.1 Z Tev +0.8 +0.7 W + LHC (7TeV) +0.7 +0.3 W − LHC (7TeV)

0.7
0.4

Z LHC (7TeV) +0.0

0.1

W + LHC (14TeV) +0.6 +0.3 W − LHC (14TeV)

0.6
0.5

Z LHC (14TeV) +0.1

0.1

Higgs TeV

0.5
1.8

Higgs LHC (7TeV) +0.2

0.1

Higgs LHC (14TeV) +0.1 +0.1 Extreme stability in total cross sections, all far inside uncertainties. Even σ(W +)/σ(W −) barely more than 1%.

PDF4LHC IPPP – September 2012 34

SLIDE 36

Seen clearly on plot. Note – uncertainty on σ¯

tt ∼

5 − 6% from PDFs + αS(M 2

Z)

at 7 TeV.

PDF4LHC IPPP – September 2012 35

SLIDE 37

Conclusions Monte Carlo approach to using PDFs based on best fit and eigenvectors is straightforward. Good accuracy obtained with similar number of sets to the case

f eigenvector approaches. Allows different PDFs to be combined just by sampling

random PDFs from each. An NLO fit using a FFNS shows qualitative differences to all GM-VFNS variations and tendency for smaller αS(M 2

Z).

MSTW08 fits current LHC data as well, or better than other sets, with exception of (particularly high-pT) lepton asymmetry. In the main need more data for constraints. Studies of parameterisation dependence suggest ∼ 4 terms in a Chebyshev polynomial about the maximum needed for very high precision. Backs up conclusion that in current MSTW fits the only need for an extended parameterisation is for small-x valence quarks. Automatically improves comparison to LHC lepton asymmetry data. Makes fit with deuterium corrections much more stable, and these lead to further slight improvements. Most cross sections practically unchanged.

PDF4LHC IPPP – September 2012 36

SLIDE 38

Can see effect of data on the gluon using reweighting technique, R = 0.4. Clearly little pull with present data.

0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x g(x) at q2=10000 (GeV)2 Before Reweighting (Npdf=1000) After Reweighting (Neff=616)

PDF4LHC IPPP – September 2012 37

SLIDE 39

0.9 0.95 1 1.05 1.1 10

5

10

4

10

3

10

2

10

1

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 ZMVFNS GMVFNSopt FFNS

x GMVFNSa/2008 at NLO for g(x,Q2)

0.9 0.95 1 1.05 1.1 10

5

10

4

10

3

10

2

10

1

MSTW08 GMVFNS1 GMVFNS2 GMVFNS3 GMVFNS4 GMVFNS5 GMVFNS6 ZMVFNS GMVFNSopt FFNS

x GMVFNSa/2008 at NLO for u(x,Q2)

PDF4LHC IPPP – September 2012 38

SLIDE 40

Contributions to χ2.

0.001 0.01 0.1 1 x 0.01 1 100 1 0.001 0.01 0.1 1 x 104 0.01 1 2 0.001 0.01 0.1 1 x 104 0.001 0.01 0.1 1 10 3 0.001 0.01 0.1 1 x 104 0.01 1 4 0.001 0.01 0.1 1 x 105 0.001 0.1 10 5 0.001 0.01 0.1 1 x 104 0.01 1 6

After 5 − 6 polynomials start fitting noise, i.e. χ2 lower than real function. Conclude 4 parameters fine. (Note first 2 just re-expression of standard MSTW parameterisation.)

PDF4LHC IPPP – September 2012 39

SLIDE 41

Can try reweighting approach and dependence on eigenvectors using modified MSTW2008 sets (B. Watt). No significant changes in fits to jet data. For W, Z rapidity data eigenvectors preferred mainly alter gluon shape and details of uV and dV still. Small preference for eigenvectors with higher strange.

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25 0.3 5 10 15 20 Χ2 per point Deviation From Central Value Eigenvector Number MSTW Eigenvectors for WZ Fit (proj)

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 0.25 5 10 15 20 Χ2 per point Deviation From Central Value Eigenvector Number MSTW Eigenvectors for WZ Fit (projdeut)

PDF4LHC IPPP – September 2012 40

SLIDE 42

Effective number of sets now much higher. After reweighting get χ2 = 39.5/30 and χ2 = 38.5/30. No noticeable pull on strange.

0.85 0.9 0.95 1 1.05 1.1 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x g(x) at q2=10000 (GeV)2 Before Reweighting (Npdf=1000) After Reweighting (Neff=422) 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.0001 0.001 0.01 0.1 Ratio to MSTW Central Value x g(x) at q2=10000 (GeV)2 Before Reweighting (Npdf=1000) After Reweighting (Neff=538)

PDF4LHC IPPP – September 2012 41

SLIDE 43

Strange Quark Recently suggested by ATLAS study that strange quark fraction at x ∼ 0.01 much larger than generally suggested - though there is quite a lot of variation.

s

r

0.2

0.2 0.4 0.6 0.8 1 1.2 1.4

ABKM09 NNPDF2.1 MSTW08 CT10 (NLO) total uncertainty experimental uncertainty

ATLAS

, x=0.023

2

= 1.9 GeV

2

Q s epWZ free

Mostly determined in many fits by dimuon data νµ → µ− + W +, W + + s → c where the charm meson decays to a muon. From CCFR, NuTeV, the latter being more constraining.

PDF4LHC IPPP – September 2012 42

SLIDE 44

x

1

10 0.1 0.2 0.3 0.4 0.5 0.6

y = 0.324 = 88.29 GeV

ν

E

x

1

10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

y = 0.558 = 88.29 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1

y = 0.771 = 88.29 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4

y = 0.324 = 174.29 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

y = 0.558 = 174.29 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

y = 0.771 = 174.29 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y = 0.324 = 247.00 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y = 0.558 = 247.00 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

y = 0.771 = 247.00 GeV

ν

E

2

X) in GeV

µ

+

µ → N

µ

ν ( dxdy σ d

ν

E

N

M

2 F

G π 100 NuTeV

= 13 for 21 DOF

2

χ MSTW 2008 NNLO PDF fit,

1cm

x

1

10 0.1 0.2 0.3 0.4 0.5

y = 0.349 = 77.88 GeV

ν

E

x

1

10 0.1 0.2 0.3 0.4 0.5 0.6 0.7

y = 0.579 = 77.88 GeV

ν

E

x

1

10 0.1 0.2 0.3 0.4 0.5 0.6

y = 0.776 = 77.88 GeV

ν

E

x

1

10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y = 0.349 = 143.74 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y = 0.579 = 143.74 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4

y = 0.776 = 143.74 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4

y = 0.349 = 226.79 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

y = 0.579 = 226.79 GeV

ν

E

x

1

10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

y = 0.776 = 226.79 GeV

ν

E

2

X) in GeV

µ

+

µ → N

µ

ν ( dxdy σ d

ν

E

N

M

2 F

G π 100 NuTeV

= 32 for 19 DOF

2

χ MSTW 2008 NNLO PDF fit,

Where Q2 = 2mpxEν. At x ∼ 0.02 Q2 ∼ 2 − 5GeV2. Lowest x bin usually Q2 = 2 − 3GeV2.

PDF4LHC IPPP – September 2012 43

SLIDE 45

Significant variation in PDFs (ABM similar to MSTW). Maybe partially explained by Q2 cuts (MSTW 2GeV2, NNPDF 3GeV2, CT10 4GeV2). Strange almost unchanged if MSTW cut 5GeV2.

x

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2

= 2 GeV

2

distribution at Q s s+

NLO PDF (68% C.L.) MSTW08 CT10 NNPDF2.1 MSTW08 (no sub.) )

2

/Q

2 c

MSTW08 (1+m

x

3

10

2

10

1

10

Ratio to MSTW 2008 NLO

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Factor of (1 + m2

c/Q2) in NNPDF2.1 lowers MSTW a little - cuts different.

Correction of contribution from initial state charm quarks/subtraction from gluon (σ ∝ s + (1 − y)2¯ c, y = 0.3 − 0.7) to be consistent with acceptance corrections moves MSTW down very slightly (smaller y → smaller charm). Plot by G. Watt.

PDF4LHC IPPP – September 2012 44

SLIDE 46

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

v

u Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

v

d Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

u Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

d Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

s Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

c Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

g Fe

R

x

2

10

1

10 1 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

2

= 20 GeV

2

at Q Nuclear corrections for iron HKN07 NLO (68% C.L.) nDS NLO NUCMOD(x) × nDS NLO RATFE(x)

Requires use of nuclear corrections. Can vary by ∼ 10% at x ∼ 0.01. A little more at low Q2. MSTW allow no penalty variation in nuclear corrections with three parameters (normalisation, low x shape and high x shape).

PDF4LHC IPPP – September 2012 45

SLIDE 47

Try various fits changing strange parameterisation. General form s(x, Q2

0) + ¯

s(x, Q2

0) = A(1 − x)η(1 + ǫx0.5 + γx)xδ,

Q2

0 = 1GeV2.

where δ set equal to light sea. Fix ǫ and γ because the fit finds no improvement if left free. A leads to suppression and η slightly greater than for light sea. Try raising strange at low x by setting A so that s(x, Q2

0) + ¯

s(x, Q2

0) is a third of the

total sea at input at low x. Try 4 variations.

k =1 where k = (s + ¯

s)/(¯ u + ¯ d) - all other parameters fixed. Strange exactly 1/3

f sea at input. ∆χ2 = −10 for ATLAS, W,Z data.
k=1 1p - η free. ∆χ2 = −11 for ATLAS, W,Z data.
k=1 2p - η, γ free. ∆χ2 = −10 for ATLAS, W,Z data.
k=1 3p - η, γ, ǫ free. ∆χ2 = −4 for ATLAS, W,Z data.

PDF4LHC IPPP – September 2012 46

SLIDE 48

0.5 1 1.5 2 10

4

10

3

10

2

10

1

MSTW08 MSTWk=1 1p MSTWk=1 2p MSTWk=1 3p MSTWk=1

Q2 = 2 GeV2 x MSTWmod/2008 at NLO for s(x,Q2)

0.8 0.9 1 1.1 1.2 1.3 10

4

10

3

10

2

10

1

MSTW08 MSTWk=1 1p MSTWk=1 2p MSTWk=1 3p MSTWk=1

x Q2 = 10000 GeV2 MSTWmod/2008 at NLO for s(x,Q2)

k = 1 - ∆χ2 = 1200. NuTeV dimuon χ2 25 times worse. All nuclear data and Drell Yan data (E866 and Tevatron) much worse. k = 1 1p - ∆χ2 = 190. NuTeV dimuon χ2120 worse. Nuclear and Drell Yan data

worse. Nuclear correction modified.

k = 1 2p - ∆χ2 = 55. NuTeV dimuon χ242 worse. Nuclear and Drell Yan data slightly worse. (Similar to CT10 strange) k = 1 3p - ∆χ2 = 43. NuTeV dimuon χ217 worse. Nuclear and Drell Yan data slightly worse. Does not resolve issues. Some pull from ATLAS data. Much more from W +c data (see Stirling and Vryonidou study).

PDF4LHC IPPP – September 2012 47