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Theoretical Uncertainties in Vector Theoretical Uncertainties in Vector Boson Production at the LHC Scott Yost The Citadel Charleston South Carolina Charleston, South Carolina with N.E. Adam, V. Halyo, W.-H. Zhu y (Princeton) PHENO 2009

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SLIDE 1

Theoretical Uncertainties in Vector Theoretical Uncertainties in Vector Boson Production at the LHC

Scott Yost

The Citadel

Charleston South Carolina Charleston, South Carolina

with N.E. Adam, V. Halyo, W.-H. Zhu

PHENO 2009 – Madison, Wisconsin – May 12, 2009

y (Princeton)

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SLIDE 2

W and Z Production at the LHC

Vector Boson Production will be an important process at p p the LHC:

Standard candle for the precision luminosity

measurement (1%).

Precision EW parameter measurements Precision EW parameter measurements Constraints on PDFs via Z/W rapidity. Important for detector calibration.

p

New physics searches: Z’ predicted by various SM

extensions – few TeV range accessible.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 2

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SLIDE 3

Precision Event Generator

An event generator is desired at the 1% precision level. The present best event generators incorporate NLO

QCD ith a parton sho er MC@NLO or POWHEG QCD with a parton shower: MC@NLO or POWHEG.

NNLO QCD is available but not interfaced to a shower: NNLO QCD is available, but not interfaced to a shower:

Vrap (Anastasiou, Dixon, Melnikov, Petriello) and FEWZ (Melnikov, Petriello).

Electroweak corrections cannot be neglected.

HORACE (Carloni Calame) HORACE (Carloni-Calame)

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 3

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SLIDE 4

Theoretical Uncertainty Studies y

We decided to study the state of the art programs to We decided to study the state of the art programs to

determine how well Z production could really be calculated at this time. [Adams, Halyo, Yost: JHEP 05 (2008) 062]

The results can be useful in selecting experimental

cuts to minimize systematic errors as well as in cuts to minimize systematic errors, as well as in identifying the most fruitful course for improving the precision.

The analysis was extended to W production.

[Adams, Halyo, Yost, Zhu: JHEP 09 (2008) 133]

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 4

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SLIDE 5

Theoretical Uncertainty Studies y

These studies focused on three areas:

Electroweak Corrections NNLO QCD Parton Distribution Functions

G

The basic generators used were HERWIG 6.5 and

MC@NLO.

Electroweak corrections were evaluated using Electroweak corrections were evaluated using

PHOTOS and HORACE 3.1.

NNLO QCD was calculated using FEWZ.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 5

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SLIDE 6

Electroweak Effects

Since α αs

2 at LHC energies, NLO QED naively s

g , Q y should enter at a comparable level to NNLO QCD.

But EW corrections are enhanced by big logs

(generically logns/m 2) which increase at high energy: NLO QED and QCD can be comparable. energy: NLO QED and QCD can be comparable.

This especially affects new physics searches (Z’, …) in

the TeV range, where the W and Z begin to look increasingly “massless”.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 6

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SLIDE 7

Electroweak Effects

We calculated the EW effects in HORACE3.1

Event Generator with LO QCD + Shower and

O (α) EW + FSR photon shower.

We also compared PHOTOS (Wąs)

Add-on program that generates photon radiation

from charged final-state particles from charged final-state particles.

What is the best way to incorporate mixed QCD/EW

effects?

PHOTOS can be run with NLO QCD. HORACE cannot, but has more complete EW.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 7

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SLIDE 8

Cut Selections

The comparisons were made for sets of experimental

cuts typical of those that might be used in a Luminosity measurement, or precision W/Z parameter measurements.

We are interested not just in the total cross section,

but also in the detector acceptances for these cuts. Th ti t f t d t t l The error estimates for acceptances and total cross sections can differ greatly. Acceptance = σ(cut)/σ(total) ccep a ce σ(cu )/σ( o a ) σ(total) already includes basic “generator-level” cuts, such as a lower bound on Mll in Z production to th h t d i t d i remove the photon-dominated region.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 8

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SLIDE 9

Cut Selections: EW Calculation

We used the following cuts: g

l l Z q q → → γ /

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2 cot log θ η CUT Mll pTl |ηl | Loose > 40 GeV > 5 GeV < 50 Tight 40 < M < 140 GeV > 20 GeV < 2 Tight 40 < Mll < 140 GeV > 20 GeV < 2

ν

± ± →

→ l W q q '

CUT pTl pTν |ηl| Basic > 25 GeV > 20 GeV < 1 Larger η > 25 GeV > 20 GeV 1 < |ηl | < 2.2 Higher > 25 GeV > 30 GeV < 1

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 9

Higher pTν > 25 GeV > 30 GeV < 1

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SLIDE 10

Electroweak Effects: Z Production

Compare HORACE and PHOTOS in Z Production:

EW correction in σ: 1 – 3%. Difference: 0.2 – 0.4% Recommendation: Use MC@NLO + PHOTOS. Fractional EW Contribution in Z Production

0.0 0.0

%) %)

Fractional EW Contribution in Z Production Cross Section Acceptance Comparison

(%)

0.0 ‐2.0 ‐1.0 ‐2.0 ‐1.0 PHOTOS HORACE

Contribution (% Contribution (% OS - HORACE (

‐0.8 ‐0.4 Cross Section ‐4.0 ‐3.0 ‐4.0 ‐3.0

EW C EW C

Cut: Cut:

se ght se ght se ght PHOTO

‐1.6 ‐1.2 Acceptance

Cut:

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 10 loos tig loos tig loos tig

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SLIDE 11

Electroweak Effects: W Production

Compare HORACE and PHOTOS for W Production: p

Using PHOTOS for W production is not as well motivated:

the W can radiate also. Use HORACE if EW is important.

Fractional EW Contribution in W Production

3 0 4.0 5.0 HORACE W+

Fractional EW Contribution in W Production Cross Section Acceptance

n (%) tion (%)

  • 0.5

0.0 1 0 0.0 1.0 2.0 3.0 PHOTOS W+ HORACE W-

W Contribution EW Contribut

  • 2.5
  • 2.0
  • 1.5
  • 1.0
  • 3.0
  • 2.0
  • 1.0

PHOTOS W-

Cut: Cut:

none basic her η er pTν basic gher η er pTν EW

Note sign difference

  • 3.5
  • 3.0
  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 11 hig highe hig high

difference.

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SLIDE 12

Number of Photons Generated

Comparison of the numbers of photons gnerated by PHOTOS (black) or HORACE (red). [Born level (no photon generation) = blue]

Z Production W+ Production

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 12

Z Production W+ Production

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SLIDE 13

Total Photon PT

Comparison of photon PT in PHOTOS and HORACE:

T

HORACE gives slightly more photon PT .

Z Production W+ Production

Larger scale

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 13

Larger scale

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SLIDE 14

Cut Selections: NNLO Calculation

We used the following cuts: (generator cut: Mll > 40GeV) g (g

ll

)

CUT Mll pTl |ηl |

l l Z q q → → γ / 11.5o – 25.2o

Basic > 40 GeV > 20 GeV < 2 Angle Slice > 40 GeV > 20 GeV 1.5 |ηl | < 2.3 Z Peak 79 < Mll < 104 GeV > 20 GeV < 2 Z Peak 79 Mll 104 GeV 20 GeV 2

ν

± ± →

→ l W q q '

CUT pTl pTν |ηl| Basic > 25 GeV > 20 GeV < 1 Larger η > 25 GeV > 20 GeV 1 < |ηl | < 2.2 Higher > 25 GeV > 30 GeV < 1

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 14

Higher pTν > 25 GeV > 30 GeV < 1

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SLIDE 15

Z: NNLO QCD Contribution

The size of the NNLO correction calculated with two PDFs:

4 5 4 5

Fractional NNLO Contribution in Z Production Cross Section Acceptance

1 2 3 4 MRST 1 2 3 4

ribution (%) tribution (%)

  • 3
  • 2
  • 1

CTEQ

  • 3
  • 2
  • 1

NNLO Contr NNLO Cont

  • 4
  • 3
  • 4
  • 3

basic gle slice Z peak none basic ngle slice Z peak

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 15 ang an

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SLIDE 16

W: NNLO QCD Contribution

The same calculation for W production: p

1 2

Fractional NNLO Contribution in W Production Cross Section Acceptance

  • 3
  • 2
  • 1

W+ MRST W+ CTEQ W- MRST 2

  • 1

1

ribution (%) tribution (%)

  • 7
  • 6
  • 5
  • 4

W- MRST W- CTEQ

  • 5
  • 4
  • 3
  • 2

NNLO Contr NNLO Cont

  • 8
  • 7
  • 6

none basic higher η gher pTν basic higher η gher pTν

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 16 hi h hig

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SLIDE 17

NNLO Dependence on PT Cut: Z p

T

NNLO contribution dependence on lepton PT cuts for Z production

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 17

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SLIDE 18

NNLO Dependence on PT Cut: W+ p

T

NNLO contribution dependence on lepton PT cuts for W+ production

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 18

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SLIDE 19

NNLO Dependence on PT Cut: W- p

T

NNLO contribution dependence on lepton PT cuts for W- production

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 19

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SLIDE 20

NNLO Dependence on η Cut: Z p η

NNLO contribution dependence on lepton η cuts for Z production

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 20

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SLIDE 21

NNLO Dependence on η Cut: W+

NNLO contribution dependence on lepton η cuts for W+ production

p η

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 21

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SLIDE 22

NNLO Dependence on η Cut: W- p η

NNLO contribution dependence on lepton η cuts for W- production

section ance cross s accept

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 22

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SLIDE 23

QCD Scale Dependence p

The QCD calculations depend on two arbitrary scales:

the factorization scale and renormalization scale. These scales are fictitious, and would cancel in a complete all-order calculation. At finite order, they must be all order calculation. At finite order, they must be chosen.

We have chosen these to be MZ or MW in our

l l ti b t d t h k th d d calculations, but need to check the dependence on them.

We varied them by a factor of 2 or ½ to see how the We varied them by a factor of 2 or ½ to see how the

cross-sections and acceptances change with scale.

NNLO calculations reduce scale dependence in the

cross section, but not necessarily in acceptances.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 23

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SLIDE 24

QCD Scale Dependence: Z p

Change by varying QCD scales by a factor of 2 or ½ : g y y g Q y

Fractional Scale Dependence in Z Production Cross Section Acceptance

7 7

ndance (%) endance (%)

4 5 6 NLO 4 5 6

Scale Depen Scale Depe

1 2 3 NNLO 1 2 3

basic gle slice Z peak none basic ngle slice Z peak

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 24 ang an

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SLIDE 25

QCD Scale Dependence: W p

The same calculation for W production: p

Fractional Scale Dependence in W Production Cross Section Acceptance

7 6

dence (%) ndence (%)

4 5 6 W+ NLO W- NLO 3 4 5

Scale Depen Scale Depen

1 2 3 W+ NNLO W- NNLO 1 2 3

none basic higher η gher pTν basic higher η gher pTν

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 25 hi h hig

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SLIDE 26

Total QCD Uncertainty

This combined QCD uncertainty includes the error for not including NNLO, with the residual scale dependence inferred at NNLO.

Estimate of Total QCD Uncertainty

4 5

ainty (%)

4 5 W+ CS

nty (%)

Cross Section Acceptance

1 2 3 Cross Section Acceptance

QCD uncerta

1 2 3 W- CS W+ Acc W- Acc

QCD uncertain none basic higher η higher pTν none basic ngle slice Z peak

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 26 a

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SLIDE 27

Convergence Issues g

Convergence is a limiting factor in calculating the

NNLO ti FEWZ 11 di i l NNLO corrections. FEWZ uses an 11-dimensional Vegas integral which converges slowly for some cuts.

The results shown here typically took a month or The results shown here typically took a month or

longer for narrow cuts.

Still, some results could not converge to better than

% 1% ff f 4%. Attaining 1% is difficult except for relatively inclusive cuts.

W production converged somewhat better W production converged somewhat better. Separating different classes of terms in FEWZw and

calculating them on different nodes of the clusters helped to make the W calculation manageable.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 27

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SLIDE 28

Convergence for Z Production g

FEWZz Run Time ≈ 1 month per data point (narrow cuts)

Cross Section Relative Error

2500 10 1500 2000 no cut 6 8

Zz error (%) σ (pb)

500 1000 basic cut angle slice 2 4

FEWZ

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 Z Peak 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 28 Vegas iteration Vegas iteration

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SLIDE 29

PDF Contribution to Error

To estimate the error due to the PDFs, we calculated

, the error in the NLO cross section and acceptance for a range of PDF sets using the eigenvector sets provided and using the asymmetric Hessian method to calculate and using the asymmetric Hessian method to calculate the error in the cross section.

Errors within a PDF set tend to be greater than the

difference between sets, as seen in the following plots for Z W+ and W- production for Z, W+, and W production.

PDF errors tend to cancel in acceptances.

PDF errors tend to cancel in acceptances.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 29

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SLIDE 30

PDF Contribution to Error

Z W+ W-

cross sections (“basic” cuts)

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 30

acceptances (“basic” cuts)

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SLIDE 31

Summary of Uncertainties y

Cross Section

Uncertainty Z W+ W - Uncertainty Z W W Missing EW 0.4 ± 0.3 1.8 ± 0.6 1.7 ± 0.6 Total QCD 1.5 ± 0.8 1.7 ± 0.7 1.3 ± 0.6 PDF 3 8 4 0 3 3

“BASIC” CUT

Z: M > 40 GeV

Acceptance

PDF 3.8 4.0 3.3 Total 4.1 ± 0.3 4.7 ± 0.5 3.9 ± 0.5

Mll > 40 GeV PTl> 20 GeV W:

Acceptance

Uncertainty Z W+ W - Missing EW 1.0 ± 0.2 2.0 ± 0.5 2.1 ± 0.6

Mlν > 40 GeV PTl > 25 GeV PTlν> 20 GeV

Total QCD 2.6 ± 0.8 1.3 ± 0.6 1.0 ± 0.8 PDF 1.3 2.2 2.3 Total 3.0 ± 0.7 3.2 ± 0.3 3.3 ± 0.3

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 31

The missing EW correction for W is based on HORACE alone. For the Z, the HORACE – PHOTOS difference is used.

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SLIDE 32

The HERWIRI Project j

High Energy Radiation With InfraRed Improvement Toward a new event generator based on YFS-like non- abelian exponentiation. [My Loopfest VIII talk, Friday]

HERWIRI 1 0 (available now) [Joseph Majhi Ward Yost] HERWIRI 1.0 (available now) [Joseph, Majhi, Ward, Yost]

HERWIG with exponentiated DGLAP kernels

HERWIRI 2.0 (this summer) [Halyo, Hejna, Ward, Yost] HERWIRI 2.0 (this summer) [Halyo, Hejna, Ward, Yost]

HERWIG + YFS3 exponentiated QCD for Z

production Hypergeometric function-based reduction techniques are being developed to facilitate better convergence of higher order corrections [Kalmykov Ward Yost] higher order corrections. [Kalmykov, Ward, Yost] .

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 32

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SLIDE 33

Summary

There is still work to do to calculate the W and Z

production for desired cuts at the 1% level production for desired cuts at the 1% level.

Convergence of FEWZ is a limiting factor in estimating

the missing NNLO contribution.

An NNLO event generator is needed. For Z production, MC@NLO + Photos provides a good

l ti NNLO b ll f t i t d

  • solution. NNLO can be small for certain cuts and

acceptances.

Horace is good for estimating the size of EW Horace is good for estimating the size of EW

  • corrections. An event generator is needed.

One approach: the HERWIRI Project. Many others are

ki hi working on this too.

  • S. Yost, The Citadel
  • S. Yost, The Citadel

PHENO 2009 – Madison, Wisconsin – May 12, 2009 33