some theoretical issues regarding method 2

Top properties workshop 11/11/05

Some theoretical issues regarding Method 2

J. Huston

Michigan State University


History

Based on a series of talks that I gave at Lepton + Jets meetings May 21, 2004 Nov. 7, 2003 Oct. 10, 2003 April 25, 2003

Plus a paper that I wrote with John Campbell “Heavy Flavor in W + Jets Production at the

Fermilab Tevatron” hep-ph/0405276 Phys. Rev. D70:094021,2004

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Method 2 In Method 2, the calculated

ratio for WbBj(j) to Wjjj(j) is used, along with the measured Wjjj(j) cross sections to estimate the heavy flavor background to top production

The ratio is calculated at LO and then multiplied by a phenomenological factor of 1.5 for use in background subtractions

It would be nicer to put this aspect of the analysis on a firmer basis

NLO is firmer than LO

The state of the art for NLO calculations is WbB and Wjj although recent advances

make the 1 loop calculation of WbBj and Wjjj realistic…but don’t hold your breath

WbB and Wjj are available now in MCFM; may give guidance

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Scale dependence

As expected, scale dependence lessened at NLO

More so for exclusive final states than inclusive

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K-factors

K-factors depend both on scale choice and pT cuts on jets

Ratio of K-factors (WbB/Wjj) is reasonably stable for scales of MW/2 and above

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Wbb/Wjj ratioVery dependent on

kinematics (jet pT) at LOMore stable at NLORatio is higher for

inclusive final states than for exclusive final states

NLO prediction for exclusive ratio is in agreement with ratio assumed in Method 2 analyses (with factor of 1.5 applied) but note that LO and NLO

predictions in MCFM are reasonably close for a jet cut of 15 GeV/c

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HT

Look at cross sections for WbB(j) and Wjj(j) as a function of the HT variable

Distributions look similar at LO but not at NLO

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Ratios

So it appears that cross sections using very exclusive variables like HT may not have the same shape at LO and NLO so this assumption

should not be made in analyses

But inclusive variables like the lead jet pT are safer

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PDF uncertainties

PDF uncertainties easily calculated using weight technique

Note talk given by Craig Group at TeV4LHC meeting in Oct on LHAPDF

Easier to use the weight technique to calculate pdf uncertainties in version 5

9


Calculation of pdf uncertainties

Note that CDF webpage seems to be recommending option 3

Option 4 is preferred

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LO vs NLO pdf’s for parton shower MC’s

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

For NLO calculations, use NLO pdf’s (duh) What about for parton shower Monte

Carlos? somewhat arbitrary assumptions (for

example fixing Drell-Yan normalization) have to be made in LO pdf fits

DIS data in global fits affect LO pdf’s in ways that may not directly transfer to LO hadron collider predictions

LO pdf’s for the most part are outside the NLO pdf error band

LO matrix elements for many of the processes that we want to calculate are not so different from NLO matrix elements

by adding parton showers, we are partway towards NLO anyway

any error is formally of NLO (my recommendation) use NLO pdf’s

pdf’s must be + definite in regions of application (CTEQ is so by def’n)

Note that this has implications for MC tuning, i.e. Tune A uses CTEQ5L

need tunes for NLO pdf’s …but at the end of the day this is still LO physics;There’s no substitute for honest-to-god NLO.

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Rick Field at TeV4LHC: CTEQ6.1 Tune

"Transverse" Charged Particle Density: dN/d ηdφ

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300 350 400 450 500

( #1) ( / )PT particle jet GeV c

" " Transverse Charged Density1.96 TeV

RDF Preliminary generator level

(|Charged Particles η|<1.0, >0.5 / ) PT GeV c

PY Tune A5CTEQ L

" "Leading Jet

PY Tune Q61CTEQ

PY Tune A61CTEQ

"Transverse" PTsum Density: dPT/d ηdφ

0.0

0.4

0.8

1.2

1.6

0 50 100 150 200 250 300 350 400 450 500

( #1) ( / )PT particle jet GeV c

" " ( / ) Transverse PTsum Density GeV c1.96 TeV (|Charged Particles η|<1.0, >0.5 / ) PT GeV c

RDF Preliminary generator level

" "Leading Jet

PY Tune A5CTEQ L

PY Tune Q61CTEQ

PY Tune A61CTEQ

I used LHAPDF! See the next talk by Craig Group!

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W + jets at NLO

Currently are working (B. Cooper, A. Messina, D. Waters, J. Dittmann) to obtain W + jets cross sections that can be compared directly to NLO correct for UE and

hadronization but not out of cone

Hadronization+UE corrections for 0.4 cone different than for 0.7 cone (used for inclusive jet analysis) from Ken Hatakeyama

R=0..4 R=0.7

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Tevatron W + jets studies

We can’t help with the VBF Higgs discovery channel at the Tevatron but we can look at the rates for central jet emission in W/Z + jet(s) events

Cross section larger for W + jets so that is primary investigation

Will compare measured cross sections to LO +PS predictions and to fixed order (LO and NLO) predictions from MCFM

In particular, are interested in comparing to CKKW cross sections generated by Steve Mrenna

Predictions will be extrapolated to the LHC

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Comparisons

Look at probability for 3rd jet to be emitted as a function of the rapidity separation of the tagging jets

Relatively flat probability, stable with CKKW scale (not shown)

Bracketed by two predictions for MCFM using mW and <pT

jet> as scales MCFM predicts a slight

decrease in the ratio as the tagging jet rapidity separation increases

CKKW and ALGEN+Herwig 3p agrees with the data ALPGEN+Herwig 3p too high

for this kinematic region

MCFM mW

MCFM pTjet

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Summary

NLO predictions for Method 2 are more reliable than LO HT is not a good variable to use if you’re expecting

similar behavior at NLO (i.e. real world) as at LO of course, best numbers for heavy flavor fractions

are given by direct measurement; it will be interesting to compare these to the theory predictions and to better understand the factor of 1.5

A lot of theory tools out there (and more on the way); up to use to make use of them

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some theoretical issues regarding method 2

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