Multi-jet production at NLO with NJet Valery Yundin - - PowerPoint PPT Presentation

Multi-jet production at NLO with NJet

Valery Yundin

Max-Planck-Institut f¨ ur Physik

in collaboration with S. Badger, B. Biedermann, A. Guffanti and P. Uwer

HP2, 3–5 August 2014, GGI Firenze

NLO QCD calculations NLO results provide more accurate predictions and theoretical uncertainties for multi-jet backgrounds in new physics searches.

NLO vs LO

◮ Reduced theoretical

uncertainty

NLO automation

◮ Great advances in the

recent years

◮ High-multiplicity still

remains a challenge

1 2 3 4 5 x, µR = x HT 500000 1000000 1500000 2000000 2500000 σ (pb) NJet + Sherpa pp → 2 jet at 7 TeV LO NLO 1 2 3 4 5 x, µR = x HT −50000 50000 100000 150000 200000 σ (pb) NJet + Sherpa pp → 3 jet at 7 TeV LO NLO 1 2 3 4 5 x, µR = x HT −10000 −5000 5000 10000 15000 20000 25000 30000 σ (pb) NJet + Sherpa pp → 4 jet at 7 TeV LO NLO 1 2 3 4 5 x, µR = x HT 500 1000 1500 σ (pb) NJet + Sherpa pp → 5 jet at 7 TeV LO NLO

— LO — NLO

• 1 / N

NLO setup

Hard process ingredients

σNLO =

• n

dσB

n + dσV n +

• 1

dσS

n+1

+

• n+1

dσR

n+1 − dσS n+1

• bottleneck

bottleneck

Complicated pieces

• 1. Virtual matrix elements

[NJet, QCDLoop]

◮ Integration over loop momentum ◮ A number of new competing advanced methods

• 2. Real + subtraction

[Sherpa, Comix]

◮ Tree-like ◮ Difficult phase-space integration

• 3. Linked with BLHA interface

0 / N

NJet 2.0

NJet version 2.01

Multi-parton matrix elements in massless QCD

[arXiv:1209.0100] ◮ Full colour-summed amplitudes for up to 5 outgoing partons ◮ Reliable accuracy estimate and rescue system ◮ BLHA interface for MC generators

New in version 2.0

◮ W ±/Z/γ with up to 5 jets and γγ with up to 4 jets. ◮ Leading/Subleading colour splitting. ◮ Hardware vectorization for scaling test. ◮ BLHA2 support. ◮ Fast analytic amplitudes for 2 and 3 jets.

1available from project homepage https://bitbucket.org/njet/njet

1 / N

Binoth Les Houches Accord interface to One Loop matrix elements

• rder.lh

njet.py contract.lh

OLP Start OLP EvalSubProcess OLP SetParameter

virt[-2] virt[-1] virt[0] born BLHA

◮ Simple uniform interface

between Monte-Carlo (MC) and One Loop Providers (OLP)

[arXiv:1001.1307, arXiv:1308.3462]

BLHA in NJet 2.0

◮ Support BLHA1 and BLHA2 ◮ Provide colour/spin-correlated trees ◮ Provide leading/subleading colour

and desymmetrized amplitudes BLHA extensions

◮ Control all settings via order file ◮ Single point of interaction with OLP

2 / N

Dealing with complexity of multi-leg NLO

Advanced methods for computing amplitudes

◮ On-shell methods to avoid unphysical degrees of freedom

(amplitudes from trees, rational terms from massive loop cuts)

◮ Efficient recursive construction of building blocks ◮ Relations between primitive amplitudes

Time per phase-space point for dominating channels T(n) ∼ 2nn6 n! , n – number of final states Getting rid of the factorial (offload to MC)

◮ Desymmetrizing final states (available in NJet) ◮ Separate integration of leading/subleading colour (available in NJet) ◮ Colour-dressed approach (available in Sherpa/COMIX)

3 / N

Why split into leading/subleading colour (at high multiplicity)

10−5 10−4 10−3 10−2

dσV /dpT,j3 NJet + Sherpa pp → γγ + 3 jet at 8 TeV full colour leading approx.

50 100 150 200

pT,j3

0.95 1.00 1.05 1.10 1.15 1.20 1.25

Subleading colour

◮ Order of magnitude slower ◮ Order of magnitude smaller ◮ Often cannot be ignored

Separate integration

◮ Full colour 5−10 times faster

Disadvantages

◮ Manual (no MC support) ◮ µR dep. has to be corrected ◮ Not standardized in BLHA

4 / N

Example: Z + jets production with NJet+Sherpa ATLAS cuts. Agreement with [1304.1253] and [1108.2229]

100 101

σ [pb] NJet + Sherpa pp → Z[→e+e−] + jets at 7 TeV LO NLO ATLAS 1304.7098

1 2 3 4

Inclusive Jet Multiplicity

0.85 0.90 0.95 1.00 1.05 1.10 1.15

Theory / data

100 101

σ [pb] NJet + Sherpa pp → Z[→µ+µ−] + jets at 7 TeV LO NLO ATLAS 1304.7098

1 2 3 4

Inclusive Jet Multiplicity

0.85 0.90 0.95 1.00 1.05 1.10 1.15

Theory / data

5 / N

Example: timing of W/Z + jets production with NJet+Sherpa Time spent in different parts of NLO calculation

1 2 3 4

# jets

0.0 0.5 1.0 1.5 2.0 2.5 3.0

time (cpu years) x25 x16 x9 x4 NJet + Sherpa pp → Z + jets B V(lead.) V(sub-lead.) I RS

1 2 3 4

# jets

10−4 10−3 10−2 10−1 100 101 102

average time per event (s) W + jets V leading Z + jets V leading W + jets V sub-leading Z + jets V sub-leading

6 / N

Efficient use of results is crucial

High multiplicity calculations are expensive

◮ Typical 5 final state calculations take ∼ 105 CPU · hours. ◮ Do not want to run it more than once.

Layered computation set-up

◮ Save generated events in ROOT NTuples. [arXiv:1003.1241] ◮ Analyze later (still several days per analysis). ◮ Interpolation grids with APPLgrid for fast PDF convolution

and scale variations.

[arXiv:1312.4460]

7 / N

Saving events for further analysis NLO calculations are expensive and we need to use the results as efficiently as possible.

ROOT NTuples output

[arXiv:1003.1241] ◮ Save weigths, PDFs,

scheme dependence

◮ Compact compressed

storage

◮ Can change scales/PDFs

during analysis

◮ Several jet algorithms

at low cost

8 / N

Interpolation grids to speed-up PDF convolution APPLgrid – interpolation grids in Q, x1, x2 for each bin in histogram.

NTuples: ∼ 1000 GB space, ∼ 30 hours to analyze, completely generic APPLgrid: ∼ 1 GB space, ∼ 0.1 hour to analyze, specific observable/binning

10−1 100

x, µR = x Hn

T

800000 1000000 1200000 1400000 1600000 1800000

σ (pb) NJet + Sherpa pp → 2 jet at 7 TeV

APPL LO APPL NLO HT/2 APPL LO APPL NLO HT/40 LO HT/2 NLO HT/2 NLO HT/40 1 2 3 4 5 x, µR = x HT −10000 −5000 5000 10000 15000 20000 25000 30000 σ (pb) NJet + Sherpa pp → 4 jet at 7 TeV

1 2 3 4 5 x, µR = x HT −1000 −500 500 1000 1500 2000 2500 3000 σ (pb) NJet + Sherpa pp → 5 jet at 7 TeV

9 / N

Analysis methods comparison

On-the-fly:

+ Zero disk space cost −− Scale/PDF vars. Extremely high CPU cost − Flexibility low + Can use standard tools: Rivet

NTuples:

− High disk space cost ± Scale/PDF vars. moderate CPU cost ++ Flexibility high − Needs custom software

APPLgrid:

+ Low disk space cost ++ Scale/PDF vars. low CPU cost − Flexibility low − Needs custom software

Most important for high-multiplicity fixed order NLO are flexibility and cheap scale/PDF variations: NTuples+APPLgrid

10 / N

NJet+Sherpa: γγ + 3j at 8 TeV, scale variations, CT10nlo PDF

1 2 3 4 5

x, µR = xµR;0

0.0 0.5 1.0 1.5 2.0

σ [pb]

NJet + Sherpa pp → γγ + 3j @ 8 TeV

µR;0 = H′

T/2

µR;0 = H′

T/2

µR;0 = √ Σ2/2 µR;0 = HT/2

σLO

γγ+3j(

H′

T /2) = 0.643(0.003)+0.278 −0.180 pb

σNLO

γγ+3j(

H′

T /2) = 0.785(0.010)+0.027 −0.085 pb

Cuts

pT,j > 30 GeV |ηj| ≤ 4.7 pT,γ1 > 40 GeV pT,γ2 > 25 GeV |ηγ| ≤ 2.5 Rγ,j = 0.5 Rγ,γ = 0.45

Scales

• HT = Σ

i∈{γ, partons}

pT,i

• H′

T = mγγ +Σ i∈partons

pT,i H′

T = mγγ +Σ i∈jets

pT,i Σ2 = m2

γγ +Σ i∈jets

p2

T,i

11 / N

NJet+Sherpa: γγ + 3j at 8 TeV, mγγ distribution and PDF uncertainties

PDF uncertainty ≈ 3−6%

10−4 10−3 10−2

dσ/dmγγ [pb GeV−2] NJet + Sherpa pp → γγ + 3 jet at 8 TeV LO NLO

100 200 300 400 500

mγγ

0.6 0.8 1.0 1.2 1.4 1.6 10−4 10−3

dσ/dmγγ [pb GeV−2] NJet + Sherpa pp → γγ + 3 jet at 8 TeV NLO CT10 NLO NNPDF23 NLO MSTW2008 NLO ABM11

100 200 300 400

mγγ

0.94 0.96 0.98 1.00 1.02 1.04 1.06

Di-photon invariant mass distribution

12 / N

NJet+Sherpa: total XS for 2, 3, 4, 5 jets at 7 TeV vs ATLAS measurements

102 103 104 105 106

σ (pb) NJet + Sherpa pp → jets at 7 TeV LO NLO ATLAS data

CERN-PH-EP-2011-098

2 3 4 5 6

Inclusive Jet Multiplicity

1 2

Theory / data

Cuts

anti-kt R = 0.4 p1st

T

> 80 GeV pother

T

> 60 GeV |η| < 2.8

NLO

µR = µF = ˆ HT /2

• vars. ˆ

HT /4 and ˆ HT αs(MZ) = 0.118 NNPDF23 PDF set

13 / N

NJet+Sherpa: jets ratios at 7 TeV with different PDFs vs ATLAS data

2 3 4

n

0.02 0.06 0.10 0.14 0.18

σn+1/σn NJet + Sherpa pp → jets at 7 TeV NNPDF2.3 MSTW2008 CT10 ABM11 ATLAS data

CERN-PH-EP-2011-098

Cuts

anti-kt R = 0.4 p1st

T

> 80 GeV pother

T

> 60 GeV |η| < 2.8

NLO

µR = µF = ˆ HT /2

• vars. ˆ

HT /4 and ˆ HT (shown for NNPDF) αs(MZ) = 0.118

14 / N

Dijet phase-space cuts choices

102 103 104 105

dσ/dHT NJet + Sherpa pp → 2 jet at 7 TeV LO NLO

150 200 250 300 350 400 450 500

HT

0.0 0.5 1.0 1.5 2.0 2.5 102 103 104 105

NJet + Sherpa pp → 2 jet at 7 TeV LO NLO

150 200 250 300 350 400 450 500

HT

0.0 0.5 1.0 1.5 2.0 2.5 102 103 104 105

NJet + Sherpa pp → 2 jet at 7 TeV LO NLO

150 200 250 300 350 400 450 500

HT

0.0 0.5 1.0 1.5 2.0 2.5

◮ Left symmetric pT cuts: pT,1 > 60 GeV, pT,2 > 60 GeV

doesn’t work for NLO (negative XS)

◮ Middle asymmetric pT cuts: pT,1 > 80 GeV, pT,2 > 60 GeV

doesn’t give full NLO accuracy (LO is symmetric)

◮ Right symmetric HT,2 cuts: pT,1 + pT,2 > 140 GeV

seems to work best

15 / N

3/2 jet ratios compared with CMS data

0.00 0.05 0.10 0.15 0.20 0.25

dσ/dp12 NJet + Sherpa r3/2 at 7 TeV LO/LO NLO/NLO CMS data

CERN-PH-EP-2014-057

400 600 800 1000 1200

p12

0.7 0.8 0.9 1.0 1.1 1.2 0.0 0.5 1.0 1.5

dσ/dHT NJet + Sherpa r3/2 at 7 TeV LO/LO NLO/NLO CMS data

CERN-PH-EP-2011-044

500 1000 1500 2000 2500

HT

0.6 0.8 1.0 1.2 1.4 1.6

pT,12 = HT,2/2 results in smaller K-factor than HT

16 / N

NJet+Sherpa: pT for jets ratios at 7 TeV

100 200 300 400 500 600 700 800

Leading Jet pT [GeV]

0.2 0.4 0.6 0.8 1.0

(dσn+1/dpT )/(d σn/dpT ) NJet + Sherpa pp → jets at 7 TeV LO 3/2 LO 4/3 LO 5/4 NLO 3/2 NLO 4/3 NLO 5/4

Cuts

anti-kt R = 0.4 p1st

T

> 80 GeV pother

T

> 60 GeV |η| < 2.8

NLO

µR = µF = ˆ HT /2

• vars. 60%, 12%, 9%

(not shown) αs(MZ) = 0.118 NNPDF23 PDF set

17 / N

Conclusions

Summary

◮ NJet library version 2 with improved speed and new processes ◮ Multi-leg NLO workflow with NTuples and APPLgrid ◮ NJet+Sherpa: pp → 3, 4, 5 jets at NLO at 7 and 8 TeV

pp → γγ + 2, 3 jets at NLO at 8 TeV

◮ 3/2 ratio is sensitive to cuts and observable definition,

4/3 and 5/4 ratios are more stable

Outlook

◮ Today: fully automated 4 final state predictions at NLO ◮ In a few years: routine calculations with 5/6 final states

N / N

Bonus material

NJet+Sherpa: pT for γγ + jets 3/2 ratio at 8 TeV

100 200 300 400 500 600 700

Leading Jet pT [GeV]

0.2 0.4 0.6 0.8 1.0

(dσn+1/dpT )/(d σn/dpT ) NJet + Sherpa at 8 TeV LO γγ 3/2 NLO γγ 3/2

Ratio

µR = µF = H′

T /2

RLO

3/2 = 0.314(0.002)

RNLO

3/2

= 0.276(0.004)

Scale

Different scales agree within 8% for R3/2

N + 1 / N

NJet+Sherpa: pT for 3/2 ratio at 7 TeV with diff. PDFs vs ATLAS data

100 200 300 400 500 600 700 800

Leading Jet pT [GeV]

0.0 0.2 0.4 0.6 0.8

(dσn+1/dpT )/(dσn/dpT ) NJet + Sherpa pp → jets at 7 TeV LO w/ NLO PDFs NNPDF2.3 LO w/ NLO PDFs MSTW2008 LO w/ NLO PDFs CT10 LO w/ NLO PDFs ABM11 NLO NNPDF2.3 NLO MSTW2008 NLO CT10 NLO ABM11 ATLAS data CERN-PH-EP-2011-098

Cuts

anti-kt R = 0.6 p1st

T

> 80 GeV pother

T

> 60 GeV |η| < 2.8

NLO

µR = µF = ˆ HT /2 αs(MZ) = 0.118

αs from 3/2 ratios

[ATLAS-CONF-2013-041] [CMS-QCD-11-003]

N + 2 / N

NJet+Sherpa: 5 jets at 7 TeV, scale variations

ATLAS cuts, NNPDF23 PDF set, αs(MZ) = 0.118

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

x, µR = x HT

500 1000 1500

σ (pb) NJet + Sherpa pp → 5 jet at 7 TeV LO NLO

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

x, µR = x HT

500 1000 1500

σ (pb) NJet + Sherpa pp → 5 jet at 7 TeV LO w/ NLO PDFs NLO

σ7TeV-LO

5

(µ = ˆ HT /2) = 0.699(0.004)+0.530

−0.280 nb

σ7TeV-NLO

5

(µ = ˆ HT /2) = 0.544(0.016)+0.0

−0.177 nb

σ8TeV-LO

5

(µ = ˆ HT /2) = 1.044(0.006)+0.770

−0.413 nb

σ8TeV-NLO

5

(µ = ˆ HT /2) = 0.790(0.021)+0.0

−0.313 nb

N + 3 / N

NJet+Sherpa: 5 jets at 7 TeV, pT and η distributions

ATLAS cuts, NNPDF23 PDF set, αs(MZ) = 0.118

10−4 10−3 10−2 10−1 100 101

dσ/dpT [pb/GeV] NJet + Sherpa pp → 5 jet at 7 TeV LO NLO

100 200 300 400 500 600 700 800 900

1st jet pT [GeV]

0.0 0.5 1.0 1.5 2.0

4 3 2 1 1

100 200 300 400 500 600 700 800 900

2nd jet pT [GeV]

5 5 100 200 300 400 500

3rd jet pT [GeV]

5 5 100 200 300 400 500

4th jet pT [GeV]

5 5 100 200 300 400 500

5th jet pT [GeV]

5 5

100 101 102 103

dσ/dη [pb] NJet + Sherpa pp → 5 jet at 7 TeV LO NLO

−2 −1 1 2

1st jet rapidity

0.0 0.5 1.0 1.5 2.0 1 2 3 −2 −1 1 2

2nd jet rapidity

5 5 1 2 3 −2 −1 1 2

3rd jet rapidity

5 5 −2 −1 1 2

4th jet rapidity

5 5 1 2 3 −2 −1 1 2

5th jet rapidity

5 5

N + 4 / N

NJet+Sherpa: 5 jets at 7 TeV, PDF uncertainties

ATLAS cuts, αs(MZ) = 0.118, PDF uncertainty ≈ 3%

10−2 10−1 100

dσ/dpT [pb / GeV] NJet + Sherpa pp → 5 jet at 7 TeV NNPDF23 MSTW2008 CT10 ABM11

100 200 300 400 500 600 700 800

1st Leading Jet pT [GeV]

0.7 0.8 0.9 1.0 1.1 1.2 10−5 10−4 10−3 10−2 1 σ dσ/dpT [GeV−1]

NJet + Sherpa pp → 5 jet at 7 TeV NNPDF23 MSTW2008 CT10 ABM11

100 200 300 400 500 600 700 800

1st Leading Jet pT [GeV]

0.7 0.8 0.9 1.0 1.1 1.2

Right plot — distributions normalized to total cross-section.

N + 5 / N