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 2500000 200000 LO LO NJet + Sherpa NLO pp → 3 jet at 7 TeV NLO 2000000 150000 ◮ Reduced theoretical 1500000 100000 σ (pb) σ (pb) uncertainty 1000000 50000 500000 0 NJet + Sherpa pp → 2 jet at 7 TeV 0 − 50000 0 1 2 3 4 5 0 1 2 3 4 5 x, µ R = x � H T x, µ R = x � H T NLO automation 30000 LO LO NJet + Sherpa pp → 4 jet at 7 TeV NLO 1500 NLO 25000 ◮ Great advances in the 20000 1000 15000 σ (pb) σ (pb) recent years 10000 500 5000 0 NJet + Sherpa 0 − 5000 pp → 5 jet at 7 TeV ◮ High-multiplicity still − 10000 0 1 2 3 4 5 0 1 2 3 4 5 x, µ R = x � x, µ R = x � H T H T remains a challenge — LO — NLO -1 / N
NLO setup Hard process ingredients � � � � dσ B � + � dσ R � σ NLO = n + dσ V dσ S n +1 − dσ S n + n +1 n +1 n 1 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 2.0 1 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. 1 available from project homepage https://bitbucket.org/njet/njet 1 / N
Binoth Les Houches Accord interface to One Loop matrix elements BLHA order.lh ◮ Simple uniform interface between Monte-Carlo (MC) and One Loop Providers (OLP) njet.py [arXiv:1001.1307, arXiv:1308.3462] BLHA in NJet 2.0 contract.lh ◮ Support BLHA1 and BLHA2 ◮ Provide colour/spin-correlated trees OLP Start ◮ Provide leading/subleading colour OLP EvalSubProcess and desymmetrized amplitudes OLP SetParameter BLHA extensions virt[-2] virt[-1] ◮ Control all settings via order file virt[0] ◮ Single point of interaction with OLP born 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 ) ∼ 2 n n 6 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) Subleading colour ◮ Order of magnitude slower full colour 10 − 2 leading approx. ◮ Order of magnitude smaller NJet + Sherpa 10 − 3 dσ V /dp T,j 3 pp → γγ + 3 jet at 8 TeV ◮ Often cannot be ignored 10 − 4 Separate integration 10 − 5 ◮ Full colour 5 − 10 times faster 1 . 25 1 . 20 1 . 15 Disadvantages 1 . 10 1 . 05 ◮ Manual (no MC support) 1 . 00 0 . 95 50 100 150 200 ◮ µ R dep. has to be corrected p T,j 3 ◮ Not standardized in BLHA 4 / N
Example: Z + jets production with NJet+Sherpa ATLAS cuts. Agreement with [1304.1253] and [1108.2229] LO LO NLO NLO ATLAS 1304.7098 ATLAS 1304.7098 10 1 10 1 σ [pb] σ [pb] 10 0 NJet + Sherpa 10 0 NJet + Sherpa pp → Z [ → e + e − ] + jet s at 7 TeV pp → Z [ → µ + µ − ] + jet s at 7 TeV 1 . 15 1 . 15 Theory / data Theory / data 1 . 10 1 . 10 1 . 05 1 . 05 1 . 00 1 . 00 0 . 95 0 . 95 0 . 90 0 . 90 0 . 85 0 . 85 1 2 3 4 1 2 3 4 Inclusive Jet Multiplicity Inclusive Jet Multiplicity 5 / N
Example: timing of W/Z + jets production with NJet+Sherpa Time spent in different parts of NLO calculation 3 . 0 B W + jets V leading 10 2 V(lead.) Z + jets V leading 2 . 5 W + jets V sub-leading V(sub-lead.) Z + jets V sub-leading I average time per event (s) 10 1 RS 2 . 0 time (cpu years) 10 0 x4 1 . 5 NJet + Sherpa 10 − 1 pp → Z + jets 1 . 0 10 − 2 x9 0 . 5 10 − 3 x16 x25 10 − 4 0 . 0 0 1 2 3 4 0 1 2 3 4 # jets # jets 6 / N
Efficient use of results is crucial High multiplicity calculations are expensive ◮ Typical 5 final state calculations take ∼ 10 5 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 , x 1 , x 2 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 APPL LO 30000 APPL NLO HT/2 LO NLO 25000 1800000 20000 15000 NJet + Sherpa σ (pb) 10000 pp → 2 jet at 7 TeV 1600000 5000 0 NJet + Sherpa − 5000 pp → 4 jet at 7 TeV 1400000 − 10000 σ (pb) 0 1 2 3 4 5 x, µ R = x � H T 3000 1200000 APPL LO APPL NLO HT/2 LO 2500 NLO 2000 1000000 1500 APPL LO APPL NLO HT/2 σ (pb) 1000 APPL LO APPL NLO HT/40 500 LO HT/2 800000 NLO HT/2 0 NJet + Sherpa NLO HT/40 pp → 5 jet at 7 TeV − 500 10 − 1 10 0 − 1000 x, µ R = x � H n 0 1 2 3 4 5 x, µ R = x � T H T 9 / N
Analysis methods comparison On-the-fly: NTuples: APPLgrid: + Zero disk space cost − High disk space cost + Low disk space cost −− Scale/PDF vars. ± Scale/PDF vars. ++ Scale/PDF vars. Extremely high moderate CPU cost low CPU cost CPU cost − Flexibility low ++ Flexibility high − Flexibility low + Can use standard − Needs custom − Needs custom tools: Rivet software software Most important for high-multiplicity fixed order NLO are flexibility and cheap scale/PDF variations: NTuples+APPLgrid 10 / N
NJet+Sherpa: γγ + 3 j at 8 TeV, scale variations, CT10nlo PDF 2 . 0 Cuts µ R ;0 = H ′ T / 2 p T,j > 30 GeV µ R ;0 = � H ′ T / 2 NJet + Sherpa √ | η j | ≤ 4 . 7 µ R ;0 = Σ 2 / 2 pp → γγ + 3 j @ 8 TeV 1 . 5 p T,γ 1 > 40 GeV µ R ;0 = � H T / 2 p T,γ 2 > 25 GeV | η γ | ≤ 2 . 5 σ [pb] R γ,j = 0 . 5 1 . 0 R γ,γ = 0 . 45 Scales H T = Σ � p T,i 0 . 5 i ∈{ γ, partons } H ′ � T = m γγ + Σ p T,i i ∈ partons 0 . 0 H ′ T = m γγ + Σ p T,i 1 2 3 4 5 x, µ R = xµ R ;0 i ∈ jets Σ 2 = m 2 γγ + Σ p 2 σ LO γγ +3 j ( � T / 2) = 0 . 643(0 . 003) +0 . 278 T,i H ′ − 0 . 180 pb i ∈ jets σ NLO γγ +3 j ( � H ′ T / 2) = 0 . 785(0 . 010) +0 . 027 − 0 . 085 pb 11 / N
NJet+Sherpa: γγ + 3 j at 8 TeV, m γγ distribution and PDF uncertainties PDF uncertainty ≈ 3 − 6% 10 − 2 LO NLO CT10 NLO NLO NNPDF23 dσ/dm γγ [pb GeV − 2 ] NLO MSTW2008 dσ/dm γγ [pb GeV − 2 ] NLO ABM11 10 − 3 10 − 3 NJet + Sherpa 10 − 4 pp → γγ + 3 jet at 8 TeV NJet + Sherpa 10 − 4 pp → γγ + 3 jet at 8 TeV 1 . 06 1 . 6 1 . 04 1 . 02 1 . 4 1 . 00 1 . 2 0 . 98 1 . 0 0 . 96 0 . 8 0 . 94 0 . 6 0 100 200 300 400 500 0 100 200 300 400 m γγ m γγ Di-photon invariant mass distribution 12 / N
NJet+Sherpa: total XS for 2, 3, 4, 5 jets at 7 TeV vs ATLAS measurements Cuts LO 10 6 NLO anti-kt R = 0 . 4 ATLAS data p 1st > 80 GeV CERN-PH-EP-2011-098 10 5 T p other > 60 GeV σ (pb) T 10 4 | η | < 2 . 8 10 3 NJet + Sherpa NLO pp → jets at 7 TeV 10 2 µ R = µ F = ˆ H T / 2 vars. ˆ H T / 4 and ˆ H T Theory / data α s ( M Z ) = 0 . 118 2 NNPDF23 PDF set 1 2 3 4 5 6 Inclusive Jet Multiplicity 13 / N
NJet+Sherpa: jets ratios at 7 TeV with different PDFs vs ATLAS data 0 . 18 Cuts NNPDF2.3 MSTW2008 anti-kt R = 0 . 4 CT10 p 1st > 80 GeV T 0 . 14 ABM11 p other > 60 GeV ATLAS data T CERN-PH-EP-2011-098 | η | < 2 . 8 σ n +1 /σ n 0 . 10 NLO µ R = µ F = ˆ H T / 2 vars. ˆ H T / 4 and ˆ H T 0 . 06 (shown for NNPDF) NJet + Sherpa α s ( M Z ) = 0 . 118 pp → jets at 7 TeV 0 . 02 2 3 4 14 / N n
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