NLO Event Generation with Herwig++ Simon Pl atzer DESY on behalf - - PowerPoint PPT Presentation

NLO Event Generation with Herwig++

Simon Pl¨ atzer

DESY

– on behalf of the Herwig++ collaboration –

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 1 / 16

Overview.

Dedicated approaches to NLO matching, largely hand-made or semi-automated. Many processes available in current release, well established.

ATLAS data

Herwig++ LO Herwig++ Powheg 0.05 0.1 0.15 0.2 0.25 0.3 Muon charge asymmetry in W decays Aµ 0.5 1 1.5 2 0.6 0.8 1 1.2 1.4 |ηµ| MC/data

pp → W

[K. Hamilton et al. – JHEP 0904 (2009) 116]

NLO LO+PS NLO+PS 0.5 1 1.5 2 2.5 3 10 1 Azimuthal angle difference between the first and second jet ∆φ12 dσ/d∆φ12 [pb]

Z+jet

[SP & S. Gieseke – Eur.Phys.J. C72 (2012) 2187]

Change in paradigm: Need for an automated, fully integrated framework. → Uncertainties and merging require full control of fixed-order input.

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 2 / 16

Dedicated NLO approaches: BSM Decay Chains.

Powheg matching integrated with fexible and generic Herwig++ BSM infrastructure.

[P. Richardson, A. Wilcock – Eur.Phys.J. C74 (2014) 2713] Jet pair mass in RS graviton decay.

Herwig++ PO Herwig++ LO 0.01 0.02 0.03 0.04 0.05 0.06 0.07 dσ/dmjj [fb/GeV] 1000 1200 1400 1600 1800 2000 2200 2400 0.6 0.8 1 1.2 1.4 mjj [GeV] Ratio

p⊥ distribution in CMSSM squark decay.

Herwig++ PO Herwig++ LO 10−7 10−6 10−5 dσ/dpT,2 [fb/GeV] 50 100 150 200 250 300 350 400 0.6 0.8 1 1.2 1.4 pT,2 [GeV] Ratio

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 3 / 16

Outline.

– (N)LO Matrix Elements for Herwig++ with Matchbox – Matching Validation & Systematics – Shower & Matching Uncertainties – Further development: BSM, EW corrections, NLO merging – Summary & Outlook

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 4 / 16

Matchbox Overview.

σNLO =

• n

dσLO |Mn,0 |Mn,0|2

• +
• n
• dσV
• |Mn,0, |Mn,1

2Re(Mn,0|Mn,1)

• +
• 1

dσA

• |Mn,0

|Mij

n,0|2

• +
• n+1
• dσPS
• P(˜

q), D(p⊥) RME(p⊥)

• − dσA
• |Mn,0

|Mij

n,0|2

• +
• n+1
• dσR

|Mn+1,0 |Mn+1,0|2

• − dσPS
• P(˜

q), D(p⊥) RME(p⊥)

• Interfaces at amplitude level

– Color bases provided, including interface to ColorFull. [M. Sj¨

• dahl, SP]

– Spinor helicity library and caching facilities. – MadGraph5. [MadGraph & J. Bellm, S. Gieseke, SP, A. Wilcock] – Some in-house calculations and parts of HJets++. [F. Campanario, T. Figy, SP, M. Sj¨

• dahl]

Interfaces at squared amplitude level

– Dedicated interfaces. [HEJ & SP] [nlojet++ & J. Kotanski, J. Katzy, SP] – BLHA2. [GoSam & J. Bellm, S. Gieseke, SP, C. Reuschle] [NJet & SP] [OpenLoops & J. Bellm, S. Gieseke] [VBFNLO & K. Arnold, S. Gieseke, SP]

Matchbox infrastructure

based on [SP & S. Gieseke – Eur.Phys.J. C72 (2012) 2187] – Process generation and bookkeeping, integration. – Automated Catani-Seymour dipole subtraction. – Diagram-based mutli-channel phase space.

Shower plugins

matching details & uncertainties [in preparation] – Dipole shower D(p⊥). – Angular ordered shower P(˜ q). – ME correction RME(p⊥), including adaptive sampling. Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 5 / 16

Matchbox Validation.

Extensive validation against e.g. MCFM [N. Fischer, D. Rauch, C. Reuschle]

MCFM Herwig + GoSam 1 10 1 ∆y between the WZ boson pair dσ/d∆y [pb] 1 2 3 4 5 0.6 0.8 1 1.2 1.4 ∆y Ratio MCFM H++ & GoSam H++ & MadGraph 10−2 10−1 1 10 1 10 2 10 3 Antitop Quark Transverse Momentum pT,¯

t

dσ/dpT,¯

t

100 200 300 400 500 600 700 800 900 0.6 0.8 1 1.2 1.4 pT,¯

t [GeV]

Ratio

Various internal cross checks: Subtraction checks, pole cancellation.

10−2 10−1 1 10 1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Singularity cancellation in u ¯ u → e+e−gg √s14 D/|M|2 du → dug gu → uug

• 16
• 14
• 12
• 10
• 8
• 6

10−2 10−1 1 10 1 1/ǫ pole cancellation in pp → 3 jets log10(∆)

• ccurence in %

pp → Z + jet (GoSam) pp → 3 jets (NJet)

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 6 / 16

NLO Calculations with Matchbox.

Electroweak H+Jets production with HJets++

[F. Campanario, T. Figy, SP, M. Sj¨

• dahl – PRL 111 (2013) 211802]

– Employs all of Matchbox’s infrastructure for a hadron collider 2 → 4 process. – Hybrid interfaces of amplitude and squared amplitude infrastructure, internal cross checks possible.

HJets++ LO NLO 10−2 10−1 1 10 1 10 2 Transverse momentum of the third jet dσ/dp⊥,3 [fb/GeV] 20 40 60 80 100 120 140 160 180 200 0.5 1 1.5 2 2.5 3 3.5 p⊥,3 [GeV] K HJets++ LO NLO 10−4 10−3 10−2 10−1 1 10 1 Transverse momentum of the third jet dσ/dpT,3 [fb/GeV] 20 40 60 80 100 120 140 160 180 200 0.6 0.8 1 1.2 1.4 pT,3 [GeV] K

Inclusive cuts. VBF cuts. pp → H + 3 jets @ 14 TeV – inlcudes all VBF and Higgs-strahlung contributions Have pp → H + 2 jets available as well.

[validated against Ciccolini, Denner, Dittmaier – Phys.Rev.Lett. 99 (2007) 161803] Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 7 / 16

Matching Validation & Systematics.

Compare fixed order, unshowered S and H events, and full simulation.

Herwig++

OpenLoops / MadGraph / ColorFull

LO + Dipoles NLO + Dipoles NLO NLO + Dipoles H 10−4 10−3 10−2 10−1 1 10 1 10 2 Z boson transverse momentum dσ/dp⊥(Z) GeV/pb 20 40 60 80 100 120 140 0.6 0.8 1 1.2 1.4 p⊥(Z)/GeV Ratio to NLO Herwig++

OpenLoops / MadGraph / ColorFull

LO + QTilde LO NLO + QTilde NLO + QTilde H NLO + QTilde S 20 40 60 80 100 120 140 160 180 Z boson rapidity dσ/dy(Z) 1/pb

• 6
• 4
• 2

2 4 6 0.6 0.8 1 1.2 1.4 y(Z) Ratio to NLO

Prime validation: inclusive Z. Non-trivial application: Z plus jet

Herwig++

OpenLoops / MadGraph / ColorFull

LO + Dipoles LO NLO + Dipoles NLO NLO + Dipoles H NLO + Dipoles S 2 4 6 8 10 10−2 10−1 1 10 1 10 2 10 3 10 4 R separation of Z and first jet ∆R(Z, j) dσ/d∆R(Z, j) 1/pb LO + QTilde LO NLO + QTilde NLO NLO + QTilde H NLO + QTilde S 100 200 300 400 500 600 700 800 900 1000 10−5 10−4 10−3 10−2 10−1 1 10 1 Transverse momentum of first jet p⊥(j) dσ/dp⊥(j) GeV/pb

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 8 / 16

Matching Validation & Systematics: Powheg-type.

[A. Wilcock, P. Richardson, SP – work in progress]

Powheg-type matching smoothly integrated into Matchbox – Adaptive sampling of ME correction Sudakov

[SP – Eur.Phys.J. C72 (2012) 1929]

– Various profile scale choices and uncertainty estimates – Can check impact of truncated showering

Matchbox POWHEGBOX Herwig++ 10 3 10 4 10 5 10 6 Number events 20 40 60 80 100 120 140 160 180 0.6 0.8 1 1.2 1.4 pT,ll[GeV] Ratio truncated shower no truncated shower 10 3 10 4 10 5 Number events 20 40 60 80 100 0.6 0.8 1 1.2 1.4 pT,ll[GeV] Ratio

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 9 / 16

Shower & Matching Uncertainties.

Shower uncertainties until now poorly understood. – Various scales in the game: µR, µF, µQ. – Role of µQ not a priory clear (no variable hard scale for a.o. showers, only p⊥ veto) – µR, µF in hard process vs. in the shower? Matching is a way more complicated setting! – Some expectations confirmed in matched setups. – Surprises in uncertainties for higher jet multiplicities. – Need to profile hard emission to avoid NNLO jumps. Upshot: Cross-benchmark between different showers with and without matching. Hopefully more insight soon – needs close connection with resummation community.

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 10 / 16

µQ variations and profile scales.

Important to validate uncertainties at leading order: Matching may hide important details. Do we see what we expect?

natural shower hfact profile resummation profile 50 100 150 200 250 0.2 0.4 0.6 0.8 1 q/GeV p power shower natural shower hfact profile resummation profile leading order 10 2 10 3 10−2 10−1 1 10 1 Transverse momentum of leading jet p⊥(jet 1) [GeV] dσ/dp⊥(jet 1) [pb/GeV] power shower natural shower hfact profile resummation profile 0.5 1 1.5 2 2.5 3 3.5 1 10 1 10 2 10 3 log10(k⊥ jet resolution 1 → 2 [GeV]) log10(d12/GeV) dσ/d log10(d12/GeV) [pb] power shower natural shower hfact profile resummation profile leading order 1 2 3 4 5 6 7 1 10 1 10 2 Separation between Z boson and leading jet ∆R(Z, 1st jet) dσ/d∆R(Z, 1st jet) [pb]

Full benchmark of uncertainties in progress – S. Gieseke & SP Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 11 / 16

Matching uncertainties.

Herwig++

OpenLoops / MadGraph / ColorFull

NLO µR,F variation NLO + Dipoles µR,F variation NLO + QTilde µR,F variation 10−1 1 10 1 10 2 Z boson transverse momentum dσ/dp⊥(Z) GeV/pb 20 40 60 80 100 120 140 0.6 0.8 1 1.2 1.4 p⊥(Z)/GeV Ratio to NLO Herwig++

OpenLoops / MadGraph / ColorFull

NLO µR,F variation NLO + Dipoles µQ variation NLO + QTilde µQ variation 10−1 1 10 1 10 2 Z boson transverse momentum dσ/dp⊥(Z) GeV/pb 20 40 60 80 100 120 140 0.6 0.8 1 1.2 1.4 p⊥(Z)/GeV Ratio to NLO

More (jetty) processes in progress, e.g. dijets:

Herwig++

NJet / MadGraph / ColorFull

NLO µR,F variation NLO + Dipoles µR,F variation 10 6 10 7 10 8 10 9 Pseudorapidity separation between jets dσ/d∆φ(j1, j2) 1/dpb 0.5 1 1.5 2 2.5 3 0.6 0.8 1 1.2 1.4 ∆φ(j1, j2) Ratio to NLO

Intricate pattern of cancellations in scale variations?

Herwig++

NJet / MadGraph / ColorFull

LO + Dipoles NLO + Dipoles NLO + Dipoles H NLO + Dipoles S 1 2 3 4 5 6 7 8

• 100
• 50

50 100 150 200 250 300 350 R separation between leading jets ∆R(j1, j2) dσ/d∆R(j1, j2) 1/mb

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 12 / 16

BSM with Matchbox.

[A. Wilcock, P. Richardson, SP – work in progress]

Study impact of matrix element corrections in t¯ t and ˜ q˜ q production. – First step to full NLO matching. – Impact on exclusion bounds. – Matching condition ↔ ‘diagram subtraction’. t¯ t and ˜ t˜ t production at 14 TeV.

Leading order Herwig++ ME correction (MadGraph+Matchbox) 100 200 300 400 500 600 10−7 10−6 10−5 10−4 10−3 10−2 10−1 pT,t¯ t [GeV] 1 σ dσ dpT,t¯

t

Leading order Herwig++ ME correction (MadGraph+Matchbox) 200 400 600 800 1000 1200 1400 10−7 10−6 10−5 10−4 10−3 10−2 pT,˜ t1˜ t∗

1 [GeV]

1 σ dσ dpT,˜

t1˜ t∗ 1

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 13 / 16

EW corrections.

[S. Gieseke, T. Kasprczik, J. K¨ uhn – arXiv:1401.3964]

Electroweak corrections to diboson production @ LHC. – Factorized ansatz to mixed corrections: (1 + δQCD)(1 + δEW) ≈ 1 + δQCD + δEW – Valid if both corrections are small → use suitable cuts to supress phase space enhanced QCD corrections – QCD corrections from builtin POWHEG cross sections – EW corrections through ˆ s,ˆ t-dependent reweighting

LO NLO EW NLO QCD NLO QCD×EW Herwig++ 2.6.3* 10−8 10−7 10−6 10−5 10−4 10−3 pp → e+e−µ+µ− at LHC, √s = 13 TeV dσ/dpT,l¯

l [pb/GeV]

100 200 300 400 500 0.6 0.8 1 1.2 1.4 pT,l¯

l/GeV

Ratio to LO

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 14 / 16

(N)LO Merging.

[J. Bellm, S. Gieseke, SP – work in progress]

Matchbox framework provides unique possibilities for exploring new merging algorithms. Follow the ‘unitarized’ approach.

[SP – JHEP 1308 (2013) 114] [L¨

• nnblad, Prestel –JHEP 1303 (2013) 166]

3LO 2LO-1NLO 3LO-2NLO 10−2 10−1 1 Z → ℓ+ℓ−, p⊥(jet) > 30 GeV, |yjet| < 4.4 dσ/dp⊥ [pb/GeV] 40 60 80 100 120 140 160 180 0.6 0.8 1 1.2 1.4 pleading jet

⊥

[GeV] MC/Data

OPAL data

LO+PS not unit., 2/3 jets

• unit. 2/3 jets

not unit 2/3/4 jets unit 2/3/4 jets 0.4 0.6 0.8 1 1.2 1.4 1.6 Modified Nachtmann-Reiter angle (parton level) 1/σ dσ/d| cos(θ∗

NR)|

0.2 0.4 0.6 0.8 1 0.9 0.95 1.0 1.05 | cos(θ∗

NR)|

MC/data

Z plus jets from ATLAS, four-jet correlations at LEP.

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 15 / 16

Summary & Outlook.

Current release: Dedicated approaches to NLO matching. Largely hand-made or semi-automated, many processes available, well established. Change in paradigm: Automated NLO × Two showers × Two matching algorithms. – Matching and uncertainties under validation for a bunch of processes. – Needs careful investigation for several process classes, especially with jets. Related: BSM applications, NLO merging, first attempts on EW corrections. Not covered: Subleading-N improvements. Matchbox 2.0 will appear with Herwig++ 2.8.0, partial beta tester in 2.7.1. Stay tuned on herwig.hepforge.org

Simon Pl¨ atzer (DESY) NLO Event Generation with Herwig++ 16 / 16