The event generator WHIZARD Jrgen R. Reuter, DESY J.R.Reuter - - PowerPoint PPT Presentation

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Jürgen R. Reuter, DESY

The event generator WHIZARD

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Jürgen R. Reuter, DESY

W,HIggs,Z And Respective Decays

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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The WHIZARD Event Generator

WHIZARD Team: Wolfgang Kilian,

Thorsten Ohl, JRR, Simon Braß/Bijan Chokoufé/C. Fleper/Marco Sekulla/ So Young Shim/Florian Staub/Christian Weiss/Zhijie Zhao + 2 Master

EPJ C71 (2011) 1742

• Universal event generator for lepton and hadron colliders
• Modular package: - Phase space parameterization (resonances, collinear emission, Coulomb etc.)
• O’Mega optimized matrix element generator (recursiveness via Directed

Acyclical Graphs)

• VAMP: adaptive multi-channel Monte Carlo integrator
• CIRCE1/2: generator/simulation tool for lepton collider beam spectra
• Lepton beam ISR Kuraev/Fadin, 1986; Skrzypek/Jadach, 1991
• Color flow formalism Stelzer/Willenbrock, 2003; Kilian/Ohl/JRR/Speckner, 2011

<whizard@desy.de>

WHIZARD v2.3.1 (25 Aug. 2016)

http://whizard.hepforge.org

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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WHIZARD: Installation and Run

Download: http://www.hepforge.org/archive/whizard/whizard-2.3.1.tar.gz Unpack it, intended to be installed in /usr/local (or locally) Create build directory and do ./configure make, [ make check ], make install Working directory: create SINDARIN steering file <input>.sin Working directory: run whizard <input>.sin Supported event formats: LHA, StdHep, LHEF (i-iii), HepMC, LCIO, div. ASCII Interfaces to external packages for Feynman rules, hadronization, event formats, analysis, jet clustering etc.: FastJet, GoSam, GuineaPig(++), HepMC,

HOPPET, LCIO, LHAPDF(4/5/6), LoopTools, OpenLoops, PYTHIA6, [PYTHIA8], StdHep [internal]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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WHIZARD: Installation and Run

Download: http://www.hepforge.org/archive/whizard/whizard-2.3.1.tar.gz Unpack it, intended to be installed in /usr/local (or locally) Create build directory and do ./configure make, [ make check ], make install Working directory: create SINDARIN steering file <input>.sin Working directory: run whizard <input>.sin Supported event formats: LHA, StdHep, LHEF (i-iii), HepMC, LCIO, div. ASCII Interfaces to external packages for Feynman rules, hadronization, event formats, analysis, jet clustering etc.: FastJet, GoSam, GuineaPig(++), HepMC,

HOPPET, LCIO, LHAPDF(4/5/6), LoopTools, OpenLoops, PYTHIA6, [PYTHIA8], StdHep [internal]

J.R.Reuter Event generator WHIZARD FCC-ee “Physics behind precision”, CERN, 2.2.16

Decay processes / auto_decays

WHIZARD cannot only do scattering processes, but also decays

Example Energy distribution electron in muon decay:

model = SM process mudec = e2 => e1, N1, n2 integrate (mudec) histogram e_e1 (0, 60 MeV, 1 MeV) analysis = record e_e1 (eval E [e1]) n_events = 100000 simulate (mudec) compile_analysis { $out_file = “test.dat” }

dN/dEe(µ− → e−¯ νeνµ)

GeV

J.R.Reuter Event generator WHIZARD FCC-ee “Physics behind precision”, CERN, 2.2.16

Decay processes / auto_decays

WHIZARD cannot only do scattering processes, but also decays

Example Energy distribution electron in muon decay:

model = SM process mudec = e2 => e1, N1, n2 integrate (mudec) histogram e_e1 (0, 60 MeV, 1 MeV) analysis = record e_e1 (eval E [e1]) n_events = 100000 simulate (mudec) compile_analysis { $out_file = “test.dat” } auto_decays_multiplicity = 2 ?auto_decays_radiative = false unstable Wp () { ?auto_decays = true }

Automatic integration of particle decays

dN/dEe(µ− → e−¯ νeνµ)

GeV

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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BSM Models in WHIZARD

MODEL TYPE with CKM matrix trivial CKM QED with e, µ, τ, γ – QED QCD with d, u, s, c, b, t, g – QCD Standard Model SM CKM SM SM with anomalous gauge coupl. SM ac CKM SM ac SM with anomalous top coupl. SMtop CKM SMtop SM for e+e top threshold — SM tt threshold SM with anom. Higgs coupl. — SM rx / NoH SM ext. for VV scattering — SSC / SSC2/ AltH SM ext. for unitarity limits — SM ul SM with Z0 — Zprime 2HDM 2HDM CKM 2HDM MSSM MSSM CKM MSSM MSSM with gravitinos — MSSM Grav NMSSM NMSSM CKM NMSSM extended SUSY models — PS/E/SSM Littlest Higgs — Littlest Littlest Higgs with ungauged U(1) — Littlest Eta Littlest Higgs with T parity — Littlest Tpar Simplest Little Higgs (anomaly-free/univ.) — Simplest[ univ] 3-site model — Threeshl UED — UED SM with gravitino and photino — GravTest Augmentable SM template — Template

Automated models: interface to SARAH/BSM Toolbox Staub, 0909.2863; Ohl/Porod/Staub/Speckner, 1109.5147 Automated models: interface to FeynRules Christensen/Duhr; Christensen/Duhr/Fuks/JRR/Speckner, 1010.3251 Automated models: UFO interface [in connection with new WHIZARD/O’Mega model format]

2.2.8: SM_dim6

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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BSM Models in WHIZARD

MODEL TYPE with CKM matrix trivial CKM QED with e, µ, τ, γ – QED QCD with d, u, s, c, b, t, g – QCD Standard Model SM CKM SM SM with anomalous gauge coupl. SM ac CKM SM ac SM with anomalous top coupl. SMtop CKM SMtop SM for e+e top threshold — SM tt threshold SM with anom. Higgs coupl. — SM rx / NoH SM ext. for VV scattering — SSC / SSC2/ AltH SM ext. for unitarity limits — SM ul SM with Z0 — Zprime 2HDM 2HDM CKM 2HDM MSSM MSSM CKM MSSM MSSM with gravitinos — MSSM Grav NMSSM NMSSM CKM NMSSM extended SUSY models — PS/E/SSM Littlest Higgs — Littlest Littlest Higgs with ungauged U(1) — Littlest Eta Littlest Higgs with T parity — Littlest Tpar Simplest Little Higgs (anomaly-free/univ.) — Simplest[ univ] 3-site model — Threeshl UED — UED SM with gravitino and photino — GravTest Augmentable SM template — Template

Automated models: interface to SARAH/BSM Toolbox Staub, 0909.2863; Ohl/Porod/Staub/Speckner, 1109.5147 Automated models: interface to FeynRules Christensen/Duhr; Christensen/Duhr/Fuks/JRR/Speckner, 1010.3251 Automated models: UFO interface [in connection with new WHIZARD/O’Mega model format]

2.2.8: SM_dim6

NEW NEW

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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BSM Models in WHIZARD

MODEL TYPE with CKM matrix trivial CKM QED with e, µ, τ, γ – QED QCD with d, u, s, c, b, t, g – QCD Standard Model SM CKM SM SM with anomalous gauge coupl. SM ac CKM SM ac SM with anomalous top coupl. SMtop CKM SMtop SM for e+e top threshold — SM tt threshold SM with anom. Higgs coupl. — SM rx / NoH SM ext. for VV scattering — SSC / SSC2/ AltH SM ext. for unitarity limits — SM ul SM with Z0 — Zprime 2HDM 2HDM CKM 2HDM MSSM MSSM CKM MSSM MSSM with gravitinos — MSSM Grav NMSSM NMSSM CKM NMSSM extended SUSY models — PS/E/SSM Littlest Higgs — Littlest Littlest Higgs with ungauged U(1) — Littlest Eta Littlest Higgs with T parity — Littlest Tpar Simplest Little Higgs (anomaly-free/univ.) — Simplest[ univ] 3-site model — Threeshl UED — UED SM with gravitino and photino — GravTest Augmentable SM template — Template

Automated models: interface to SARAH/BSM Toolbox Staub, 0909.2863; Ohl/Porod/Staub/Speckner, 1109.5147 Automated models: interface to FeynRules Christensen/Duhr; Christensen/Duhr/Fuks/JRR/Speckner, 1010.3251 Automated models: UFO interface [in connection with new WHIZARD/O’Mega model format]

2.2.8: SM_dim6

NEW NEW

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Unitarity bounds in VBS with WHIZARD

200 400 600 800 1000 1200 1400 1600 1800 2000 M(W +W +)[GeV] 10−4 10−3 10−2 10−1 100 101

∂σ ∂M

⇥

fb 100GeV

⇤

pp → W +W +jj

FS,0 = 480 TeV−4 FS,1 = 480 TeV−4 FHD = 30 TeV−2 SM

General cuts: Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5

200 400 600 800 1000 1200 1400 1600 1800 2000 M(W +W −)[GeV] 10−4 10−3 10−2 10−1 100 101

⇥

⇤

pp → W +W −jj

200 400 600 800 1000 1200 1400 1600 1800 2000 M(W +Z)[GeV] 10−4 10−3 10−2 10−1 100 101

∂σ ∂M

⇥

fb 100GeV

⇤

pp → WZjj

FS,0 = 480 TeV−4 FS,1 = 480 TeV−4 FHD = 30 TeV−2 SM

Kilian/Ohl/JRR/Sekulla: PRD91(15),096007 [1408.6207] Alboteanu/Kilian/Ohl/JRR: JHEP 0811.010 [0806.4145]

model = SM_rx model = SM_ul

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Differential spectra in VBS

pp → e+µ+νeνµjj √s = 14 TeV L = 1 ab−1

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5; p` T > 20 GeV

Kilian/Ohl/JRR/Sekulla: PRD91(15),096007 [1408.6207]

model = SM_rx

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Differential spectra in VBS

pp → e+µ+νeνµjj √s = 14 TeV L = 1 ab−1

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5; p` T > 20 GeV

0.5 1.0 1.5 2.0 2.5 3.0

∆φeµ

50 100 150 200 250 300 350

N

bare unit SM

500 1000 1500 2000

P

l=e,µ |pT(l)|

100 101 102 103 104

N

bare unit SM

FHD = 30 TeV−2

Kilian/Ohl/JRR/Sekulla: PRD91(15),096007 [1408.6207]

model = SM_rx

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Differential spectra in VBS

pp → e+µ+νeνµjj √s = 14 TeV L = 1 ab−1

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5; p` T > 20 GeV

0.5 1.0 1.5 2.0 2.5 3.0

∆φeµ

50 100 150 200 250 300 350

N

bare unit SM

500 1000 1500 2000

P

l=e,µ |pT(l)|

100 101 102 103 104

N

bare unit SM

FS,0 = 480 TeV−4

Kilian/Ohl/JRR/Sekulla: PRD91(15),096007 [1408.6207]

model = SM_rx

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Differential spectra in VBS

pp → e+µ+νeνµjj √s = 14 TeV L = 1 ab−1

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5; p` T > 20 GeV

0.5 1.0 1.5 2.0 2.5 3.0

∆φeµ

50 100 150 200 250 300 350

N

bare unit SM

500 1000 1500 2000

P

l=e,µ |pT(l)|

100 101 102 103 104

N

bare unit SM

FS,1 = 480 TeV−4

Kilian/Ohl/JRR/Sekulla: PRD91(15),096007 [1408.6207]

model = SM_rx

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Comparison: Simplified Models & EFT

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5

Black dashed line: saturation of A22(W +W +)/A00(ZZ)

400 600 800 1000 1200 1400 1600 1800 2000 M(ZZ)[GeV] 10−2 10−1 100 101

∂σ ∂M

⇥

fb 100GeV

⇤

pp → ZZjj

FS,1 = 12.3 TeV−4 Fσ = 4.0 TeV−1 SM limit of A00

Mσ = 800 GeV Γσ = 80 GeV

• EFT fails at resonance
• aQGC describe rise of

resonance

• Unitarization applied
• Tensor resonances better

visible than scalars

ATLAS PRL 113(2014)14, 141803 [1405.6241]

Kilian/Ohl/JRR/Sekulla: PRD93(16),3. 036004 [1511.00022]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Comparison: Simplified Models & EFT

Mjj > 500 GeV; ∆ηjj > 2.4; pj

T > 20 GeV; |∆ηj| < 4.5

Black dashed line: saturation of A22(W +W +)/A00(ZZ)

400 600 800 1000 1200 1400 1600 1800 2000 M(ZZ)[GeV] 10−2 10−1 100 101

∂σ ∂M

⇥

fb 100GeV

⇤

pp → ZZjj

FS,1 = 12.3 TeV−4 Fσ = 4.0 TeV−1 SM limit of A00

Mσ = 800 GeV Γσ = 80 GeV

• EFT fails at resonance
• aQGC describe rise of

resonance

• Unitarization applied
• Tensor resonances better

visible than scalars

400 600 800 1000 1200 1400 1600 1800 2000 M(W +W +)[GeV] 10−2 10−1 100 101

∂σ ∂M

⇥

fb 100GeV

⇤

pp → W +W +jj

FS,0 = 19.2 TeV−4FS,1 = -134.1 TeV−4 FX = 38.6 TeV−1 SM limit of A22

MX = 1800 GeV ΓX = 720 GeV

ATLAS PRL 113(2014)14, 141803 [1405.6241]

Kilian/Ohl/JRR/Sekulla: PRD93(16),3. 036004 [1511.00022]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Complete LHC VBS process at 14 TeV

500 1000 1500 2000

M (e+, e−, µ+, µ−) [GeV]

50 100 150 200 250

N

pp → e+e−µ+µ−jj at 3 ab−1

Ff = 17.4 TeV−1 SM

Mf = 1.0 TeV

Work in progress: unitarization for transversal polarisations & for tribosons (pp → VVV)

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Recent WHIZARD Study for CLIC

Fleper/Kilian/JRR/Sekulla: 1607.03030 (tbp EPJC)

e− ¯ νe νe W − e+ W + Z W − W + e− ¯ νe νe W − e+ W + H W − W + e− ¯ νe νe W − e+ W + W − W +

Signal

e− ¯ νe e− Z, γ νe W − e+ W + e+ e− ¯ νe e− Z νe W − e+ W + W + e− ¯ νe νe W e+ W − W + νe e+

Bkgd.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Recent WHIZARD Study for CLIC

Fleper/Kilian/JRR/Sekulla: 1607.03030 (tbp EPJC)

e− ¯ νe νe W − e+ W + Z W − W + e− ¯ νe νe W − e+ W + H W − W + e− ¯ νe νe W − e+ W + W − W +

Signal

e− ¯ νe e− Z, γ νe W − e+ W + e+ e− ¯ νe e− Z νe W − e+ W + W + e− ¯ νe νe W e+ W − W + νe e+

Bkgd.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Recent WHIZARD Study for CLIC

Fleper/Kilian/JRR/Sekulla: 1607.03030 (tbp EPJC)

e− ¯ νe νe W − e+ W + Z W − W + e− ¯ νe νe W − e+ W + H W − W + e− ¯ νe νe W − e+ W + W − W +

Signal

e− ¯ νe e− Z, γ νe W − e+ W + e+ e− ¯ νe e− Z νe W − e+ W + W + e− ¯ νe νe W e+ W − W + νe e+

Bkgd.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Recent WHIZARD Study for CLIC

Fleper/Kilian/JRR/Sekulla: 1607.03030 (tbp EPJC)

e− ¯ νe νe W − e+ W + Z W − W + e− ¯ νe νe W − e+ W + H W − W + e− ¯ νe νe W − e+ W + W − W +

Signal

e− ¯ νe e− Z, γ νe W − e+ W + e+ e− ¯ νe e− Z νe W − e+ W + W + e− ¯ νe νe W e+ W − W + νe e+

Bkgd.

J.R.Reuter Event generator WHIZARD FCC-ee “Physics behind precision”, CERN, 2.2.16

Spin Correlation and Polarization in Cascades

Cascade decay, factorize production and decay

200 400 600 800 200 400 600 Minv(jℓ) #evt/bin 200 400 600 800 1000 200 400 600 Minv(jℓ) #evt/bin 200 400 600 800 200 400 600 Minv(jℓ) #evt/bin

simulate (fullproc)

200 400 600 800 200 400 600 Minv(jℓ) #evt/bin

simulate (casc) ?diagonal_decay = true ?isotropic_decay = true

J.R.Reuter Event generator WHIZARD FCC-ee “Physics behind precision”, CERN, 2.2.16

Spin Correlation and Polarization in Cascades

Cascade decay, factorize production and decay

200 400 600 800 200 400 600 Minv(jℓ) #evt/bin 200 400 600 800 1000 200 400 600 Minv(jℓ) #evt/bin 200 400 600 800 200 400 600 Minv(jℓ) #evt/bin

simulate (fullproc)

200 400 600 800 200 400 600 Minv(jℓ) #evt/bin

simulate (casc) ?diagonal_decay = true ?isotropic_decay = true unstable “W+” { decay_helicity = 0 }

Possibility to select specific helicity in decays!

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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WHIZARD Parton Shower

Two independent implementations: kT

• ordered QCD and Analytic QCD shower

Analytic shower: no shower veto ⇒ exact shower history known, allows reweighting

Kilian/JRR/Schmidt/Wiesler, JHEP 1204 013 (2012)

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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WHIZARD Parton Shower

Two independent implementations: kT

• ordered QCD and Analytic QCD shower

Analytic shower: no shower veto ⇒ exact shower history known, allows reweighting

Kilian/JRR/Schmidt/Wiesler, JHEP 1204 013 (2012)

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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WHIZARD Parton Shower

Two independent implementations: kT

• ordered QCD and Analytic QCD shower

Analytic shower: no shower veto ⇒ exact shower history known, allows reweighting

Kilian/JRR/Schmidt/Wiesler, JHEP 1204 013 (2012)

First tunes of kT

• ordered & Analytic QCD shower

Chokoufe/Englert/JRR, 2015 Di-/Multijet LEP as given in RIVET analysis Usage of the PROFESSOR tool for best fit [Buckley et al., 2009]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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NLO Development in WHIZARD

QCD corrections done, start work on QED and electroweak corrections Automated FKS subtraction WHIZARD provides Born, reals, all subtraction terms Virtual amplitudes linked externally Working NLO interfaces to:

GoSam [G. Cullen et al.] OpenLoops [F. Cascioli et al.] Recola (wip) [A. Denner et al.] ↪︎ Talk by Ansgar

work by summer student! [A. Motornenko]

• Plan to also support NJet [Badger et al.]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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NLO Development in WHIZARD

QCD corrections done, start work on QED and electroweak corrections Automated FKS subtraction WHIZARD provides Born, reals, all subtraction terms Virtual amplitudes linked externally Working NLO interfaces to:

GoSam [G. Cullen et al.] OpenLoops [F. Cascioli et al.] Recola (wip) [A. Denner et al.] ↪︎ Talk by Ansgar

WHIZARD v2.3.1 contains beta version QCD corrections (massless and massive emitters)

alpha_power = 2 alphas_power = 0 process eett = e1,E1 => t, tbar { nlo_calculation = “full” }

work by summer student! [A. Motornenko]

• Plan to also support NJet [Badger et al.]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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NLO Development in WHIZARD

QCD corrections done, start work on QED and electroweak corrections Automated FKS subtraction WHIZARD provides Born, reals, all subtraction terms Virtual amplitudes linked externally Working NLO interfaces to:

GoSam [G. Cullen et al.] OpenLoops [F. Cascioli et al.] Recola (wip) [A. Denner et al.] ↪︎ Talk by Ansgar

WHIZARD v2.3.1 contains beta version QCD corrections (massless and massive emitters)

alpha_power = 2 alphas_power = 0 process eett = e1,E1 => t, tbar { nlo_calculation = “full” }

work by summer student! [A. Motornenko]

• Plan to also support NJet [Badger et al.]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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NLO Development in WHIZARD

QCD corrections done, start work on QED and electroweak corrections Automated FKS subtraction WHIZARD provides Born, reals, all subtraction terms Virtual amplitudes linked externally Working NLO interfaces to:

GoSam [G. Cullen et al.] OpenLoops [F. Cascioli et al.] Recola (wip) [A. Denner et al.] ↪︎ Talk by Ansgar

WHIZARD v2.3.1 contains beta version QCD corrections (massless and massive emitters)

alpha_power = 2 alphas_power = 0 process eett = e1,E1 => t, tbar { nlo_calculation = “full” }

work by summer student! [A. Motornenko]

• Plan to also support NJet [Badger et al.]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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NLO Development in WHIZARD

QCD corrections done, start work on QED and electroweak corrections Automated FKS subtraction WHIZARD provides Born, reals, all subtraction terms Virtual amplitudes linked externally Working NLO interfaces to:

GoSam [G. Cullen et al.] OpenLoops [F. Cascioli et al.] Recola (wip) [A. Denner et al.] ↪︎ Talk by Ansgar

WHIZARD v2.3.1 contains beta version QCD corrections (massless and massive emitters)

alpha_power = 2 alphas_power = 0 process eett = e1,E1 => t, tbar { nlo_calculation = “full” }

work by summer student! [A. Motornenko]

• Plan to also support NJet [Badger et al.]

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Examples and Validation

Simplest benchmark process:

e+e− → q¯ q with

• σNLO − σLO

/σLO = αs/π

Excerpt of validated QCD NLO processes

• Cross-checks with MG5_aMC@NLO, Sherpa, MUNICH
• Phase space integration performs great (V, R, S)
• e+e− → q¯

q

• e+e− → q¯

qg

• e+e− → `+`−q¯

q

• e+e− → `+⌫`q¯

q

• e+e− → t¯

t

• e+e− → tW −b
• e+e− → W +W −b¯

b

• e+e− → t¯

tH

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Examples and Validation

Simplest benchmark process:

e+e− → q¯ q with

• σNLO − σLO

/σLO = αs/π

Excerpt of validated QCD NLO processes

• Cross-checks with MG5_aMC@NLO, Sherpa, MUNICH
• Phase space integration performs great (V, R, S)
• e+e− → q¯

q

• e+e− → q¯

qg

• e+e− → `+`−q¯

q

• e+e− → `+⌫`q¯

q

• e+e− → t¯

t

• e+e− → tW −b
• e+e− → W +W −b¯

b

• e+e− → t¯

tH

Add weights of real emission events to weight of Born kinematics using the FKS mapping Output weighted events in WHIZARD (e.g. using HepMC), then analysis with Rivet NLO Fixed Order Events

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Resonance mappings for NLO processes

Amplitudes (except for pure QCD/QED) contain resonances (Z, W, H, t) In general: resonance masses not respected by modified kinematics of subtraction terms Collinear (and soft) radiation can lead to mismatch between Born and subtraction terms

↪︎ Talk by Carlo

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Resonance mappings for NLO processes

Amplitudes (except for pure QCD/QED) contain resonances (Z, W, H, t) In general: resonance masses not respected by modified kinematics of subtraction terms Collinear (and soft) radiation can lead to mismatch between Born and subtraction terms Algorithm to include resonance histories [Ježo/Nason, 1509.09071] Avoids double logarithms in the resonances’ width Most important for narrow resonances (H ➝ bb) Separate treatment of Born and real terms, soft mismatch [, collinear mismatch]

↪︎ Talk by Carlo

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Resonance mappings for NLO processes

Amplitudes (except for pure QCD/QED) contain resonances (Z, W, H, t) In general: resonance masses not respected by modified kinematics of subtraction terms Collinear (and soft) radiation can lead to mismatch between Born and subtraction terms Algorithm to include resonance histories [Ježo/Nason, 1509.09071] Avoids double logarithms in the resonances’ width Most important for narrow resonances (H ➝ bb) Separate treatment of Born and real terms, soft mismatch [, collinear mismatch]

↪︎ Talk by Carlo

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

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Resonance mappings for NLO processes

Amplitudes (except for pure QCD/QED) contain resonances (Z, W, H, t) In general: resonance masses not respected by modified kinematics of subtraction terms Collinear (and soft) radiation can lead to mismatch between Born and subtraction terms Algorithm to include resonance histories [Ježo/Nason, 1509.09071] Avoids double logarithms in the resonances’ width Most important for narrow resonances (H ➝ bb) Separate treatment of Born and real terms, soft mismatch [, collinear mismatch] WHIZARD complete automatic implementation: example e+ e− ➝ μμbb (ZZ, ZH histories)

standard FKS

↪︎ Talk by Carlo

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 15

Resonance mappings for NLO processes

Amplitudes (except for pure QCD/QED) contain resonances (Z, W, H, t) In general: resonance masses not respected by modified kinematics of subtraction terms Collinear (and soft) radiation can lead to mismatch between Born and subtraction terms Algorithm to include resonance histories [Ježo/Nason, 1509.09071] Avoids double logarithms in the resonances’ width Most important for narrow resonances (H ➝ bb) Separate treatment of Born and real terms, soft mismatch [, collinear mismatch] WHIZARD complete automatic implementation: example e+ e− ➝ μμbb (ZZ, ZH histories)

standard FKS FKS with resonance mappings

↪︎ Talk by Carlo

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 16

Automated POWHEG Matching, e.g.: e+e− →jj

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 17

WHIZARD LHC example: Drell-Yan

• Simplest hadron collider processes: pp → (Z →ll) + X, pp → (W →lν) + X, pp → ZZ + X
• Standard candle processes

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 17

WHIZARD LHC example: Drell-Yan

• Simplest hadron collider processes: pp → (Z →ll) + X, pp → (W →lν) + X, pp → ZZ + X
• Standard candle processes

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 17

WHIZARD LHC example: Drell-Yan

• Simplest hadron collider processes: pp → (Z →ll) + X, pp → (W →lν) + X, pp → ZZ + X
• Standard candle processes
• Flavor sums in fixed-order event generation
• Color in initial and final state (already validated for top decay)
• Gluons in the initial state
• Next processes: pp → Zj + X, pp → tt + X, pp → jj + X
• automated POWHEG matching for hadron collider

To be fully validated:

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 18

WHIZARD ee example: tt & ttH (on-/off-shell)

Paradigm processes at lepton colliders: precision determination of mt and Yt Major bkgd. for EW processes (VVV, VBS); many BSM searches Processes of increasing complexity: 2→2, 2→4, 2→6

double-resonant single top non-resonant single top

Cross checks for 2→2, 2→4 with Sherpa, Munich, Madgraph5_aMC@NLO Using massive b quarks: no cuts necessary for e+e− → W+W−bb Full process e+e− → μ+νμe−νebb exhibits collinear singularity: Typical pentagon/hexagon diagrams:

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 19

WHIZARD ee example: tt & ttH (on-/off-shell)

complex mass scheme:

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 19

Choose = 800 GeV because its the maximum of the ttH cross section

√s

WHIZARD ee example: tt & ttH (on-/off-shell)

complex mass scheme:

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 19

Choose = 800 GeV because its the maximum of the ttH cross section

√s

WHIZARD ee example: tt & ttH (on-/off-shell)

complex mass scheme:

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 20

WHIZARD ee example: tt & ttH (on-/off-shell)

Eh = 1 2√s ⇥ s + M 2

h − (k1 + k2)2⇤

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 20

WHIZARD ee example: tt & ttH (on-/off-shell)

Eh = 1 2√s ⇥ s + M 2

h − (k1 + k2)2⇤

Determination of top Yukawa coupling (ttH)

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 20

WHIZARD ee example: tt & ttH (on-/off-shell)

Eh = 1 2√s ⇥ s + M 2

h − (k1 + k2)2⇤

Determination of top Yukawa coupling (ttH) Polarized Results (tt)

• ILC will always run polarized
• Polarized 1-loop amplitudes beyond BLHA

Chokoufé/Kilian/Lindert/Pozzorini/JRR/Weiss, 1608.XXXXX

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 21

POWHEG-matched results for tt and ttH

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 22

Threshold-continuum matching: e.g. top

ILC top threshold scan best-known method to measure top quark mass, ΔΜ ~ 30-50 MeV Threshold region: top velocity v ~ αs ⪡ 1

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 22

Threshold-continuum matching: e.g. top

ILC top threshold scan best-known method to measure top quark mass, ΔΜ ~ 30-50 MeV Threshold region: top velocity v ~ αs ⪡ 1

330.0 337.5 345.0 352.5 360.0 √s [GeV] 250 500 750 1000 σ [fb] σNLL,full

σexpanded,NLL,full

[αH, αH] σoffshell,NLO,full

σmatched

Bach/Chokoufé/Hoang/ Kilian/JRR/Stahlhofen/ Teubner/Weiss, 2016 & work in progress

For (almost) fully exclusive description: proper matching between vNRQCD NLL resummation and NLO QCD continuum

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 22

Threshold-continuum matching: e.g. top

ILC top threshold scan best-known method to measure top quark mass, ΔΜ ~ 30-50 MeV Threshold region: top velocity v ~ αs ⪡ 1 Similar matching for WW threshold ! (in prep.)

330.0 337.5 345.0 352.5 360.0 √s [GeV] 250 500 750 1000 σ [fb] σNLL,full

σexpanded,NLL,full

[αH, αH] σoffshell,NLO,full

σmatched

Bach/Chokoufé/Hoang/ Kilian/JRR/Stahlhofen/ Teubner/Weiss, 2016 & work in progress

For (almost) fully exclusive description: proper matching between vNRQCD NLL resummation and NLO QCD continuum

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 23

Conclusions & Outlook

WHIZARD 2.3 event generator for collider physics (ee, pp, ep) BSM: focus on VBS simplified models / unitarization / full dim. 6 SM EFT Unitarization for transversal bosons & for tribosons [work in progress] UFO support [still in validation phase] NLO automation: reals and FKS subtraction [+ virtuals externally] [QCD almost completed, EW started] ➝ WHIZARD 3.0 Can produce NLO fixed-order histograms Automated POWHEG matching [other schemes in progress] NLL NRQCD threshold / NLO continuum matching (e.g. in ee → tt ) Performance: Virtual Machine for MEs, MPI parallelization [validated], … Plans & projects: showers, merging, MPI, inclusion in CheckMate, … , …

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 24

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23

BACKUP SLIDES

25

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 26

WHIZARD: Manual

WHIZARD Manual @ HepForge

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 27

The Optimizing Matrix Element Generator (O’Mega)

O’Mega [Ohl, 2000; Moretti/Ohl/JRR, 2001; JRR, 2002] computes amplitudes with

1-particle off-shell wave functions (1POWs)

• x

p q q = x p q q + x p q q + x p q q

• Possible to construct set of all currents recursively (tree-/1-loop level)

Keystones K to replace sum

• ver Feynman diagrams

Calculation forms Directed Acyclical Graphs (DAGs), optimized to consist only of the minimal number of connections by O’Mega

F (n)

X

i=1

Di =

P (n)

X

k,l,m=1

K(3)

fkflfm(pk, pl, pm)Wfk(pk)Wfl(pl)Wfm(pm)

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 28

Phase Space Setup

WHIZARD algorithm: heuristics to classify phase-space topology, adaptive multi-channel

mapping ⟹ resonant, t-channel, radiation, infrared, collinear, off-shell Complicated processes: factorization into production and decay with the unstable option

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 29

FKS Subtraction (Frixione/Kunszt/Signer)

Subtraction formalism to make real and virtual contributions separately finite

dσNLO = Z

n+1

• dσR − dσS

| {z }

finite

+ Z

n+1

dσS + Z

n

dσV | {z }

finite

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 29

FKS Subtraction (Frixione/Kunszt/Signer)

Subtraction formalism to make real and virtual contributions separately finite

dσNLO = Z

n+1

• dσR − dσS

| {z }

finite

+ Z

n+1

dσS + Z

n

dσV | {z }

finite

✴ Find all singular pairs ✴ Partition phase space according to singular regions ✴ Generate subtraction terms for singular regions

I = {(1, 5), (1, 6), (2, 5), (2, 6), (5, 6)}

1 = X

α∈I

Sα(Φ)

Automated subtraction terms in WHIZARD, algorithm:

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 29

FKS Subtraction (Frixione/Kunszt/Signer)

Subtraction formalism to make real and virtual contributions separately finite

dσNLO = Z

n+1

• dσR − dσS

| {z }

finite

+ Z

n+1

dσS + Z

n

dσV | {z }

finite

✴ Find all singular pairs ✴ Partition phase space according to singular regions ✴ Generate subtraction terms for singular regions

I = {(1, 5), (1, 6), (2, 5), (2, 6), (5, 6)}

1 = X

α∈I

Sα(Φ)

Automated subtraction terms in WHIZARD, algorithm:

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 30

Automated POWHEG Matching in WHIZARD

Soft gluon emissions before hard emission generate large logs Perturbative αs : Consistent matching of NLO matrix element with shower POWHEG method: hardest emission first [Nason et al.]

|Msoft|2 ∼ 1 k2

T

→ log kmax

T

kmin

T

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 30

Automated POWHEG Matching in WHIZARD

Soft gluon emissions before hard emission generate large logs Perturbative αs : Consistent matching of NLO matrix element with shower POWHEG method: hardest emission first [Nason et al.]

|Msoft|2 ∼ 1 k2

T

→ log kmax

T

kmin

T

• Complete NLO events
• POWHEG generate events according to the formula:
• Uses the modified Sudakov form factor:

B(Φn) = B(Φn) + V (Φn) + Z dΦradR(Φn+1)

dσ = B(Φn)  ∆NLO

R

(kmin

T

) + ∆NLO

R

(kT )R(Φn+1) B(Φn) dΦrad

• ∆NLO

R

(kT ) = exp  − Z dΦrad R(Φn+1) B(Φn) θ(kT (Φn+1) − kT )

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 30

Automated POWHEG Matching in WHIZARD

Soft gluon emissions before hard emission generate large logs Perturbative αs : Consistent matching of NLO matrix element with shower POWHEG method: hardest emission first [Nason et al.]

|Msoft|2 ∼ 1 k2

T

→ log kmax

T

kmin

T

• Complete NLO events
• POWHEG generate events according to the formula:
• Uses the modified Sudakov form factor:

B(Φn) = B(Φn) + V (Φn) + Z dΦradR(Φn+1)

dσ = B(Φn)  ∆NLO

R

(kmin

T

) + ∆NLO

R

(kT )R(Φn+1) B(Φn) dΦrad

• ∆NLO

R

(kT ) = exp  − Z dΦrad R(Φn+1) B(Φn) θ(kT (Φn+1) − kT )

• Hardest emission: ; shower with imposing a veto

if virtual and real terms larger than Born: shouldn’t happen in perturbative regions Reweighting such that for all events POWHEG: Positive Weight Hardest Emission Generator own implementation in WHIZARD

kmax

T

B < 0 B > 0

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 31

Top-Forward Backward Asymmetry

AFB of the top quark AFB of the anti-top quark Gluon emission symmetric in θ ⇒ NLO QCD corrections small

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 32

Top Threshold Resummation in (p)NRQCD

NRQCD is EFT for non-relativistic quark-antiquark systems: separate M·v and M·v Integrate out hard quark and gluon d.o.f. Resummation of singular terms close to threshold (v = 0) Hoang/Teubner, 1999; Hoang et al., 2001

2

R ≡ σt¯

t

σµµ = v X

k

⇣αs v ⌘k X

i

(αs ln v)i × ×

• 1 (LL); αs, v (NLL); α2

s, αsv, v2 (NNLL)

Phase space of two massive particles (p/v)NRQCD EFT w/ RG improvement

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 32

Top Threshold Resummation in (p)NRQCD

NRQCD is EFT for non-relativistic quark-antiquark systems: separate M·v and M·v Integrate out hard quark and gluon d.o.f. Resummation of singular terms close to threshold (v = 0) Hoang/Teubner, 1999; Hoang et al., 2001

2

R ≡ σt¯

t

σµµ = v X

k

⇣αs v ⌘k X

i

(αs ln v)i × ×

• 1 (LL); αs, v (NLL); α2

s, αsv, v2 (NNLL)

Phase space of two massive particles

Rγ,Z(s) = F v(s)Rv(s) | {z }

s-wave: LL+NLL

+ F a(s)Ra(s) | {z }

p-wave∼v2:NNLL

but contributes at NLL differentially! (p/v)NRQCD EFT w/ RG improvement

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 32

Top Threshold Resummation in (p)NRQCD

NRQCD is EFT for non-relativistic quark-antiquark systems: separate M·v and M·v Integrate out hard quark and gluon d.o.f. Resummation of singular terms close to threshold (v = 0) Hoang/Teubner, 1999; Hoang et al., 2001

2

R ≡ σt¯

t

σµµ = v X

k

⇣αs v ⌘k X

i

(αs ln v)i × ×

• 1 (LL); αs, v (NLL); α2

s, αsv, v2 (NNLL)

Phase space of two massive particles Coulomb potential gluon ladder resumption

Rγ,Z(s) = F v(s)Rv(s) | {z }

s-wave: LL+NLL

+ F a(s)Ra(s) | {z }

p-wave∼v2:NNLL

but contributes at NLL differentially! (p/v)NRQCD EFT w/ RG improvement

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 32

Top Threshold Resummation in (p)NRQCD

NRQCD is EFT for non-relativistic quark-antiquark systems: separate M·v and M·v Integrate out hard quark and gluon d.o.f. Resummation of singular terms close to threshold (v = 0) Hoang/Teubner, 1999; Hoang et al., 2001

2

R ≡ σt¯

t

σµµ = v X

k

⇣αs v ⌘k X

i

(αs ln v)i × ×

• 1 (LL); αs, v (NLL); α2

s, αsv, v2 (NNLL)

Phase space of two massive particles Coulomb potential gluon ladder resumption

Rγ,Z(s) = F v(s)Rv(s) | {z }

s-wave: LL+NLL

+ F a(s)Ra(s) | {z }

p-wave∼v2:NNLL

but contributes at NLL differentially!

| {z }

can be mapped onto effective ttV vertex

C 3 Gv/a

(N)LL = Gv/a (N)LL(↵s, M pole t

, ps, |~ pt| , Γt)

differential in off-shell tt phase space far away from threshold (p/v)NRQCD EFT w/ RG improvement

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 33 with B. Chokoufé/A. Hoang/M. Stahlhofen/T. Teubner/C. Weiss

Top Threshold in WHIZARD

Implement resummed threshold effects as effective vertex [form factor] in WHIZARD from TOPPIK code [Jezabek/Teubner], included in WHIZARD Gv,a(0, pt, E + iΓt, ν)

M1S = 172 GeV, Γt = 1.54 GeV, αs(MZ) = 0.118

Default parameters:

M 1S = M pole

t

(1 − ∆LL/NLL

(Coul.) )

Marquard et al.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 33 with B. Chokoufé/A. Hoang/M. Stahlhofen/T. Teubner/C. Weiss

Top Threshold in WHIZARD

Implement resummed threshold effects as effective vertex [form factor] in WHIZARD from TOPPIK code [Jezabek/Teubner], included in WHIZARD Gv,a(0, pt, E + iΓt, ν)

M1S = 172 GeV, Γt = 1.54 GeV, αs(MZ) = 0.118

Default parameters:

M 1S = M pole

t

(1 − ∆LL/NLL

(Coul.) )

Marquard et al.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 33 with B. Chokoufé/A. Hoang/M. Stahlhofen/T. Teubner/C. Weiss

Top Threshold in WHIZARD

Implement resummed threshold effects as effective vertex [form factor] in WHIZARD from TOPPIK code [Jezabek/Teubner], included in WHIZARD Gv,a(0, pt, E + iΓt, ν)

M1S = 172 GeV, Γt = 1.54 GeV, αs(MZ) = 0.118

Default parameters:

M 1S = M pole

t

(1 − ∆LL/NLL

(Coul.) )

Theory uncertainties from scale variations: hard and soft scale

µh = h · mt µs = f · mtv

Marquard et al.

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 34

Sanity checks: correct limit for αs ⟶ 0, stable against variation of cutoff ΔM [15-30 GeV] Why include LL/NLL in a Monte Carlo event generator? Important effects: beamstrahlung; ISR; LO electroweak terms More exclusive observables accessible

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 34

Sanity checks: correct limit for αs ⟶ 0, stable against variation of cutoff ΔM [15-30 GeV] Why include LL/NLL in a Monte Carlo event generator? Important effects: beamstrahlung; ISR; LO electroweak terms More exclusive observables accessible

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 34

Sanity checks: correct limit for αs ⟶ 0, stable against variation of cutoff ΔM [15-30 GeV] Why include LL/NLL in a Monte Carlo event generator? Important effects: beamstrahlung; ISR; LO electroweak terms More exclusive observables accessible Forward-backward asymmetry (norm. ⇒ good shape stability)

Afb := σ(pt

z > 0) − σ(pt z) < 0)

σ(pt

z > 0) + σ(pt z < 0)

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 35

Matching to continuum at (LO and) NLO

• Transition region between relativistic and

resummation effects

• CLIC benchmark energies:

0.38 TeV, 1.4 TeV, 3.0 TeV

• Remove double-counting NLO / (N)LL

340 350 360 370 380 390 400 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 35

Matching to continuum at (LO and) NLO

• Transition region between relativistic and

resummation effects

• CLIC benchmark energies:

0.38 TeV, 1.4 TeV, 3.0 TeV

• Remove double-counting NLO / (N)LL

340 350 360 370 380 390 400 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell 344.0 344.5 345.0 345.5 346.0 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell

Resummed formfactor, expanded to O(αs)

⌫ = r√s − 2mt + iΓt m p = |~ p| p0 = Et − mt

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 35

Matching to continuum at (LO and) NLO

• Transition region between relativistic and

resummation effects

• CLIC benchmark energies:

0.38 TeV, 1.4 TeV, 3.0 TeV

• Remove double-counting NLO / (N)LL

340 350 360 370 380 390 400 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell 344.0 344.5 345.0 345.5 346.0 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell

Resummed formfactor, expanded to O(αs)

⌫ = r√s − 2mt + iΓt m p = |~ p| p0 = Et − mt

Matching formula

J.R.Reuter WHIZARD MBI 2016, U. Wisconsin, Madison, 25.08.16

/23 35

Matching to continuum at (LO and) NLO

• Transition region between relativistic and

resummation effects

• CLIC benchmark energies:

0.38 TeV, 1.4 TeV, 3.0 TeV

• Remove double-counting NLO / (N)LL

340 350 360 370 380 390 400 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell 344.0 344.5 345.0 345.5 346.0 √s [GeV] 200 400 600 800 1000 σ [fb]

• nshell, NLO

expanded FF, onshell, mpole = m1S expanded FF, onshell, mpole = m1S, nopwave AnalyticOneloop, mpole = m1S, onshell analytic+whizard-onshell

Resummed formfactor, expanded to O(αs)

⌫ = r√s − 2mt + iΓt m p = |~ p| p0 = Et − mt

Matching formula Switch-off function