Recent Developments of the WHIZARD Event Generator

Christian Weiss

DESY Hamburg

AWLC2017, SLAC, June 26th

1 / 19 The WHIZARD Event Generator

WHIZARD 2.5.0 - May 6, 2017( http://whizard.hepforge.org) Multi-purpose event generator for lepton and hadron colliders. Modular structure:

I O’Mega: Matrix element generator

I VAMP: Adaptive multi-channel Monte Carlo integrator

I CIRCE: Simulation tool for lepton collider beam spectra

I SINDARIN: Script language for simulation and analysis

I Lepton beam ISR

EPJ C71 (2011) 1742, [arXiv:0708.4233], whizard@desy.de

2 / 19 Team members

Senior members:

I Wolfgang Kilian (Siegen University)

I J¨urgenReuter (DESY)

I Thorsten Ohl (W¨urzburgUniversity) Junior members:

I Bijan Chokouf´e(DESY, Fixed-order NLO and threshold matching, parton showers)

I Vincent Rothe (DESY, Electroweak NLO)

I Simon Braß (Siegen U., Parallelization, Fixed-order NLO)

I Christian Fleper (Siegen U., Vector-Boson Fusion)

3 / 19 Overview

1 Higher-order computations with WHIZARD

2 Parallelization with MPI

3 Miscellaneous features

4 / 19 WHIZARD+NLO

I Uses FKS subtraction. I Validation of QCD corrections almost done. I Work on EW corrections has been picked up. Expect ﬁrst numbers at LCWS in October.

+ + + e e− tt¯ and e e− W W −b¯b → → 875 3.00 LO tt¯ NLO tt¯ + LO W W −b¯b 700 + 2.00 NLO W W −b¯b K-factor

525 1.00

[fb] 300 350 400 √ σ s [GeV] alpha power = 2 350 alphas power = 0 175 0 WHIZARD+OPENLOOPS process eett = e1, E1 => t, T 1.15 1.10 nlo calculation = "Full" 1.05 K-factor 1.00 { } 0.95 ¯ t 2.0 t 1.75 /σ b ¯ b

− 1.5 W

+ 1.25

W 1.0 σ 500 1000 1500 2000 2500 3000 √s [GeV] Supported One-Loop-Providers: I GoSam [G. Cullen et.al.] I OpenLoops [F. Cascioli et.al.] I RECOLA [A. Denner et.al.] 5 / 19 Comparison with MG5aMC@NLO

MG5 aMC Whizard Final state σLO[fb] σNLO[fb] K σLO[fb] σNLO[fb] K jj 622.3(5) 639(1) 1.02684 622.73(4) 639.7(2) 1.02725 b¯b 92.73(6) 94.89(1) 1.0233 92.32(1) 94.78(7) 1.02664 tt¯ 166.2(2) 174.5(6) 1.04994 166.4(1) 175.1(1) 1.05228 ttj¯ 48.13(5) 53.43(1) 1.11012 48.3(2) 53.66(9) 1.11098 4 4 4 4 ttt¯ t¯ 6.45(1) 10− 12.21(5) 10− 1.89302 6.463(2) 10− 12.16(2) 10− 1.88147 · 1 · 1 · 1 · 1 b¯bb¯b 1.644(3) 10− 3.60(1) 10− 2.1897 1.64(2) 10− 3.67(4) 10− 2.2378 · 1 · 1 · 1 · 1 ttb¯ ¯b 1.819(3) 10− 2.92(1) 10− 1.6052 1.86(1) 10− 2.93(2) 10− 1.5752 · · · · jjj 340.1(2) 316(2) 0.92914 342.4(5) 319(1) 0.93166 jjjj 104.7(1) 109.0(6) 1.04106 105.1(4) 118(1) 1.12274 5 5 5 5 ttt¯ tj¯ 2.719(5) 10− 5.34(3) 10− 1.96394 2.722(1) 10− 4.471(5) 10− 1.64253 · · · · Madgraph numbers from [Alwall et.al., 1405.0301].

6 / 19 Comparison with Madgraph

MG5 aMC WHIZARD Final State σLO[fb] σNLO[fb] K σLO[fb] σNLO[fb] K ttH¯ 2.018(3) 1.911(6) 0.9461 2.022(3) 1.913(3) 0.9461 ttγ¯ 12.7(2) 13.3(4) 1.04726 12.71(4) 13.78(4) 1.08418 ttZ¯ 4.642(6) 4.95(1) 1.06636 4.64(1) 4.94(1) 1.06467 2 2 2 2 ttZ¯ 3.600(6) 10− 3.58(1) 10− 0.99445 3.596(1) 10− 3.581(2) 10− 0.99571 ttγZ¯ 0.2212(3)· 0.2364(6)· 1.06873 0.220(1)· 0.240(2) · 1.09094 2 2 2 2 ttγH¯ 9.75(1) 10− 9.42(3) 10− 0.96614 9.748(6) 10− 9.58(7) 10− 0.98277 · · · · ttγγ¯ ∗ 0.383(5) 0.416(2) 1.08618 0.382(3) 0.420(3) 1.09952 2 2 2 2 ttZZ¯ 3.788(4) 10− 4.00(1) 10− 1.05597 3.756(4) 10− 4.005(2) 10− 1.06621 · 2 · 2 · 2 · 2 ttHH¯ 1.358(1) 10− 1.206(3) 10− 0.888 1.367(1) 10− 1.218(1) 10− 0.8909 + · · · · ttW¯ W − 0.1372(3) 0.1540(6) 1.1225 0.1370(4) 0.1538(4) 1.12257 4 4 4 4 ttW¯ ±jj 2.400(4) 10− 3.72(1) 10− 1.541 2.41(1) 10− 3.74(2) 10− 1.55186 · · · · ttHj¯ 0.2533(3) 0.2658(9) 1.04935 0.254(1) 0.307(1) 1.20874 ttγj¯ 2.355(2) 2.62(1) 1.11253 2.47(1) 3.14(2) 1.27124 ttZj¯ 0.6059(6) 0.694(3) 1.14548 0.610(4) 0.666(5) 1.09187

Madgraph numbers from [Alwall et.al., 1405.0301].

7 / 19 Resonance-aware FKS

Factorization in the soft limit 100 Numerical instabilties arise from + + I e e− µ µ−b¯b Standard FKS very narrow resonances (e.g. → Resonance-aware FKS internal Higgs bosons). 10

I Resonance-aware modiﬁcation α soft α 1 R of FKS [Jeˇzo/Nason,1509.0907] R implemented in

WHIZARD leads to 0.1 signiﬁcant improvements.

I Additional soft mismatch 0.01 0.00 0.01 0.02 0.03 0.04 0.04 integration component. Eg [GeV]

σreal[fb] σmism[fb] ncalls standard 1.90485 0.99% n/a 5 100000 resonances −9.15077 ± 0.52% 0.97930 0.94% 5 20000(real×) + 5 20000(mism.) − ± − ± × ×

8 / 19 Powheg matching

+ e e− tt,¯ √s = 500GeV 2 → 10 NLO

GeV] Powheg h =1 / Powheg h =5 [fb 1

dσ 10 Powheg h = 10 dm Powheg h = 50 Powheg h = 100 1 Powheg I WHIZARD can generate

1 10− weighted ﬁxed-order NLO Whizard+OpenLoops events. Large logarithms 2 10−10 9 → 8 and double counting when 7 6 NLO 5 4 interfaced to parton shower. σ/σ 3 2 1 I Powheg matching [Nason, 300 350 400 450 500 m(pt + pt¯) hep-ph/0409146] overcomes this + e e− tt,¯ √s = 500GeV → NLO issue, keeping NLO accuracy in

[fb] 500 Powheg h =1 jets dσ

dN Powheg h =5 the parton shower. 400 Powheg h = 10 Powheg h = 50 300 Powheg h = 100 I Available out-of-the box in Powheg

200 WHIZARD , with grids being ﬁlled during integration. 100 Whizard+OpenLoops

0 I Setup also allows for matrix 1.4 1.2 element method at NLO.

NLO 1

σ/σ 0.8 0.6 1.5 2 2.5 3 3.5 4 4.5 5 9 / 19 Njets Top Threshold Resummation and Matching to Continuum

∆mt = 30 GeV, NLL, only s-wave contributions

1000

800

600 [fb] σ 400

200 Fixed-order approximation fails Whizard signal I Analytic Whizard factorized close to the top production 0 1.50 threshold. Require resummation 1.25 1.00

of large logarithms. Whizard factorized 0.75

σ/σ 0.50 I Available in WHIZARD via 330 340 350 360 370 380 √s [GeV]

interface to TOPPIK 1000

900 I Activate: 800

model = sm tt threshold 700 I Fixed-order NLO contributions 600

[fb] 500

are consistently taken into σ 400

account. 300 matched, v1 = 1000, v2 = 10000 200 matched, v1 = 0.10, v2 = 0.30 matched, v1 = 0.10, v2 = 0.40 matched, v1 = 0.15, v2 = 0.30 100 NLO NLL 0

330 340 350 360 370 380 √s [GeV]

10 / 19 Top Threshold Resummation and Matching to Continuum

∆mt = 30 GeV, NLL, only s-wave contributions

1000

800

600 [fb] σ 400

200 Fixed-order approximation fails Whizard signal I Analytic Whizard factorized close to the top production 0 1.50 threshold. Require resummation 1.25 1.00

of large logarithms. Whizard factorized 0.75

σ/σ 0.50 I Available in WHIZARD via 330 340 350 360 370 380 √s [GeV]

interface to TOPPIK 1000

900 I Activate: 800

model = sm tt threshold 700 I Fixed-order NLO contributions 600

[fb] 500

are consistently taken into σ 400

account. 300 matched, v1 = 1000, v2 = 10000 200 matched, v1 = 0.10, v2 = 0.30 matched, v1 = 0.10, v2 = 0.40 matched, v1 = 0.15, v2 = 0.30 100 NLO NLL 0

330 340 350 360 370 380 √s [GeV]

10 / 19

Talk on Thursday → Overview

1 Higher-order computations with WHIZARD

2 Parallelization with MPI

3 Miscellaneous features

11 / 19 Parallelization using MPI

I Event generation can be split up into several individual jobs Trivial parallelization. → I Serial integration takes Several days for grid computation until event generation can→ start. The integration is the performance bottleneck for many simulations. I Thread-parallelization with OpenMP [Chokouf´eet.al, 1602.07242] Parallel performance of 2 (n 2)g amplitudes → −

p = 100% 1.0 n = 6 (PS) 10 n = 6 (A) n = 7 (PS) 0.9 n = 7 (A) n = 8 (PS) n = 8 (A) 8 p = 95% 0.8 s

s/n 0.7 6

speedup 0.6 efﬁciency

4 0.5

0.4 2

0.3 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 threads N threads N

I Core-parallelization: Non-trivial setup of integration required due to communication for grid adaption.

12 / 19 Parallelization using MPI

WHIZARD can compute on multiple cores usingMessagePassing Interface (MPI). Do not confuse with OpenMP, which uses several threads on same core.

I total integral: Result of indiviual workers. call MPI Ireduce (total integral, root total integral, 1, I root total integral: MPI DOUBLE PRECISION, MPI SUM, 0, Collected result. MPI COMM WORLD, status(1)) I MPI SUM: Operation to be performed. Usage in WHIZARD:

I Download Open MPI; Install with either gfortran or ifort.

I Conﬁgure WHIZARD: FC=mpifort F77=mpifort --enable-fc-mpi.

I In Sindarin ﬁle: $integration method = "vamp2" and $rng method = "rng stream".

13 / 19 Parallelization using MPI – speedup

100

gg → Wqq gg → Wqq g gg → Wqq gg j j → Wj j j → Wj j 10 j j → Wj j j

Speedup j j → WWbb 푝 = 1.0 푝 = 0.9

1 1 10 100

푁Tasks

I Speedup of 10 to 30 achieved.

I Saturation occurs at (100) tasks. O 1 I Amdahl’s law: Speedup = 1 p+p/N − 14 / 19 Parallelization using MPI – execution time

100

gg → Wqq

] 1 gg → Wqq g h gg → Wqq gg j j → Wj j j → Wj j

Time [ 0.1 j j → Wj j j j j → WWbb

0.01

0.001 1 10 100

푁Tasks Processes which took one week to compute can now be computed within hours.

15 / 19 Overview

1 Higher-order computations with WHIZARD

2 Parallelization with MPI

3 Miscellaneous features

16 / 19 The UFO interface [Degrande et.al., 1108.2040]

WHIZARD default: Manually create Ocaml and Fortran code. New UFO interface: Implementation of new physics models with python code.

O’Mega Whizard

UFO: python ﬁles Fortran code

particles.py proc id.f90 vertices.py model parameters.f90 lorentz.py ... couplings.py default lib.f90 ...

17 / 19

1 Update on LC generator group issues

Validation of WHIZARD 2.5.0 against WHIZARD 1.9.5 mostly completed.

I Existing LCIO interface since 2.2.4. (generator) status code correctly set.

I Tauola interface validated against 1.9.5

I All 2 8 and 2 10 processes work. → → I Mismatch of post-shower photon and hadron multiplicities solved by a generic hard ME matching based on resonance histories.

I pT spectrum of ISR photons: Need to create event transformation after shower.

18 / 19 Summary & Outlook

I WHIZARD 2.5.0 leading-order validation is mostly done.

I Fixed-order NLO QCD and top threshold matching can now be used out-of-the box.

I Parallelized integration leads to signiﬁcant performance gains. Future work

I First eﬀorts on electroweak NLO.

I Consistent matching of lepton beam structures and NLO eﬀects.

19 / 19 Overview

4 Appendix

20 / 19 Section 4

Appendix

21 / 19 Resonance-aware FKS subtraction [Jeˇzo/Nason,1509.0907]

The studied processes contain very narrow resonances, e.g. ΓH = (100MeV ). e+ b O 1 Born h 2 2 2 2 2 i− ¯b I DH = p¯bb mH + mH ΓH , H ν − µ 1 + 2 Z µ Real 2 2 2 2 − I D = p m + m Γ e− H bbg − H H H e− ν¯e Parameterize deviation from resonance: 2 2 2 pbbg =p ¯bb + ∆bbg

Born p¯2 m2 ∆4 DH bb→ H bbg Divergence close to resonance: Real = 1 + 2 2 DH mH ΓH

22 / 19 Resonance-aware FKS subtraction [Jeˇzo/Nason,1509.0907]

Born p¯2 m2 ∆4 DH bb→ H bbg Divergence close to resonance: Real = 1 + 2 2 DH mH ΓH

Solution: Fix ∆bbg = 0. The real phase space is constructed in such a way that the invariant mass of the resonance system including the radiated particle (gluon) is conserved.

22 / 19 Problems in top-pair production

Emission from b-quark regularised, but no suitable mapping for top-associated emissions exist!

W − W − ¯b ¯b m + m¯ − m + m¯ − b bW g ≈ bW ≈ b bW ≈ bW g ≈ g mt X g mt W + W +

I Internal top quarks not treated correctly!

I Initial-state phase-space mappings required.

I This study: Naive ﬁxed beam setting. Leave out top resonance histories (only a performance issue).

23 / 19 Resonance aware FKS subtraction: soft mismatch

Soft part of virtual integral: Z 1 ε 3 2ε 2 Is,α dΦns − dΩ − lim ξ α ∼ ξ 0 R → Resonance FKS: s k2 for each resonance history, → res Z 2 1 ε 3 2ε 2 Is,α dΦn kres − dΩ − lim ξ α ∼ ξ 0 R → Globality has to be restored soft mismatch →

Z Z Z 1 Z 2π 2k·kres ∞ sξ 2 − kres ξ Imism,α = dΦn dξ dy dφ 3 s,α e e− 0 1 0 (4π) × R − α − 0 " 2k·kres ki # ) 32πα C 2 0 s j(fb) 1 − kres k ξ (1 y)− e j e− , − sξ2 Bfb − − α (1)

24 / 19 Resonance aware FKS subtraction: application to + ¯ + e e− bbµ µ− →

e+e µ+µ b¯b − → − 239 + LO µ µ−b¯b + ¯ NLO µ µ−bb Factorization in the soft limit 191 100 + + e e− µ µ−b¯b Standard FKS → Resonance-aware FKS 143 [fb] 10 σ 96

48 α soft α 1 R R 0

1.08

1.04 0.1

0.99

K-factor 0.95 0.01 0.90 30 110 190 270 350 0.00 0.01 0.02 0.03 0.04 0.04 √s [GeV] Eg [GeV]

σreal[fb] σmism[fb] ncalls standard 1.90485 0.99% n/a 5 100000 resonances −0.915077± 0.52% 0.97930 0.94% 5 20000(real×) + 5 20000(mism) − ± − ± × ×

25 / 19 Polarized beams

Whizard can include beam polarization and ISR eﬀects in NLO predictions. + Results for e e− tt¯: → √s = 800 GeV √s = 1500 GeV + LO NLO LO NLO P (e−) P (e ) σ [fb] σ [fb] K-factor σ [fb] σ [fb] K-factor 0% 0% 253.7 272.8 1.075 75.8 79.4 1.049 80% 0% 176.5 190.0 1.077 98.3 103.1 1.049 −80% 0% 176.5 190.0 1.077 53.2 55.9 1.049 80% 30% 420.8 452.2 1.074 124.9 131.0 1.048 −80% 60% 510.7 548.7 1.074 151.6 158.9 1.048 −80% 30% 208.4 224.5 1.077 63.0 66.1 1.049 80% −60% 240.3 258.9 1.077 72.7 76.3 1.049 −

26 / 19