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Merging NNLO calculations with higher-order resummation and partons showers in GENEVA http://geneva.physics.lbl.gov Simone Alioli LoopFest XVIII Fermilab 13 August 2019 SA, C. Bauer, C. Berggren, A. Hornig, F . Tackmann, C. Vermilion, J.

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SLIDE 1

Merging NNLO calculations with higher-order resummation and partons showers in GENEVA

http://geneva.physics.lbl.gov

Simone Alioli

LoopFest XVIII Fermilab 13 August 2019

SA, C. Bauer, C. Berggren, A. Hornig, F . Tackmann, C. Vermilion, J. Walsh, S. Zuberi JHEP09(2013)120 SA, C. Bauer, C. Berggren, F . Tackmann, J. Walsh, S. Zuberi JHEP06(2014)089 SA, C. Bauer, C. Berggren, F . Tackmann, J. Walsh, Phys.Rev. D92 (2015) 9 SA, C. Bauer, F . Tackmann, S. Guns, Eur.Phys.J. C76 (2016) 614 SA, A. Broggio, M. Lim, S. Kallweit, L. Rottoli ArXiv 1908.xxxx

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Introduction

GENEVA combines the 3 theoretical tools we use for QCD predictions into a single framework: 1) Fully differential fixed-order calculations

◮ up to NNLO via N-jettiness or qT-subtraction

2) Higher-logarithmic resummation

◮ up to NNLL′ via SCET or more traditional QCD

approaches 3) Parton showering, hadronization and MPI

◮ recycling standard SMC. Using PYTHIA8 now, any

SMC supporting LHEF and user-hook vetoes is OK Resulting Monte Carlo event generator has many advantages:

◮ consistently improves perturbative accuracy away from FO regions ◮ provides event-by-event systematic estimate of theoretical perturbative

uncertainties and correlations

◮ gives a direct interface to SMC hadronization, MPI modeling and

detector simulations.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 2

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GENEVA in a nutshell: color singlet production

  • 1. Design IR-finite definition of

events, based e.g. on resolution parameters T cut (or pcut

T ).

  • 2. Associate differential

cross-sections to events such that 0-jet events are (N)NLO accurate and T0 is resummed at NNLL ’ accuracy

  • 3. Shower events imposing

conditions to avoid spoiling NNLL ’ accuracy reached at step 2

  • 4. Hadronize, add multi-parton

interactions (MPI) and decay without further restrictions

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 3

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IR-safe definitions of events beyond LO

Using 0- and 1-jettiness an IR safe definition of color-single events with any number of extra emissions can be devised:

◮ Emissions below T cut N

are unresolved ( i.e. integrated over) and the kinematic considered is the one of the event before the extra emission(s).

◮ Emissions above T cut N

are retained and the kinematics is fully specified.

An M-parton event is interpreted as an N-jet event, N ≤ M, fully differential in

ΦN, without using a standard “jet-algo”

  • Price to pay: power corrections in T cut

N

due to PS projection.

  • Advantage: vanish for IR-safe observables as T cut

N

→ 0

Iterating the procedure, the phase space is sliced into jet-bins

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 4

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Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 6

Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 0−jet exclusive cross section

dσMC dΦ0 (T cut ) = dσNNLL′ dΦ0 (T cut ) + dσnons dΦ0 (T cut ) dσNNLL′ dΦ0 (T cut ) = T cut dT0

  • ij

dσB

ij

dΦ0 Hij(Q2, µH) UH(µH, µ) ×

  • Bi(xa, µB) ⊗ UB(µB, µ)
  • ×
  • Bj(xb, µB) ⊗ UB(µB, µ)
  • ⊗
  • S(µS) ⊗ US(µS, µ)
  • ,

SCET factorization: hard, beam and soft function depend on a single scale. No large logarithms present when scales are at their characteristic values:

µH = Q, µB =

  • QT0,

µS = T0

Resummation performed via RGE evolution factors U to a common scale µ. At NNLL ’ all singular contributions to O

  • α2

s

already included by definition.

Two-loop virtual corrections properly spread to nonzero T0 by resummation.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 0−jet exclusive cross section

dσMC dΦ0 (T cut ) = dσNNLL′ dΦ0 (T cut ) + dσnons dΦ0 (T cut ) dσnons dΦ0 (T cut ) = dσNNLO0 dΦ0 (T cut ) − dσNNLL′ dΦ0 (T cut )

  • NNLO0

Nonsingular matching constrained by requirement of NNLO0 accuracy.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 8

Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 1−jet inclusive cross section

dσMC

≥1

dΦ1 (T0 > T cut ) = dσNNLL′

≥1

dΦ1 θ(T0 > T cut ) + dσnons

≥1

dΦ1 (T0 > T cut )

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 9

Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 1−jet inclusive cross section

dσMC

≥1

dΦ1 (T0 > T cut ) = dσNNLL′

≥1

dΦ1 θ(T0 > T cut ) + dσnons

≥1

dΦ1 (T0 > T cut ) dσNNLL′

≥1

dΦ1 θ(T0 > T cut ) = dσNNLL′ dΦ0dT0 P(Φ1) θ(T0 > T cut )

Resummed formula only differential in Φ0, T0. Need to make it differential in 2 more variables, e.g. energy ratio z = EM/ES and azimuthal angle φ We use a normalized splitting probability to make the resummation differential in Φ1.

P(Φ1) = psp(z, φ)

  • sp

zmax(T0)

zmin(T0) dzdφ psp(z, φ)

dΦ0dT0dzdφ dΦ1 ,

  • dΦ1

dΦ0dT0 P(Φ1) = 1 psp are based on AP splittings for FSR, weighted by PDF ratio for ISR.

All singular O

  • α2

s

terms again included at NNLL

’ by definition.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 10

Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 1−jet inclusive cross section

dσMC

≥1

dΦ1 (T0 > T cut ) = dσNNLL′ dΦ0dT0 P(Φ1) + dσnons

≥1

dΦ1 (T0 > T cut ) dσnons

≥1

dΦ1 (T0 > T cut ) = dσNLO1

≥1

dΦ1 (T0 > T cut ) − dσNNLL′ dΦ0dT0 P(Φ1)

  • NLO1

θ(T0 > T cut )

Nonsingular matching fixed by NLO1 requirement

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 11

Combining resummation with fixed-order in GENEVA

For color-singlet at NNLO provide partonic formulae for up to 2 extra partons.

◮ 1−jet inclusive cross section ◮ The separation between 1 and 2 jets is determined by the NLL resummation of T cut 1

Results in lengthier expressions. Need to include both the T0 and T1

  • resummations. See arXiv: 1508.01475 and arXiv: 1605.07192 for derivation.

dσMC

1

dΦ1 (T0 > T cut ; T cut

1

) = dσC

≥1

dΦ1 U1(Φ1, T cut

1

) θ(T0 > T cut ) + dσmatch

1

dΦ1 (T0 > T cut ; T cut

1

) dσMC

≥2

dΦ2 (T0 > T cut , T1 > T cut

1

) = dσC

≥1

dΦ1 U′

1(Φ1, T1) θ(T0 > T cut

)

  • Φ1=ΦT

1 (Φ2)×

P(Φ2) θ(T1 > T cut

1

) + dσmatch

≥2

dΦ2 (T0 > T cut , T1 > T cut

1

) dσC

≥1

dΦ1 = dσNNLL′

≥1

dΦ1 + (B1 + V C

1 )(Φ1) −

dσNNLL′

≥1

dΦ1

  • NLO1

The fully differential T0 information is contained trough

dσNNLL′

≥1

dΦ1 Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5

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SLIDE 12

Drell-Yan production

◮ Both NC and, more recently, CC contributions included

[Phys.Rev. D92 (2015) 9]

◮ Interface to the parton showers, hadronization and MPI carefully studied

[Eur.Phys.J. C76 (2016) 614]

◮ Ongoing study for W/Z transverse distribution ratio.

b b b b b b b b b b b b

Atlas

b

Geneva+Py8 Geneva+Py8(no MPI) Pythia8 Tune 11 Tune 14 Tune 17 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Z → µ+µ−, 7 TeV 1/N dN/dTCM [GeV] 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1.0 1.1 TCM [GeV] MC/Data

b b b b b b b b b b b b b b b b b b b b b b b b b b

Data

b

Geneva+Py8(as=0.114, kT=0.5) Geneva+Py8(as=0.118, kT=0.5) Pythia8 AZ 10−7 10−6 10−5 10−4 10−3 10−2 Z → ee ”bare”, Inclusive

1 σfid dσfid dpT [GeV−1]

1 10 1 10 2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Z pT [GeV] MC/Data

b b b b b

Geneva+Py8 αs = 0.114 Geneva+Py8 αs = 0.118 Pythia8 AZ ATLAS Data

b

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Ratio of normalized pT distribution of W and Z RW/Z 10 20 30 40 50 60 70 0.9 0.95 1 1.05 pT MC/Data

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 6

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Public code release candidate http://geneva.physics.lbl.gov

◮ Release candidate version is publicly available since 2016 at DESY git repo

  • r

LBNL mirror. Please report back issues to geneva@lbl.gov . ◮ Installation by CMake, external packages either found or automatically

installed.

◮ As most NNLO codes, GENEVA needs reasonable parallelization and

runtime to produce accurate results.

◮ Python interface available to steer the running on several systems (own

laptop, NERSC clusters, etc.). Can also just provide the list of commands to be run and their grouping, to extend it to other systems.

◮ Running is best organized into 4 separate stages: setup, generate,

reweight and shower. All accessible and managed through the Python interface

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 7

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SLIDE 14

New implementations: HiggsStrahlung

◮ Third largest Higgs boson production channel. Observed last year by ATLAS and

CMS.

◮ Allows possibility to study V V H vertex, Hb¯

b when also considering decay

◮ Similar to DY production, complications coming from diagrams with top-quark loops ◮ Including all top-quark mass effects at 1 loop, currently neglecting top-quark mass

diagrams VI and VII only known in top-quark mass expansion.

◮ Beam-thrust resummation at NNLL

’ matched to NNLO0 via SCET

◮ Scale profiles adapted to the process, not extremely dependendent on leading-order

kinematics

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 8

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NNLO validation

◮ NNLO xsec and inclusive distributions validated against MATRIX Kallweit et al. Eur.Phys.J.

C78 (2018).

◮ Non-trivial correlations for scales variations, dedicated profiled used to reproduce

fixed-order variations for inclusive quantities.

◮ Smallness of scale variations makes it numerically very challenging. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 9

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NNLO validation

◮ NNLO xsec and inclusive distributions validated against MATRIX Kallweit et al. Eur.Phys.J.

C78 (2018).

◮ Non-trivial correlations for scales variations, dedicated profiled used to reproduce

fixed-order variations for inclusive quantities.

◮ Smallness of scale variations makes it numerically very challenging. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 9

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SLIDE 17

NNLO validation

◮ NNLO xsec and inclusive distributions validated against MATRIX Kallweit et al. Eur.Phys.J.

C78 (2018).

◮ Non-trivial correlations for scales variations, dedicated profiled used to reproduce

fixed-order variations for inclusive quantities.

◮ Smallness of scale variations makes it numerically very challenging. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 9

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SLIDE 18

NNLO validation

◮ NNLO xsec and inclusive distributions validated against MATRIX Kallweit et al. Eur.Phys.J.

C78 (2018).

◮ Non-trivial correlations for scales variations, dedicated profiled used to reproduce

fixed-order variations for inclusive quantities.

◮ Smallness of scale variations makes it numerically very challenging. ◮ Power-suppressed corrections effects on distributions small. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 9

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Adding the parton shower.

◮ Purpose of the parton shower is to fill the 0− and 1−jet exclusive bins with radiation

and add more emissions to the inclusive 2−jet bin

◮ Not allowed to change accuracy reached at partonic level. ◮ If shower ordered in N-jettiness setting starting scales is enough. ◮ For different ordering variable (i.e. any real shower), jet-boundaries constraints T cut k

need to be imposed on hardest radiation (largest jet resolution scale)

◮ Impose the first emission has the largest jet resolution scale, by performing a

splitting by hand using a NLL Sudakov and the Tk-preserving map. Showering setting starting scales T cut

k

does not spoil NNLL ’+NNLO accuracy:

  • Φ0 events only constrained by normalization, shape given by PYTHIA
  • Φ1 events vanish forced to vanish by splitting down to Λ1 100 MeV.
  • Φ2 events: PYTHIA showering can be shown to shift T0 distribution at the same

α3

s /T0 order of the dominant term beyond NNLL

’. Beyond claimed accuracy.

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 10

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SLIDE 20

Showered and hadronized results for HiggsStrahlung

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 11

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Showered and hadronized results for HiggsStrahlung

◮ Inclusive quantities not modified, expected changes in exclusive ones. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 12

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Including the gluon-fusion channel

◮ Sizeable contribution due to gluon luminosity. Nonsingular contribution added at

fixed-order only.

◮ Scale unc. dominated by gg channel, desirable to have NLO corrections. ◮ Shower effects more marked, as already seen in other gg-initiated processes. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 13

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Handling the decay at NNLO

◮ In the NWA it is possible to factorize production from decay and correctly match two

GENEVA

◮ Beam-thrust T0 resolution parameter for production, 2-jettiness (thrust) τ dec 2

for decay

dσMC dΦℓ+ℓ−b¯ b

(T cut ;τdec,cut

2

)

=

dσMC dΦℓ+ℓ−H

(T cut )×

dΓ(0) H→b¯ b dΦH→b¯ b

+

dσ(0) ℓ+ℓ−H dΦℓ+ℓ−H

×

dΓMC dΦH→b¯ b

(τdec,cut

2

) −

dσ(0) ℓ+ℓ−H dΦℓ+ℓ−H

×

dΓ(0) H→b¯ b dΦH→b¯ b

+

dσNLO ℓ+ℓ−H dΦℓ+ℓ−H

(T cut )×

dΓNLO H→b¯ b dΦH→b¯ b

(τdec,cut

2

) ◮ There are now 2 contributions to the 1-jet bin, coming from production or decay

dσMC 1 dΦℓ+ℓ−b¯ bj

(T0>T cut ;T cut

1

;τdec,cut

2

)

dσMC 1 dΦℓ+ℓ−b¯ bj

(T cut ;τdec

2

>τdec,cut

2

;τdec,cut

3

) ◮ And 3 contributions to the 2-jets bin, coming from production, decay or both

dσMC 2 dΦℓ+ℓ−b¯ bjj

(T0>T cut ;T1>T cut

1

;τdec,cut

2

)

dσMC 2 dΦℓ+ℓ−b¯ bjj

(T0>T cut ;T cut

1

;τdec

2

>τdec,cut

2

;τdec,cut

3

)

dσMC 2 dΦℓ+ℓ−b¯ bjj

(T cut ;T cut

1

;τdec

2

>τdec,cut

2

;τdec

3

>τdec,cut

3

) ◮ Implementation is work in progress ... Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 14

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SLIDE 24

Accuracy for other observables : qT, φ∗ and jet-veto

◮ For DY one can compare with dedicated tools DYqT Bozzi et al. arXiv:1007.2351 , BDMT Banfi et al. arXiv:1205.4760 and JetVHeto Banfi et al. 1308.4634 ◮ Analytic NNLL predictions formally higher log accuracy than GENEVA ◮ Results are in better agreement with higher-order resummation, despite lack of

perturbative ingredients.

◮ Difficult to formally quantify the accuracy achieved due to parton shower. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 15

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SLIDE 25

Changing the resolution parameter: qT

◮ Using qT as 0-jet resolution parameter

guarantees target NNLL ’qT +NNLO0 accuracy

◮ RadISH performs qT resummation up

to N3LL directly in qT space

Bizon et al. arXiv:1905.05171

◮ Its internal structure requiring Monte

Carlo generation of unphysical events makes it hard to directly link.

◮ We proceeded building interpolating

grids with Chebyshev polynomials and calling these interpolating grids from Geneva.

◮ Usage of Chebyshev polynomials is key

in easily obtaining spectrum from cumulant.

◮ Results are in good agreement with dedicated RadISH+NNLOJET NNLL

’+NNLO0 control runs.

◮ Shower interface slightly simplified compared to T0, currently under testing ... Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 16

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SLIDE 26

Summary and Outlook

performs matching of NNLO+NNLL′+PS.

◮ Higher-order resummation of resolution parameters provides a natural link

between NNLO and PS.

◮ Provides theoretical perturbative uncertainties coming from both

fixed-order and resummation on a event-by-event basis.

◮ Allows for realistic event simulation and interface to detectors.

Current status:

◮ pp → V is publicly available. ◮ pp → V H will be released soon.

Outlook:

◮ Other processes (Higgs, VV, γγ, etc.) in the pipeline. ◮ Adding NNLO decay in NWA ◮ Use different resolution parameters: qT ◮ Increase accuracy

Thank you for your attention!

Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 17