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
Introduction G ENEVA 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 q T -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
GENEVA in a nutshell: color singlet production 1. Design IR-finite definition of events, based e.g. on resolution parameters T cut (or p cut T ). 0 2. Associate differential cross-sections to events such that 0-jet events are (N)NLO accurate and T 0 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
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 are unresolved ( i.e. integrated over) and the kinematic N considered is the one of the event before the extra emission(s). ◮ Emissions above T cut are retained and the kinematics is fully specified. N An M -parton event is interpreted as an N -jet event, N ≤ M , fully differential in Φ N , without using a standard “jet-algo” • Price to pay: power corrections in T cut due to PS projection. N • Advantage: vanish for IR-safe observables as T cut → 0 N Iterating the procedure, the phase space is sliced into jet-bins Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 4
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
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 ) = d σ NNLL ′ d σ MC ) + d σ nons 0 ( T cut 0 ( T cut 0 ( T cut ) 0 0 0 dΦ 0 dΦ 0 dΦ 0 � T cut d σ NNLL ′ d σ B 0 ij ( T cut � H ij ( Q 2 , µ H ) U H ( µ H , µ ) ) = d T 0 0 dΦ 0 dΦ 0 0 ij � � � � × B i ( x a , µ B ) ⊗ U B ( µ B , µ ) × B j ( x b , µ B ) ⊗ U B ( µ B , µ ) � � ⊗ S ( µ S ) ⊗ U S ( µ S , µ ) , SCET factorization: hard, beam and soft function depend on a single scale. No large logarithms present when scales are at their characteristic values: � µ H = Q, µ B = Q T 0 , µ S = T 0 Resummation performed via RGE evolution factors U to a common scale µ . � already included by definition. α 2 At NNLL ’ all singular contributions to O � s Two-loop virtual corrections properly spread to nonzero T 0 by resummation. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 ) = d σ NNLL ′ ) + d σ nons d σ MC 0 ( T cut ( T cut 0 ( T cut ) 0 0 0 dΦ 0 dΦ 0 dΦ 0 � d σ NNLL ′ ) = d σ NNLO 0 d σ nons � 0 ( T cut 0 ( T cut ( T cut ) − ) 0 0 0 dΦ 0 dΦ 0 dΦ 0 NNLO 0 Nonsingular matching constrained by requirement of NNLO 0 accuracy. Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 d σ NNLL ′ d σ MC d σ nons ≥ 1 ≥ 1 ≥ 1 ( T 0 > T cut θ ( T 0 > T cut ( T 0 > T cut ) = ) + ) 0 0 0 dΦ 1 dΦ 1 dΦ 1 Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 d σ NNLL ′ d σ MC d σ nons ≥ 1 ≥ 1 ≥ 1 ( T 0 > T cut θ ( T 0 > T cut ( T 0 > T cut ) = ) + ) 0 0 0 dΦ 1 dΦ 1 dΦ 1 d σ NNLL ′ ) = d σ NNLL ′ ≥ 1 θ ( T 0 > T cut P (Φ 1 ) θ ( T 0 > T cut ) 0 0 dΦ 1 dΦ 0 d T 0 Resummed formula only differential in Φ 0 , T 0 . Need to make it differential in 2 more variables, e.g. energy ratio z = E M /E S and azimuthal angle φ We use a normalized splitting probability to make the resummation differential in Φ 1 . p sp ( z, φ ) dΦ 0 d T 0 d z d φ � dΦ 1 P (Φ 1 ) = , P (Φ 1 ) = 1 � z max ( T 0 ) dΦ 1 dΦ 0 d T 0 � z min ( T 0 ) d z d φ p sp ( z, φ ) sp p sp are based on AP splittings for FSR, weighted by PDF ratio for ISR. � terms again included at NNLL α 2 All singular O � ’ by definition. s Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 ) = d σ NNLL ′ d σ nons d σ MC ≥ 1 ≥ 1 ( T 0 > T cut ( T 0 > T cut P (Φ 1 ) + ) 0 0 dΦ 1 dΦ 0 d T 0 dΦ 1 � d σ NNLL ′ d σ NLO 1 d σ nons � ≥ 1 ≥ 1 ( T 0 > T cut ( T 0 > T cut θ ( T 0 > T cut ) = ) − P (Φ 1 ) ) 0 0 0 dΦ 1 dΦ 1 dΦ 0 d T 0 NLO 1 Nonsingular matching fixed by NLO 1 requirement Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 T 0 and T 1 resummations. See arXiv: 1508.01475 and arXiv: 1605.07192 for derivation. d σ C d σ MC ≥ 1 1 ( T 0 > T cut ; T cut U 1 (Φ 1 , T cut ) θ ( T 0 > T cut ) = ) + 0 1 1 0 dΦ 1 dΦ 1 d σ match 1 ( T 0 > T cut ; T cut ) 0 1 dΦ 1 d σ MC d σ C ≥ 2 ≥ 1 � ( T 0 > T cut , T 1 > T cut U ′ 1 (Φ 1 , T 1 ) θ ( T 0 > T cut ) = ) 1 (Φ 2 ) × � 0 1 0 dΦ 2 dΦ 1 � Φ 1 =Φ T d σ match ≥ 2 P (Φ 2 ) θ ( T 1 > T cut ( T 0 > T cut , T 1 > T cut ) + ) 1 0 1 dΦ 2 � d σ NNLL ′ d σ NNLL ′ d σ C � ≥ 1 ≥ 1 ≥ 1 + ( B 1 + V C = 1 )(Φ 1 ) − dΦ 1 dΦ 1 dΦ 1 NLO 1 d σ NNLL ′ ≥ 1 The fully differential T 0 information is contained trough dΦ 1 Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 5
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 b b b b b b b b b b b b b b b b b b b b 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. Z → µ + µ − , 7 TeV 1/ N d N /d T CM [GeV] 0 . 14 Z → ee ”bare”, Inclusive Ratio of normalized p T distribution of W and Z A tlas 1 . 3 d p T [ GeV − 1 ] R W/Z G eneva +P y8 0 . 12 Geneva+Py 8 α s = 0.114 1 . 2 G eneva +P y8 (no MPI) 10 − 2 Geneva+Py 8 α s = 0.118 Pythia 8 0 . 1 1 . 1 Pythia 8 AZ d σ fid Tune 11 10 − 3 ATLAS Data σ fid 1 0 . 08 Tune 14 1 Data Tune 17 10 − 4 0 . 9 0 . 06 Geneva+Py 8 (as= 0 . 114 , kT= 0 . 5 ) Geneva+Py 8 (as= 0 . 118 , kT= 0 . 5 ) 0 . 8 10 − 5 Pythia 8 AZ 0 . 04 0 . 7 10 − 6 0 . 02 0 . 6 10 − 7 0 . 5 0 1 . 3 1 . 1 1 . 2 1 . 05 MC/Data MC/Data 1 . 1 1 . 0 MC/Data 1 1 0 . 9 0 . 9 0 . 8 0 . 8 0 . 7 0 . 95 0 . 6 0 . 7 0 . 5 0 . 9 1 10 1 10 2 0 10 20 30 40 50 70 0 . 6 60 Z p T [GeV] p T 0 . 5 0 10 20 30 40 50 60 T CM [GeV] Simone Alioli | GENEVA | LoopFest XVIII 13/8/2019 | page 6
Public code release candidate http://geneva.physics.lbl.gov DESY git repo ◮ Release candidate version is publicly available since 2016 at LBNL mirror. Please report back issues to geneva@lbl.gov . or ◮ Installation by CMake, external packages either found or automatically installed. ◮ As most NNLO codes, G ENEVA 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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