Full NLO corrections to 3-jet production and R 32 at the LHC Max Reyer University of Freiburg (University of G¨ ottingen) Eur. Phys. J. C79 no. 4, (2019) 321 arXiv:1902.01763 [hep-ph] In collaboration with Steffen Schumann Marek Sch¨ onherr Loopfest XVIII @ Fermilab August 13th, 2019
Outline Motivation EW NLO Calculation Setup 3/2jet Production Results and R 32 Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 1/14
Motivation jet production: • most abundant process at LHC ⇒ allows multi-differential measurements into high- p T regions ⇒ benchmark for theoretical predictions • important SM background to many analyses • pure jet final state is BSM search ground ⇒ enhancements in high p T -tails • determination of PDFs and α s at high Q 2 ⇒ consistency check of RGE evolution over large range of scales EW corrections: • naˆ ıve relative magnitude of α ∼ 1% to inclusive XS • weak Sudakov logarithms ⇒ O (10%) corr in TeV range ⇒ inclusion necessitated by high p T reach • many subprocesses, all dipole kinematics and types involed ⇒ strong test case for automized NLO tools Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 2/14
Previous Studies of Jet Production • NLO QCD up to 5 final state jets [Ellis et al. , 1992] [Bern et al. , 2012] [Giele et al. , 1993] [Badger et al. , 2014] [Nagy, 2003] • NLO QCD combined with parton showers [Alioli et al. , 2011] [H¨ oche et al. , 2012] • NNLO QCD dijet completed [Currie et al. , 2016] [Ridder et al. , 2019] [Currie et al. , 2017] [Czakon et al. , 2019] (full color) • pure weak corrections for dijet (no γ ; O � α 2 � � α 2 � s α , O ( α s α ), O ) [Dittmaier et al. , 2012] • full SM NLO for dijet [Frederix et al. , 2017] • full SM NLO for 3jet, inclusive cross section [Frederix et al. , 2018] here: full SM NLO for 3/2jet, (double) differential in Sherpa Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 3/14
Features of EW NLO Massive W ± and Z : Massless photons γ : • IR divergences necessitate • real emission distinct process class subtraction • IR finite loop contributions: ⇒ descends from QCD via � Q 2 � ∼ α log 2 , T ( ij ) ˆ ˆ T k → Q ( ij ) Q k m 2 • add γ to jet clustering ⇒ Sudakov logs ∼ 10% @ 1TeV • unambiguous definition of NLO correction by perturbative order: O L α n s α m N E W D C N Q L O α n − 1 α m α n s α m − 1 s ⇒ simultaneous QCD and QED subtraction with distinct underlying Borns r . QCD subtr. b t s u D X + g + γ E Q final state X + g X + γ ⇒ forces γ in process definition • photon jet removal desired, requires e.g. fragmentation functions Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 4/14
Automation of EW NLO • public full SM one-loop provider are becoming available • Recola • OpenLoops2 • GoSam ⇒ paving road for automatic SM NLO event generator ⇒ already public: MadGraph5 aMC@NLO [Frederix et al. , 2018] ⇒ still-private version of Sherpa [Sch¨ onherr, 2018] • bookkeeping in mixed coupling scenario • tree level ME • simultaneous QCD&QED subtraction: dipole terms, I-operators, ... • (approximate) procedures for combination with PS Validated in growing set of processes Sherpa + GoSam • γγ W and γγ Z [Greiner et al. ] Sherpa + OpenLoops • γγ j [Chiesa et al. ] • V + jets [Kallweit et al. , 2015] Sherpa + Recola [Kallweit et al. , 2016] • 2 ℓ 2 ν • V + j , t ¯ tH , e + e − µ + µ − [Kallweit et al. , 2017] • t ¯ t + jets [Biedermann et al. , 2017] [G¨ utschow et al. , 2018] • off-shell WWW [Sch¨ onherr, 2018] (approximate multijet merging) Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 5/14
Calculation Setup - Process Definition • partonic processes [ ewj ∈ { q , g , γ, l , ν } → no external W , Z !] 3 jet : ewj + ewj → ewj + ewj + ewj (+ ewj ) , 2 jet : ewj + ewj → ewj + ewj (+ ewj ) , • perturb. orders α n s α m 3 jet : m + n = 3 , 4 2 jet : m + n = 2 , 3 , • sensitive to full SM spectrum (tops, Higgs, . . . ) O ( α 4 O ( α 3 O ( α 2 s α 2 ) O ( α s α 3 ) O ( α 4 ) s ) s α ) Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 6/14
Calculation Setup - Input and Observable • Sherpa interfaced to Recola • pp @ 13 TeV, PDF: NNPDF31 nlo as 0118 luxqed 2 ˆ • scale choice µ R = µ F = 1 H T ⇒ missing higher orders estimated by 7 point scale variation • G µ scheme ⇒ mass logs from γ → f ¯ f splittings absorbed • complex mass scheme jet def and fiducial phase space cuts: • 3 resp. 2 democratic anti- k T jets with R = 0 . 4 and [no ν !] p i ≥ 2 p 1 | η | < 2 . 8; T ≥ 80GeV , ≥ 60GeV T • reject ’lepton jets’: | η j | < 2 . 5 and net lepton number ⇒ collinear same-flavor lepton pairs survive (IR safety!) ⇒ leptons outside tracker survive Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 7/14
XS Nomenclature • nomenclature for n -jet XS: � � � � σ LO i σ ∆NLO i = α n +1 − i = α n − i α i , α i , O O s s nj nj • combination of QCD and EW NLO: σ NLO QCD+EW = σ LO 0 + σ ∆NLO 0 + σ ∆NLO 1 additive: nj nj nj nj � σ ∆NLO 0 � � σ ∆NLO 1 � σ NLO QCD × EW = σ LO 0 nj nj multiplicative: 1 + 1 + nj nj σ LO 0 σ LO 0 nj nj • estimate of unknown O ( α s α ) NNLO corrections: QCD+EW = δσ NLO QCD × δσ NLO EW σ NLO QCD × EW − σ NLO σ LO Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 8/14
p T -Spectra LO QCD NLO QCD×EW LO QCD NLO QCD×EW LO QCD NLO QCD×EW NLO QCD NLO QCD NLO QCD NLO QCD+EW full NLO NLO QCD+EW full NLO NLO QCD+EW full NLO 10 2 10 2 10 2 p 1 T , 3j p 2 T , 3j p 3 T , 3j 10 0 | i | < 2.8 | i | < 2.8 | i | < 2.8 10 0 10 0 T [pb/GeV] p 1 T [pb/GeV] p 1 T [pb/GeV] p 1 T > 80 GeV T > 80 GeV T > 80 GeV 10 2 p 2, 3 > 60 GeV 10 2 p 2, 3 > 60 GeV p 2, 3 > 60 GeV 10 2 T T T 10 4 10 4 d /d p 1 10 4 d /d p 2 d /d p 3 10 6 10 6 10 6 10 8 10 8 10 8 2.75 2.25 2.50 1.75 2.00 2.25 2.00 1.75 1.50 Ratio over NLO QCD Ratio over NLO QCD Ratio over NLO QCD 1.75 1.50 1.50 1.25 1.25 1.25 1.00 1.00 1.00 0.75 0.75 0.75 0.50 0.50 0.25 0.50 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 p 1 T [GeV] p 2 T [GeV] p 3 T [GeV] • large negative Sudakov-type EW NLO corrections ⇒ grow with i in p i T ( − 10% , − 15% , − 15% at 2TeV) • scale uncertainties asymmetric, grow from QCD to QCD+EW • accidental cancellation with subleading LO and NLO contributions • mainly ∆NLO 2 , LO 1 , LO 2 • grow larger than ∆NLO 1 for p T > 2 . 5TeV ⇒ highly dependent on observable & fiducial phase space Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 9/14
p T -Spectra LO 0 ( s ) 3 NLO 0 ( s ) 4 NLO 4 ( 4 ) LO 0 ( s ) 3 NLO 0 ( 4 s ) NLO 4 ( 4 ) LO 0 ( 3 s ) NLO 0 ( s ) 4 NLO 4 ( 4 ) LO 1 ( 2 1 ) NLO 1 ( 3 1 ) LO 1 ( 2 1 ) NLO 1 ( 3 1 ) LO 1 ( 2 1 ) NLO 1 ( 3 1 ) s s s s s s LO 2 ( 1 2 ) NLO 2 ( 2 2 ) LO 2 ( 1 2 ) NLO 2 ( 2 2 ) LO 2 ( 1 2 ) NLO 2 ( 2 2 ) s s s s s s LO 3 ( 3 ) NLO 3 ( 1 3 ) LO 3 ( 3 ) NLO 3 ( 1 3 ) LO 3 ( 3 ) NLO 3 ( 1 3 ) full NLO full NLO full NLO s s s 10 3 10 3 10 1 10 1 10 1 p 1 T , 3j p 2 T , 3j p 3 T , 3j | i | < 2.8 | i | < 2.8 | i | < 2.8 10 1 10 1 10 1 T [pb/GeV] p 1 T > 80 GeV T [pb/GeV] p 1 T > 80 GeV T [pb/GeV] p 1 T > 80 GeV 10 3 p 2, 3 > 60 GeV 10 3 p 2, 3 > 60 GeV p 2, 3 > 60 GeV 10 3 T T T 10 5 10 5 10 5 d /d p 1 d /d p 2 d /d p 3 10 7 10 7 10 7 10 9 10 9 10 9 10 11 10 11 10 11 10 0 10 0 10 0 10 1 10 1 Ratio over full NLO Ratio over full NLO Ratio over full NLO 10 1 10 2 10 2 10 2 10 3 10 3 10 3 10 4 10 4 10 5 4 10 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 p 1 T [GeV] p 2 T [GeV] p 3 T [GeV] • large negative Sudakov-type EW NLO corrections ⇒ grow with i in p i T ( − 10% , − 15% , − 15% at 2TeV) • scale uncertainties asymmetric, grow from QCD to QCD+EW • accidental cancellation with subleading LO and NLO contributions • mainly ∆NLO 2 , LO 1 , LO 2 • grow larger than ∆NLO 1 for p T > 2 . 5TeV ⇒ highly dependent on observable & fiducial phase space Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 9/14
R 32 Observable T ) = d σ 3 j / d H (2) R 32 ( H (2) T d σ 2 j / d H (2) T • reduced experimental uncertainties ⇒ e.g. luminosity, jet energy scale • factorizing contributions in theory predictions cancel • strongly dependent on α s ( H (2) T ) ⇒ allows for measurement [Chatrchyan et al. , 2013] (fit of theory predictions to data) ⇒ consistency check of RGE evolution at high scales ⇒ possibly sensitive to BSM physics [Becciolini et al. ] • sensitive to gluon PDF Full NLO corrections to 3-jet production and R32 at the LHC Max Reyer (Univ. Freiburg) 10/14
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