Higgs Pair Production: NLO Matching Uncertainties

Higgs Pair Production: NLO Matching Uncertainties Silvan Kuttimalai in collaboration with Stephen Jones November 7th, 2017 Higgs Couplings Workshop, Heidelberg

Introduction

Motivation: the Higgs Potential V = 2 v 2 H 2 + 3 vh 3 + 4 v 2 H 4 SM 2 = SM 3 = SM 4 = m2 H 2v 2 3 can be measured in Higgs pair production Experimentally challenging (pp! HH) (pp! H) 10 3 Prospects for HL-LHC: around 10 % - 50 % precision on 3 Theoretically also extremely challenging 1

Higgs Pair Production at NLO Born Virtual Real Born and real corrections Automated 1-loop tools: OpenLoops, GoSam, MadLoop, Recola,... Infrared subtraction Born UV finite, use standard techniques: Catani-Seymour, FKS,... Virtual corrections Two-loop integrals, massive propagators, external masses Very hard ) not available until recently 2

Low-Energy Approximation t HEFT m t!1 Higgs E ective Field Theory Take into account only top quark contributions Work in low-energy limit: ŝ mt 2 ) Gives rise to point-like Higgs-gluon interactions ) Reduces complexity immensely ) Validity highly questionable, however: m HH > m t 3

New Level of Precision Borowka et al. JHEP 10 (2016) Two-loop virtuals numerically evaluated Details: Gudrun Heinrich s talk HEFT-based approximations inaccurate NLO corrections large, well outside LO uncertainties 4

Motivation New level of precision NLO corrections Full finite top mass e ects ) Meaningful fixed-order uncertainties Fixed-order NLO not su cient Small p? HH region: spoiled by logs n s log m p? HH/m HH Requires matching to parton shower / resummation ) Need careful re-assessment of PS / matching uncertainties 5

Motivation Heinrich et al.: JHEP 08 (2017) 6

Loop-Induced Processes at NLO in Sherpa Born and real corrections Interfaced from OpenLoops Interface extended for color- and spin-correlated amplitudes Infrared Substraction Use Catani-Seymour method Re-implemented for loop-induced external amplitudes Process handling and interface to parton showers Re-implemented for loop-induced external amplitudes Two parton showers available: CS shower / Dire shower [Schumann, Krauss, JHEP 03 (2008)] [Höche, Prestel, Eur.Phys.J. C75 (2015)] 7

Parton Shower E ects at LO

ds/dp? HH [pb/gev] 10 10 10 11 Ratio 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1.6 0.8 SHERPA HEFT pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s LO+PS Results p s = 14 TeV HEFT 10 1 10 2 10 3 p HH? [GeV] P M 2 1 M 2 P: process independent parton shower kernels 8

ds/dp? HH [pb/gev] 10 10 10 11 Ratio 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1.6 0.8 SHERPA HEFT pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s LO+PS Results p s = 14 TeV HEFT P M 2 M 2 10 1 10 2 10 3 p HH? [GeV] Uncertainty bands on LO+PS: 1 µ PS 2{ m HH 4, m HH 2, m HH 1 } µ PS implements phase space restriction: t( 1 ) <µ 2 PS µ PS = p s power shower, full phase space open 8

LO+PS Results ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA HEFT pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV HEFT ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA Full SM pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV Full SM Ratio 1.6 0.8 Ratio 1.6 0.8 10 1 10 2 10 3 p HH? [GeV] Qualitative di erences between HEFT and full SM HEFT: PS approximation underestimates fixed-order Full SM: PS approximation overestimates fixed-order Sharply falling spectrum above m t in full SM 10 1 10 2 10 3 p HH? [GeV] Parton shower kernels don t know hard process 8

Parton Shower E ects at NLO

NLO Parton Shower Matching: S-MC@NLO NLO = Z apple Z B( B )+V( B )+ B( B )P( 1 ) (µ 2 PS t)d 1 d B Z h i + R( R ) B( B )P( 1 ) (µ 2 PS t) d R Modified subtraction Use parton shower splitting kernels P for subtraction Restrict subtraction terms to parton shower phase space 9

NLO Parton Shower Matching: S-MC@NLO NLO = Z B( B )d B S-events M 2 Z h i + R( R ) B( B )P( 1 ) (µ 2 PS t) d R H-events M 2 Interplay between parton shower and fixed order 10

NLO Parton Shower Matching: S-MC@NLO MC@NLO = Z apple B( B ) Z (µ 2 PS, t 0 )+ Sudakov factor: no-emission probability between µ 2 PS and t 0 (µ 2 PS, t)p( 1 ) (µ 2 PS t)d 1 d B Z h i + R( R ) B( B )P( 1 ) (µ 2 PS t) d R P: splittingkernel Interplay between parton shower and fixed order 11

NLO Parton Shower Matching: S-MC@NLO MC@NLO = Z apple B( B ) Z (µ 2 PS, t 0 )+ (µ 2 PS, t)p( 1 ) (µ 2 PS t)d 1 d B Z h i + R( R ) B( B )P( 1 ) (µ 2 PS t) d R Interplay between parton shower and fixed order Consider observable insensitive to born kinematics (p HH? ) 11

NLO Parton Shower Matching: S-MC@NLO MC@NLO = Z B( B ) (µ 2 PS, t)p( 1 ) (µ 2 PS t)d 1 d B + S-events Z h i + R( R ) B( B )P( 1 ) (µ 2 PS t) d R H-events Interplay between parton shower and fixed order Consider observable insensitive to born kinematics (p HH? ) Focus on soft region: t µ 2 PS ) recover LO+PS with local K-factor 11

NLO Results ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 SHERPA Fixed-Order MC@NLO, CS shower pp! HH p s = 14 TeV HEFT HEFT approximation µ PS cancellation between S- and H-events PS uncertainties reduced Recover fixed-order in tail Ratio to FO Ratio to MC@NLO 1.6 0.8 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV] B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events 12

NLO Results ds/dp? HH [pb/gev] Ratio to FO Ratio to MC@NLO 10 2 10 3 10 4 10 5 10 6 10 7 1.6 0.8 1.5 0.0 SHERPA Fixed-Order MC@NLO, CS shower S-events H-events pp! HH p s = 14 TeV HEFT 10 1 10 2 10 3 p HH? [GeV] HEFT approximation µ PS cancellation between S- and H-events PS uncertainties reduced Recover fixed-order in tail B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events ( B B) P R 12

NLO Results ds/dp? HH [pb/gev] Ratio to FO Ratio to MC@NLO 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 1.6 0.8 1.5 0.0 SHERPA Fixed-Order MC@NLO, CS shower S-events H-events pp! HH p s = 14 TeV Full SM 10 1 10 2 10 3 p HH? [GeV] Full SM much larger uncertainties PS e ects extend into tail large µ PS ) don t recover fixed order B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events ( B B) P R 13

NLO Results ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Ratio to FO Ratio to MC@NLO 1.6 0.8 1.5 pp! HH p s = 14 TeV Full SM SHERPA Fixed-Order MC@NLO, CS Dire shower S-events H-events 0.0 10 1 10 2 10 3 p? HH Full SM much larger uncertainties PS e ects extend into tail large µ PS ) don t recover fixed order B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events ( B B) P R 13

Comparison to Literature: NLO+PS ds/dp? HH [fb/gev] 0.5 0.4 0.3 0.2 Sherpa, Dire Shower Sherpa, CS Shower MadGraph5 + Pythia Powheg-Box + Pythia Heinrich et al.: JHEP 08 (2017) Larger di erences in peak region due to di erences in algorithms beyond choice of µ PS : 15 % 10 20 30 40 50 60 70 80 2.5 Ratio to fixed-order 2.0 1.5 1.0 MC@NLO results within uncertainties in tail MadGraph uncertainties larger 2.5 2.0 1.5 1.0 0 200 400 600 800 1000 Ratio to fixed-order 0 200 400 600 800 1000 p HH? [GeV] POWHEG: flat excess in tail known feature of matching method somewhat suppressed through damping factor h damp = 250 GeV 14

Comparison to Literature: Analytic Resummation ds/dp? HH [fb/gev] 0.4 0.3 0.2 SHERPA pp! HH p s = 14 TeV Full SM Ferrera, Pires: JHEP 02 (2017) Next-to-leading log (NLL) parametrically equivalent to parton shower Ratio to NLO+NLL 0.1 0.0 1.3 1.1 0.9 0.7 NLO+NLL [Ferrera, Pires, 2017] MC@NLO, Dire shower MC@NLO, CS shower 10 1 10 2 p HH? [GeV] Uncertainties on NLO+NLL: 3% near p? HH 20GeV 10 % near p? HH 100GeV Good agreement within uncertainties 15

Conclusions Recent advances at fixed-order ) reduced uncertainties Studied uncertainties introduced though parton shower matching Found good agreement with analytic resummation Matching to fixed-order at large p HH? requires judicious choice of µ PS µ PS variations may exceed FO uncertainties ) Is µ PS source of uncertainty or tuning parameter? 16

Backup

E ects on Fixed-Order Uncertainties ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 SHERPA µ f /r variations Fixed-Order MC@NLO, Dire shower pp! HH p s = 14 TeV Full SM Full SM At small p? HH : NLO uncertainties seed cross section ( B) moreinclusive At large p HH? : LO uncertainties seed cross section (R) 1-jet exclusive Ratio to FO Ratio to MC@NLO 1.6 0.8 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV] B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events

NLO+PS: Alternative Comparison Plot ds/dp? HH [fb/gev] 0.5 0.4 0.3 0.2 Sherpa, Dire Shower Sherpa, CS Shower MadGraph5 + Pythia Powheg-Box + Pythia 0.1 0.0 2.5 2.0 1.5 1.0 2.5 2.0 1.5 1.0 0 50 100 150 200 250 300 Ratio to fixed-order 0 200 400 600 800 1000 Ratio to fixed-order 0 200 400 600 800 1000 p HH? [GeV]

Replacing B by B ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 SHERPA Fixed-Order MC@NLO, Dire shower ( B! B) pp! HH p s = 14 TeV Full SM Ratio to FO Ratio to MC@NLO 1.6 0.8 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV] B( B ) (µ 2 PS, t)p( 1) (µ 2 PS t)d B d 1 S-events h i R( R ) B( B )P( 1) (µ 2 PS t) d R H-events

LO+PS Results: CS Shower ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA HEFT pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV HEFT ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA Full SM pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV Full SM Ratio 1.6 0.8 Ratio 1.6 0.8 10 1 10 2 10 3 p HH? [GeV] 10 1 10 2 10 3 p HH? [GeV] Uncertainty bands on LO+PS: µ CS PS 2{m HH 4, m HH 2, m HH 1 } µ Dire PS 2{m HH 8, m HH 4, m HH 2 } µ CS PS = p s power shower µ Dire PS = m HH 2 power shower

LO+PS Results: Dire Shower ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA HEFT pp! HH + j pp! HH +Direshower p s = 14 TeV HEFT ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 SHERPA Full SM pp! HH + j pp! HH +Direshower p s = 14 TeV Full SM Ratio 1.6 0.8 Ratio 1.6 0.8 10 1 10 2 10 3 p HH? [GeV] 10 1 10 2 10 3 p HH? [GeV] Uncertainty bands on LO+PS: µ CS PS 2{m HH 4, m HH 2, m HH 1 } µ Dire PS 2{m HH 8, m HH 4, m HH 2 } µ CS PS = p s power shower µ Dire PS = m HH 2 power shower

CS shower vs Dire: HEFT ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 SHERPA Fixed-Order MC@NLO, CS shower pp! HH p s = 14 TeV HEFT ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 SHERPA Fixed-Order MC@NLO, Dire shower pp! HH p s = 14 TeV HEFT 10 7 10 7 Ratio to FO 1.6 0.8 Ratio to FO 1.6 0.8 Ratio to MC@NLO 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV] Ratio to MC@NLO 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV]

CS shower vs Dire: Full SM ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 SHERPA Fixed-Order MC@NLO, CS shower pp! HH p s = 14 TeV Full SM ds/dp? HH [pb/gev] 10 2 10 3 10 4 10 5 10 6 10 7 10 8 SHERPA Fixed-Order MC@NLO, Dire shower pp! HH p s = 14 TeV Full SM 10 9 10 9 Ratio to FO 1.6 0.8 Ratio to FO 1.6 0.8 Ratio to MC@NLO 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV] Ratio to MC@NLO 1.5 0.0 S-events H-events 10 1 10 2 10 3 p HH? [GeV]

Other Observables ds/dp j? [pb/gev] 10 3 10 4 10 5 10 6 10 7 10 8 SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM ds/dht 10 4 10 5 10 6 10 7 SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM Ratio to FO 10 9 1.6 1.2 0.8 Ratio to Dire 10 8 1.25 1.00 10 2 10 3 p j? [GeV] 10 2 10 3 HT [GeV]

Other Observables ds/d HH [pb/gev] 10 1 10 2 10 3 SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM Ratio to FO 1.5 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 HH

Single Higgs ds/dp H? [pb/gev] 1 10 1 10 2 10 3 10 4 10 5 2 1.5 Higgs boson transverse momentum Fixed-order HEFT Fixed-order LO+PS µ PS = Ratio 1 0.5 0 10 1 10 2 10 3 p H? [GeV]

p a p b Parton shower kinematics Q p j H H ˆt =(p a p j ) 2 û =(p b p j ) 2 ŝ =(p a + p b ) 2 v = p ap j p a p b = ˆt ŝ 0 w = p bp j p a p b = û ŝ 0 ŝ + ˆt +û = Q 2 ) v + w =(1 Q 2 ŝ ) < 1 ) vw < 1 4 t Dire Q 2 = (p ap j )(p b p j ) (p a p b ) 2 = vw t Dire < Q2 4 t CSS Q 2 = vw 1 (v + w).

Parton Shower Simulations 1 M 2 P M 2 + P M 2 1 Soft and Collinear Limit Hardness parameter / evolution variable t( 1 )! 0 Matrix elements factorize Derive process independent splitting kernels P Generate soft/collinear emissions probabilistically according to P Parton shower scale implements phase space restriction: t( 1 ) <µ 2 PS

Parton Shower Simulations M 2 P 1 M 2 + P M 2 1 Sudakov form factor " Z # t1 (t 1, t 0 )=exp P( 1 )d 1 t 0 No-emission probability between scales t 0 and t 1 Parton shower scale implements phase space restriction: t( 1 ) <µ 2 PS

Parton Shower Simulations M 2 P 1 M 2 + P M 2 1 Leading order plus parton shower cross section LO+PS = Z apple B( B ) Z µ 2 (µ 2 PS PS, t 0 )+ (µ 2 PS, t( 1 ))P( 1 ) d 1 d B t 0 no emission hardest emission at t( 1 ) Parton shower scale implements phase space restriction: t( 1 ) <µ 2 PS

POWHEG NLO = Z apple Z B( B )+V( B )+ R( B, 1)d 1 d B + Z R( R ) R( R ) d R P = R B

POWHEG NLO = Z apple Z B( B )+V( B )+ + Z " R( R ) h 2 damp h 2 damp p? 2 + R( R ) h2 damp p? 2 + R( B, 1)d 1 d B h2 damp # d R P = h damp 2 p? 2 R +h2 damp B