Higgs Pair Production: NLO Matching Uncertainties
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1 Higgs Pair Production: NLO Matching Uncertainties Silvan Kuttimalai in collaboration with Stephen Jones November 7th, 2017 Higgs Couplings Workshop, Heidelberg
2 Introduction
3 Motivation: the Higgs Potential V = 2 v 2 H vh 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
4 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
5 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
6 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
7 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
8 Motivation Heinrich et al.: JHEP 08 (2017) 6
9 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
10 Parton Shower E ects at LO
11 ds/dp? HH [pb/gev] Ratio SHERPA HEFT pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s LO+PS Results p s = 14 TeV HEFT p HH? [GeV] P M 2 1 M 2 P: process independent parton shower kernels 8
12 ds/dp? HH [pb/gev] Ratio 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 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
13 LO+PS Results ds/dp? HH [pb/gev] 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] SHERPA Full SM pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV Full SM Ratio Ratio 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 p HH? [GeV] Parton shower kernels don t know hard process 8
14 Parton Shower E ects at NLO
15 NLO Parton Shower Matching: 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
16 NLO Parton Shower Matching: 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
17 NLO Parton Shower Matching: 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
18 NLO Parton Shower Matching: 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
19 NLO Parton Shower Matching: = 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
20 NLO Parton Shower Matching: = 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
21 NLO Parton Shower Matching: = 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? ) 11
22 NLO Parton Shower Matching: = 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
23 NLO Parton Shower Matching: = 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 Focus on hard region: t µ 2 PS ) recover fixed order, assuming B B 11
24 NLO Results ds/dp? HH [pb/gev] 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 S-events H-events 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
25 NLO Results ds/dp? HH [pb/gev] Ratio to FO Ratio to SHERPA Fixed-Order MC@NLO, CS shower S-events H-events pp! HH p s = 14 TeV HEFT 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
26 NLO Results ds/dp? HH [pb/gev] Ratio to FO Ratio to SHERPA Fixed-Order MC@NLO, CS shower S-events H-events pp! HH p s = 14 TeV Full SM 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
27 NLO Results ds/dp? HH [pb/gev] Ratio to FO Ratio to MC@NLO pp! HH p s = 14 TeV Full SM SHERPA Fixed-Order MC@NLO, CS Dire shower S-events H-events 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
28 Comparison to Literature: NLO+PS ds/dp? HH [fb/gev] 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 % Ratio to fixed-order MC@NLO results within uncertainties in tail MadGraph uncertainties larger Ratio to fixed-order p HH? [GeV] POWHEG: flat excess in tail known feature of matching method somewhat suppressed through damping factor h damp = 250 GeV 14
29 Comparison to Literature: Analytic Resummation ds/dp? HH [fb/gev] 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 NLO+NLL [Ferrera, Pires, 2017] MC@NLO, Dire shower MC@NLO, CS shower p HH? [GeV] Uncertainties on NLO+NLL: 3% near p? HH 20GeV 10 % near p? HH 100GeV Good agreement within uncertainties 15
30 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
31 Backup
32 E ects on Fixed-Order Uncertainties ds/dp? HH [pb/gev] 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 S-events H-events 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
33 NLO+PS: Alternative Comparison Plot ds/dp? HH [fb/gev] Sherpa, Dire Shower Sherpa, CS Shower MadGraph5 + Pythia Powheg-Box + Pythia Ratio to fixed-order Ratio to fixed-order p HH? [GeV]
34 Replacing B by B ds/dp? HH [pb/gev] SHERPA Fixed-Order MC@NLO, Dire shower ( B! B) pp! HH p s = 14 TeV Full SM Ratio to FO Ratio to MC@NLO S-events H-events 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
35 LO+PS Results: CS Shower ds/dp? HH [pb/gev] 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] SHERPA Full SM pp! HH + j pp! HH +CSshower pp! HH +CSshower,µ PS = p s p s = 14 TeV Full SM Ratio Ratio p HH? [GeV] 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
36 LO+PS Results: Dire Shower ds/dp? HH [pb/gev] SHERPA HEFT pp! HH + j pp! HH +Direshower p s = 14 TeV HEFT ds/dp? HH [pb/gev] SHERPA Full SM pp! HH + j pp! HH +Direshower p s = 14 TeV Full SM Ratio Ratio p HH? [GeV] 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
37 CS shower vs Dire: HEFT ds/dp? HH [pb/gev] SHERPA Fixed-Order MC@NLO, CS shower pp! HH p s = 14 TeV HEFT ds/dp? HH [pb/gev] SHERPA Fixed-Order MC@NLO, Dire shower pp! HH p s = 14 TeV HEFT Ratio to FO Ratio to FO Ratio to MC@NLO S-events H-events p HH? [GeV] Ratio to MC@NLO S-events H-events p HH? [GeV]
38 CS shower vs Dire: Full SM ds/dp? HH [pb/gev] SHERPA Fixed-Order MC@NLO, CS shower pp! HH p s = 14 TeV Full SM ds/dp? HH [pb/gev] SHERPA Fixed-Order MC@NLO, Dire shower pp! HH p s = 14 TeV Full SM Ratio to FO Ratio to FO Ratio to MC@NLO S-events H-events p HH? [GeV] Ratio to MC@NLO S-events H-events p HH? [GeV]
39 Other Observables ds/dp j? [pb/gev] SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM ds/dht SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM Ratio to FO Ratio to Dire p j? [GeV] HT [GeV]
40 Other Observables ds/d HH [pb/gev] SHERPA Fixed-Order MC@NLO, Dire shower MC@NLO, CS shower pp! HH p s = 14 TeV Full SM Ratio to FO HH
41 Single Higgs ds/dp H? [pb/gev] Higgs boson transverse momentum Fixed-order HEFT Fixed-order LO+PS µ PS = Ratio p H? [GeV]
42 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).
43 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
44 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
45 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
46 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
47 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
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