MadGolem: Automated NLO predictions for SUSY and beyond

Transcription

1 David López-Val D. Gonçalves Netto (MPI, Munich), T. Plehn (Heidelberg U.), I. Wigmore (Edinburgh U.), K. Mawatari (Vrije U.) together with ITP - Universität Heidelberg SUSY 2013, Trieste (Italy) - August 29th 2013

2 Outline Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

3 MadGolem a 3-slide overview Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

4 AUTOMATION NEXT-TO-LEADING ORDER NEW PHYSICS

5 MadGolem a 3-slide overview Modules & flowchart Modules & flowchart Golem one-loop amplitude MadGraph tree-level NLO Real emission process card.dat run card.dat parameter card.dat Qgraf one-loop amplitude NLO cross sections MadGolem NLO distributions MadDipole IR subtraction Counterterm generator UV renormalization MadOS OS subtraction

6 MadGolem a 3-slide overview Modules & flowchart Modules & flowchart Golem one-loop amplitude MadGraph tree-level NLO Real emission process card.dat run card.dat parameter card.dat Qgraf one-loop amplitude NLO cross sections MadGolem NLO distributions MadDipole IR subtraction Counterterm generator UV renormalization MadOS OS subtraction PROSPINO

7 MadGolem a 3-slide overview Modules & flowchart Modules & flowchart Golem one-loop amplitude MadGraph tree-level NLO Real emission process card.dat run card.dat parameter card.dat Qgraf one-loop amplitude NLO cross sections MadGolem NLO distributions MadDipole IR subtraction Counterterm generator UV renormalization MadOS OS subtraction PROSPINO

8 MadGolem a 3-slide overview Modules & flowchart Modules & flowchart Golem one-loop amplitude MadGraph tree-level NLO Real emission process card.dat run card.dat parameter card.dat Qgraf one-loop amplitude NLO cross sections MadGolem NLO distributions MadDipole IR subtraction Counterterm generator UV renormalization MadOS OS subtraction Automating PROSPINO Generalizing

9 MadGolem architecture Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

10 MadGolem architecture Automating NLO the major hurdles Loops Divergences

11 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams

12 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude

13 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

14 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

15 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

16 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

17 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

18 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors

19 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors CALCULATION Golem [Binoth et al.] Amplitude BASH,PERL,FORM,MAPLE Reduced amplitude

20 MadGolem architecture One-loop amplitude One-loop amplitude The lo GENERATION Qgraph [Nogueira] Model files FORTRAN Feynman diagrams TRANSLATION Qgraf-Golem Feynman diagrams BASH,PERL,FORM Amplitude vertices propagators color Lorentz structures rel. signs sym. factors CALCULATION Golem [Binoth et al.] Amplitude BASH,PERL,FORM,MAPLE Reduced amplitude M NLO = M NLO [color/helicity/1l function] }{{} partial amplitudes B color B hel B 1Lfunction }{{} basis

21 MadGolem architecture One-loop amplitude One-loop amplitude Analytical results accessible at any time Dedicated coding: efficient generation & numerical evaluation Loop filtering Grouping of topologically equivalent one-loop diagrams Amplitude coefficients as split dynamic libraries loaded at runtime Genuine New Physics structures treatable Majorana fermions (clashing arrows!) complex color & spin structures MSSM renormalization including heavy flavor squarks & SUSY restoration. Most easily interfaced with MG tools : FeynRules, MadAnalysis,...

22 MadGolem performance Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

23 MadGolem performance Running MadGolem 3-stage procedure 3 interfaces 3 executables Stage 1: PROCESS GENERATION process_card./newprocess_snlo

24 MadGolem performance Feynman Virtual corrections O(α s) virtual gluon/gluino/squark exchange Real corrections : quark and gluon emission off the initial partons and the final-state squark i) self-energy insertions; ii) vertex corrections; iii) box diagrams; iv) real emission

25 MadGolem performance Feynman Virtual corrections O(α s) virtual gluon/gluino/squark exchange Real corrections : quark and gluon emission off the initial partons and the final-state squark i) self-energy insertions; ii) vertex corrections ; iii) box diagrams; iv) real emission

26 MadGolem performance Feynman Virtual corrections O(α s) virtual gluon/gluino/squark exchange Real corrections : quark and gluon emission off the initial partons and the final-state squark i) self-energy insertions; ii) vertex corrections; iii) box diagrams ; iv) real emission

27 MadGolem performance Feynman Virtual corrections O(α s) virtual gluon/gluino/squark exchange Real corrections : quark and gluon emission off the initial partons and the final-state squark i) self-energy insertions; ii) vertex corrections; iii) box diagrams; iv) real emission

28 MadGolem performance Feynman The Feynman diagrams get generated...

29 MadGolem performance Running MadGolem 3-stage procedure 3 interfaces 3 executables Stage 1: PROCESS GENERATION process_card./newprocess_snlo Stage 2: AMPLITUDE CALCULATION./run_golem_pl At this point the user is able to: Select diagram topologies detailed analysis of the virtual corrections Access the analytical output in several stages very useful for cross-checking (and to dig out some physics!)

30 MadGolem performance Feynman The scattering amplitudes are further translated...

31 MadGolem performance Feynman and analytically reduced

32 MadGolem performance Running MadGolem 3-stage procedure 3 interfaces 3 executables Stage 1: PROCESS GENERATION process_card./newprocess_snlo Stage 2: AMPLITUDE CALCULATION./run_golem_pl At this point the user is able to: Select diagram topologies detailed analysis of the virtual corrections Access the analytical output in several stages very useful for cross-checking (and to dig out some physics!) Stage 3: NUMERICAL EVALUATION param_card.dat, run_card.dat./generate_events_nlo 2 2 myrun

33 MadGolem performance Running MadGolem And the user retrieves the results!

34 MadGolem performance Automated NLO BSM phenomenology First complete fully automated NLO calculations of BSM 2 2

35 MadGolem performance Automated NLO BSM phenomenology First complete fully automated NLO calculations of BSM 2 2 pp q χ 0 arxiv: pp [ q q, q q, q g, g g] arxiv: pp GG arxiv: pp l 8 l8 arxiv:

36 MadGolem performance Automated NLO BSM phenomenology First complete fully automated NLO calculations of BSM 2 2 pp q χ 0 arxiv: pp [ q q, q q, q g, g g] arxiv: pp GG arxiv: pp l 8 l8 arxiv: Total NLO rates and K factors unconstrained Parameter space surveys BSM NLO Anatomy of the NLO quantum effects separated contributions for each one-loop topology & partonic sub-channel Analytical expression for the one-loop amplitudes Scale dependences NLO distributions & comparison to jet merging

37 MadGolem an application: MSSM 3rd generation Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

38 MadGolem an application: MSSM 3rd generation 3rd generation at the LHC Phenomenological case Light 3rd generation squarks are motivated Naturalness little hierarchy Natural SUSY Unconstrained MSSM no high-scale relations Higgs physics a viable non-decoupling SUSY Higgs sector Han et al. [ 13] Astrophysics & Cosmology EW phase transition & baryogenesis Experimentally : Compelling decay patterns eventually rich in t/b t/b-rich final-states from g decays Loose mass constraints (e.g. for compressed m m χ 0 spectra) 1

39 MadGolem an application: MSSM 3rd generation Benchmarks Benchmarks 3rd generation phenomenology pmssm Berger et al [ 08]; Cahill-Rowley [ 13]: no high-scale relations R-parity ; MFV ; degenerated 1st & 2nd generations ; suppressed Yukawas & trilinears for 1st & 2nd generations Light 3rd generation & Higgs physics Han [ 13] NSUSY Dine, Dimopoulos, Espinosa, Giudice, Weiler [ 93 13] light soft-masses for strong Yukawas ; light µ term Specific benchmarks as laid out in Buchmuller [ 13]; Baer, List [ 13]

40 MadGolem an application: MSSM 3rd generation Benchmarks Benchmarks 3rd generation phenomenology pmssm Berger et al [ 08]; Cahill-Rowley [ 13]: no high-scale relations R-parity ; MFV ; degenerated 1st & 2nd generations ; suppressed Yukawas & trilinears for 1st & 2nd generations Light 3rd generation & Higgs physics Han [ 13] NSUSY Dine, Dimopoulos, Espinosa, Giudice, Weiler [ 93 13] light soft-masses for strong Yukawas ; light µ term Specific benchmarks as laid out in Buchmuller [ 13]; Baer, List [ 13] m t1 m t2 m b1 m b2 m χ 0 1 m χ 1 NSUSY NSCMSSM Light m g

41 MadGolem an application: MSSM 3rd generation Automated t t & b b production to NLO t t & b NLO: rates [preliminary] g g t g g g (all rates in fb)

42 MadGolem an application: MSSM 3rd generation Automated t t & b b production to NLO t t & b NLO: rates [preliminary] g g t g g g pp pp b 1 b1 σ LO σ NLO K σ LO σ NLO K NSUSY NSUSY NSUSY NSCMSSM ,47 NSCMSSM NSCMSSM Light (all rates in fb)

43 MadGolem an application: MSSM 3rd generation Automated t t & b b production to NLO t t & b NLO: distributions [preliminary] g g t g g g NSCMSSM NSCMSSM pp > ~ t ~ t1 1 real real 8 TeV -virtual -virtual LO NLO dσ/dp T [GeV -1 ] jet merging p T (t ~ 1 ) [GeV] LO dσ/dy NLO pp > ~ t ~ t1 1 8 TeV jet merging y (t ~ 1 ) NSCMSSM NSCMSSM pp > ~ t ~ t1 µ 0 /2 pp > ~ t ~ 1 t1 1 8 TeV TeV NLO 2µ 0 K factor 2.0 2µ 0 jet merging 1/σ dσ/dp T [GeV -1 ] p T (t ~ 1 ) [GeV] µ 0 / p T (t ~ 1 ) [GeV]

44 MadGolem an application: MSSM 3rd generation Automated t t & b b production to NLO t NLO [preliminary] b g b χ 1 t χ 1 t g t b g χ 1 t χ 1 t g g b g χ 1 t pp χ 1 σ LO σ NLO K NSUSY NSUSY NSUSY NSCMSSM NSCMSSM NSCMSSM Light NSCMSSM NSCMSSM pp > ~ t χ1 pp > ~ t χ1 ~ 1 µ 0 /2 1 8 TeV 8 TeV NLO 2µ 0 1/σ dσ/dy y (t ~ 1 ) K factor 2µ 0 µ 0 / y (t ~ 1 )

45 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO 4 versus 5 active flavors

46 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO 4 versus 5 active flavors 4FS m b 0 Q 2 m 2 b initial-state b-quarks final-state b-quarks 5FS m b = 0 Q 2 m 2 b b-quark PDF log(q 2 /m 2 b ) Maltoni, Ridolfi, Ubiali [ 12]

47 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO 4 versus 5 active flavors 4FS m b 0 Q 2 m 2 b initial-state b-quarks final-state b-quarks 5FS m b = 0 Q 2 m 2 b b-quark PDF log(q 2 /m 2 b ) Maltoni, Ridolfi, Ubiali [ 12] σ (pp b l n 1 ) [fb] 2000 (1) µ F 5 (2) µ R =10 µ 0 (3) µ F =0.1 µ 0 (4) µ R =0.1 µ 0 (5) µ F =10 µ S = 14 TeV µ R 5FS 500 4FS µ R,F / µ 0 µ F / µ 0 1 µ R / µ 0 1 µ F / µ 0 1 µ R / µ 0

48 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO Automated on-shell subtraction gg χ 1 + b-jet gg χ 1 + b-jet

49 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO Automated on-shell subtraction gg χ 1 + b-jet gg χ 1 + b-jet dσ R ] dσ R + ] dσ R regular O(1/(p 2 m 2 )) gg χ 1 + b-jet + gg t 1(OS) t 1(OS) χ 1 + b-jet

50 MadGolem an application: MSSM 3rd generation Automated tχ 1 production to NLO Automated on-shell subtraction gg χ 1 + b-jet gg χ 1 + b-jet dσ R dσ R ] regular + dσ R ] O(1/(p 2 m 2 )) gg χ 1 + b-jet + gg t 1(OS) t 1(OS) χ 1 + b-jet ( dσ OS = σ Born m t1 Γ t1 /π + O dm 2 (M 2 m 2 t )+m 2 t Γ (M 2 m 2 ) ) phase-space singularity & double counting avoided gauge-invariance & spin correlations preserved Beenakker, Höpker, Spira, Zerwas [ 99]

51 Summary Outline 1 MadGolem a 3-slide overview 2 MadGolem architecture 3 MadGolem performance 4 MadGolem an application: MSSM 3rd generation 5 Summary

52 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies

53 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies

54 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies

55 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies

56 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies

57 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies MadGolem ITS APPLICATION 3rd NLO :, b 1 b1, χ 1 NLO rate s, K-factors, scale dependences, distributions, theory uncertainties, flavor schemes

58 Summary Take-home ideas Take-home ideas MadGolem THE TOOL Automated NLO cross-sections & distributions for 2 2 processes Highly modular, independent add-on to MadGraph/MadEvent Analytical, Feynman-diagrammatic one-loop amplitudes Automated renormalization & subtraction Tailored for BSM & NLO studies MadGolem ITS APPLICATION 3rd NLO :, b 1 b1, χ 1 NLO rate s, K-factors, scale dependences, distributions, theory uncertainties, flavor schemes Standalones for numerical evaluation available upon request!