Geneva: Event Generation at NLO

Transcription

1 Geneva: Event Generation at NLO Saba Zuberi UC Berkeley/LBL Christian Bauer, Calvin Berggren, Nicholas Dunn, Andrew Hornig, Frank Tackmann, Jesse Thaler, Christopher Vermilion, Jonathan Walsh, SZ

2 Outline Report on progress towards Event Generation at NLO Important Features of Monte Carlos Why merging NLO with Resummation is important and challenging Current Approaches Geneva Approach First Results Conclusions Saba Zuberi 2

3 Important Features of MC Monte Carlos indispensable at colliders Goal: Connect most precise theory predictions possible to experiment. Key Feature: Monte Carlos are exclusive Basic role of event generator: return weight for each point in N-body phase space dσ/dφ N Can implement arbitrary experimental cuts Major challenge for analytic calculations. {η cut,p cut T,R} Leading small pt resummation and large pt fixed order Allows one to be exclusive in jet multiplicities Eg. pp H +0, 1, 2 jets have different backgrounds and sensitivities Fully hadronized events Saba Zuberi 3

4 Parts of the Monte Carlo dσ MC = Hard Interaction Parton Hadronization Underlying Event Hard Interaction: Fixed order partonic matrix elements. Legs + Loops. Parton : Collinear and soft splittings. High Multiplicity final state. Logs α s ln 2 µ PS. µ H Hard Interaction Evolution µ hard dφn LO Matrix Element dφn+1 Parton dφn+2 Parton dφn+3 Parton Hadronization µ PS Hadronization/ UE: Model non-perturbative physics. Partons to hadrons Λ QCD Saba Zuberi 4

5 Combining Fixed Order and Resummation Example pp H WW lνlν : Large fixed order corrections. Vary with pt cut Anastasiou, Dissertori, Stockli (2007) α s FO expansion describe large pt cut region Unreliable at small pt cut Need α s ln pcut T m H resummation (parton shower) Combine Hard Matrix Element NLO with Resummation (parton shower) Anastasiou, Dissertori, Stockli, Webber (2008) Goal of Geneva: Combine different jet multiplicities all at NLO with resummation Saba Zuberi 5

6 Challenge : Fixed Order and Parton dφn dφn+1 dφn+2 dφn+3 At LO: LO Matrix Element Parton Parton Parton Beyond LO: N-body Phase Space = N-parton Phase Space IR finite NLO = dφn + dφn+1 Make each weight well defined. Both Parton and NLO ME include real emission corrections FO: exact n+1 body, PS collinear/soft limit. dφn dφn+1 dφn+2 dφn+3 At NLO: LO +Virtual Real PS Parton Parton Avoid Double Counting Saba Zuberi 6

7 Current Approaches: Fixed Order Parton *touch on just a few MC@NLO/ POWHEG Divergences: Define Subtraction (NLO for single jet multiplicity) (LL Parton ) ] dφ n [V n + dφ n+1 n S +dφ n+1 [R n+1 S] Maps N-Body Phase Space to N-Parton Phase Space [Frixione, Webber; Nason; Frixione, Nason, Oleari] Double Counting: Modify 1st emission of parton shower. Inclusive jet observable at NLO Multi-jets at LO Partonic LO ME Parton Hadronization µ hard µ PS Λ QCD (LO for all jet multiplicities) (LL Parton ) [Catani, Krauss, Kuhn, Webber; Lönnblad; Mangano] Hard matrix element µ res combined with Sudakov to cancel µ res dependence. MENLOPS (NLO single jet + LO rest jet multiplicities) Saba Zuberi 7 (LL Parton ) [Bauer, Tackmann, Thaler; Hamilton, Nason; Hoche, Krauss, Schonherr, Siegert]

8 The Geneva Approach Goal: Exclusive jet multiplicities all at NLO + resummation pp H/W +0, 1, 2 jets Start with e + e 2, 3, 4 jets. Naively 4 jets NLO would require 2 jet to N 3 LO to be IR finite. Geneva: relevant pieces obtained from resummation Divergences: Map N-jet Phase Space to N-body Phase Space Divide Phase Space : Resolution variable, N-jettiness defined for any number of partonic final states. T N. Vetos > N jets. Well [Stewart, Tackmann, Waalewijn ] µ hard Resummed Calculation SCET µ res T cut dσ excl 2 : T cut > T 2 dσ excl 3 : T 2 > T cut > T 3 dσ incl }4 : T3 > Tcut } } Parton µ PS Hadronization Λ QCD Saba Zuberi 8

9 Systematic Improvement of MC Using EFT For given N-jet [Bauer, Fleming, Luke, Pirjol, Stewart] Small T 2 : Soft Collinear Effective Theory - framework to calculate resummed QCD distributions. Systematically include: α n s matching and resum renormalization group α n s ln m (T /Q)/T dσ2 s dω dt = dσ B dω H 2(Ecm,µ) 2 ( ds 1 ds 2 J 1 (s 1,µ) J 2 (s 2,µ) S 2 T s 1 s ) 2,µ Q 1 Q 2 Hard Function: NLO matrix elements Jet and Soft functions: Collinear and soft limit Hard Jet E cm Ecm T Soft T Parton Hadronization µ PS Λ QCD Saba Zuberi 9

10 Systematic Improvement of MC Using EFT Combine with large dσ 2 dω dt = dσs 2 dω dt + } T 2 in 2-jet bin [ Resummed NLL = NLO FO+ α n s L 2n 1 dσ QCD 2 dω dt dσs 2 dω dt ] exp } Non-singular NLO σ2(tcut) [pb] E cm = 500 GeV NLO NLL NLL +NLO T cut [GeV] Saba Zuberi 10

11 Combining Higher Jet Multiplicities Focus on 2-jet NLL+NLO, 3 jet LO (MC@NLO/POWHEG equivalent) Distribute events according to: dσ 2 dφ 2 (T cut )= 2-body events Tcut 0 dt 2 dσ 2 dω dt 2 + dσ 3 dφ 3 = Now straightforward to extend to 3 jet NLO. ( dσ2 dω 2 dt 2 Constant T 2 Has full Φ3 dependence for Large dependence T 2 : Resummation 2-body events starts to turn off. Ratio starts at O(αs) 2 3-body events / dσ2 ) exp dσ FO 3 θ(t 2 > T cut ) dω 2 d T 2 dφ 3 } } Small important : Resummation Ratio starts at NNLL Saba Zuberi 11 T 2

12 First Results Distribute events according to Monte Carlo with theory (scale) uncertainties not MC statistics! Exactly matches analytic central value + uncertainty. dσ/dt2 [fb/gev] dσ 3 dφ 3 T 2 = 2(1 T ) E cm = 500 GeV NLL +NLO NLL GENEVA T 2 [GeV] Saba Zuberi 12

13 First Results Consider variable sensitive to Φ3 angular dependence. Using Should reproduce shape. dφ 3 =dφ 2 dz dt 2 dφ Definition of variables consistent for 3-jets (at any order). dσ/dz [pb] dσ 3 dφ 3 = ( dσ2 dω 2 dt 2 T cut < T 2 < / dσ2 ) exp dσ FO 3 θ(t 2 > T cut ) dω 2 d T 2 dφ 3 Singular behavior turned off by Qz 1 z 2 E cm = 500 GeV T 2 10 GeV LO GENEVA shift from resummed terms ~ α 2 s z = E 1 E 1 + E z Saba Zuberi

14 Conclusions Want event generators with best possible accuracy to connect theory and experiment Goal of Geneva: Combining several jet multiplicities at NLO with resummation/ parton shower Method: Use resummed exclusive cross-sections from SCET Status: 2 jet NLL + NLO and 3 jet LO; 3 jet NLO almost complete. Expect pp H +0, 1 jets, pp W +0, 1 jets at NLO soon! Saba Zuberi 14

15 END Saba Zuberi PANIC July 2011

16 Back Up Slides Saba Zuberi PANIC July 2011

17 α 2 s corrections are Large NLL much larger than α s contribution [Abbate, Fickinger, Hoang, Mateu, Stewart] Saba Zuberi 17

18 } } } Perturbative Structure Perturbative structure of hard interaction σ 1 + α s L 2 + α s L + α s " parton shower NLO L ln µ PS µ hard + α 2 sl 4 + α 2 sl 3 + α 2 sl 2 + α 2 sl + α 2 s N 2 LO LL NLL N 2 LL Saba Zuberi 18