Determination of the strong coupling constant from multi-jet production with the ATLAS detector

Transcription

1 Determination of the strong coupling constant from multi-jet production with the ATLAS detector WNPPC 22 Marc-André Dufour McGill University February 22 Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS

2 ATLAS & LHC LHC Proton-proton collider with 7 TeV center-of-mass energy Currently in operation Located 5-5m under the Swiss-French border just outside Geneva ATLAS One of 4 main experiments taking place at the LHC Multi-purpose particle detector Collaboration of 3 scientists from 38 countries & 74 universities and labs Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 2

3 Analysis Goals Measure the QCD strong coupling constant α S Study the running of the strong coupling at energies> 29 GeV Approach Calculate the inclusive ratio distribution = σ N jets 3 σ Njets 2 in data at the particle level 2 Match to next-to-leading order (NLO) predictions at particle level & extract a value for QCD s strong coupling α S Predictions generated from the ratio are largely independent of PDFs, allowing the study of α S at energies > 29 GeV Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 3

4 Analysis Cuts and Parameters Analysis Cuts All jets p T > 4 GeV & η <2.8 Leading jet p T > 6 GeV Exactly primary vertex with more than 5 tracks ATLAS pre-defined loose jet quality cuts (hadronic end-cap spikes, coherent noise, non-collision background) (bad/ugly jets) Data quality cuts recommended by ATLAS standard model group Analysis Parameters Data: ATLAS 2 periods A to I ( 38pb ) Triggers: A combination of all of ATLAS single jet triggers Jet algorithm: Anti-k t.6 jets built from topological clusters & corrected for η offset and jet energy scale (JES) Independent variable: Q = N jets j= ( p (j) T ) 2 Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 4

5 Parton-jet Level (NLOJet++) NLO Predictions α S (M ) Z [GeV/c] NLOJet++ Generate 2 & 3 jet NLO samples with different α S (M Z ) values & matching PDF M events / sample Use MSTW8nlo9cl PDF set (. α S (M Z ).3) Compute (Q ) for each α S (M Z ) value Hard scale parametrization choice consistent with independent variable (Q ) Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 5

6 ) r ) r Parton-jet Level (NLOJet++) NLO Calculations 8 GeV < < 23 GeV.6 & MSTW 28 NLO Anti-k t 8 GeV < < 23 GeV.6 & MSTW 28 NLO Anti-k t (µ log [nb] / d 2-jets d σ (µ log / d [nb] 3-jets d σ log (µ ) f log (µ ) Application of the principle of minimal sensitivity Find the renormalization (µ R = µ r Q ) and factorization (µ F = µ f Q ) scales corresponding to the most stable NLO predictions, i.e. the saddle point. f.2 Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 6

7 Parton-jet Level (NLOJet++) NLO Uncertainties Relative uncertainties Scale: Obtained by varying the renormalization and factorization scales independently according to µ (saddle) r /2 µ r 2 µ (saddle) r /2 µ f 2 µ (saddle) µ (saddle) f f µ r /2 µ f 2µ r PDF: Obtained by generating M events with the full eigenvector PDF sets and combining the resulting values with the master equation X + max = X max = N i= N i= [ ( max X + i X,X i )] 2 X, [ ( max X X + i,x X )] 2 i, () (2) Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 7

8 Parton-jet Level (NLOJet++) NLO Uncertainties (continued) uncertainty / value Statistical Scale PDF NLOJet++, α S =.28.8 MSTW 28 PDF [GeV/c] Total theoretical uncertainty / value NLOJet++, α S =.28 MSTW 28 PDF [GeV/c] NLO theoretical uncertainties are dominated by the scale uncertainty Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 8

9 Folding-in non-pertubative effects AlpGen Parton Particle (Truth) Level C non-perturbative () [GeV/c] Details NLO results do not include any hadronization or underlying event (UE) Use AlpGen+Herwig/Jimmy samples to calculate corrections, and AlpGen+Pythia samples to estimate a model uncertainty Compute a correction factor C non perturbative as (particle+ue,alpgen) (parton+noue,alpgen) (particle)=c non pertubative (parton) Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 9

10 Trigger Accounting for Trigger Data (reconstructed) [GeV/c] Details Use single jet triggers Jet p T selection criteria range from to 95 GeV Use a single trigger per bin Trigger must be fully efficient Use trigger with smallest prescale Assign each event a weight w = prescale Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS

11 Unfolding Detector Particle (Truth) Level Unfolding C unfolding () [GeV/c] Approach Use AlpGen+Herwig/Jimmy sample to compute unfolding factor s value C unfolding as (particle) (reconstructed) Estimate uncertainty on factor by computing it from AlpGen+Pythia and Pythia samples Take maximum shift in each bin used as symmetric uncertainty (particle)=c unfolding (reconstructed) Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS

12 Systematic Uncertainties on Unfolded Data Estimating Pile-Up Effect in Unfolding Reconstructed-level No pile-up In-time pile-up Bunch-train pile-up 2 Data [GeV/c] Approach Use Monte-Carlo sample without pile-up for unfolding Calculate an uncertainty on reconstructed due to pile-up Compute with in-time & bunch-train pile-up samples Take the maximum shift in each bin as additional uncertainty due to pile-up on reconstructed Propagate additional uncertainty to unfolded ratio Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 2

13 Systematic Uncertainties on Unfolded Data Jet Energy Scale (JES) Uncertainty / Value Particle-level 2 Data Uncertainties: Data statistics Jet energy scale [GeV/c] Toy Monte-Carlo Approach Vary jet p T in AlpGen by an amount proportional to the jet s JES uncertainty Use the same proportionality factor for all jets per toy MC iteration Unfold the data using the modified MC sample The standard deviation is calculated for each point and used as JES uncertainty on the unfolded ratio Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 3

14 Systematic Uncertainties on Unfolded Data Jet Energy Resolution (JER) & η Resolution Uncertainty / Value Particle-level 2 Data Uncertainties: Data statistics Jet energy resolution [GeV/c] Uncertainty / Value Particle-level 2 Data Uncertainties: Data statistics Jet angular resolution [GeV/c] A similar toy MC approach to the JES calculation is used The jet p T and η are varied independently in Monte-Carlo Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 4

15 α S Measurement Procedure α s Measurement Procedure Data (particle) NLOJet++ (particle) α S =., MSTW [GeV/c] Least-squares fit with Hessian approach Data (particle) NLOJet++ (particle) α S =.3, MSTW [GeV/c] Define the chi-squared function as [ R (theory) (α χ 2 3/2 S (M Z ),i) R (measured) 3/2 (i)+ λ s λ (correlated) iλ = [ i λ (uncorrelated) ] 2 i,λ λ ] 2 + where iλ are correlated and uncorrelated uncertainties for each Q bin i, and s λ are nuisance parameters associated with each correlated source of uncertainty λ. Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 5 s 2 λ,

16 α S Results α s Measurement Procedure ) R ( µ S α MSTW 28 PDF ATLAS results D results H results ZEUS results ATLAS overall World average D average CDF average 2 3 Renormalization scale µ [GeV/c] R α S (M Z ) results: ATLAS fit: World average:.84 ±.7 DØ: CDF: Obtain an α S (M Z ) measurement in each Q bin, then evolve it with a 2-loop approximation of the renormalization group equation solution Obtain an overall α S (M Z ) measurement by fitting all bins simultaneously Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 6

17 Conclusion Summary Measured distributions in good agreement with with NLO predictions from NLOJet++ The application of the principle of minimal sensitivity is a robust method to tune renormalization and factorization scales in NLO predictions α S (M Z ) results in statistical agreement with the world average and results from similar measurements at CDF and DØ Results are consistent with the running of the coupling as predicted by the RGE Running of the coupling observed for the first time at energy scales > 29 GeV ATLAS note & paper preparation in progress for 22 approval Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 7

18 Backup - Variations in optimal µ r & µ Saddle ) Factorization scale factor Renormalization scale Saddle ) Factorization scale factor Renormalization scale factor (µ (µ log r,f r,f - log NLOJet++; N 2 jets [GeV/c] -.5 NLOJet++; N 3 jets [GeV/c] Details Renormalization (µ r ) and factorization (µ f ) scales optimized by applying the principle of minimal sensitivity Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 8

19 Backup - Raw differential cross-section distributions leading jet T p σ Njets 2 Simulation / Data Details Data AlpGen+Jimmy/Herwig leading jet p [GeV/c] T leading jet T p σ Njets 3 Uncertainties are only statistical Simulation / Data Data AlpGen+Jimmy/Herwig leading jet p [GeV/c] T Distributions are corrected for triggering effects but are otherwise un-altered Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 9

20 Backup - Raw differential cross-section distributions σ Njets σ Njets Simulation / Data Details Data AlpGen+Jimmy/Herwig [GeV/c] Uncertainties are only statistical Simulation / Data Data AlpGen+Jimmy/Herwig [GeV/c] Distributions are corrected for triggering effects but are otherwise un-altered Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 2

21 Backup - Systematic uncertainties Data Measurement Theoretical Predictions Type of Uncertainty Correlated Data Statistics No Trigger Selection Yes Jet Energy Scale Yes Jet Energy Resolution Yes Angular Resolution Yes Jet Quality Yes Unfolding Correction Jet Energy Scale Yes Jet Energy Resolution Yes Angular resolution Yes Pile-up No Monte-Carlo Modelling No ALPGEN Statistics No NLOJET++ Statistics No Scale Yes PDF Yes Non-pQCD correction factor ALPGEN Statistics No Monte-Carlo Modelling Yes List of all sources of uncertainties considered in the analysis, and whether they are treated as correlated between Q bins. Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 2

22 Backup - Uncertainty from jet quality requirements, default /, test Reconstructed-level With bad, with ugly With bad, no ugly No bad, with ugly 2 Data [GeV/c] Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 22

23 Backup - agreement between data and NLO predictions Data (particle) NLOJet++ (particle) α S =., MSTW [GeV/c] Marc-André Dufour February 22 Determination of strong coupling constant at ATLAS 23