1. A study on AlpGen and Sherpa in Z+jets events Piergiulio Lenzi Università di Firenze & INFN CTEQ-MCnet Summer School Debrecen, 8-16 August 2008

2. Introduction ­ I’m a PhD student based in Florence; I’m in my third year (the last in Italy), working on CMS ­ Florence group has been deeply involved in the CMS Inner Tracker construction, so I’ve been working on: ­ Construction and commissioning of the detector ­ Development of track reconstruction algorithms ­ In the last year we dedicated more effort on the physics, and we have chosen the Z+jets channel ­ As I was starting to study the new subject the “MCnet short-term studentship” announcement appeared on one of the CMS mailing lists!! ­ I immediately decided to apply!

3. Outline ­ Something about what I used to do before my studentship… ­ Building the CMS tracker ­ Track Reconstruction @ CMS ­ The Matrix Element – Parton Shower matching problem ­ Two different approaches to the matching: ­ CKKW (Catani, Kuhn, Krauss, Webber), the SHERPA way ­ MLM (M. Mangano), the AlpGen way ­ Production of Z+jets events at LHC (14 TeV) ­ Sherpa and its systematics ­ AlpGen and its systematics ­ A comparison between the two

4. CMS Tracker construction I’ve been involved in all the steps of the tracker construction, from sensor quality tests to the full detector commissioning Beam test, Oct 2004 Cosmic rays in a tracker prototype, June 2005 Layer assembly, Feb 2006 Final Inner Barrel assembly, Oct 2007 Final assembly and tests, Mar-Jul 2007

5. Track reconstruction ­ I’ve worked on the development of CMS track reconstruction algorithms; in particular ­ Commissioning of detector and reconstruction software with cosmic ray real data Track reconstruction efficiency on cosmic rays as a function of track θ. Black simulation; Red data ­ Development of the Kalman Filter based pattern recognition ­ Development of track fitting methods based on soft hit-to-track assignment (DAF). Should perform better in dense or noisy environment Transverse and longitudinal impact parameter resolution; Blue standard tracking Red DAF preliminary

6. My studentship ­ I spent my studentship at University College London (UCL) from Jan to Apr 2008, supervised by Prof. Jon Butterworth ­ I was working in close contact with developers of the RIVET package and with MC experts http://projects.hepforge.org/rivet/trac/wiki/ http://projects.hepforge.org/rivet/trac/wiki/ ­ RIVET (Robust Independent Validation of Experiment and Theory) is part of the CEDAR (Combined e-Science Data Analysis Resource) [1] project ­ Rivet main objective is to provide a general framework for MC validation/tuning and comparison with experimental results ­ The main idea is to reproduce in Rivet experimental analyses; results obtained running such analyses on MC samples are then easily compared with experimental results stored in HEP-DATA DB [2] [1] J.M. Butterworth et al. “The CEDAR Project”, hep-ph/0412139 [2] http://hepdata.cedar.ac.ukhttp://hepdata.cedar.ac.uk

7. RIVET ­ Interface to many generators is provided by the separate AGILe library http://projects.hepforge.org/agile/http://projects.hepforge.org/agile/ ­ RIVET is a C++ package, with two main kind of objects ­ Projections: these classes calculate event observables. Projections are handled through a smart caching system avoiding the same observable being calculated twice for the same event ­ Analyses: RIVET comes with many analyses that reproduce experimental papers from LEP, HERA, TVT.  User analyses can be easily plugged in the RIVET framework with a plugin system ­ Comparison with experimental results is straightforward, thanks to the use of the low weight AIDA-xml plot format, the same used when exporting experimental results from HEP-DATA database

8. ME and PS ­ Matrix Element (ME) calculations are based on the computation of the Feynman amplitudes of the processes contributing to the final state ­ Parton showers (PS) describe the final state starting from a hard 2  2 process as a successive series of 1  2 splittings. ­ Splitting probability is calculated in the limit of collinear emission ­ Divergences in this limit are tamed imposing the conservation of total probability using form factors (Sudakov)

9. The ME-PS matching problem ­ Matrix Element calculations: ✓ Describe well separated jets configurations ✓ Are exact at a given order ✕ Run into troubles in the soft and collinear regions ✕ Can’t describe the internal structure of jets - Parton Shower calculations: ✓ PS is universal, given the basic hard process the PS recipe will produce reasonable parton configurations ✓ The use of Sudakov form factors ensures controlled behavior in the soft and collinear region, so jet evolution is well described ✕ Cannot steer the shower evolution too much, some regions of the phase space are not efficiently filled, e.g. well separated parton configurations - It would be very convenient to use the ME to predict hard parton configuration and the PS to describe the evolution of jets, but beware double counting and holes in the phase space

10. SHERPA approach to the matching: CKKW ­ Jet production and jet evolution regions are well separated using a k t measure (y=min(Pt 1 2, Pt 2 2 )*ΔR 2 /D 2 ) cutoff y cut =Q cut 2 /E cm 2 ­ Calculate the ME cross sections for all the desired parton multiplicities; y cut is used to cutoff divergences; a fixed  s ME is used ­ Select one parton multiplicity according to ME cross sections and produce jet momenta according to the corresponding ME squared ­ a “shower history” is reconstructed through k t clustering until a 2  2 process is found  In other words this answers to the question: “How could a PS have produced this parton configuration?” ­ A running coupling correction weight is applied ­ Apply a Sudakov form factor correction for each clustering  The effect of this correction is to weight the event as if it were produced by a PS but substituting the collinear splitting function with the exact ME ­ Evolve the event with a PS, vetoing emission above the cut Cluster Above y cut Below y cut

11. AlpGen approach to the matching: MLM ­ The MLM algorithm proceeds exactly as the CKKW up to the reweighting of  s ­ Events emerging from the ME are fully showered using a conventional shower (PYTHIA or HERWIG) ­ Partons are clustered into jets (with a cone algorithm in the AlpGen implementation) ­ Jets are matched to original partons ­ If not all the jets match to the original partons event is rejected ­ This effectively reproduces Sudakov reweighting ­ Effectively vetoes PS emission above the merging scale

12. Z+jets event generation ­ SHERPA ­ SHERPA-MC-1.0.11 was used ­ pp  e+ e- + up to 3 jets at 14TeV ­ CTEQ6l pdf ­ No underlying event ­ 66. GeV < mass(e + e - ) < 116. GeV ­ Matching parameter Q cut = 20GeV ­ AlpGen ­ V2.13 was used ­ pp  e+ e- + n jets (n = 0, 1, 2, 3) at 14TeV ­ CTEQ6l pdf ­ 66.GeV < mass(e + e - ) < 116. GeV ­ - Matching parameters:  E t (clus) = 25 GeV  R(clus) = 0.7  ηmax = 5 ­ Pythia and Herwig UE was switched off

13. Analysis ­ Final state particles with |η| < 5 were selected ­ No pt cut on the final state particles ­ Kt jets were reconstructed using the FastJets package by M. Cacciari, G. Salam ­ Ptmin = 30 GeV, D = 0.4 ­ Many lepton and jet observables have been calculated ­ For each generator a collection of observables is shown and the effect of a change in the matching parameters and in the scale choice is described ­ A comparison between AlpGen and Sherpa is shown

14. Sherpa observables Pt lepton pair Pt e - Jet multiplicityPt leading jet

15. Sherpa, differential jet rates ­ Distribution of the kt resolution variable making a n jet turn into a n-1 jet event ­ Critical region around the cut (log 10 (20)~1.3) ­ The ME kinematics is altered by the PS, so mismatches around the cut can occur MEPS

16. Sherpa systematics: change of the matching scale ­ I tired three values for Q cut : 20GeV (default), 30GeV, 50GeV ­ The effect on the overall cross section is summarized below ­ The effect on lepton observables, and the relative difference with respect to the default is shown in the plots below ­ As the Q cut is increased, the ME phase space fraction is reduced ­ Since the ME is responsible for the hardest parton kinematics the increase in the merging scale results in spectra with softer tails Qcut=20GeVQcut=30GeVQcut=50GeV 1594.1 pb1411.3 pb1399.8 pb Pt lepton pair Pt e -

17. Sherpa systematics: change of scales ­ Sherpa was run with the default choice for renormalization (  R ) and factorization (  F ) scales,  R and  F times 0.5 and  R and  F times 2 ­ The effect on the overall cross secion is summarized below: Default scalesScales*0.5Scales*2 1594.1 pb1292.4 pb1646.5 pb ­ The effect is more evident in the first bins where the 0 jet contribution dominates ­ The effect changes sign for higher boson pt ­ This agrees with previous studies, where it was shown that the LO cross section for 0 jets grows with the scale, while the LO cross section for >0jets decreases as the scale grows [hep-ph/ 0308195 ] Pt lepton pair

18. AlpGen systematics, change of the merging scale ­ Two values were used for the E t (min) of the cone algorithm used to steer the matching: 25GeV and 40 GeV ­ The overall cross section effect is summarized below ­ The effect on lepton observables is almost negligible Et(min)=25GeVEt(min)=40GeV 1534.5 pb1516.4 pb

19. AlpGen systematics, Change of scales ­ AlpGen+Pythia was run with the default scale choice,  R times 0.5 and  R times 2 ­ The effect on the overall cross section is summarized below: Default scalesScale*0.5Scale*2 1534.5 pb1449.1 pb1672.2 pb ­ The effect is similar to the one observed in Sherpa ­ The low pt region, dominated by the 0jet contribution shows a behavior similar to Sherpa

20. AlpGen-SHERPA comparisons: lepton observables ­ AlpGen has been showered both with Pythia and Herwig ­ The inclusive cross sections are ­ Sherpa shows the hardest spectrum, Pythia the softest ­ Differences between Pythia and Herwig are due to the different way the two PS alter the ME kinematics ­ The Pt spectrum differences translate into the η spectrum, with PYTHIA showing the less central Z and SHERPA the most central one SHERPAAlpGen+PYTHIAAlpGen+Herwig 1594.1 pb1534.5 pb1523.0 pb

21. AlpGen-SHERPA comparisons: jet observables ­ Sherpa shows a harder leading jet spectrum ­ The jet multiplicity is maximum for Sherpa and minimum for AlpGen+Pythia

22. Conclusion ­ About my work ­ AlpGen and SHERPA implement two different approaches to the matching of ME and PS predictions ­ A study of the “theoretical uncertainties” has been carried out for both generators, varying the matching parameters and the scales ­ When comparing AlpGen with SHERPA, some not negligible differences have been spotted ­ And in general about my studentship: ­ I worked in close contact with MC experts ­ I got an insight on the differences among some of the MC tools available, and on the systematics of such tools ­ ….and I spent some nice time in London! ­ Many thanks to Jon Butterworth, James Monk, Andy Buckley, Frank Krauss, Frank Siegert

23. Backup

24. Track reconstruction ­ Track reconstruction is a complex pattern recognition problem ­ A combinatorial approach together with a Kalman filter estimation of track parameters is used pixel Inner Barrel Outer Barrel Endcaps Inner Disks 5.6 m 1.2 m ­ Track candidates found in this way are then fitted in order to estimate track parameters on each surface

25. The ME-PS matching problem ­ The PS response coincides with the ME in the soft/collinear region x i ~1 ­ The divergence of the cross section in this region is tamed in the PS using a reweighting factor called Sudakov form factor ­ It would be very convenient to use the ME to predict hard parton configuration and the PS to describe the evolution of jets ­ BUT beware double counting and holes in the phase space!

26. The PS formulae Divergent in z = 0 and z = 1 Divergencies are tamed with a cutoff. Evolving the shower a big splitting probability will turn into big probabilities for successive branchings. If we want to conserve total probability the splitting probability a  bc at scale Q has to be multiplied by the probability that that splitting did not happen before (at > Q). This “non branching probability” is the “Sudakov form factor”

27. PYTHIA approach to the matching: ME corrections ­ Let’s consider the LO e+e-  qqbar and the NLO real emission one e+e-  qqbar g ­ If the shower populates the phase space according to W PS, then a factor W ME /W PS needs to be applied ­ W ME is substituted to W PS in the Sudakov form factor ­ In the hard region, where the Sudavov ~1, the ME results holds, in the soft region, where W ME ~W PS the PS result holds

28. CKKW (continued) ­ For each internal line in the “shower history” connecting scale i to scale k reweight events with a factor ­ For each external line reweight events with a factor  Δ k (q i, q j ) is the Sudakov form factor associated to clustering k, connecting scales q i and q j  The net effect of this procedure is similar to what is achieved with the Pythia’s ME corrections: the splitting functions present in the Sudakov form factor are replaced by their ME version ­ The PS is then applied to the weighted events, with a VETO on hard (avove the merging scale) emission

29. Sherpa, jet observables

30. AlpGen+Pythia, default settings ­ Lepton observables Pt lepton pair η lepton pair Pt e- η e-

31. AlpGen+Pythia, default settings ­ Jet observables

32. AlpGen+Pythia, default settings

33. Change of the matching scale (continued) ­ Jet observables: ­ The mean multiplicity decreases as the merging scale grows ­ Diff jet rates are depleted in the ME region, and are enhanced in the PS region ­ The smoothest transition seems to be the one for the highest merging scale used

34. Jet observables (continued) ­ The differential jet rates show many differences: ­ AlpGen+Pythia and AlpGen+Herwig show similar rates for 2  1 and 3  2 transition, while the shape is quite different for 1  0 ­ Sherpa always fills the ME region more ­ This seems to be in agreement with the harder spectra observed for sherpa, since the ME is responsible for the hardest parton kinematics

35. Change of the merging scale (continued) ­ Leading jet Pt show a bump around 40 GeV for the non- default sample ­ Small differences observed in the jet multiplicity ­ Differential jet rate plots show some modification at the merging scale

36. Change of scales (continued) ­ The effect on the jet multiplicity: ­ The scales*0.5 sample shows the highest jet multiplicity, while the scales*2 samples shows the smallest ­ This agrees with what was observed in the boson p t spectrum, where the tail due to >0 jet events was enhanced in the scales*0.5 case and depleted in the scales*2 case ­ The effect of the jet pt spectrum is not very evident

37. Lepton observables (continued) ­ As for the Z spectrum, the e - P t spectrum is harder for Sherpa and softer for Pythia ­ The e - η are similar (within 8%)

38. Conclusions ­ AlpGen and SHERPA implement two different approaches to the matching of ME and PS predictions ­ A study of the “theoretical uncertainties” has been carried out for both generators, varying the matching parameters and the scales ­ The change on the shape of the distributions is similar for the two generators when changing the scales ­ When changing the matching parameters AlpGen shows minor changes in the shape of the distributions than Sherpa ­ When comparing AlpGen with SHERPA, some not negligible differences have been spotted: ­ The boson lepton and jet spectra are harder for SHERPA ­ The Sherpa mean jet multiplicity is higher then the AlpGen one ­ It might be interesting to see how differential jet rates look on data, and see how well the MC can reproduce these plots, since these observables are very sensitive to the way in which the phase space is filled