General Stuff

What is AlpGen?

ALPGEN is a tree-level matrix element (ME) calculator for a fixed number of partons (legs) in the final-state for hadronic collisions with emphasis on configurations with high jet multiplicities. ALPGEN describes multi-partonic final states at leading order without virtual corrections (loops) in perturbation theory and is based on the exact evaluation of the relevant Feynman diagrams in QCD and EW interactions. The evaluation of matrix elements gives a more exact description for processes with high jet multiplicities with large transverse momenta than the parton shower approach where additional jets (with respect to the initial 2->2 process) are generated only during the shower evolution.

What does Matching mean?

AlpGen generates only the hard process and does not include any form of hadronization. Thus, the output consists of bare quarks and gluons only. The soft/colinear showering and hadronization has to be done in a separate step with routines as they are implemented in general-purpose generators like PYTHIA or HERWIG. Interfacing the AlpGen output to an external showering package involves the risk that a theoretically equivalent parton to one already generated in the matrix element calculation is added once again during the shower evolution. Although the partons generated in the fragmentation step are generally softer than or collinear to the former ones, this leads to the problem of double counting some portions of the phase space. A solution for this problem is known as the matching procedure for matrix elements and parton showers to remove events which occur twice. In case of ALPGEN, the approach to remove double counted jet configurations is slightly different and implemented as so-called MLM matching.

How does the Matching work technically?

The jets produced in the showering routine (e.g. PYTHIA or HERWIG) are matched to the partons obtained from the matrix element calculation. For this purpose, a jet clustering algorithm (so far, IC or kt have been investigated) is applied to the final-state particles. The event is kept if each hard parton in the event can be matched to a jet based on a distance in eta-phi-space otherwise it is rejected. The parton-level configuration for the samples is generated for a particular number of hard jets (``exclusive sample''). Only for the sample with the highest jet multiplicity, extra jets which do not match to hard partons are allowed to be present after the showering is performed (``inclusive sample''). Although the parameters used for the clustering and the matching are a bit arbitrary, usually the cuts with respect to the separation and minimum momentum applied at parton level are used. See VIDEO of M. Mangano presentation on ALPGEN with details on the Weighting/Unweighting process and on the MLM Matching procedure.

Is the unweighting efficiency something I have to care about?

No. In the first step of the event generation with ALPGEN, only weighted events are produced. The weight (differential cross section) is associated with each event and refers to its probability of occurring with respect to its matrix element (subprocess) and its phase space location. At this point the events are distributed flat in phase space and there is no physical information in the distribution. The unweighting procedure is the second step in the ALPGEN event generation and produces events with the frequency predicted by the theory. After the unweighting procedure the individual event represents what might be observed in experiment. The acceptance-rejection method is normally used to perform the unweighting technically. The unweighting efficiencies given for the listed processes on the CmsAlpgen pages are for documentation only and used in the production to estimate how many events need to be requested.

Why are some sample generated in different pt(hat) bins?

To decrease the statistical error of events which occur less frequently. For a proper prediction of e.g. long tails, parts of the distribution need to be enriched so the overall number of events which are generated for each particular pt(hat) bin are approximately equal.

How do I combine the samples from different parton multiplicities?

To cover a complete multijet sample, you have to run over over all exclusive samples + highest inclusive bin and take their respective cross sections into account.

What values can be varied to determine the systematic error

Scale Functional Form:

• Funtion which determines the Factorization scale for the PDF
• iqopt = 1 (M_V²+Σm_T²), 2 (M_V²), 3 (M_V²+P_TV²)
• Default: iqopt = 1

Factorization Scale Factor:

• Multiplicitive factor to the Functional Form
• Due to technical issues the Factorization scale is determined from the Renormalization scale
• Default: qfac = 1.

α_s-reweighting for additional radiation:

• Enable the CKKW matching scheme nodal reweighting.
• This is also what should be used for the MLM matching as in the case of AlpGen
• Default: ickkw=0 (ie off)

α_s-reweighting scale used when ickkw=1 is specified:

• Multiplicative factor to the appearance of the nodes at which AlpGen showering occurs.
• Default: ktfac = 1 (implies k_T = sqrt(t) z (1-z) > Q_min is the branch cut)

P_T Parton Cut:

• Minimum P_T to meet the definition of a hard parton.
• The ME will not generate partons with P_T less than this value
• Default: ptjmin = 15 GeV

P_T Jet Cut:

• Minimum P_T to meet the definition of a Jet for parton-jet MLM matching.
• Default ETCLUS = ptjmin + 5

Delta-R Parton Cut:

• Minimum Parton separation from ME in Delta-R.
• Default: drjmin = 0.7

Delta-R Jet Cut:

• Minimum jet separation in Delta-R to meet the definition of a Jet for parton-jet MLM matching.
• Default: RCLUS = drjmin

New Questions

Why does the given cross-section not drop continuously as a function of the jet multiplicity?

Several reasons:

• Since the ALPGEN sample with the hightest jet multiplicty (N) is generated in inclusive mode, its cross-section can be of the same order of magnitude or even larger than the one of the N-1 sample. Depends on the matching scale.
• The sample is generated at a low matching scale (~ 20 GeV) where the LO calculation has problems with the perturbative expansion. Can be solved by increasing the matching and the factorization/renormalization scales. For ttbar+jets see Maurizio's and Maria's CMS IN Note 2007/038

Why does the ALPGEN distribution look significantly different from the one obtained with PYTHIA?

Have you taken all pt(hat) and all jet multiplicity bin (exclusive + inclusive) into account and scaled the different distributions correctly?

• Z+jets: A discrepency of the Z boson transverse momentum both in the low and the high pt region between ALPGEN and PYTHIA is currently under investigation See Martina's talk.

Glossary

• Phase Space: Multi-dimensional hypercube which spans all of the degrees of freedom.
• Matrix Element: The matrix element describes the collision at the smallest scales in time and distance (hard subprocess) when the colliding partons can be considered as free and therefore treated perturbatively.
• Parton Showering: In AlpGen the Matrix Elements are calculated at leading order (LO), every further order in perturbation theory is rather cumbersome to calculate. However, for some regions of phase space higher-order terms are enhanced and cannot be neglected (e.g. collinear and soft emission of partons). The Parton Shower is a probabilistic way to obtain an approximative result including all these enhancements to all orders.
• Renormalization Scale: Scale at which the perturbative nodes in &alpha are calculated. After this scale the strong coupling is not small enough any more to allow perturbative calculations, subsequent nodes have to rely on models (e.g. Hadronization).
• Factorization Scale: Scale at with the hard process strong coupling is calculated using the PDF.
• Hadronization: In this last step of the event generation the resulting partons are grouped together into color-singlet hadrons and unstable particles are decayed.
• Exclusive Sample: Might refer to different meanings. In case of e.g. the ALPGEN W/Z+jets samples, the sample contains events with a fixed number of (hard) jets. In case of the ttbar, the sample might contain only specific t final states (e.g. leptonic ones). Slang.
• Inclusive Sample: The sample contains either several jet multiplicities or all possible e.g. t decay modes. In case of the ALPGEN W/Z+jet samples, the last jet bin is generated in exclusive mode hence covering all jet multiplicities (n>=N). Slang.
• Sudakov Suppression: Gluon radiation which can not be resolved (ie collinear and soft emission of partons) are not included in the interference between processes with the same external structure. This usually gives errors at the NLL.

Further Reading...

• ALPGEN manual
• PYTHIA manual
• HERWIG manual
• Les Houches Guidebook to MC Generators

-- UlrichFelzmann - 28 Mar 2008