Changes between Version 1 and Version 2 of IntroMatching


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Timestamp:
04/06/12 16:33:03 (8 years ago)
Author:
trac
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  • IntroMatching

    v1 v2  
    1111   * The Matrix Element (ME) description diverges as partons become soft or collinear, while the parton shower description breaks down when partons become hard and widely separated.
    1212
    13 We can distinguish two different philosophies/method types: either based on shower veto and therefore a event reweighting (CKKW method) or events rejection. The latter is the method adopted in the MLM-based schemes. Note that in the CKKW case, partons are clustered in jets with the %$K_{T}$% algorithm while the original MLM method uses a cone algorithm and minimum %$P_{T}$% cut. In MadGraph/MadEvent, there are currently three matching schemes implemented, all based on MLM method. They are called cone- and %$K_{T}$%-jet MLM and Shower-%$K_{T}$% respectively. In all cases the parton shower generator is Pythia.
     13We can distinguish two different philosophies/method types: either based on shower veto and therefore a event reweighting (CKKW method) or events rejection. The latter is the method adopted in the MLM-based schemes. Note that in the CKKW case, partons are clustered in jets with the $K_{T}$ algorithm while the original MLM method uses a cone algorithm and minimum $P_{T}$ cut. In MadGraph/MadEvent, there are currently three matching schemes implemented, all based on MLM method. They are called cone- and $K_{T}$-jet MLM and Shower-$K_{T}$ respectively. In all cases the parton shower generator is Pythia.
    1414
    15 The dependence to the parton-shower evolution variable is here important. The MLM schemes can be used with both "old" virtuality-ordered showers ( '''MSTP(81)=0 or 1''' in Pythia) and "new" %$P_{T}$%-ordered showers (( '''MSTP(81)=20 or 21''' in Pythia)), whereas the Shower-%$K_{T}$% has been designed only for the latter.
     15The dependence to the parton-shower evolution variable is here important. The MLM schemes can be used with both "old" virtuality-ordered showers ( '''MSTP(81)=0 or 1''' in Pythia) and "new" $P_{T}$-ordered showers (( '''MSTP(81)=20 or 21''' in Pythia)), whereas the Shower-$K_{T}$ has been designed only for the latter.
    1616
    17    * Cone- or %$K_{T}$%-jet MLM: The final-state partons in an MG/ME event are clustered according to the %$K_{T}$%-jet algorithm to find the "equivalent parton shower history'' of the event. The Feynman diagram information from !MadGraph is used to allow only clusterings that correspond to diagrams existing in the generated matrix element. For the cone jet algorithm, a minimum %$P_T$% and %$\Delta R$% must be defined for all partons. For the %$K_T$% scheme, the smallest %$K_{T}$% value is restricted to be above the cutoff scale "xqcut". In order to closely mimic the behaviour of the parton shower, the %$K_{T}$% value for each clustering vertex corresponding to a QCD emission is used as renormalization scale for %$\alpha_{s}$% in that vertex. As factorization scale, as well as renormalization scale for the central hard %$2\to1$% or %$2\to2$% process, the transverse mass %$m_{T}^2 = P_{T}^2 + m^2$% of the particle(s) produced in the central process is used. This event is then passed to Pythia for parton showering. After showering, but before hadronization and decays, the final-state partons are clustered into jets; for the cone jet MLM scheme using cone jets, with minimum %$P_T > P_T^{ME}$% and %$\Delta R=\Delta R^{ME}$%, and for the %$K_{T}$%-jet scheme using %$K_{T}$% jets with a cutoff scale %$Qcut > xqcut$%. These jets are then compared to the original partons from the matrix element event. A jet is considered to be matched to the closest parton if, for the cone jet scheme, the jet is within 1.5%$\Delta R$% from the parton, and for the %$K_{T}$%-jet scheme, if the jet measure %$K_{T}(parton,jet)$% is smaller than the cutoff %$Qcut$%. The event is rejected unless each jet is matched to a parton, except for the highest multiplicity sample, where extra jets are allowed below the %$P_T$% or %$K_{T}$% scale (for the respective schemes) of the softest matrix element parton in the event. These matching schemes can be used with both the old (vituality-ordered) and the new (%$\pt$%-ordered) shower implementations of \pythia.
     17   * Cone- or $K_{T}$-jet MLM: The final-state partons in an MG/ME event are clustered according to the $K_{T}$-jet algorithm to find the "equivalent parton shower history'' of the event. The Feynman diagram information from !MadGraph is used to allow only clusterings that correspond to diagrams existing in the generated matrix element. For the cone jet algorithm, a minimum $P_T$ and $\Delta R$ must be defined for all partons. For the $K_T$ scheme, the smallest $K_{T}$ value is restricted to be above the cutoff scale "xqcut". In order to closely mimic the behaviour of the parton shower, the $K_{T}$ value for each clustering vertex corresponding to a QCD emission is used as renormalization scale for $\alpha_{s}$ in that vertex. As factorization scale, as well as renormalization scale for the central hard $2\to1$ or $2\to2$ process, the transverse mass $m_{T}^2 = P_{T}^2 + m^2$ of the particle(s) produced in the central process is used. This event is then passed to Pythia for parton showering. After showering, but before hadronization and decays, the final-state partons are clustered into jets; for the cone jet MLM scheme using cone jets, with minimum $P_T > P_T^{ME}$ and $\Delta R=\Delta R^{ME}$, and for the $K_{T}$-jet scheme using $K_{T}$ jets with a cutoff scale $Qcut > xqcut$. These jets are then compared to the original partons from the matrix element event. A jet is considered to be matched to the closest parton if, for the cone jet scheme, the jet is within 1.5$\Delta R$ from the parton, and for the $K_{T}$-jet scheme, if the jet measure $K_{T}(parton,jet)$ is smaller than the cutoff $Qcut$. The event is rejected unless each jet is matched to a parton, except for the highest multiplicity sample, where extra jets are allowed below the $P_T$ or $K_{T}$ scale (for the respective schemes) of the softest matrix element parton in the event. These matching schemes can be used with both the old (vituality-ordered) and the new ($\pt$-ordered) shower implementations of \pythia.
    1818
    19    * Shower-%$K_{T}$%: In this scheme, events are generated by MG/ME as described above, including the reweighting of %$\alpha_{s}$%. The event is then passed to Pythia and showered using the %$P_{T}$%-ordered showers. In this case, Pythia reports the scale of the first (hardest) emission in the shower, %$Q_{hard}$%. For events from lower-multiplicity samples, the event is rejected if %$Q_{hard}$% is above the matching scale %$Qcut$%, while events from the highest multiplicity sample are rejected if %$Q_{hard} > Q^{ME}''{low}$%, the scale of the softest matrix element parton in the event. This matching scheme is simpler and yet effectively mimics the workings of the %$K''{T}$%-jet MLM scheme. However, it allows for the matching scale %$Qcut$% to be set equal to the matrix element cutoff scale %$xqcut$%, and it more directly samples the Sudakov form factor used in the shower. Furthermore, the treatment of the highest multiplicity sample more closely mimics that used in the CKKW matching scheme.
     19   * Shower-$K_{T}$: In this scheme, events are generated by MG/ME as described above, including the reweighting of $\alpha_{s}$. The event is then passed to Pythia and showered using the $P_{T}$-ordered showers. In this case, Pythia reports the scale of the first (hardest) emission in the shower, $Q_{hard}$. For events from lower-multiplicity samples, the event is rejected if $Q_{hard}$ is above the matching scale $Qcut$, while events from the highest multiplicity sample are rejected if $Q_{hard} > Q^{ME}''{low}$, the scale of the softest matrix element parton in the event. This matching scheme is simpler and yet effectively mimics the workings of the $K''{T}$-jet MLM scheme. However, it allows for the matching scale $Qcut$ to be set equal to the matrix element cutoff scale $xqcut$, and it more directly samples the Sudakov form factor used in the shower. Furthermore, the treatment of the highest multiplicity sample more closely mimics that used in the CKKW matching scheme.
    2020
    2121=== Practical aspects ===
    2222
    23 For a discussion of the parameters used in the !MadEvent-Pythia matching, please see the page [:Software/Matching:Matching of jets between MadEvent and Pythia].
     23For a discussion of the parameters used in the !MadEvent-Pythia matching, please see the page [wiki:Software/Matching Matching of jets between MadEvent and Pythia].
    2424
    25 We now give a concrete example of how to generate properly a matched sample using MadGraph/MadEvent/Pythia and %$K_{T}$%-MLM scheme. In this example, we show how it is possible to produce a matched sample of tt + 0, 1, 2 jets (inclusively).
     25We now give a concrete example of how to generate properly a matched sample using MadGraph/MadEvent/Pythia and $K_{T}$-MLM scheme. In this example, we show how it is possible to produce a matched sample of tt + 0, 1, 2 jets (inclusively).
    2626
    2727The first step consists in modifying the proc card.dat file, which will contain all the information about the process itself. In our case we will use (the headers and footers have been removed in order to save place):
     
    4545}}}
    4646
    47    * Remark 1: The number of QED vertices has to be reduced as much as possible: the reason is twofold: first a parton emitted by a QED vertex cannot be renormalized with %$\alpha_{s}$%. Second, in the parton shower there is no QED emission of parton, and the matching procedure is supposed to be precisely merge similar things at the point of view of the content.
    48    * Remark 2: the maximal number of extra-partons is strongly related to the process and model used, because of the practical limitation of the number of diagrams in Madgraph: While in the Standard Model we can easily reach 4 extra-partons for W/Z+jets, in the MSSM this number is limited to 2 for processes like %$\tilde{g}\tilde{g}$%+jets.
     47   * Remark 1: The number of QED vertices has to be reduced as much as possible: the reason is twofold: first a parton emitted by a QED vertex cannot be renormalized with $\alpha_{s}$. Second, in the parton shower there is no QED emission of parton, and the matching procedure is supposed to be precisely merge similar things at the point of view of the content.
     48   * Remark 2: the maximal number of extra-partons is strongly related to the process and model used, because of the practical limitation of the number of diagrams in Madgraph: While in the Standard Model we can easily reach 4 extra-partons for W/Z+jets, in the MSSM this number is limited to 2 for processes like $\tilde{g}\tilde{g}$+jets.
    4949
    5050After generating the processes, the run card.dat can be edited as well as the pythia card.dat. Those two files will contains everything needed to perform the matching procedure.
     
    5353      * ickkw has to be set to 1 to perform MLM-type matching.
    5454      * xqcut defines the minimal distance in the phase space allowed between extra partons (u,d,s,c, and also b if '''maxjetflavor'''=5 in the run_card). For t t~ a value around 15 or 20 is reasonable.
    55       * drjj is the distance in the eta-phi plan between partons. As the whole matching procedure uses the %$K_{T}$% measure to control this parameter, the drjj can be set to a very low value (like 0.001) to not influence the xqcut. For MG/ME v. 4.4.16 and higher, drjj can be set to 0 if xqcut is > 0.
     55      * drjj is the distance in the eta-phi plan between partons. As the whole matching procedure uses the $K_{T}$ measure to control this parameter, the drjj can be set to a very low value (like 0.001) to not influence the xqcut. For MG/ME v. 4.4.16 and higher, drjj can be set to 0 if xqcut is > 0.
    5656      * etaj should be set to 5 for the LHC (which is the maximal rapidity used in the matching procedure ).
    57       * The xqcut definition is of %$K_{T}$% type, it means then also related to %$P_{T}$%. Therefore, in order to optimize the speed of even generation by restricting the phase-space on which calculation is allowed, ptj can be set equal to xqcut. This is not necessary for MG/ME v. 4.4.16 and higher, where ptj can be set to 0.
     57      * The xqcut definition is of $K_{T}$ type, it means then also related to $P_{T}$. Therefore, in order to optimize the speed of even generation by restricting the phase-space on which calculation is allowed, ptj can be set equal to xqcut. This is not necessary for MG/ME v. 4.4.16 and higher, where ptj can be set to 0.
    5858
    5959   * For the pythia step, where the matching procedure takes effectively place the card can be written as follows:
     
    7070}}}
    7171
    72 The result is a file in .hep format (STDHEP) which is inclusive in the multiplicities of extra jet radiation. If the user want to use the Shower-%$K_{T}$% instead of the %$K_{T}$%-MLM scheme, the parameter "showerkt=T" has to be included in the pythia_card.
     72The result is a file in .hep format (STDHEP) which is inclusive in the multiplicities of extra jet radiation. If the user want to use the Shower-$K_{T}$ instead of the $K_{T}$-MLM scheme, the parameter "showerkt=T" has to be included in the pythia_card.
    7373
    7474==== Suggested scale choices ====
    7575
    76    * For W or Z boson production, suggested xqcut scale is 10 !GeV with QCUT=15 !GeV for virtuality-ordered Pythia showers, or 30 !GeV for %$P_T$%-ordered showers with the Shower-%$K_T$% scheme.
    77    * For t t~ production, suggested xqcut scale is 20 !GeV with QCUT=30 !GeV for virtuality-ordered Pythia showers, or 80 !GeV for %$P_T$%-ordered showers with the Shower-%$K_T$% scheme.
    78    * For 600 !GeV SUSY particle pair production, suggested xqcut scale is 30 !GeV with QCUT=40 !GeV for virtuality-ordered Pythia showers, or 100 !GeV for %$P_T$%-ordered showers with the Shower-%$K_T$% scheme.
     76   * For W or Z boson production, suggested xqcut scale is 10 !GeV with QCUT=15 !GeV for virtuality-ordered Pythia showers, or 30 !GeV for $P_T$-ordered showers with the Shower-$K_T$ scheme.
     77   * For t t~ production, suggested xqcut scale is 20 !GeV with QCUT=30 !GeV for virtuality-ordered Pythia showers, or 80 !GeV for $P_T$-ordered showers with the Shower-$K_T$ scheme.
     78   * For 600 !GeV SUSY particle pair production, suggested xqcut scale is 30 !GeV with QCUT=40 !GeV for virtuality-ordered Pythia showers, or 100 !GeV for $P_T$-ordered showers with the Shower-$K_T$ scheme.
    7979
    8080==== Matching in BSM processes ====
     
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